rlab/web/rlab.js

(function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
var O = require("./field");

var acc = {
	sum:{init:0,op:'+'}, 
	product:{init:1,op:'*'},
	min:{init:Number.MAX_VALUE,op:'min'},
	max:{init:-Number.MAX_VALUE,op:'max'},
}

O.vfill=function(size, value) {
	var v=[];
	for (var i=0; i<size; i++)
		v[i] = value;
	return v;
}

O.vextend=function(a, size) {
	var v = a.slice();
	for (var i=a.length; i<size; i++) {
		v.push(0);
	}
	return v;
}

O.vdot=function(x,y) {
	var sum = 0;
	for (var i=0; i<x.length; i++) {
		sum = sum.add(x[i].mul(y[i]));
	}
	return sum;
}

O.vop=function(op,x,y) {
	var c=[],result=(O.isUndefined(acc[op]))?undefined:acc[op].init;
  if (O.isArray(x)) {
		for (var i=0; i<x.length; i++) {
			if (!O.isUndefined(result)) {
				var xi = x[i];
				if (O.isArray(x[i])) // x[i] is subArray
					xi = O.op(op, x[i]);
				else {
					if (!O.isUndefined(y))
						xi = y(x[i]); // y should be a function
				}
				result = O.op(acc[op].op, xi, result);
//				if (op==='min') console.log("xi=%d result=%d", xi, result);
			}
			else {
				var yi = O.isArray(y)?y[i]:y;
				c[i] = O.op(op, x[i], yi);
			}
		}
	} else {
		throw Error('vop fail:op,x,y=', op, x, y);
	}
	if (x.length === c.length)
		return c;
	else
		return result;
}

O.op = function(op,x,y) {
  if (O.isField(x)) {
		if (!O.isUndefined(acc[op])) {
			switch (op) {
				case 'max': return Math.max(x,y);
				case 'min': return Math.min(x,y);
				default:return x;
			}
		}	else if (x instanceof O.FieldObj || 
		    (O.isNumber(x) && y instanceof O.FieldObj)) {
			x = O.Complex.toComplex(x); 
			y = O.isNumber(y)?O.Complex.toComplex(y):y;
			switch (op) {
				case 'eval': var exp = y; return exp(x);
				case 'neg':return x.neg();
				case 'inv':return x.inv();
				case 'bnot':return x.bnot();				
				case '+':return x.add(y);
				case '-':return x.sub(y);
				case '*':return x.mul(y);
				case '/':return x.div(y);
				case 'power':return x.power(y);
				case 'sqrt':return x.sqrt();
				case 'eq':return x.eq(y);
				case 'neq':return x.neq(y);
				case 'geq':return x.geq(y);
				case 'leq':return x.leq(y);
				case 'gt':return x.gt(y);
				case 'lt':return x.lt(y);
			}
		} else if (O.isBool(x) || O.isNumber(x)) {
			switch (op) {
				case 'eval': var exp = y; return exp(x);
				case 'not':return !x;
				case 'neg':return -x;
				case 'inv':return 1/x;
				case 'bnot':return ~x;
				case 'and':return x&&y;
				case 'or':return x||y;
				case 'xor':return x!==y;
				case '+':return x+y;
				case '-':return x-y;
				case '*':return x*y;
				case '/':return x/y;
				case '%':return x%y;
				case 'eq':return x===y;
				case 'neq':return x!==y;
				case 'geq':return x>=y;
				case 'leq':return x<=y;
				case 'gt':return x>y;
				case 'lt':return x<y;
				case '&':return x&y;
				case '|':return x|y;
				case 'bxor':return x^y;
				case '<<':return x<<y;
				case '>>':return x>>y;
				case 'and':return x&&y;
				case 'or':return x||y;
				case 'xor':return x!==y;
				case 'sqrt':
				  if (x>=0) return Math.sqrt(x);
					else {
						var c = new O.Complex(x,0);
						return c.sqrt();
					}
				case 'power':
				  if (x>=0 || O.isInteger(y))
						return Math.pow(x,y);
					else
						return new O.Complex(x,0).power(y);
				case 'log':return Math.log(x);
				case 'exp':return Math.exp(x);
				case 'abs':return Math.abs(x);;
				case 'sin':return Math.sin(x);
				case 'cos':return Math.cos(x);
				case 'tan':return Math.tan(x);
				case 'asin':return Math.asin(x);
				case 'acos':return Math.acos(x);
				case 'atan':return Math.atan(x);
				case 'sinh':return Math.sinh(x);
				case 'cosh':return Math.cosh(x);
				case 'tanh':return Math.tanh(x);
				case 'ceil':return Math.ceil(x);
				case 'floor':return Math.floor(x);
				case 'round':return Math.round(x);
				case 'log1p':return Math.log1p(x);
				case 'log10':return Math.log10(x);
				case 'log2':return Math.log2(x);
				case 'random':return Math.random();
				case 'sign':return Math.sign(x);
				case 'abs':return Math.abs(x);
				case 'cbrt':return Math.cbrt(x); // cubic root
			}
		}
	} else if (O.isFunction(x)) {
		if (O.isFunction(y)) {
			switch (op) {
				case 'neg':return O.fneg(x);
				case 'inv':return O.finv(x);
				case '+':return O.fadd(x,y);
				case '-':return O.fsub(x,y);
				case '*':return O.fmul(x,y);
				case '/':return O.fdiv(x,y);
				case 'compose':return O.fcompose(x,y);
			}			
		} else {
			switch (op) {
				case 'eval':return x(y);
			}
		}
	}	else if (O.isArray(x)) {
		return O.vop(op,x,y);
	}
	throw Error('op fail:op,x,y=', op, x, y);
}

O.sum=function(x) { return O.vop('sum', x) }
O.product=function(x) { return O.vop('product', x) }
O.max=function(x) { return O.vop('max', x) }
O.min=function(x) { return O.vop('min', x) }
O.eval=function(x,y) { return O.op('eval', x,y) }
O.norm=function(x) {
	var norm2 = O.vop('sum', x, (x)=>x*x);
	return Math.sqrt(norm2);
}

// +-*/%^
O.add=function(x,y) {	return O.op('+',x,y) }
O.sub=function(x,y) {	return O.op('-',x,y) }
O.mul=function(x,y) {	return O.op('*',x,y) }
O.div=function(x,y) {	return O.op('/',x,y) }
O.mod=function(x,y) {	return O.op('%',x,y) }
O.power=function(x,y) { return O.op('power', x, y) }
O.neg=function(x) { return O.op('neg', x) }
O.inv=function(x) { return O.op('inv', x) }
// logical
O.not=function(x) { return O.op('not', x) }
O.and=function(x,y) { return O.op('&&', x, y) }
O.or=function(x,y) { return O.op('||', x, y) }
O.xor=function(x,y) { return O.op('xor', x, y) }
O.bnot=function(x) { return O.op('bnot', x) }
O.band=function(x,y) { return O.op('&', x, y) }
O.bor=function(x,y) { return O.op('|', x, y) }
O.bxor=function(x,y) { return O.op('bxor', x, y) }
O.lshift=function(x,y) { return O.op('<<', x, y) }
O.rshift=function(x,y) { return O.op('>>', x, y) }
// compare
O.eq=function(x,y) { return O.op('eq', x, y) }
O.neq=function(x,y) { return O.op('neq', x, y) }
O.geq=function(x,y) { return O.op('geq', x, y) }
O.leq=function(x,y) { return O.op('leq', x, y) }
O.gt=function(x,y) { return O.op('gt', x, y) }
O.lt=function(x,y) { return O.op('lt', x, y) }
// number function
O.sqrt=function(x) { return O.op('sqrt', x) }
O.log=function(x) { return O.op('log', x) }
O.exp=function(x) { return O.op('exp', x) }
O.abs=function(x) { return O.op('abs', x) }
O.sin=function(x) { return O.op('sin', x) }
O.cos=function(x) { return O.op('cos', x) }
O.tan=function(x) { return O.op('tan', x) }
O.asin=function(x) { return O.op('asin', x) }
O.acos=function(x) { return O.op('acos', x) }
O.atan=function(x) { return O.op('atan', x) }
O.atan2=function(x) { return O.op('atan2', x) }
O.ceil=function(x) { return O.op('ceil', x) }
O.floor=function(x) { return O.op('floor', x) }
O.round=function(x) { return O.op('round', x) }
 
O.parse = function(s) {
	if (s.indexOf(';')>=0) {
		var m = split(s, ";"), matrix;
		for (var i=0; i<m.length; i++) {
			matrix[i] = O.parse(m[i]);
		}
		return matrix;
	} if (s.indexOf(',')>=0) {
		var a = split(s, ","), array;
		for (var i=0; i<a.length; i++) {
			array[i] = O.parse(a[i]);
		}
		return array;
	}
	else if (s.indexOf('/')>=0)
		return O.Ratio.parse(s);
	else if (s.indexOf('i')>=0)
		return O.Complex.parse(s);
	else {
		return parseFloat(s);
	}
}

// =========== Polynomial Ring ==============
O.PolynomialRing=extend({}, O.Field);

class Polynomial extends O.FieldObj {
  constructor(c) {
    super(O.PolynomialRing);
    this.c = c; // sum(ci x^i)
  }
	
	eval(x) {
		var c = this.c, i=c.length-1, sum=c[i];
		for (i--;i>=0; i--) {
			sum = c[i].add(x.mul(sum));
		}
		return sum;
	}
	
	size() { return this.c.length }
	
	toString() {
		var s = [], c=this.c;
		for (var i=c.length-1; i>=0; i--) {
			s.push(c[i]+'x^'+i);
		}
		return s.join('+');
	}
	
	root() {
		var p = this.normalize(); // 正規化
		switch (this.size()) {
		  case 2:return p.c[0].neg();
		  case 3:return p.root2(p.c[1], p.c[0]);
			case 4:return p.root3(p.c[2], p.c[1], p.c[0]);
			default:throw Error('root() fail');
		}
			
	}

	root2(b,c) { // x^2 + bx + c	=0
		var d = b.mul(b).sub(c.mul(4)).sqrt();
		return [b.neg().add(d), b.neg().sub(d)];
	}
	
	root3(a,b,c) { // x^3+ax^2+bx+c=0
		var q=((2*a*a*a/27)-(a*b/3)+c)/2;
		var p=(b-a*a/3)/3;
		var D=p*p*p+q*q;
		var Dsqrt = D.sqrt(), _q=q.neg();
		var u_p=_q.add(Dsqrt).power(1/3); // (-q+sqrt(D))^1/3
		var u_m=_q.sub(Dsqrt).power(1/3); // (-q-sqrt(D))^1/3
		console.log("q=%s p=%s D=%s u+=%s u-=%s", q, p, D, u_p, u_m);
		var rho_p = (1/2).mul(O.parse('-1+3i'));
		var rho_m = (1/2).mul(O.parse('-1-3i'));
		console.log("rho_p=%s rho_m=%s", rho_p, rho_m);
		var y1=u_p.add(u_m);
		var y2=rho_p.add(u_p).add(rho_m.mul(u_m));
		var y3=rho_p.sub(u_p).add(rho_p.mul(u_m));
		return [y1, y2, y3];
	}	
	
	normalize() {
		var a = this.c[this.size()-1];
		var nc = this.c.div(a);
		return new Polynomial(nc);
	}
}

O.Polynomial = Polynomial;
/*

function root3(a,b,c) { // x^3+ax^2+bx+c=0
  var q=((2*a*a*a/27)-(a*b/3)+c/2);
	var p=(b-a*a/3)/3;
	var D=p*p*p+q*q;
	var u_p=Math.sqrt(3, -q+Math.sqrt(D));
	var u_m=Math.sqrt(3, -q-Math.sqrt(D));
	var rho_p = 1/2*(-1+3i);
	var rho_m = 1/2*(-1-3i);
  var y1=u_p+u_m;
  var y2=rho_p+u_p+ rho_m*u_m;
  var y3=rho_p-u_p+ rho_p*u_m;
}
*/
O.PolynomialAddGroup={
  e:new Polynomial([0]), // 到底應該設幾個？
  op:function(x,y) {
		var size = Math.max(x.size(), y.size());
		var a=O.vextend(x.c,size), b=O.vextend(y.c,size);
	  var c=O.add(a,b);
		return new Polynomial(c);
	},
  inv:function(x) {
		var c = O.neg(x.c);
		return new Polynomial(c);
	},
}
  
extend(O.PolynomialAddGroup, O.Group);

O.PolynomialMulSemiGroup={
  e:new Polynomial([1]),
  op:function(x,y) { 
	  var c=[];
	  for (var xi=0; xi<x.c.length; xi++) {
			for (var yi=0; yi<y.c.length; yi++) {
				var cxy = (typeof c[xi+yi]==='undefined')?0:c[xi+yi];
				c[xi+yi] = cxy+x.c[xi]*y.c[yi];
			}
		}
		return new Polynomial(c);
	},
  inv:function(x) { throw Error('PolynomialMulSemiGroup.inv not defined') },
}

extend(O.PolynomialMulSemiGroup, O.Group);

O.PolynomialRing.init(O.PolynomialAddGroup, O.PolynomialMulSemiGroup);

module.exports = O;

},{"./field":4}],2:[function(require,module,exports){
// http://blog.smartbear.com/testing/four-serious-math-libraries-for-javascript/

// Four Serious Math Libraries for JavaScript

var B = {};

B.slice = function(a) {
	return Array.prototype.slice.call(a);
}

B.bind=function(o, member) {
	if (typeof o[member]==='Function')
		return o[member].bind(o); 
	else
		return o[member];
}

B.ncall = function() {
  var args = B.slice(arguments);
  var n = args[0];
  var o = args[1];
  var fname = args[2];
  var params = args.slice(3);
  var a=[];
  for (var i=0; i<n; i++)
    a.push(o[fname].apply(o, params));
  return a;
}

B.mapFunctions=function(host, obj, pairs) {
	for (var h in pairs) {
		var o = pairs[h];
		if (typeof host[h] !=='undefined')
			console.log('mapBind: error!', h, ' has been defined!');
		host[h]=B.bind(obj, o);
	}
}

B.copyFunctions=function(host, obj, names) {
	for (var name of names) {
		if (typeof host[name] !=='undefined')
			console.log('namesBind: error!', name, ' has been defined!');
		host[name]=B.bind(obj, name);
	}
}

B.mix=function(self, members) {
	for (var name in members) {
		var member = members[name];
		if (typeof self[name] === 'undefined') {
			Object.defineProperty(self, name, {
				enumerable: true,
				writable: true,
				value: member,
			});
		} else {
	    console.log("B.mix fail:", name, " already exists!");
		}
	}
}

B.arg1this = function(f,obj) { // 傳回一個已經綁定 f, obj 的函數
  return function() { 
		var args = B.slice(arguments);
    return f.apply(obj, [this].concat(args)); // 效果相當於 obj.f(this, args)
  }
}

B.mixThis=function(proto, obj, fmembers) {
	for (var fname of fmembers) {
		var f = obj[fname];
		if (typeof proto[fname] === 'undefined') {
			Object.defineProperty(proto, fname, {
				enumerable: false,
				writable: true,
				value: B.arg1this(f,obj), // proto.f(args) => obj.f(this, args) , 這行盡量不要動，除非想得很清楚了！
			});
		} else {
	    console.log("B.mixThis:", fname, " fail!");
		}
	}
}

B.mixThisMap=function(proto, obj, poMap) {
	for (var pname in poMap) {
		var oname = poMap[pname];
		var f = obj[oname];
		if (typeof proto[pname] === 'undefined') {
			Object.defineProperty(proto, pname, {
				enumerable: false,
				writable: true,
				value: B.arg1this(f,obj), // proto.f(args) = f(this, args) , 這行盡量不要動，除非想得很清楚了！
			});
		} else {
			console.log('pname=', pname, 'proto[pname]=', proto[pname]);
	    console.log("B.mixThisMap:", oname, " fail!");
		}
	}
}

B.ctrim=function(s, set, side) {
  side = side||"both";
  for (var b=0; b<s.length; b++)
    if (set.indexOf(s[b])<0) break;
  for (var e=s.length-1; e>=0; e--)
    if (set.indexOf(s[e])<0) break;
  if (side === "right") b=0;
  if (side === "left") e=s.length-1;
  return s.substring(b, e+1);
}

B.lpad=function(s, width, ch) {
  return s.length >= width ? s : new Array(width - s.length + 1).join(ch) + s;
}

B.def = function(x, value) {
	return (typeof x !== 'undefined')?x:value;
}

B.precision=2;

B.nstr = function(n, precision=B.precision) {
	if (n % 1 === 0) return n.toString();
	return n.toFixed(precision);
}

B.astr = function(a, precision=B.precision) {
	var s=[];
	for (var i in a) {
		s.push(a[i].str(precision));
	}
	return "["+s.join(', ')+"]";
}

B.sstr = function(s) { return s.toString(); }

B.ostr = function(o, precision=B.precision) {
  var s = [];
  for (var k in o)
    s.push(k+":"+B.str(o[k], precision));
  return "{"+s.join(", ")+"}";
}

B.str = function(o, precision=B.precision) {
	if (typeof o ==='undefined')
		return 'undefined';
	else
		return o.str(precision);
}

module.exports = B;

/*
B.calls = function() {
  var args = B.slice(arguments);
  var n = args[0];
  var f = args[1];
  var params = args.slice(2);
  var a=[];
  for (var i=0; i<n; i++)
    a.push(f.apply(null, params));
  return a;
}
*/
/*
B.slice = function(a) {
	return Array.prototype.slice.call(a);
}

B.curry = function(f,o) {
  return function() {
		var args = Array.prototype.slice.call(arguments);
    return f.apply(null, [o].concat(args));
  }
}

B.mixThis=function(proto, fmap) {
	for (var name in fmap) {
		var f = fmap[name];
		if (typeof proto[name] === 'undefined') {
			Object.defineProperty(proto, name, {
				enumerable: false,
				writable: true,
				value: B.arg1this(f), // proto.f(args) = f(this, args)
			});
		} else {
	    console.log("B.mixThis:", name, " fail!");
		}
	}
}
B.thisAsArg1 = function(f) {
  return function() {
		var args = B.slice(arguments);
    return f.apply(null, [this].concat(args));
  }
}

*/

/*
B.mixThis=function(proto, obj, fmembers) {
	for (var fname of fmembers) {
//		var f = B.bind(obj, fname);
		var f = obj[fname];
		if (typeof proto[fname] === 'undefined') {
			Object.defineProperty(proto, fname, {
				enumerable: false,
				writable: true,
				value: B.arg1this(f,obj), // proto.f(args) = f(this, args)
			});
		} else {
	    console.log("B.mixThis:", fname, " fail!");
		}
	}
}
*/
},{}],3:[function(require,module,exports){
module.exports = O = require("./matrix");

// =========== Calculus =================
O.dx = 0.01;

// 微分 differential calculus
O.fdiff = O.fdifferential = function(f, x, dx) {
	dx = dx || O.dx;
  var dy = f(x.add(dx)).sub(f(x.sub(dx)));
  return dy.div(dx.mul(2));
}

// 積分 integral calculus
O.fint = O.fintegral = function(f, a, b, dx) {
	dx = dx || O.dx;
  var area = 0.0;
  for (var x=a; x<b; x=x+dx) {
    area = area + f(x).mul(dx);
  }
  return area;
}

// 偏微分 partial differential calculus
// f=[f1,f2,....] , x=[x1,x2,...] , dx=[dx1,dx2,....]
O.pdiff = O.pdifferential = function(f, x, i) {
	f = O.fa(f);
	var dx = O.vfill(x.length, 0);
	dx[i] = O.dx;
//	var df = f.apply(null, x.add(dx)).sub(f.apply(null, x.sub(dx)));
	var df = f(x.add(dx)).sub(f(x.sub(dx)));
	return df.div(dx.norm().mul(2));
}

// multidimensional integral calculus
// f=[f1,f2,....] , a=[a1,a2,...] , b=[b1,b2,....]
O.pint = O.pintegral = function(f, a, b) {
	
}

// 梯度 gradient : grad(f,x)=[pdiff(f,x,0), .., pdiff(f,x,n)]
O.fgrad = O.fgradient = function(f, x) {
	var gf = [];
	for (var i=0; i<x.length; i++) {
		gf[i] = O.pdiff(f, x, i);
	}
	return gf;
}

// 散度 divergence : div(F,x) = sum(pdiff(F[i],x,i))
O.fdiv = O.fdivergence = function(F, x) {
	var Fx = F(x);
	var f=[], d=[];
	for (var i=0; i<x.length; i++) {
		f[i] = (xt)=>F(xt)[i];
		d[i] = O.pdiff(f[i],x,i);
	}
	return d.sum();
}

// 旋度 curl : curl(F) = div(F)xF 
O.fcurl = O.fcurlance = function(F, x) {
	
}

// 線積分： int F●dr = int F(r(t))●r'(t) dt
O.vint = O.vintegral = function(F, r, a, b, dt) {
	dt = dt||O.dx;
	var sum = 0;
	for (var t=a; t<b; t+=dt) {
		sum += F(r(t)).dot(r.diff(t));
	}
	return sum;
}

// 定理：int F●dr  = int(sum(Qxi dxi))

// 向量保守場： F=grad(f) ==> int F●dr = f(B)-f(A)

// 定理： 向量保守場 F, pdiff(Qxi,xj) == pdiff(Qxj,xi)  for any i, j
// ex: F=[x^2y, x^3] 中， grad(F)=[x^2, 3x^2] 兩者不相等，所以不是保守場

// 格林定理：保守場中 《線積分=微分後的區域積分》
// int P dx + Q dy = int int pdiff(Q,x) - pdiff(P, y) dx dy

// 散度定理：通量 = 散度的區域積分
// 2D : int F●n ds = int int div F dx dy
// 3D : int int F●n dS = int int int div F dV

// 史托克定理：  F 在曲面 S 上的旋度總和 = F 沿著邊界曲線 C 的線積分
// int int_D curl(F)●n dS = int_C F●dr


},{"./matrix":8}],4:[function(require,module,exports){
// module : Field & Group Theory
var F = require("./set");
F.Integer=require("./integer");
var eq = F.eq;
// ========== Group =================
// 注意： 箭頭函數會自動將 this 變數綁定到其定義時所在的物件，因此以下很多地方不能用箭頭函數。
// 參考： https://developer.mozilla.org/zh-TW/docs/Web/JavaScript/Reference/Functions/Arrow_functions
F.Group={ 
  invOp:function(x,y) { 
    return this.op(x,this.inv(y)); 
  },
  power:function(x,n) {
    var p=this.e;
    for (var i=0;i<n;i++) {
      p=this.op(p,x);
    }
    return p;
  },
	leftCoset:function(g, H) {
		var set = new F.Set();
		for (var i in H)
		  set.add(this.op(g,H[i]));
		return set;
	},
	rightCoset:function(H, g) {
		var set = new F.Set();
		for (var i in H)
		  set.add(this.op(g,H[i]));
		return set;
	},
  // ref:https://en.wikipedia.org/wiki/Group_(mathematics)
  // 封閉性：For all a, b in G, a • b, is also in G
  closability:function(a,b) {
		var ab = this.op(a,b);
    var close=this.has(ab);
    return this.has(this.op(a,b));
  },
  // 結合性：For all a, b and c in G, (a • b) • c = a • (b • c).
  associativity:function(a,b,c) {
    var op = this.op.bind(this);
    return eq(op(op(a,b),c), op(a,op(b,c)))
  },
  // 單位元素：Identity element
  identity:function(a) {
    return eq(this.op(this.e,a),a)
  },
  // 反元素：Inverse element
  inversability:function(a) {
    return eq(this.op(a,this.inv(a)),this.e);
  },
}

// PermutationGroup
F.PermutationGroup={
  op:function(x,y) {
	  var z = [];
		for (var i in x)
			z[i] = y[x[i]];
		return z;
  },
  inv:function(x) { 
	  var nx = [];
		for (var i in x) {
			nx[x[i]] = i;
		}
	  return nx;
	},
}

extend(F.PermutationGroup, F.Group);

// Cyclic Group :  a group that is generated by a single element (g)
F.CyclicGroup={
	G:[],
//	g:g,
  op:function(x,y) {
  },
  inv:function(x) {
	},
	create(g) {
		var t = e;
		for (var i=0; !t.eq(e); i++) {
			G[i]=t;
			t=op(g,G[i]);
		}
	}
}

extend(F.CyclicGroup, F.Group);

// NormalSubGroup : 正規子群
F.NormalSubGroup={
  op:function(x,y) {
  },
  inv:function(x) {
	},
	normality(g,n) {
		return this.has(g.op(n).op(g.inv()));
	},
}

extend(F.NormalSubGroup, F.Group);

// Quotent Group : aggregating similar elements of a larger group using an equivalence relation that preserves the group structure

F.QuotentGroup={
	eq:function(x,y) {
		
	},
  op:function(x,y) {
  },
  inv:function(x) {
	},
}

extend(F.QuotentGroup, F.Group);

// Normal SubGroup : gH = Hg
// https://en.wikipedia.org/wiki/Normal_subgroup
F.NormalSubGroup={
  op:function(x,y) {
  },
  inv:function(x) {
	},
}

extend(F.NormalSubGroup, F.Group);

// 群同構第一定理： 給定 GG和 G ′ 兩個群，和 f : G → G ′ 群同態。則 Ker ⁡ f 是一個 G 的正規子群。
// 群同構第二定理：給定群 G 、其正規子群 N、其子群 H，則 N ∩ H 是 H 的正規子群，且我們有群同構如下： H / ( H ∩ N ) ≃ H N / N
// 群同構第三定理： 給定群 G， N 和 M，M 為 G 的正規子群，滿足 M 包含於 N ，則 N / M 是 G / M 的正規子群，且有如下的群同構： ( G / M ) / ( N / M ) ≃ G / N .

// ========== Field =================
F.Field={
  sub:function(x,y) { return this.addGroup.invOp(x,y) },
  div:function(x,y) { return this.mulGroup.invOp(x,y) },
//  mod:function(x,y) { return x.sub(x.div(y).mul(y)) },
  power:function(x,n) { return this.mulGroup.power(x,n) },
  init:function(addGroup, mulGroup) {
    this.addGroup = addGroup;
    this.mulGroup = mulGroup;
    this.zero = addGroup.e;
    this.add  = function(x,y) { return this.addGroup.op(x,y) }
    this.neg  = function(x) { return this.addGroup.inv(x) }
    this.one  = mulGroup.e;
    this.mul  = function(x,y) { return this.mulGroup.op(x,y) }
    this.inv  = function(x) { return this.mulGroup.inv(x) }
    this.power= function(x,n) { return this.mulGroup.power(x,n) }
		this.eq   = function(x,y) { return F.eq(x,y); }
		this.neq  = function(x,y) { return !this.eq(x,y); }
		this.isZero = function(x) { 
		  return this.field.eq(this, F.proto(this).zero) 
		}
		this.isOne = function(x) { 
		  return this.field.eq(this, F.proto(this).one)
		}
		this.gcd  = function(x,y) {
			if (y.isZero()) return x;
			return gcd(y, mod(x,y));
		}
  },
	ldistribute:function(a,b,c) {
		return this.mul(a, this.add(b,c)).eq(this.add(this.mul(a,b), this.mul(a,c)));
	},
	rdistribute:function(a,b,c) {
		return this.ldistribute(b,c,a);
	},
	associativity:function(a,b,c) {
		return this.mul(a,this.mul(b,c)).eq(this.mul(this.mul(a,b),c));
	},
}

F.Ring = F.Field;  // Ring  (環)  : 可能沒有乘法單位元素和反元素的 Field
F.Module = F.Field;// Module(模)  : (R +) is Ring, (R × M → M)
F.Ideal = F.Field; // Ideal (理想): 子環，且 i·r ∈ I (左理想), r·i ∈ I (右理想)

// ref : https://en.wikipedia.org/wiki/Group_homomorphism
//  https://en.wikipedia.org/wiki/Fundamental_theorem_on_homomorphisms
// 同態：h(a • b) = h(a) x h(b) 
F.homomorphism=function(h, g1, g2) {
  var a=g1.random(), b=g2.random();
  return eq(h(group1.op(a,b)), group2.op(h(a), h(b)))
}

// ref : https://en.wikipedia.org/wiki/Isomorphism
//  https://en.wikipedia.org/wiki/Isomorphism_theorem
// 同構：h(a • b) = h(a) • h(b)
F.isomorphism=function(h1, h2, g1, g2) {
  var a1=g1.random(), b1=g2.random();
  var a2=g1.random(), b2=g2.random();
  return homorphism(h1,g1,g2)&&homorphism(h2,g2,g1);
}

// ========== Float Field =================
F.FloatAddGroup={
  e:0,
  op:function(x,y) { return x+y },
  inv:function(x) { return -x},
}

extend(F.FloatAddGroup, F.Group, F.Set.Float);

F.FloatMulGroup={
  e:1,
  op:function(x,y) { return x*y },
  inv:function(x) { return 1/x},
}

extend(F.FloatMulGroup, F.Group, F.Set.Float);

F.FloatField=extend({}, F.Field, F.Set.Float);

F.FloatField.init(F.FloatAddGroup, F.FloatMulGroup);

// ========== Finite Field =================
F.FiniteAddGroup={
  e:0,
  op:function(x,y) { return (x+y)%this.n },
  inv:function(x) { return (this.n-x) }
}

extend(F.FiniteAddGroup, F.Group);

F.FiniteMulGroup={
  e:1,
  op:function(x,y) { return (x*y)%this.n }, 
  inv:function(x) { return this.invMap[x] },
  setOrder:function(n) {
    this.n = n;
    let invMap = new Map();
    for (var x=1; x<n; x++) {
      var y = this.op(x,x);
      invMap.set(x,y);
    }
    this.invMap = invMap;
  }
}

extend(F.FiniteMulGroup, F.Group);

F.FiniteField=extend({}, F.Field);

F.FiniteField.create=function(n) {
  var finiteField = extend(F.Finite(n), F.FiniteField);
  var addGroup = extend(F.Finite(n), {n:n}, F.FiniteAddGroup);
  var mulGroup = extend(F.Finite(n), {n:n}, F.FiniteMulGroup);
  finiteField.init(addGroup, mulGroup);
  mulGroup.setOrder(n);
  return finiteField;
}

class MathObj {
  constructor() {}
  str() { return this.toString() }
}

F.MathObj = MathObj;

// =========== Field Object ==============
class FieldObj extends MathObj {
  constructor(field) { 
    super();
    this.field = field;
		var p = Object.getPrototypeOf(this);
		p.zero = field.zero;
		p.one = field.one;
  }
  
  add(y) { return this.field.add(this,y) }
  mul(y) { return this.field.mul(this,y) }
  neg() { return this.field.neg(this) }
  inv() { return this.field.inv(this) }
  div(y) { return this.field.div(this,y) }
  sub(y) { return this.field.sub(this,y) }
  power(n) { return this.field.power(this,n) }
	isZero(x) { return this.field.isZero(this) }
	isOne(x) { return this.field.isOne(this) }
  eq(y) { return this.field.eq(this, y) }
	neq(y) { return this.field.neq(this, y) }
	mod(y) { return this.field.mod(this, y) }
	gcd(y) { return this.field.gcd(this, y) }
}

F.FieldObj = FieldObj;

// =========== Complex Field ==============
F.ComplexField=extend({}, F.Field);

class Complex extends FieldObj {
  constructor(a,b) {
    super(F.ComplexField);
    this.a = a; this.b = b; 
  }
  conj() { return new Complex(this.a, -1*this.b); }
  
	str() { 
    var op = (this.b<0)?'':'+';
	  return this.a.str()+op+this.b.str()+'i';
	}
  toString() { return this.str() }
  
	toPolar() {
    var a=this.a, b=this.b, r=Math.sqrt(a*a+b*b);
    var theta = Math.acos(a/r);
		return {r:r, theta:theta}
	}
	
	power(k) {
		var p = this.toPolar();
		return Complex.polarToComplex(Math.pow(p.r,k), k*p.theta);
	}
	
	sqrt() {
		return this.power(1/2);
	}
	
	static toComplex(o) {
		if (F.isFloat(o))
			return new Complex(o, 0);
		else if (o instanceof Complex)
			return o;
		console.log('o=', o);
		throw Error('toComplex fail');
	}
	
	static polarToComplex(r,theta) {
    var a=r*Math.cos(theta), b=r*Math.sin(theta);
		return new Complex(a, b);
	}
	
  static parse(s) {
    var m = s.match(/^([^\+]*)(\+(.*))?$/);
    var a = parseFloat(m[1]);
    var b = typeof m[3]==='undefined'?1:parseFloat(m[3]);
    return new Complex(a, b)
  }
}

F.Complex = Complex;
var C = (a,b)=>new Complex(a,b);
var enumComplex=[C(1,0),C(0,1),C(0,0),C(2,3),C(-5,4),C(-10,-7)];
F.ComplexSet=new F.Set(enumComplex);
F.ComplexSet.has = (a)=>a instanceof Complex;

F.ComplexAddGroup={
  e:new Complex(0,0),
  op:function(x,y) { 
	  x = Complex.toComplex(x), y=Complex.toComplex(y);
	  return new Complex(x.a+y.a, x.b+y.b) 
	},
  inv:function(x) { 
	  x = Complex.toComplex(x);
	  return new Complex(-x.a, -x.b) 
	}
}

extend(F.ComplexAddGroup, F.Group, F.ComplexSet);

F.ComplexMulGroup={
  e:new Complex(1,0),
  op:function(x,y) {
	  x = Complex.toComplex(x), y=Complex.toComplex(y);
    return new Complex(x.a*y.a-x.b*y.b, x.a*y.b+x.b*y.a);
  },
  inv:function(x) {
	  x = Complex.toComplex(x);
    var a=x.a,b=x.b, r=(a*a+b*b);
    return new Complex(a/r, -b/r);
  } 
}

extend(F.ComplexMulGroup, F.Group, F.ComplexSet);

extend(F.ComplexField, F.ComplexSet);

F.ComplexField.init(F.ComplexAddGroup, F.ComplexMulGroup);

// =========== Ratio Field ==============
F.RatioField=extend({}, F.Field);

class Ratio extends FieldObj {
  constructor(a,b) {
    super(F.RatioField);
    this.a = a; this.b = b; 
  }

  reduce() {
    var a = this.a, b=this.b;
    var c = F.Integer.gcd(a, b);
    return new Ratio(a/c, b/c);
  }
  
  toString() { return this.a+'/'+this.b; }

  static parse(s) {
    var m = s.match(/^(\d+)(\/(\d+))?$/);
    var a = parseInt(m[1]);
    var b = typeof m[3]==='undefined'?1:parseInt(m[3]);
    return new Ratio(a, b)
  } 
}

F.Ratio = Ratio;

F.RatioAddGroup={
  e:new Ratio(0,1),
  op:function(x,y) { return new Ratio(x.a*y.b+x.b*y.a, x.b*y.b) },
  inv:function(x) { return new Ratio(-x.a, x.b); },
}
  
extend(F.RatioAddGroup, F.Group);

F.RatioMulGroup={
  e:new Ratio(1,1),
  op:function(x,y) { return new Ratio(x.a*y.a, x.b*y.b) },
  inv:function(x) { return new Ratio(x.b, x.a) },
}

extend(F.RatioMulGroup, F.Group);

F.RatioField.init(F.RatioAddGroup, F.RatioMulGroup);

// =========== Function Operation ==============
F.fneg=function(fx) { return function(v) {
	return -1*fx(v);
}}

F.finv=function(fx) { return function(v) {
	return 1/fx(v);
}}

F.fadd=function(fx,fy) { return function(v) {
	return fx(v).add(fy(v));
}}

F.fsub=function(fx,fy) { return function(v) {
	return fx(v).sub(fy(v));
}}

F.fmul=function(fx,fy) { return function(v) {
	return fx(v).mul(fy(v));
}}

F.fdiv=function(fx,fy) { return function(v) {
	return fx(v).div(fy(v));
}}

F.fcompose=function(fx,fy) { return function(v) {
	return fx(fy(v));
}}

F.feval=function(f,x) { return f(x) }

// f=(x,y)=>x*y+x*x;
// f0=fa(f); f0([x,y]);
F.fa=function(f) {
	return function(x) {
		return f.apply(null, x);
	}
}

// =========== Function Field ==============
F.FunctionField=extend({}, F.Field);

F.FunctionAddGroup={
  e:function(x) { return 0 },
  op:function(x,y) { return F.fadd(x,y) },
  inv:function(x) { return F.fneg(x) },
}
  
extend(F.FunctionAddGroup, F.Group);

F.FunctionMulGroup={
  e:function(x) { return f(x) },
  op:function(x,y) { return F.fsub(x,y) },
  inv:function(x) { return F.finv(x) },
}

extend(F.FunctionMulGroup, F.Group);

F.FunctionField.init(F.FunctionAddGroup, F.FunctionMulGroup);

// Function
F.isField=function(x) {
	return F.isBool(x) || F.isNumber(x) || x instanceof F.FieldObj;
}

module.exports = F;


},{"./integer":6,"./set":9}],5:[function(require,module,exports){
var G = require("./statistics");

// 各種 space : https://en.wikipedia.org/wiki/Space_(mathematics)#/media/File:Mathematical_implication_diagram_eng.jpg

G.Space={} // Space = HllbertSpace + BanachSpace + Manifold (流形)

G.HilbertSpace={} // HilbertSpace => InnerProductSpace => LocallyConvaxSpace => VectorSpace (LinearSpace)

G.InnerProductSpace={}

G.LocallyConvaxSpace={}

G.LinearSpace=G.VectorSpace={} // (Algebraic)

G.BanachSpace={} // BanachSpace => NormedVectorSpace => MetricSpace => TopologicalSpace

G.NormedVectorSpace={}

G.MetricSpace={}

G.TopologicalSpace={} // (Analytic)

G.Manifold={}

G.Rn = {} // (R,R,....)

G.steps = function(from, to, step) {
	step=step || 1;
	var a=[];
	for (var t=from; t<=to; t+=step)
		a.push(t);
	return a;
}

G.curve=function(f, from=-10, to=10, step=0.1) {
	var x=G.steps(from, to, step);
	var y=x.map(f);
	return { type:"curve", x:x,	y:y	};
}

G.hist=function(a, from, to, step=1) {
//	console.log("from=%d to=%d step=%d", from, to, step);
	from = from||a.min();
	to = to||a.max();
  var n = Math.ceil((to-from+G.EPSILON)/step);
  var xc = G.steps(from+step/2.0, to, step);
//	console.log("from=%d to=%d step=%d xc=%j", from, to, step, xc);
  var bins = G.newV(n, 0);
  for (var i in a) {
    var slot=Math.floor((a[i]-from)/step);
    if (slot>=0 && slot < n)
      bins[slot]++;
  }
	return { type:'histogram', xc:xc, bins:bins, from:from, to:to, step:step};
}
/*
G.ihist=function(a) {
	console.log("a.min()=%d a.max()=%d", a.min(), a.max());
	return G.hist(a, a.min()-0.5, a.max()+0.5, 1);
}
*/
module.exports=G;
},{"./statistics":10}],6:[function(require,module,exports){
var I = {};

I.gcd = function(a, b) {
  if (!b) return a;
  return I.gcd(b, a % b);
}

I.lcm = function(a, b) {
  return (a * b) / gcd(a, b);   
}

I.isPrime=function(n) {
	for (var i=2; i<=Math.sqrt(n); i++)
		if (n%i===0) return false;
	return n%1===0;
}

module.exports = I;
},{}],7:[function(require,module,exports){
// var M = require("./calculus");
var M = require("./geometry");

module.exports=M;

},{"./geometry":5}],8:[function(require,module,exports){
var N = require("numeric");
var M = require("./algebra");
// var M = N;
// Advance mathematics
M.ode=N.dopri; // dopri(x0,x1,y0,f,tol,maxit,event) #Ordinary Diff Eq
M.minimize=N.uncmin; // uncmin(f,x0,tol,gradient,maxit,callback,options) # Unconstrained optimization
M.sparse=N.ccsSparse; // Matrix => Sparse
M.sparse2full=N.ccsFull; // Sparse => Matrix
// M.complex=N.t;
// matrix
M.svd = N.svd;
M.det = N.det;
M.inv = N.inv;
M.lu = N.cLU;
M.luSolve = N.cLUsolve;
M.dot = N.dot;
M.rep = N.rep;
M.tr = N.transpose;
M.diag = N.diag;
M.mstr = M.strM = N.prettyPrint;
// M.sumM = N.sum;
M.rows=function(m) { return m.length; }
M.cols=function(m) { return m[0].length; }
M.row =function(m,i) { return m[i]; }
M.col =function(m,j) { 
  var cols = m.cols();
  var c = M.vnew(cols);
	for (var i=0;i<cols;i++) {
		c[i] = m[i][j];
	}
	return c;
}

M.newV = function(n, value) {
	return M.rep([n], value||0);
}

M.newM = function(rows, cols, value) {
	return M.rep([rows, cols], value||0);
}

M.randomV = function(n, a, b) { 
  return N.random([n]).mul(b-a).add(a); 
}

M.randomM = function(rows, cols, a, b) {
  return N.random([rows, cols]).mul(b-a).add(a); 
}

M.rowSum = function(m) {
	var rows = M.rows(m);
	var s=M.newV(rows, 0);
	for (var i=0; i<rows; i++) {
		s[i] = m[i].sum();
	}
	return s;
}

M.colSum = function(m) {
	var mt = M.tr(m);
	return M.rowSum(mt);
}

M.rowMean = function(m) { 
  return M.rowSum(m).div(m.cols());
}

M.colMean = function(m) { 
  return M.colSum(m).div(m.rows());
}

M.addMV = function(m,v) {
  var result = [];
  for(var i=0;i<m.length;i++) {
    result.push(m[i].add(v));
	}
  return result;
}

M.mapM = function(m, f) {
	var fm = M.clone(m);
	var rows = M.rows(m), cols=M.cols(m);
  for(i=0;i<rows;i++) {
    for(j=0;j<cols;j++)
      fm[i][j]=f(m[i][j]);
  }
  return fm;
}

M.mapMM = function(m1,m2,f) {
	var fm = M.clone(m1);
	var rows = m1.rows(), cols=m1.cols();
  for(i=0;i<rows;i++) {
    for(j=0;j<cols;j++)
      fm[i][j]=f(m1[i][j],m2[i][j]);
  }
  return fm;
}

M.flatM=function(m) {
	var a=[];
	var ai = 0;
	for (var i=0; i<m.length;i++)
		for (var j=0; j<m[i].length; j++)
			a[ai++] = m[i][j];
	return a;
}

M.fillVM=function(v,rows,cols) {
	var m = M.newM(rows,cols);
	for (var r=0; r<rows; r++) {
		for (var c=0; c<cols; c++) {
			m[r][c] = v[r*cols+c];
		}
	}
	return m;
}

M.fillMM=function(m,rows,cols) {
	var v = M.flatM(m);
	return M.fillVM(m,rows,cols);
}

M.eig=function(m) {
	var E = N.eig(m);
	return {lambda:E.lambda.x, E:E.E.x};
}

module.exports = M;
},{"./algebra":1,"numeric":16}],9:[function(require,module,exports){
var S = {}
var I = require("./integer");

S.PI = Math.PI;
S.E  = Math.E;

extend = S.extend = Object.assign;
// ================= Rule =====================
var check = S.check = S.assert = function(cond, msg) {
	if (cond)
		console.log("O:"+msg);
	else {
		console.log("X:"+msg);
		if (S.throwError) throw Error('check fail!');
	}
}

be = S.be =function(msg,cond) { return check(cond, msg) }

S.proto=function(o) { return Object.getPrototypeOf(o) }

// relation
var eq=S.eq=function(a,b)  {
  return (typeof a === typeof b) && a.toString()===b.toString() 
}
S.neq=function(a,b)  { return !S.eq(a,b) }
S.leq=function(a,b)  { return a<=b }
S.geq=function(a,b)  { return a>=b }
S.lt =function(a,b)  { return a<b  }
S.gt =function(a,b)  { return a>b  }

// ========= type checking =================
S.yes=function(a) { return true }
S.no=function(a) {return false }
S.isBool=function(a) { 
  return typeof a === 'boolean' || a instanceof Boolean 
}
S.isFunction=function(a) { 
  return typeof a==='function' || a instanceof Function 
}
S.isString=function(a) { 
  return typeof a==='string' || a instanceof String 
}
S.isObject=function(a) { 
  return typeof a==='object' || a instanceof Object 
}
S.isArray=function(a) { 
  return a instanceof Array 
}
S.isUndefined=function(a) { 
  return typeof a === 'undefined' 
}
S.isSet=function(a) { 
  return a instanceof Set 
}
S.isFloat=S.isNumber=function(a) { 
  return typeof a === 'number' || a instanceof Number 
}
S.isInteger=function(a) { return S.isFloat(a) && a%1===0 }
S.isZero=function(a) { return a===0 }
S.isPositive=function(a) { return a>0 }
S.isNegative=function(a) { return a<0 }
S.isEven=function(a) { return (S.isInteger(a) && a%2===0) }
S.isOdd=function(a) { return (S.isInteger(a) && a%2===1) }

// ========== Random ==============
S.random=function(a,b) {
  return a+Math.random()*(b-a);
}

S.randomInt=function(a,b) {
  return Math.floor(S.random(a,b));
}

S.sample=function(a) {
  return a[S.randomInt(0,a.length)]; 
}

// ========= Set ===================
Set.prototype.union = function(setB) {
    var union = new Set(this);
    for (var elem of setB) {
        union.add(elem);
    }
    return union;
}

Set.prototype.intersection = function(setB) {
    var intersection = new Set();
    for (var elem of setB) {
        if (this.has(elem)) {
            intersection.add(elem);
        }
    }
    return intersection;
}

Set.prototype.difference = function(setB) {
    var difference = new Set(this);
    for (var elem of setB) {
        difference.delete(elem);
    }
    return difference;
}

Set.prototype.enumerate = function(n) {
	var array=[], values = this.values();
	for (var i=0; i<n; i++) {
		array.push(values.next().value);
	}
	return array;
}

class EnumSet {
	constructor(enumHead) { 
	  this.set = new Set(enumHead);
	  this.enumHead = S.isUndefined(enumHead)?[]:enumHead;	
	}
	add(e) { this.set.add(e) }
	has(e) { return this.set.has(e) }
	sample(n) { 
	  if (S.isUndefined(n))
			return S.sample(this.enumHead);
		else {
			var a=[];
			for (var i=0; i<n; i++) a.push(this.sample());
			return a;
		}
	}
	enumerate() { return this.enumHead }
	intersection(y) {
		var x=this, xy=new EnumSet();
		xy.has=function(e) { return x.has(e)&&y.has(e) }
		return xy;
	}
	union(y) {
		var x=this, xy=new EnumSet();
		xy.has=function(e) { return x.has(e)||y.has(e) }
		return xy;
	}
	difference(y) {
		var x=this, xy=new EnumSet();
		xy.has=function(e) { return x.has(e)&&!y.has(e) }
		return xy;
	}
	symmetricDifference(y) {
		var x=this;
		return x.union(y).difference(x.intersection(y));
	}
	cartesianProduct(y) { 
		var x=this, xy=new EnumSet();
		xy.has=function(e) { return x.has(e[0]) && y.has(e[1]) }
		return xy;
	}
}

S.Set = EnumSet

function steps(a,b,step) {
	var array=[];
	for (var i=a; i<=b; i+=step) 
		array.push(i);
	return array;
}

var enumFloat = [-3.2,-1, 0, 1, 2.3, 4.7];
var enumInt   = [-10,-5,-1,0,1,3,5,6];
var enumN0    = steps(0,10,1);
var enumN1    = steps(1,10,1);
var enumOdd   = steps(1,15,2);
var enumEven  = steps(2,15,2);
var enumPrime = [2,3,5,7,11,13,17,19,23,29,31,37];
var enumAll   = ["hi", 5, Math.PI, EnumSet, S.isBool, enumPrime, new Set() ];

// 全體集合
S.All = new EnumSet(enumAll);
S.All.has = S.yes;

// 空集合
S.Empty = new EnumSet([]);
S.Empty.has = S.no;

// 浮點數集合
S.Float=new EnumSet(enumFloat);
S.Float.has=S.isFloat;

// 整數集合
S.Z=S.Integer=new EnumSet(enumInt);
S.Z.has=S.isInteger;

// 自然數集合 N0
S.N0=new EnumSet(enumN0);
S.N0.has=(e)=>S.isInteger(e)&&e>=0;

// 自然數集合 N1
S.N1=new EnumSet(enumN1);
S.N1.has=(e)=>S.isInteger(e)&&e>1;

// 偶數集合
S.Even=new EnumSet(enumEven);
S.Even.has=S.isEven;

// 奇數集合
S.Odd=new EnumSet(enumOdd);
S.Odd.has=S.isOdd;

// 質數集合
S.Prime=new EnumSet(enumPrime)
S.Prime.has=I.isPrime;

// 有限集合 0...n-1
S.Finite=(n)=>new EnumSet(steps(0,n-1,1));

// 羅素集合悖論
S.RussellSet=new EnumSet(enumAll);
S.RussellSet.has=function(e) { return !e.has(e) }

module.exports=S;

},{"./integer":6}],10:[function(require,module,exports){
var B = require('./base');
var J = require('jStat').jStat;
var S = require('./calculus');
var ncall = B.ncall;
// var T, R;

// ========== 離散分佈的 r, q 函數 ============
S.qcdf=function(cdf, q, N, p) {
  for (var i=0; i<=N; i++) {
    if (cdf(i, N, p) > q) return i;
  }
  return N;
}

S.rcdf=function(cdf, n, N, p) {
  var a = [];
  for (var i=0; i<n; i++) {
    var q = Math.random();
    a.push(cdf(q, N, p));
  }
  return a;
}

S.EPSILON=0.0000000001;
// 均等分布 : jStat.uniform( a, b )
S.dunif=(x,a=0,b=1)=>J.uniform.pdf(x,a,b);
S.punif=(q,a=0,b=1)=>J.uniform.cdf(q,a,b);
S.qunif=(p,a=0,b=1)=>J.uniform.inv(p,a,b);
S.runif=(n,a=0,b=1)=>ncall(n, J.uniform, 'sample', a, b);
// 常態分布 : jStat.normal( mean, sd )
S.dnorm=(x,mean=0,sd=1)=>J.normal.pdf(x,mean,sd);
S.pnorm=(q,mean=0,sd=1)=>J.normal.cdf(q,mean,sd);
S.qnorm=(p,mean=0,sd=1)=>J.normal.inv(p,mean,sd);
S.rnorm=(n,mean=0,sd=1)=>ncall(n, J.normal, 'sample', mean, sd);
// F 分布 : jStat.centralF( df1, df2 )
S.df=(x,df1,df2)=>J.centralF.pdf(x,df1,df2);
S.pf=(q,df1,df2)=>J.centralF.cdf(q,df1,df2);
S.qf=(p,df1,df2)=>J.centralF.inv(p,df1,df2);
S.rf=(n,df1,df2)=>ncall(n, J.centralF, 'sample', df1, df2);
// T 分布 : jStat.studentt( dof )
S.dt=(x,dof)=>J.studentt.pdf(x,dof);
S.pt=(q,dof)=>J.studentt.cdf(q,dof);
S.qt=(p,dof)=>J.studentt.inv(p,dof);
S.rt=(n,dof)=>ncall(n, J.studentt, 'sample', dof);
// Beta 分布 : jStat.beta( alpha, beta )
S.dbeta=(x,alpha,beta)=>J.beta.pdf(x,alpha,beta);
S.pbeta=(q,alpha,beta)=>J.beta.cdf(q,alpha,beta);
S.qbeta=(p,alpha,beta)=>J.beta.inv(p,alpha,beta);
S.rbeta=(n,alpha,beta)=>ncalls(n, J.beta, 'sample', alpha, beta);
// 柯西分布 : jStat.cauchy( local, scale )
S.dcauchy=(x,local,scale)=>J.cauchy.pdf(x,local,scale);
S.pcauchy=(q,local,scale)=>J.cauchy.cdf(q,local,scale);
S.qcauchy=(p,local,scale)=>J.cauchy.inv(q,local,scale);
S.rcauchy=(n,local,scale)=>ncall(n, J.cauchy, 'sample', local, scale);
// chisquare 分布 : jStat.chisquare( dof )
S.dchisq=(x,dof)=>J.chisquare.pdf(x,dof);
S.pchisq=(q,dof)=>J.chisquare.cdf(q,dof);
S.qchisq=(p,dof)=>J.chisquare.inv(p,dof);
S.rchisq=(n,dof)=>ncall(n, J.chisquare, 'sample', dof);
// 指數分布 : jStat.exponential( rate )
S.dexp=(x,rate)=>J.exponential.pdf(x,rate);
S.pexp=(q,rate)=>J.exponential.cdf(q,rate);
S.qexp=(p,rate)=>J.exponential.inv(p,rate);
S.rexp=(n,rate)=>ncall(n, J.exponential, 'sample', rate);
// Gamma 分布 : jStat.gamma( shape, scale )
S.dgamma=(x,shape,scale)=>J.gamma.pdf(x,shape,scale);
S.pgamma=(q,shape,scale)=>J.gamma.cdf(q,shape,scale);
S.qgamma=(p,shape,scale)=>J.gamma.inv(p,shape,scale);
S.rgamma=(n,shape,scale)=>ncall(n, J.gamma, 'sample', shape, scale);
// 反 Gamma 分布 : jStat.invgamma( shape, scale )
S.rinvgamma=(n,shape,scale)=>ncall(n, J.invgamma, 'sample', shape, scale);
S.dinvgamma=(x,shape,scale)=>J.invgamma.pdf(x,shape,scale);
S.pinvgamma=(q,shape,scale)=>J.invgamma.cdf(q,shape,scale);
S.qinvgamma=(p,shape,scale)=>J.invgamma.inv(p,shape,scale);
// 對數常態分布 : jStat.lognormal( mu, sigma )
S.dlognormal=(n, mu, sigma)=>J.lognormal.pdf(x,sigma);
S.plognormal=(n, mu, sigma)=>J.lognormal.cdf(q,sigma);
S.qlognormal=(n, mu, sigma)=>J.lognormal.inv(p,sigma);
S.rlognormal=(n, mu, sigma)=>ncall(n, J.dlognormal, 'sample', mu, sigma);
// Pareto 分布 : jStat.pareto( scale, shape )
S.dpareto=(n, scale, shape)=>J.pareto.pdf(x,scale,shape);
S.ppareto=(n, scale, shape)=>J.pareto.cdf(q,scale,shape);
S.qpareto=(n, scale, shape)=>J.pareto.inv(p,scale,shape);
S.rpareto=(n, scale, shape)=>ncall(n, J.pareto, 'sample', scale, shape);
// Weibull 分布 jStat.weibull(scale, shape)
S.dweibull=(n, scale, shape)=>J.weibull.pdf(x,scale,shape);
S.pweibull=(n, scale, shape)=>J.weibull.cdf(q,scale,shape);
S.qweibull=(n, scale, shape)=>J.weibull.inv(p,scale,shape);
S.rweibull=(n, scale, shape)=>ncall(n, J.weibull, 'sample', scale, shape);
// 三角分布 : jStat.triangular(a, b, c)
S.dtriangular=(n, a, b, c)=>J.triangular.pdf(x,a,b,c);
S.ptriangular=(n, a, b, c)=>J.triangular.cdf(q,a,b,c);
S.qtriangular=(n, a, b, c)=>J.triangular.inv(p,a,b,c);
S.rtriangular=(n, a, b, c)=>ncall(n, J.triangular, 'sample', a, b, c);
// 類似 Beta 分布，但計算更簡單 : jStat.kumaraswamy(alpha, beta)
S.dkumaraswamy=(n, alpha, beta)=>J.kumaraswamy.pdf(x,alpha,beta);
S.pkumaraswamy=(n, alpha, beta)=>J.kumaraswamy.cdf(q,alpha,beta);
S.qkumaraswamy=(n, alpha, beta)=>J.kumaraswamy.inv(p,alpha,beta);
S.rkumaraswamy=(n, alpha, beta)=>ncalls(n, J.kumaraswamy, 'sample', alpha, beta);

// ========== 離散分佈的 r, q 函數 ============
// 二項分布 : jStat.binomial(n, p0)
S.dbinom=(x, size, prob)=>J.binomial.pdf(x, size, prob);
S.pbinom=(q, size, prob)=>J.binomial.cdf(q, size, prob);
S.qbinom=(p, size, prob)=>S.qcdf(S.pbinom, p, size, prob);
S.rbinom=(n, size, prob)=>S.rcdf(S.qbinom, n, size, prob);
// 負二項分布 : jStat.negbin(r, p)
S.dnbinom=(x, size, prob)=>J.negbin.pdf(x, size, prob);
S.pnbinom=(q, size, prob)=>J.negbin.cdf(q, size, prob);
S.qnbinom=(p, size, prob)=>S.qcdf(S.pnbinom, p, size, prob);
S.rnbinom=(n, size, prob)=>S.rcdf(S.qnbinom, n, size, prob);
// 超幾何分布 : jStat.hypgeom(N, m, n)
S.dhyper=(x, m, n, k)=>J.hypgeom.pdf(k, m, n, k);
S.phyper=(q, m, n, k)=>J.hypgeom.cdf(q, m, n, k);
S.qhyper=(p, m, n, k)=>S.qcdf(S.phyper, p, m, n, k);
S.rhyper=(nn,m, n, k)=>S.rcdf(S.qhyper, nn, m, n, k);
// 布瓦松分布 : jStat.poisson(l)
S.dpois=(x, lambda)=>J.poisson.pdf(x, lambda);
S.ppois=(q, lambda)=>J.poisson.cdf(q, lambda);
S.qpois=(p, lambda)=>S.qcdf(S.ppois, p, lambda);
S.rpois=(n, lambda)=>S.rcdf(S.qpois, n, lambda);

// ====================== statistics =================================
// extend function

S.normalize=function(a) {
	var sum = S.sum(a);
	return a.map(function(x) { return x/sum});
}

// Vector Functionality
B.copyFunctions(S, J, "sumsqrt,sumsqerr,sumrow,mean,meansqerr,geomean,median,cumsum,cumprod,diff,mode,range,variance,stdev,meandev,meddev,skewness,kurtosis,coeffvar,quartiles,quantiles,percentile,percentileOfScore,histogram,covariance,corrcoeff,calcRdx,betafn,betacf,ibetainv,ibeta,gammafn,gammaln,gammap,lowRegGamma,gammapinv,factorialln,factorial,combination,combinationln,permutation,erf,erfc,erfcinv,randn,randg".split(","));

B.mapFunctions(S, J, {
	C:'combination',// C(n,m)
	choose:'combination',// C(n,m)
	lchoose:'combinationln',// log C(n,m)
	P:'permutation', // P(n,m)
	sd:'stdev',
	cov:'covariance',
	cor:'corrcoeff',
});

// =============== 檢定 ==============================
B.mix(S, B);

var T = S;

T.test = function(o) { // name, D, x, mu, sd, y, alpha, op
  Object.assign(o, {alpha:0.05, op:"="});
  var alpha = o.alpha;
  var pvalue, interval;
  var D      = o.D;
  var q1     = D.o2q(o); // 單尾檢定的 pvalue
  
  if (o.op === "=") {
    if (q1>0.5) q1 = 1-q1; // (q1>0.5) 取右尾，否則取左尾。
    pvalue= 2*q1; // 對稱情況：雙尾檢定的 p 值是單尾的兩倍。
    interval = [D.q2p(alpha/2, o, "L"), D.q2p(1-alpha/2, o, "R")];
  } else {
    if (o.op === "<") { // 右尾檢定 H0: q < 1-alpha, 
      interval = [ D.q2p(alpha, o, "L"), Infinity ]; 
      pvalue = 1-q1;
    }
    if (o.op === ">") { // 左尾檢定 H0: q > alpha
      interval=[-Infinity, D.q2p(1-alpha, o, "R")];
      pvalue = q1;
    }
  }
  return { 
    name: o.name,
    h: D.h(o),
    alpha: alpha,
    op: o.op, 
    pvalue: pvalue, 
    ci : interval, 
    df : D.df(o),
    report: function() { S.report(this) }
  };
}

T.report = function(o) {
  console.log("=========== report ==========");
  for (var k in o) {
    if (typeof o[k] !== "function")
      console.log(k+"\t: "+S.str(o[k]));
  }
}

var t1 = { // 單樣本 T 檢定 t = (X-mu)/(S/sqrt(n))
  h:function(o) { return "H0:mu"+o.op+o.mu; }, 
  o2q:function(o) {
    var x = o.x, n = x.length;
    var t = (S.mean(x)-o.mu)/(S.sd(x)/Math.sqrt(n)); 
    return S.pt(t, n-1);
  },
  // P(X-mu/(S/sqrt(n))<t) = q ; 信賴區間 P(T<q)
  // P(mu > X-t*S/sqrt(n)) = q ; 這反而成了右尾檢定，所以左尾與右尾確實會反過來
  q2p:function(q, o) {
    var x = o.x, n = x.length;
    return S.mean(x) + S.qt(q, n-1) * S.sd(x) / Math.sqrt(n);
  },
  df:function(o) { return o.x.length-1; }
}

var t2vareq = { // σ1=σ2, 合併 T 檢定 (雙樣本)
  h:function(o) { return "H0:mu1"+o.op+"mu2" }, 
  // S^2 = (n1-1)*S1^2+(n2-1)*S2^2)/(n1-1+n2-1)
  sd:function(o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    var S1= S.sd(x), S2 = S.sd(y);
    var S = Math.sqrt(((n1-1)*S1*S1+(n2-1)*S2*S2)/(n1-1+n2-1)); 
    return S;
  },
  // T = ((X-Y)-(mu1-mu2))/(sqrt(1/n1+1/n2)*S)
  o2q:function(o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    var S = this.sd(o);
    var t = (S.mean(x)-S.mean(y)-o.mu)/(Math.sqrt(1/n1+1/n2)*S);
    return S.pt(t, n1+n2-2);
  },
  // t=((X-Y)-mu)/(sqrt(1/n1+1/n2)*S), (X-Y)-t*sqrt(1/n1+1/n2)*S = mu
  q2p:function(q, o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    var S = this.sd(o);
    return S.mean(x)-S.mean(y)+ S.qt(q, n1+n2-2)*Math.sqrt(1/n1+1/n2)*S;
  },
  df:function(o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;  
    return n1+n2-2; 
  }
}

var t2paired = { // 成對 T 檢定 T = (X-Y-mu)/(S/sqrt(n)) (雙樣本)
  h:function(o) { return "H0:mu1"+o.op+"mu2" }, 
  sd:function(o) { // S = sd(x-y)
    var x = o.x, n = x.length, y=o.y;
    var S= S.sd(S.sub(x,y));
    return S;
  },
  o2q:function(o) { 
    var x = o.x, n = x.length, y=o.y;
    var S = this.sd(o);
    var t = (S.mean(S.sub(x,y))-o.mu)/(S/Math.sqrt(n));
    return S.pt(t, n-1);
  },
  // mean(x-y)+t*S/sqrt(n)
  q2p:function(q, o) {
    var x = o.x, n = x.length, y=o.y;
    var S = this.sd(o);
    return S.mean(S.sub(x,y))+ S.qt(q, n-1)*S/Math.sqrt(n);
  },
  df:function(o) {
    return o.x.length-1; 
  }
}

var t2varneq = { // σ1≠σ2, Welch's t test (雙樣本) (又稱 Smith-Satterwaite 程序)
// 參考：http://en.wikipedia.org/wiki/Welch's_t_test
  h:function(o) { return "H0:mu1"+o.op+"mu2" }, 
  // T = ((X-Y)-(mu1-mu2))/sqrt(S1^2/n1+S2^2/n2)
  o2q:function(o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    var S1 = S.sd(x), S2=S.sd(y);
    var t = (S.mean(x)-S.mean(y)-o.mu)/Math.sqrt(S1*S1/n1+S2*S2/n2);
    return S.pt(t, this.df(o));
  },
  // t=((X-Y)-mu)/sqrt(S1^2/n1+S2^2/n2), (X-Y)-t*sqrt(S1^2/n1+S2^2/n2) = mu
  q2p:function(q, o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    var S1 = S.sd(x), S2=S.sd(y);
    return S.mean(x)-S.mean(y)+ S.qt(q, this.df(o))*Math.sqrt(S1*S1/n1+S2*S2/n2);
  },
  df:function(o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;  
    var S1 = S.sd(x), S2=S.sd(y);
    var Sn1 = S1*S1/n1, Sn2 = S2*S2/n2, Sn12 = Sn1+Sn2;
    var df = (Sn12*Sn12)/((Sn1*Sn1)/(n1-1)+(Sn2*Sn2)/(n2-1));
    return df;
  }
}

T.ttest = function(o) { 
  var t;
  if (typeof o.y === "undefined") {
    o.name = "ttest(X)";
    o.D = t1;
    t = T.test(o);
    t.mean = S.mean(o.x);
    t.sd   = S.sd(o.x);
  } else {
    var varequal = o.varequal || false;
    var paired = o.paired || false;
    if (varequal) {
      o.name = "ttest(X,Y,mu="+o.mu+",varequal=true) (pooled)";
      o.D = t2vareq;
      t = T.test(o);
    } else if (paired) {
      o.name = "ttest(x,y,mu="+o.mu+",paired=true)";
      o.D = t2paired;
      t = T.test(o);
      t.mean = "mean(x-y)="+S.str(S.mean(S.sub(o.x, o.y)));
      t.sd   = "sd(x-y)="+S.str(S.sd(S.sub(o.x, o.y)));
    } else {
      o.name = "ttest(x,y,mu="+o.mu+",varequal=false), Welch t-test";
      o.D = t2varneq;
      t = T.test(o);
    }
    if (typeof t.mean === "undefined") {
      t.mean = "mean(x)="+S.str(S.mean(o.x))+" mean(y)="+S.str(S.mean(o.y));
      t.sd   = "sd(x)="+S.str(S.sd(o.x))+" sd(y)="+S.str(S.sd(o.y));
    }
  }
  return t;
}

var f2 = { // 檢定 σ1/σ2 = 1? 
  h:function(o) { return "H0:σ1/σ2"+o.op+"1"; }, 
  // F = S1^2/S2^2
  o2q:function(o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    var S1 = S.sd(x), S2=S.sd(y);
    var f = (S1*S1)/(S2*S2);
    var pf = S.pf(f, n1-1, n2-1);
    return pf;
  },
  // 信賴區間公式： S1^2/(S2^2*F(1-α/2), S1^2/(S2^2*F(α/2))
  // 也就是要用 S1^2/(S2^2*f(1-q)) ，參考 R 軟體、應用統計方法 (陳景祥) 389 頁。
  q2p:function(q, o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    var S1 = S.sd(x), S2=S.sd(y);
    var qf = S.qf(1-q, n1-1, n2-1);
    return (S1*S1)/(S2*S2*qf);
  },
  df:function(o) {
    var x = o.x, n1 = x.length, y=o.y, n2=y.length;
    return [n1-1, n2-1];
  }
}

T.ftest = function(o) { 
  o.name = "ftest(X, Y)";
  o.D = f2;
  var t = T.test(o);
  var rsd = S.sd(o.x)/S.sd(o.y);
  t.ratio = (rsd*rsd);
  return t;
}

// R 軟體沒有此函數，測試請看湯銀才 143 頁
var chisq1 = { // 檢定 σ1 = σ ?
  h:function(o) { return "H0:σ1"+o.op+"σ"; }, 
  // χ(n-1) = (n-1)S^2/σ^2
  o2q:function(o) {
    var x = o.x, n = x.length, S=S.sd(x);
    var v = (n-1)*S*S/(o.sd*o.sd);
    return S.pchisq(v, n-1);
  },
  // 信賴區間公式： (n-1)S^2/χ^2(1-q)，參考 R 語言與統計分析 (湯銀才) 142 頁。
  q2p:function(q, o) {
    var x = o.x, n = x.length, S=S.sd(x);
    return (n-1)*S*S/S.qchisq(1-q, n-1);
  },
  df:function(o) {
    var x = o.x, n = x.length;
    return n-1;
  }
}

T.chisqtest = function(o) { 
  o.name = "chisqtest(X)";
  o.D = chisq1;
  return T.test(o);
}

T.vartest = function(o) {
  if (typeof o.y === "undefined")
    return S.chisqtest(o);
  else
    return S.ftest(o);
}

var z1 = { // 單樣本 Z 檢定
  h:function(o) { return "H0:mu"+o.op+o.mu+" when sd="+o.sd; }, 
  o2q:function(o) {
    var x = o.x, n = x.length;
    var z = (S.mean(x)-o.mu)/(o.sd/Math.sqrt(n)); // z=(X-mu)/(sd/sqrt(n))
    return S.pnorm(z, 0, 1);
  },
  q2p:function(q, o) {
    var x = o.x, n = x.length;
    return S.mean(x) + S.qnorm(q, 0, 1) * S.sd(x) / Math.sqrt(n);
  },
  df:function(o) { return o.x.length; }
}

T.ztest = function(o) { 
  o.name = "ztest(X)";
  o.D = z1;
  return T.test(o);
}

var zprop1 = { // 比例的檢定， n 較大時的近似解 o={ x, n, p } // x 為數值，n 個中出現 x 個 1
  h:function(o) { return "H0:p"+o.op+o.p; }, 
  // Z = (p1-p)/sqrt(p(1-p)/n)
  o2q:function(o) {
    var x=o.x, n=o.n, p1=x/n, p=o.p||p1;
    var z = (p1-p)/Math.sqrt(p*(1-p)/n);
    return S.pnorm(z, 0, 1);
  },
  // 信賴區間公式： p1+z*sqrt(p1*(1-p1)/n)，參考 R 語言與統計分析 (湯銀才) 149 頁。
  q2p:function(q, o) {
    var x=o.x, n=o.n, p1=x/n, p=p1;
    var z = S.qnorm(q, 0, 1);
    var z22n = z*z/(2*n);
    return (p1+z22n+z*Math.sqrt( p*(1-p)/n + z22n/(2*n) ))/(1+2*z22n); // R 的版本，比較複雜的估計公式
//  return p1+z*Math.sqrt(p*(1-p)/n); //  語言與統計分析 (湯銀才) 149 頁的版本。
  },
  df:function(o) { return 1; }
}

var zprop2 = { // 比例的檢定， n 較大時的近似解 o={ x, y, n1, n2 }
  h:function(o) { return "H0:p1-p2"+o.op+o.p; }, 
  // Z = (p1-p2)/sqrt(p*(1-p)*(1/n1+1/n2)), p = (n1p1+n2p2)/(n1+n2)，參考 R 語言與統計分析 (湯銀才) 175 頁。
  o2q:function(o) {
    var x=o.x, y=o.y, n1=o.n1, n2=o.n2, p1=x/n1, p2=y/n2, p=(n1*p1+n2*p2)/(n1+n2);
    var z = (p1-p2)/Math.sqrt(p*(1-p)*(1/n1+1/n2));
    return S.pnorm(z, 0, 1);
  },
  // 信賴區間公式： p1-p2+z*sqrt(p*(1-p)*(1/n1+1/n2));
  q2p:function(q, o) {
    var x=o.x, y=o.y, n1=o.n1, n2=o.n2, p1=x/n1, p2=y/n2, p=(n1*p1+n2*p2)/(n1+n2);
    var z = S.qnorm(q, 0, 1);
    return p1-p2+z*Math.sqrt(p*(1-p)*(1/n1+1/n2));
  },
  df:function(o) { return 1; }
}

/* 在 prop.test.R 當中，雙邊檢定的 pvalue 是用 pchisq, 單邊才是用 z ，為何呢？ ( 但是信賴區間則是全部用 z)
 if (alternative == "two.sided")
  PVAL <- pchisq(STATISTIC, PARAMETER, lower.tail = FALSE)
    else {
  if (k == 1)
      z <- sign(ESTIMATE - p) * sqrt(STATISTIC)
  else
      z <- sign(DELTA) * sqrt(STATISTIC)
  PVAL <- pnorm(z, lower.tail = (alternative == "less"))
    }
*/

T.proptest = function(o) {
  o.p = o.p || 0.5;
  o.name = "proptest("+S.str(o)+")";
  o.correct = o.correct|| false;
  if (o.correct) {
    o.name += ", binomtest";
    o.D += binom1;
  } else {
    if (typeof o.y === "undefined") {
      o.name += ", zprop1";
      o.D = zprop1;
    } else {
      o.p = 0; // p1-p2 = 0
      o.name += ", zprop2";
      o.D = zprop2;
    }
  }
  var t=T.test(o);
  if (typeof o.y === "undefined")
    t.p = o.x/o.n;
  else
    t.p = [o.x/o.n1, o.y/o.n2];
  return t;
}

// 參考： https://github.com/SurajGupta/r-source/blob/master/src/library/stats/R/binom.test.R
var binom1 = { // 比例的檢定， n 較大時的近似解 o={ x, n, p } // x 為數值，n 個中出現 x 個 1
  h:function(o) { return "H0:p"+o.op+o.p; }, 
  
  // Z = C(n, k)*p1^k*(1-p1)^(n-k), CDF(z: from 1 to x)
  o2q:function(o) {
    var x=o.x, n=o.n, p = o.p, q;
    var dx = S.dbinom(x, n, p);
    if (o.op === "=") { // 雙尾檢定，去雙尾後 / 2
      var q = 0;
      for (var i=0; i<=n; i++) {
        var di = S.dbinom(i, n, p);
        if (di > dx+1e-5) q += di; // 為何 x 本身不算，如果算應該用 di > dx-1e-5 才對。
      }
      q=1-((1-q)/2); // 因為 test 會 * 2 所進行的減半調整
    } else { // 單尾檢定
      if (Math.abs(x - n*p)<1e-5) // 正確預測， q=1
        q = 1;
      else {
        if (o.op === ">")
          q = S.pbinom(x, n, p); // 去右尾
        else // op=== "<"
          q = S.pbinom(x-1, n, p); // 去右尾
      }
    }
    return q;
  },
/* 注意上述 R 原始碼另一尾的計算方式，是用 < pbinom(最接近 x 者) 的算法，而不是直接 * 2。 問題是我們在 test 中是直接用*2 的方式。
  d <- dbinom(x, n, p)
  ...
  else if (x < m) {
      i <- seq.int(from = ceiling(m), to = n)
      y <- sum(dbinom(i, n, p) <= d * relErr)
      pbinom(x, n, p) 左尾 + pbinom(n - y, n, p, lower.tail = FALSE) 右尾
  } else {
      i <- seq.int(from = 0, to = floor(m))
      y <- sum(dbinom(i, n, p) <= d * relErr)
      pbinom(y - 1, n, p) 左尾 + pbinom(x - 1, n, p, lower.tail = FALSE) 右尾
  }
*/               
  // 信賴區間公式： P(T>c) = Σ (n, i) C(n, i) p1^i (1-p1)^(n-i) for i>c < q
  
  q2p:function(q, o, side) { 
    var x=o.x, n=o.n, p=o.p, op=o.op;
    if (side === "L")
      return S.qbeta(q, x, n - x + 1); // 這裏採用 qbeta 是 R 的作法; 直覺上應該採用 S.qbinom(q, n, p);
    else
      return S.qbeta(q, x + 1, n - x);
  },
  df:function(o) { return 1; }
}

T.binomtest = function(o) {
  o.p = o.p || 0.5;
  o.name = "binomtest("+S.str(o)+")";
  o.D = binom1;
  var t=T.test(o);
  t.p = o.x/o.n;
  t.ci[0]=(o.op === ">")?0:t.ci[0];
  t.ci[1]=(o.op === "<")?1:t.ci[1];
  return t;
}

// anova f-test : array1, array2, array3, ...
T.anovaftest = function() {
  return { 
    h0 : "σ1=σ2=...=σ"+arguments.length, 
    pvalue: J.anovaftest(), 
    score: J.anovafscore(),
  };
}

module.exports = S;

},{"./base":2,"./calculus":3,"jStat":14}],11:[function(require,module,exports){
var Symbol = require('algebrite')

module.exports = Symbol;
},{"algebrite":12}],12:[function(require,module,exports){
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factors, factpoly_expo, fill_buf, filter, filter_main, filter_sum, filter_tensor, findroot, fixed_top_level_eval, fixup_fraction, fixup_power, flag, fmt_index, fmt_level, fmt_x, frame, free_stack, gamma, gamma_of_sum, gammaf, gcd, gcd_expr, gcd_expr_expr, gcd_factor_term, gcd_main, gcd_numbers, gcd_term_factor, gcd_term_term, gen, get_arglist, get_binding, get_factor, get_next_token, get_printname, get_size, get_token, getdisplaystr, glyph, gp, guess, hasImaginaryCoeff, hermite, hilbert, imag, imaginaryunit, index_function, init, initNRoots, inited, inner, inner_f, input_str, integral, integral_of_form, integral_of_product, integral_of_sum, inv, inverse, invert_number, invg, is_denominator, is_factor, is_small_integer, is_square_matrix, isadd, isalnum, isalpha, iscomplexnumber, iscons, isdenominator, isdigit, isdouble, iseveninteger, isfactor, isfactorial, isfloating, isfraction, isimaginarynumber, isimaginaryunit, isinteger, isintegerfactor, iskeyword, isminusone, isminusoneoversqrttwo, ismultiply, isnegative, isnegativenumber, isnegativeterm, isnonnegativeinteger, isnpi, isnum, isoneover, isoneoversqrttwo, isplusone, ispoly, ispoly_expr, ispoly_factor, ispoly_term, isposint, ispower, isquarterturn, isrational, isspace, isstr, issymbol, issymbolic, istensor, iszero, itab, laguerre, laguerre2, lcm, leading, legendre, length, lessp, level, list, logarithm, logbuf, lookupsTotal, lu_decomp, madd, mag, makePositive, makeSignSameAs, mask, mcmp, mcmpint, mdiv, mdivrem, meta_mode, mgcd, mini_solve, mint, mmod, mmul, mod, monic, move, mp_clr_bit, mp_denominator, mp_numerator, mp_set_bit, mpow, mprime, mroot, mshiftright, msub, mtotal, multinomial_sum, multiply, multiply_all, multiply_all_noexpand, multiply_denominators, multiply_denominators_factor, multiply_denominators_term, multiply_noexpand, multiply_numbers, n_factor_number, negate, negate_expand, negate_noexpand, negate_number, new_string, newline_flag, nil_symbols, normalize_angle, nroots_a, nroots_b, nroots_c, nroots_df, nroots_dx, nroots_fa, nroots_fb, nroots_x, nroots_y, nterms, numerator, numericRootOfPolynomial, o, one, oneElement, out_buf, out_count, out_of_memory, outer, p0, p1, p2, p3, p4, p5, p6, p7, p8, p9, parse, parse_internal, parse_p1, parse_p2, partition, peek, peek2, polar, polycoeff, polyform, pop, pop_double, pop_frame, pop_integer, power, power_str, power_sum, power_tensor, prime, primetab, print1, print_a_over_b, print_char, print_denom, print_double, print_expr, print_factor, print_factorial_function, print_it, print_multiply_sign, print_number, print_str, print_subexpr, print_tensor, print_tensor_inner, print_term, printchar, printchar_nowrap, printline, program_buf, promote_tensor, push, push_cars, push_double, push_factor, push_frame, push_identity_matrix, push_integer, push_rational, push_symbol, push_term_factors, push_terms, push_zero_matrix, qadd, qdiv, qmul, qpow, qpowf, quickfactor, quickpower, rational, rationalize, rationalize_coefficients, real, reciprocate, rect, ref, ref1, remove_negative_exponents, reset_after_error, restore, rewrite_args, rewrite_args_tensor, roots, roots2, roots3, run, save, scalar_times_tensor, scan, scan_error, scan_expression, scan_factor, scan_function_call, scan_meta, scan_power, scan_relation, scan_stmt, scan_str, scan_string, scan_subexpr, scan_symbol, scan_term, scanned, setM, setSignTo, set_binding, set_binding_and_arglist, set_component, setq_indexed, sfac_product, sfac_product_f, sgn, shape, sign, sign_of_term, simfac, simfac_term, simplify, simplify_main, simplify_polar, simplify_tensor, simplify_trig, simplifyfactorials, sine, sine_of_angle, sine_of_angle_sum, sort_stack, square, ssqrt, stack, stackAddsCount, std_symbol, step, step2, stop, strcmp, stringToBePrinted, subf, subst, subtract, subtract_numbers, swap, symbol, symnum, symtab, tangent, taylor, tensor, tensor_plus_tensor, tensor_times_scalar, test_flag, text_metric, theRandom, token, token_buf, token_str, top_level_eval, tos, transform, transpose, trigmode, trivial_divide, try_kth_prime, ucmp, unique, unique_f, update_token_buf, usr_symbol, verbosing, will_be_displayed_as_fraction, ybinomial, ycosh, ydirac, yerf, yerfc, yfloor, yindex, ysinh, yyarg, yybesselj, yybessely, yyceiling, yycondense, yycontract, yycosh, yydegree, yydetg, yydivpoly, yyerf, yyerfc, yyexpand, yyfactorpoly, yyfloat, yyfloor, yyhermite, yyhermite2, yyinvg, yylcm, yylog, yymag, yymultiply, yyouter, yypower, yyrationalize, yysgn, yysimfac, yysinh, yytangent, zero,
    slice = [].slice;

  bigInt = require('big-integer');

  SELFTEST = 1;

  NSYM = 1000;

  DEBUG = false;

  PRINTOUTRESULT = false;

  rational = (function() {
    function rational() {}

    rational.prototype.a = null;

    rational.prototype.b = null;

    return rational;

  })();

  U = (function() {
    U.prototype.cons = null;

    U.prototype.printname = "";

    U.prototype.str = "";

    U.prototype.tensor = null;

    U.prototype.q = null;

    U.prototype.d = 0.0;

    U.prototype.k = 0;

    U.prototype.tag = 0;

    U.prototype.toString = function() {
      return collectResultLine(this);
    };

    function U() {
      this.cons = {};
      this.cons.car = null;
      this.cons.cdr = null;
      this.q = new rational();
    }

    return U;

  })();

  errorMessage = "";

  CONS = 0;

  NUM = 1;

  DOUBLE = 2;

  STR = 3;

  TENSOR = 4;

  SYM = 5;

  counter = 0;

  ABS = counter++;

  ADD = counter++;

  ADJ = counter++;

  AND = counter++;

  ARCCOS = counter++;

  ARCCOSH = counter++;

  ARCSIN = counter++;

  ARCSINH = counter++;

  ARCTAN = counter++;

  ARCTANH = counter++;

  ARG = counter++;

  ATOMIZE = counter++;

  BESSELJ = counter++;

  BESSELY = counter++;

  BINDING = counter++;

  BINOMIAL = counter++;

  CEILING = counter++;

  CHECK = counter++;

  CHOOSE = counter++;

  CIRCEXP = counter++;

  CLEAR = counter++;

  CLOCK = counter++;

  COEFF = counter++;

  COFACTOR = counter++;

  CONDENSE = counter++;

  CONJ = counter++;

  CONTRACT = counter++;

  COS = counter++;

  COSH = counter++;

  DECOMP = counter++;

  DEFINT = counter++;

  DEGREE = counter++;

  DENOMINATOR = counter++;

  DERIVATIVE = counter++;

  DET = counter++;

  DIM = counter++;

  DIRAC = counter++;

  DISPLAY = counter++;

  DIVISORS = counter++;

  DO = counter++;

  DOT = counter++;

  DRAW = counter++;

  DSOLVE = counter++;

  EIGEN = counter++;

  EIGENVAL = counter++;

  EIGENVEC = counter++;

  ERF = counter++;

  ERFC = counter++;

  EVAL = counter++;

  EXP = counter++;

  EXPAND = counter++;

  EXPCOS = counter++;

  EXPSIN = counter++;

  FACTOR = counter++;

  FACTORIAL = counter++;

  FACTORPOLY = counter++;

  FILTER = counter++;

  FLOATF = counter++;

  FLOOR = counter++;

  FOR = counter++;

  GAMMA = counter++;

  GCD = counter++;

  HERMITE = counter++;

  HILBERT = counter++;

  IMAG = counter++;

  INDEX = counter++;

  INNER = counter++;

  INTEGRAL = counter++;

  INV = counter++;

  INVG = counter++;

  ISINTEGER = counter++;

  ISPRIME = counter++;

  LAGUERRE = counter++;

  LCM = counter++;

  LEADING = counter++;

  LEGENDRE = counter++;

  LOG = counter++;

  MAG = counter++;

  MOD = counter++;

  MULTIPLY = counter++;

  NOT = counter++;

  NROOTS = counter++;

  NUMBER = counter++;

  NUMERATOR = counter++;

  OPERATOR = counter++;

  OR = counter++;

  OUTER = counter++;

  POLAR = counter++;

  POWER = counter++;

  PRIME = counter++;

  PRINT = counter++;

  PRODUCT = counter++;

  QUOTE = counter++;

  QUOTIENT = counter++;

  RANK = counter++;

  RATIONALIZE = counter++;

  REAL = counter++;

  YYRECT = counter++;

  ROOTS = counter++;

  SETQ = counter++;

  SGN = counter++;

  SIMPLIFY = counter++;

  SIN = counter++;

  SINH = counter++;

  SHAPE = counter++;

  SQRT = counter++;

  STOP = counter++;

  SUBST = counter++;

  SUM = counter++;

  TAN = counter++;

  TANH = counter++;

  TAYLOR = counter++;

  TEST = counter++;

  TESTEQ = counter++;

  TESTGE = counter++;

  TESTGT = counter++;

  TESTLE = counter++;

  TESTLT = counter++;

  TRANSPOSE = counter++;

  UNIT = counter++;

  ZERO = counter++;

  NIL = counter++;

  AUTOEXPAND = counter++;

  BAKE = counter++;

  LAST = counter++;

  TRACE = counter++;

  TTY = counter++;

  YYE = counter++;

  DRAWX = counter++;

  METAA = counter++;

  METAB = counter++;

  METAX = counter++;

  SECRETX = counter++;

  PI = counter++;

  SYMBOL_A = counter++;

  SYMBOL_B = counter++;

  SYMBOL_C = counter++;

  SYMBOL_D = counter++;

  SYMBOL_I = counter++;

  SYMBOL_J = counter++;

  SYMBOL_N = counter++;

  SYMBOL_R = counter++;

  SYMBOL_S = counter++;

  SYMBOL_T = counter++;

  SYMBOL_X = counter++;

  SYMBOL_Y = counter++;

  SYMBOL_Z = counter++;

  C1 = counter++;

  C2 = counter++;

  C3 = counter++;

  C4 = counter++;

  C5 = counter++;

  C6 = counter++;

  USR_SYMBOLS = counter++;

  E = YYE;

  TOS = 100000;

  BUF = 10000;

  MAX_PROGRAM_SIZE = 100001;

  MAXPRIMETAB = 10000;

  MAXDIM = 24;

  tensor = (function() {
    tensor.prototype.ndim = 0;

    tensor.prototype.dim = null;

    tensor.prototype.nelem = 0;

    tensor.prototype.elem = null;

    function tensor() {
      this.dim = (function() {
        var o, ref, results;
        results = [];
        for (o = 0, ref = MAXDIM; 0 <= ref ? o <= ref : o >= ref; 0 <= ref ? o++ : o--) {
          results.push(0);
        }
        return results;
      })();
      this.elem = [];
    }

    return tensor;

  })();

  display = (function() {
    function display() {}

    display.prototype.h = 0;

    display.prototype.w = 0;

    display.prototype.n = 0;

    display.prototype.a = [];

    return display;

  })();

  text_metric = (function() {
    function text_metric() {}

    text_metric.prototype.ascent = 0;

    text_metric.prototype.descent = 0;

    text_metric.prototype.width = 0;

    return text_metric;

  })();

  tos = 0;

  expanding = 0;

  fmt_x = 0;

  fmt_index = 0;

  fmt_level = 0;

  verbosing = 0;

  primetab = (function() {
    var ceil, i, j, primes;
    primes = [2];
    i = 3;
    while (primes.length < MAXPRIMETAB) {
      j = 0;
      ceil = Math.sqrt(i);
      while (j < primes.length && primes[j] <= ceil) {
        if (i % primes[j] === 0) {
          j = -1;
          break;
        }
        j++;
      }
      if (j !== -1) {
        primes.push(i);
      }
      i += 2;
    }
    primes[MAXPRIMETAB] = 0;
    return primes;
  })();

  esc_flag = 0;

  draw_flag = 0;

  mtotal = 0;

  trigmode = 0;

  logbuf = "";

  program_buf = "";

  symtab = [];

  binding = [];

  arglist = [];

  stack = [];

  frame = 0;

  p0 = null;

  p1 = null;

  p2 = null;

  p3 = null;

  p4 = null;

  p5 = null;

  p6 = null;

  p7 = null;

  p8 = null;

  p9 = null;

  zero = null;

  one = null;

  imaginaryunit = null;

  symtab = [];

  out_buf = "";

  out_count = 0;

  test_flag = 0;

  draw_stop_return = null;

  symbol = function(x) {
    return symtab[x];
  };

  iscons = function(p) {
    return p.k === CONS;
  };

  isrational = function(p) {
    return p.k === NUM;
  };

  isdouble = function(p) {
    return p.k === DOUBLE;
  };

  isnum = function(p) {
    return isrational(p) || isdouble(p);
  };

  isstr = function(p) {
    return p.k === STR;
  };

  istensor = function(p) {
    if (p == null) {
      debugger;
    } else {
      return p.k === TENSOR;
    }
  };

  issymbol = function(p) {
    return p.k === SYM;
  };

  iskeyword = function(p) {
    return issymbol(p) && symnum(p) < NIL;
  };

  car = function(p) {
    if (iscons(p)) {
      return p.cons.car;
    } else {
      return symbol(NIL);
    }
  };

  cdr = function(p) {
    if (iscons(p)) {
      return p.cons.cdr;
    } else {
      return symbol(NIL);
    }
  };

  caar = function(p) {
    return car(car(p));
  };

  cadr = function(p) {
    return car(cdr(p));
  };

  cdar = function(p) {
    return cdr(car(p));
  };

  cddr = function(p) {
    return cdr(cdr(p));
  };

  caadr = function(p) {
    return car(car(cdr(p)));
  };

  caddr = function(p) {
    return car(cdr(cdr(p)));
  };

  cadar = function(p) {
    return car(cdr(car(p)));
  };

  cdadr = function(p) {
    return cdr(car(cdr(p)));
  };

  cddar = function(p) {
    return cdr(cdr(car(p)));
  };

  cdddr = function(p) {
    return cdr(cdr(cdr(p)));
  };

  caaddr = function(p) {
    return car(car(cdr(cdr(p))));
  };

  cadadr = function(p) {
    return car(cdr(car(cdr(p))));
  };

  caddar = function(p) {
    return car(cdr(cdr(car(p))));
  };

  cdaddr = function(p) {
    return cdr(car(cdr(cdr(p))));
  };

  cadddr = function(p) {
    return car(cdr(cdr(cdr(p))));
  };

  cddddr = function(p) {
    return cdr(cdr(cdr(cdr(p))));
  };

  caddddr = function(p) {
    return car(cdr(cdr(cdr(cdr(p)))));
  };

  cadaddr = function(p) {
    return car(cdr(car(cdr(cdr(p)))));
  };

  cddaddr = function(p) {
    return cdr(cdr(car(cdr(cdr(p)))));
  };

  caddadr = function(p) {
    return car(cdr(cdr(car(cdr(p)))));
  };

  cdddaddr = function(p) {
    return cdr(cdr(cdr(car(cdr(cdr(p))))));
  };

  caddaddr = function(p) {
    return car(cdr(cdr(car(cdr(cdr(p))))));
  };

  isadd = function(p) {
    return car(p) === symbol(ADD);
  };

  ismultiply = function(p) {
    return car(p) === symbol(MULTIPLY);
  };

  ispower = function(p) {
    return car(p) === symbol(POWER);
  };

  isfactorial = function(p) {
    return car(p) === symbol(FACTORIAL);
  };

  MSIGN = function(p) {
    if (p.isPositive()) {
      return 1;
    } else if (p.isZero()) {
      return 0;
    } else {
      return -1;
    }
  };

  MLENGTH = function(p) {
    return p.toString().length;
  };

  MZERO = function(p) {
    return p.isZero();
  };

  MEQUAL = function(p, n) {
    if (p == null) {
      debugger;
    }
    return p.equals(n);
  };

  $ = typeof exports !== "undefined" && exports !== null ? exports : this;

  $.isadd = isadd;

  $.ismultiply = ismultiply;

  $.ispower = ispower;

  $.isfactorial = isfactorial;

  $.car = car;

  $.cdr = cdr;

  $.caar = caar;

  $.cadr = cadr;

  $.cdar = cdar;

  $.cddr = cddr;

  $.caadr = caadr;

  $.caddr = caddr;

  $.cadar = cadar;

  $.cdadr = cdadr;

  $.cddar = cddar;

  $.cdddr = cdddr;

  $.caaddr = caaddr;

  $.cadadr = cadadr;

  $.caddar = caddar;

  $.cdaddr = cdaddr;

  $.cadddr = cadddr;

  $.cddddr = cddddr;

  $.caddddr = caddddr;

  $.cadaddr = cadaddr;

  $.cddaddr = cddaddr;

  $.caddadr = caddadr;

  $.cdddaddr = cdddaddr;

  $.caddaddr = caddaddr;

  $.symbol = symbol;

  $.iscons = iscons;

  $.isrational = isrational;

  $.isdouble = isdouble;

  $.isnum = isnum;

  $.isstr = isstr;

  $.istensor = istensor;

  $.issymbol = issymbol;

  $.iskeyword = iskeyword;

  $.CONS = CONS;

  $.NUM = NUM;

  $.DOUBLE = DOUBLE;

  $.STR = STR;

  $.TENSOR = TENSOR;

  $.SYM = SYM;

  Eval_abs = function() {
    push(cadr(p1));
    Eval();
    return absval();
  };

  absval = function() {
    var h;
    h = 0;
    save();
    p1 = pop();
    if (istensor(p1)) {
      absval_tensor();
      restore();
      return;
    }
    if (isnum(p1)) {
      push(p1);
      if (isnegativenumber(p1)) {
        negate();
      }
      restore();
      return;
    }
    if (iscomplexnumber(p1)) {
      push(p1);
      push(p1);
      conjugate();
      multiply();
      push_rational(1, 2);
      power();
      restore();
      return;
    }
    if (car(p1) === symbol(POWER) && isnegativeterm(caddr(p1))) {
      push(p1);
      reciprocate();
      absval();
      reciprocate();
      restore();
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      h = tos;
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        absval();
        p1 = cdr(p1);
      }
      multiply_all(tos - h);
      restore();
      return;
    }
    if (isnegativeterm(p1) || (car(p1) === symbol(ADD) && isnegativeterm(cadr(p1)))) {
      push(p1);
      negate();
      p1 = pop();
    }
    push_symbol(ABS);
    push(p1);
    list(2);
    return restore();
  };

  absval_tensor = function() {
    if (p1.tensor.ndim !== 1) {
      stop("abs(tensor) with tensor rank > 1");
    }
    push(p1);
    push(p1);
    conjugate();
    inner();
    push_rational(1, 2);
    power();
    simplify();
    return Eval();
  };


  /*
   Symbolic addition
  
  	Terms in a sum are combined if they are identical modulo rational
  	coefficients.
  
  	For example, A + 2A becomes 3A.
  
  	However, the sum A + sqrt(2) A is not modified.
  
  	Combining terms can lead to second-order effects.
  
  	For example, consider the case of
  
  		1/sqrt(2) A + 3/sqrt(2) A + sqrt(2) A
  
  	The first two terms are combined to yield 2 sqrt(2) A.
  
  	This result can now be combined with the third term to yield
  
  		3 sqrt(2) A
   */

  flag = 0;

  Eval_add = function() {
    var h;
    h = tos;
    p1 = cdr(p1);
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      p2 = pop();
      push_terms(p2);
      p1 = cdr(p1);
    }
    return add_terms(tos - h);
  };

  stackAddsCount = 0;

  add_terms = function(n) {
    var ac, ad, h, i, o, ref, ref1, results, s, subsetOfStack;
    stackAddsCount++;
    i = 0;
    h = tos - n;
    s = h;
    if (DEBUG) {
      console.log("stack before adding terms #" + stackAddsCount);
    }
    if (DEBUG) {
      for (i = o = 0, ref = tos; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
        print1(stack[i]);
      }
    }
    for (i = ac = 0; ac < 10; i = ++ac) {
      if (n < 2) {
        break;
      }
      flag = 0;
      subsetOfStack = stack.slice(h, h + n);
      subsetOfStack.sort(cmp_terms);
      stack = stack.slice(0, h).concat(subsetOfStack).concat(stack.slice(h + n));
      if (flag === 0) {
        break;
      }
      n = combine_terms(h, n);
    }
    tos = h + n;
    switch (n) {
      case 0:
        push_integer(0);
        break;
      case 1:
        break;
      default:
        list(n);
        p1 = pop();
        push_symbol(ADD);
        push(p1);
        cons();
    }
    if (DEBUG) {
      console.log("stack after adding terms #" + stackAddsCount);
    }
    if (DEBUG) {
      results = [];
      for (i = ad = 0, ref1 = tos; 0 <= ref1 ? ad < ref1 : ad > ref1; i = 0 <= ref1 ? ++ad : --ad) {
        results.push(print1(stack[i]));
      }
      return results;
    }
  };

  cmp_terms_count = 0;

  cmp_terms = function(p1, p2) {
    var i, o, ref, t;
    cmp_terms_count++;
    i = 0;
    if (isnum(p1) && isnum(p2)) {
      flag = 1;
      return 0;
    }
    if (istensor(p1) && istensor(p2)) {
      if (p1.tensor.ndim < p2.tensor.ndim) {
        return -1;
      }
      if (p1.tensor.ndim > p2.tensor.ndim) {
        return 1;
      }
      for (i = o = 0, ref = p1.tensor.ndim; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
        if (p1.tensor.dim[i] < p2.tensor.dim[i]) {
          return -1;
        }
        if (p1.tensor.dim[i] > p2.tensor.dim[i]) {
          return 1;
        }
      }
      flag = 1;
      return 0;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
      if (isnum(car(p1))) {
        p1 = cdr(p1);
        if (cdr(p1) === symbol(NIL)) {
          p1 = car(p1);
        }
      }
    }
    if (car(p2) === symbol(MULTIPLY)) {
      p2 = cdr(p2);
      if (isnum(car(p2))) {
        p2 = cdr(p2);
        if (cdr(p2) === symbol(NIL)) {
          p2 = car(p2);
        }
      }
    }
    t = cmp_expr(p1, p2);
    if (t === 0) {
      flag = 1;
    }
    return t;
  };


  /*
   Compare adjacent terms in s[] and combine if possible.
  
  	Returns the number of terms remaining in s[].
  
  	n	number of terms in s[] initially
   */

  combine_terms = function(s, n) {
    var ac, ad, ae, af, i, j, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, t;
    i = 0;
    while (i < (n - 1)) {
      check_esc_flag();
      p3 = stack[s + i];
      p4 = stack[s + i + 1];
      if (istensor(p3) && istensor(p4)) {
        push(p3);
        push(p4);
        tensor_plus_tensor();
        p1 = pop();
        if (p1 !== symbol(NIL)) {
          stack[s + i] = p1;
          for (j = o = ref = i + 1, ref1 = n - 1; ref <= ref1 ? o < ref1 : o > ref1; j = ref <= ref1 ? ++o : --o) {
            stack[s + j] = stack[s + j + 1];
          }
          n--;
          i--;
        }
        i++;
        continue;
      }
      if (istensor(p3) || istensor(p4)) {
        i++;
        continue;
      }
      if (isnum(p3) && isnum(p4)) {
        push(p3);
        push(p4);
        add_numbers();
        p1 = pop();
        if (iszero(p1)) {
          for (j = ac = ref2 = i, ref3 = n - 2; ref2 <= ref3 ? ac < ref3 : ac > ref3; j = ref2 <= ref3 ? ++ac : --ac) {
            stack[s + j] = stack[s + j + 2];
          }
          n -= 2;
        } else {
          stack[s + i] = p1;
          for (j = ad = ref4 = i + 1, ref5 = n - 1; ref4 <= ref5 ? ad < ref5 : ad > ref5; j = ref4 <= ref5 ? ++ad : --ad) {
            stack[s + j] = stack[s + j + 1];
          }
          n--;
        }
        i--;
        i++;
        continue;
      }
      if (isnum(p3) || isnum(p4)) {
        i++;
        continue;
      }
      p1 = one;
      p2 = one;
      t = 0;
      if (car(p3) === symbol(MULTIPLY)) {
        p3 = cdr(p3);
        t = 1;
        if (isnum(car(p3))) {
          p1 = car(p3);
          p3 = cdr(p3);
          if (cdr(p3) === symbol(NIL)) {
            p3 = car(p3);
            t = 0;
          }
        }
      }
      if (car(p4) === symbol(MULTIPLY)) {
        p4 = cdr(p4);
        if (isnum(car(p4))) {
          p2 = car(p4);
          p4 = cdr(p4);
          if (cdr(p4) === symbol(NIL)) {
            p4 = car(p4);
          }
        }
      }
      if (!equal(p3, p4)) {
        i++;
        continue;
      }
      push(p1);
      push(p2);
      add_numbers();
      p1 = pop();
      if (iszero(p1)) {
        for (j = ae = ref6 = i, ref7 = n - 2; ref6 <= ref7 ? ae < ref7 : ae > ref7; j = ref6 <= ref7 ? ++ae : --ae) {
          stack[s + j] = stack[s + j + 2];
        }
        n -= 2;
        i--;
        i++;
        continue;
      }
      push(p1);
      if (t) {
        push(symbol(MULTIPLY));
        push(p3);
        cons();
      } else {
        push(p3);
      }
      multiply();
      stack[s + i] = pop();
      for (j = af = ref8 = i + 1, ref9 = n - 1; ref8 <= ref9 ? af < ref9 : af > ref9; j = ref8 <= ref9 ? ++af : --af) {
        stack[s + j] = stack[s + j + 1];
      }
      n--;
      i--;
      i++;
    }
    return n;
  };

  push_terms = function(p) {
    var results;
    if (car(p) === symbol(ADD)) {
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        push(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else if (!iszero(p)) {
      return push(p);
    }
  };

  add = function() {
    var h;
    save();
    p2 = pop();
    p1 = pop();
    h = tos;
    push_terms(p1);
    push_terms(p2);
    add_terms(tos - h);
    return restore();
  };

  add_all = function(k) {
    var h, i, o, ref, s;
    i = 0;
    save();
    s = tos - k;
    h = tos;
    for (i = o = 0, ref = k; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      push_terms(stack[s + i]);
    }
    add_terms(tos - h);
    p1 = pop();
    tos -= k;
    push(p1);
    return restore();
  };

  subtract = function() {
    negate();
    return add();
  };

  Eval_adj = function() {
    push(cadr(p1));
    Eval();
    return adj();
  };

  adj = function() {
    var ac, doNothing, i, j, n, o, ref, ref1;
    i = 0;
    j = 0;
    n = 0;
    save();
    p1 = pop();
    if (istensor(p1) && p1.tensor.ndim === 2 && p1.tensor.dim[0] === p1.tensor.dim[1]) {
      doNothing = 1;
    } else {
      stop("adj: square matrix expected");
    }
    n = p1.tensor.dim[0];
    p2 = alloc_tensor(n * n);
    p2.tensor.ndim = 2;
    p2.tensor.dim[0] = n;
    p2.tensor.dim[1] = n;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      for (j = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
        cofactor(p1, n, i, j);
        p2.tensor.elem[n * j + i] = pop();
      }
    }
    push(p2);
    return restore();
  };

  Eval_arccos = function() {
    push(cadr(p1));
    Eval();
    return arccos();
  };

  arccos = function() {
    var d, errno, n;
    n = 0;
    d = 0.0;
    save();
    p1 = pop();
    if (car(p1) === symbol(COS)) {
      push(cadr(p1));
      restore();
      return;
    }
    if (isdouble(p1)) {
      errno = 0;
      d = Math.acos(p1.d);
      if (errno) {
        stop("arccos function argument is not in the interval [-1,1]");
      }
      push_double(d);
      restore();
      return;
    }
    if (isoneoversqrttwo(p1)) {
      push_rational(1, 4);
      push_symbol(PI);
      multiply();
      restore();
      return;
    }
    if (isminusoneoversqrttwo(p1)) {
      push_rational(3, 4);
      push_symbol(PI);
      multiply();
      restore();
      return;
    }
    if (!isrational(p1)) {
      push_symbol(ARCCOS);
      push(p1);
      list(2);
      restore();
      return;
    }
    push(p1);
    push_integer(2);
    multiply();
    n = pop_integer();
    switch (n) {
      case -2:
        push_symbol(PI);
        break;
      case -1:
        push_rational(2, 3);
        push_symbol(PI);
        multiply();
        break;
      case 0:
        push_rational(1, 2);
        push_symbol(PI);
        multiply();
        break;
      case 1:
        push_rational(1, 3);
        push_symbol(PI);
        multiply();
        break;
      case 2:
        push(zero);
        break;
      default:
        push_symbol(ARCCOS);
        push(p1);
        list(2);
    }
    return restore();
  };

  Eval_arccosh = function() {
    push(cadr(p1));
    Eval();
    return arccosh();
  };

  arccosh = function() {
    var d;
    d = 0.0;
    save();
    p1 = pop();
    if (car(p1) === symbol(COSH)) {
      push(cadr(p1));
      restore();
      return;
    }
    if (isdouble(p1)) {
      d = p1.d;
      if (d < 1.0) {
        stop("arccosh function argument is less than 1.0");
      }
      d = Math.log(d + Math.sqrt(d * d - 1.0));
      push_double(d);
      restore();
      return;
    }
    if (isplusone(p1)) {
      push(zero);
      restore();
      return;
    }
    push_symbol(ARCCOSH);
    push(p1);
    list(2);
    return restore();
  };

  Eval_arcsin = function() {
    push(cadr(p1));
    Eval();
    return arcsin();
  };

  arcsin = function() {
    var d, errno, n;
    n = 0;
    d = 0;
    save();
    p1 = pop();
    if (car(p1) === symbol(SIN)) {
      push(cadr(p1));
      restore();
      return;
    }
    if (isdouble(p1)) {
      errno = 0;
      d = Math.asin(p1.d);
      if (errno) {
        stop("arcsin function argument is not in the interval [-1,1]");
      }
      push_double(d);
      restore();
      return;
    }
    if (isoneoversqrttwo(p1)) {
      push_rational(1, 4);
      push_symbol(PI);
      multiply();
      restore();
      return;
    }
    if (isminusoneoversqrttwo(p1)) {
      push_rational(-1, 4);
      push_symbol(PI);
      multiply();
      restore();
      return;
    }
    if (!isrational(p1)) {
      push_symbol(ARCSIN);
      push(p1);
      list(2);
      restore();
      return;
    }
    push(p1);
    push_integer(2);
    multiply();
    n = pop_integer();
    switch (n) {
      case -2:
        push_rational(-1, 2);
        push_symbol(PI);
        multiply();
        break;
      case -1:
        push_rational(-1, 6);
        push_symbol(PI);
        multiply();
        break;
      case 0:
        push(zero);
        break;
      case 1:
        push_rational(1, 6);
        push_symbol(PI);
        multiply();
        break;
      case 2:
        push_rational(1, 2);
        push_symbol(PI);
        multiply();
        break;
      default:
        push_symbol(ARCSIN);
        push(p1);
        list(2);
    }
    return restore();
  };

  Eval_arcsinh = function() {
    push(cadr(p1));
    Eval();
    return arcsinh();
  };

  arcsinh = function() {
    var d;
    d = 0.0;
    save();
    p1 = pop();
    if (car(p1) === symbol(SINH)) {
      push(cadr(p1));
      restore();
      return;
    }
    if (isdouble(p1)) {
      d = p1.d;
      d = Math.log(d + Math.sqrt(d * d + 1.0));
      push_double(d);
      restore();
      return;
    }
    if (iszero(p1)) {
      push(zero);
      restore();
      return;
    }
    push_symbol(ARCSINH);
    push(p1);
    list(2);
    return restore();
  };

  Eval_arctan = function() {
    push(cadr(p1));
    Eval();
    return arctan();
  };

  arctan = function() {
    var d, errno;
    d = 0;
    save();
    p1 = pop();
    if (car(p1) === symbol(TAN)) {
      push(cadr(p1));
      restore();
      return;
    }
    if (isdouble(p1)) {
      errno = 0;
      d = Math.atan(p1.d);
      if (errno) {
        stop("arctan function error");
      }
      push_double(d);
      restore();
      return;
    }
    if (iszero(p1)) {
      push(zero);
      restore();
      return;
    }
    if (isnegative(p1)) {
      push(p1);
      negate();
      arctan();
      negate();
      restore();
      return;
    }
    if (Find(p1, symbol(SIN)) && Find(p1, symbol(COS))) {
      push(p1);
      numerator();
      p2 = pop();
      push(p1);
      denominator();
      p3 = pop();
      if (car(p2) === symbol(SIN) && car(p3) === symbol(COS) && equal(cadr(p2), cadr(p3))) {
        push(cadr(p2));
        restore();
        return;
      }
    }
    if (car(p1) === symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), -1, 2)) {
      push_rational(1, 6);
      push(symbol(PI));
      multiply();
      restore();
      return;
    }
    if (equaln(p1, 1)) {
      push_rational(1, 4);
      push(symbol(PI));
      multiply();
      restore();
      return;
    }
    if (car(p1) === symbol(POWER) && equaln(cadr(p1), 3) && equalq(caddr(p1), 1, 2)) {
      push_rational(1, 3);
      push(symbol(PI));
      multiply();
      restore();
      return;
    }
    push_symbol(ARCTAN);
    push(p1);
    list(2);
    return restore();
  };

  Eval_arctanh = function() {
    push(cadr(p1));
    Eval();
    return arctanh();
  };

  arctanh = function() {
    var d;
    d = 0.0;
    save();
    p1 = pop();
    if (car(p1) === symbol(TANH)) {
      push(cadr(p1));
      restore();
      return;
    }
    if (isdouble(p1)) {
      d = p1.d;
      if (d < -1.0 || d > 1.0) {
        stop("arctanh function argument is not in the interval [-1,1]");
      }
      d = Math.log((1.0 + d) / (1.0 - d)) / 2.0;
      push_double(d);
      restore();
      return;
    }
    if (iszero(p1)) {
      push(zero);
      restore();
      return;
    }
    push_symbol(ARCTANH);
    push(p1);
    list(2);
    return restore();
  };


  /*
   Argument (angle) of complex z
  
  	z		arg(z)
  	-		------
  
  	a		0
  
  	-a		-pi			See note 3 below
  
  	(-1)^a		a pi
  
  	exp(a + i b)	b
  
  	a b		arg(a) + arg(b)
  
  	a + i b		arctan(b/a)
  
  Result by quadrant
  
  	z		arg(z)
  	-		------
  
  	1 + i		1/4 pi
  
  	1 - i		-1/4 pi
  
  	-1 + i		3/4 pi
  
  	-1 - i		-3/4 pi
  
  Notes
  
  	1. Handles mixed polar and rectangular forms, e.g. 1 + exp(i pi/3)
  
  	2. Symbols in z are assumed to be positive and real.
  
  	3. Negative direction adds -pi to angle.
  
  	   Example: z = (-1)^(1/3), mag(z) = 1/3 pi, mag(-z) = -2/3 pi
  
  	4. jean-francois.debroux reports that when z=(a+i*b)/(c+i*d) then
  
  		arg(numerator(z)) - arg(denominator(z))
  
  	   must be used to get the correct answer. Now the operation is
  	   automatic.
   */

  Eval_arg = function() {
    push(cadr(p1));
    Eval();
    return arg();
  };

  arg = function() {
    save();
    p1 = pop();
    push(p1);
    numerator();
    yyarg();
    push(p1);
    denominator();
    yyarg();
    subtract();
    return restore();
  };

  yyarg = function() {
    save();
    p1 = pop();
    if (isnegativenumber(p1)) {
      push(symbol(PI));
      negate();
    } else if (car(p1) === symbol(POWER) && equaln(cadr(p1), -1)) {
      push(symbol(PI));
      push(caddr(p1));
      multiply();
    } else if (car(p1) === symbol(POWER) && cadr(p1) === symbol(E)) {
      push(caddr(p1));
      imag();
    } else if (car(p1) === symbol(MULTIPLY)) {
      push_integer(0);
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        arg();
        add();
        p1 = cdr(p1);
      }
    } else if (car(p1) === symbol(ADD)) {
      push(p1);
      rect();
      p1 = pop();
      push(p1);
      real();
      p2 = pop();
      push(p1);
      imag();
      p3 = pop();
      if (iszero(p2)) {
        push(symbol(PI));
        if (isnegative(p3)) {
          negate();
        }
      } else {
        push(p3);
        push(p2);
        divide();
        arctan();
        if (isnegative(p2)) {
          push_symbol(PI);
          if (isnegative(p3)) {
            subtract();
          } else {
            add();
          }
        }
      }
    } else {
      push_integer(0);
    }
    return restore();
  };

  bake = function() {
    var h, s, t, x, y, z;
    h = 0;
    s = 0;
    t = 0;
    x = 0;
    y = 0;
    z = 0;
    expanding++;
    save();
    p1 = pop();
    s = ispoly(p1, symbol(SYMBOL_S));
    t = ispoly(p1, symbol(SYMBOL_T));
    x = ispoly(p1, symbol(SYMBOL_X));
    y = ispoly(p1, symbol(SYMBOL_Y));
    z = ispoly(p1, symbol(SYMBOL_Z));
    if (s === 1 && t === 0 && x === 0 && y === 0 && z === 0) {
      p2 = symbol(SYMBOL_S);
      bake_poly();
    } else if (s === 0 && t === 1 && x === 0 && y === 0 && z === 0) {
      p2 = symbol(SYMBOL_T);
      bake_poly();
    } else if (s === 0 && t === 0 && x === 1 && y === 0 && z === 0) {
      p2 = symbol(SYMBOL_X);
      bake_poly();
    } else if (s === 0 && t === 0 && x === 0 && y === 1 && z === 0) {
      p2 = symbol(SYMBOL_Y);
      bake_poly();
    } else if (s === 0 && t === 0 && x === 0 && y === 0 && z === 1) {
      p2 = symbol(SYMBOL_Z);
      bake_poly();
    } else if (iscons(p1)) {
      h = tos;
      push(car(p1));
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        bake();
        p1 = cdr(p1);
      }
      list(tos - h);
    } else {
      push(p1);
    }
    restore();
    return expanding--;
  };

  polyform = function() {
    var h;
    h = 0;
    save();
    p2 = pop();
    p1 = pop();
    if (ispoly(p1, p2)) {
      bake_poly();
    } else if (iscons(p1)) {
      h = tos;
      push(car(p1));
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        push(p2);
        polyform();
        p1 = cdr(p1);
      }
      list(tos - h);
    } else {
      push(p1);
    }
    return restore();
  };

  bake_poly = function() {
    var a, h, i, k, n, o, ref;
    h = 0;
    i = 0;
    k = 0;
    n = 0;
    a = tos;
    push(p1);
    push(p2);
    k = coeff();
    h = tos;
    for (i = o = ref = k - 1; o >= 0; i = o += -1) {
      p1 = stack[a + i];
      bake_poly_term(i);
    }
    n = tos - h;
    if (n > 1) {
      list(n);
      push(symbol(ADD));
      swap();
      cons();
    }
    p1 = pop();
    tos -= k;
    return push(p1);
  };

  bake_poly_term = function(k) {
    var h, n;
    h = 0;
    n = 0;
    if (iszero(p1)) {
      return;
    }
    if (k === 0) {
      if (car(p1) === symbol(ADD)) {
        p1 = cdr(p1);
        while (iscons(p1)) {
          push(car(p1));
          p1 = cdr(p1);
        }
      } else {
        push(p1);
      }
      return;
    }
    h = tos;
    if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        p1 = cdr(p1);
      }
    } else if (!equaln(p1, 1)) {
      push(p1);
    }
    if (k === 1) {
      push(p2);
    } else {
      push(symbol(POWER));
      push(p2);
      push_integer(k);
      list(3);
    }
    n = tos - h;
    if (n > 1) {
      list(n);
      push(symbol(MULTIPLY));
      swap();
      return cons();
    }
  };


  /*
   Bessel J function
  
  	1st arg		x
  
  	2nd arg		n
  
  Recurrence relation
  
  	besselj(x,n) = (2/x) (n-1) besselj(x,n-1) - besselj(x,n-2)
  
  	besselj(x,1/2) = sqrt(2/pi/x) sin(x)
  
  	besselj(x,-1/2) = sqrt(2/pi/x) cos(x)
  
  For negative n, reorder the recurrence relation as
  
  	besselj(x,n-2) = (2/x) (n-1) besselj(x,n-1) - besselj(x,n)
  
  Substitute n+2 for n to obtain
  
  	besselj(x,n) = (2/x) (n+1) besselj(x,n+1) - besselj(x,n+2)
  
  Examples
  
  	besselj(x,3/2) = (1/x) besselj(x,1/2) - besselj(x,-1/2)
  
  	besselj(x,-3/2) = -(1/x) besselj(x,-1/2) - besselj(x,1/2)
   */

  Eval_besselj = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    return besselj();
  };

  besselj = function() {
    save();
    yybesselj();
    return restore();
  };

  yybesselj = function() {
    var d, n;
    d = 0.0;
    n = 0;
    p2 = pop();
    p1 = pop();
    push(p2);
    n = pop_integer();
    if (isdouble(p1) && n !== 0x80000000) {
      d = jn(n, p1.d);
      push_double(d);
      return;
    }
    if (iszero(p1) && iszero(p2)) {
      push_integer(1);
      return;
    }
    if (iszero(p1) && n !== 0x80000000) {
      push_integer(0);
      return;
    }
    if (p2.k === NUM && MEQUAL(p2.q.b, 2)) {
      if (MEQUAL(p2.q.a, 1)) {
        push_integer(2);
        push_symbol(PI);
        divide();
        push(p1);
        divide();
        push_rational(1, 2);
        power();
        push(p1);
        sine();
        multiply();
        return;
      }
      if (MEQUAL(p2.q.a, -1)) {
        push_integer(2);
        push_symbol(PI);
        divide();
        push(p1);
        divide();
        push_rational(1, 2);
        power();
        push(p1);
        cosine();
        multiply();
        return;
      }
      push_integer(MSIGN(p2.q.a));
      p3 = pop();
      push_integer(2);
      push(p1);
      divide();
      push(p2);
      push(p3);
      subtract();
      multiply();
      push(p1);
      push(p2);
      push(p3);
      subtract();
      besselj();
      multiply();
      push(p1);
      push(p2);
      push_integer(2);
      push(p3);
      multiply();
      subtract();
      besselj();
      subtract();
      return;
    }
    if (isnegativeterm(p1)) {
      push(p1);
      negate();
      push(p2);
      power();
      push(p1);
      push(p2);
      negate();
      power();
      multiply();
      push_symbol(BESSELJ);
      push(p1);
      negate();
      push(p2);
      list(3);
      multiply();
      return;
    }
    if (isnegativeterm(p2)) {
      push_integer(-1);
      push(p2);
      power();
      push_symbol(BESSELJ);
      push(p1);
      push(p2);
      negate();
      list(3);
      multiply();
      return;
    }
    push(symbol(BESSELJ));
    push(p1);
    push(p2);
    return list(3);
  };

  Eval_bessely = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    return bessely();
  };

  bessely = function() {
    save();
    yybessely();
    return restore();
  };

  yybessely = function() {
    var d, n;
    d = 0.0;
    n = 0;
    p2 = pop();
    p1 = pop();
    push(p2);
    n = pop_integer();
    if (isdouble(p1) && n !== 0x80000000) {
      d = yn(n, p1.d);
      push_double(d);
      return;
    }
    if (isnegativeterm(p2)) {
      push_integer(-1);
      push(p2);
      power();
      push_symbol(BESSELY);
      push(p1);
      push(p2);
      negate();
      list(3);
      multiply();
      return;
    }
    push_symbol(BESSELY);
    push(p1);
    push(p2);
    list(3);
  };

  MP_MIN_SIZE = 2;

  MP_MAX_FREE = 1000;

  mtotal = 0;

  free_stack = [];

  mint = function(a) {
    return bigInt(a);
  };

  setSignTo = function(a, b) {
    if (a.isPositive()) {
      if (b < 0) {
        return a.multiply(bigInt(-1));
      }
    } else {
      if (b > 0) {
        return a.multiply(bigInt(-1));
      }
    }
    return a;
  };

  makeSignSameAs = function(a, b) {
    if (a.isPositive()) {
      if (b.isNegative()) {
        return a.multiply(bigInt(-1));
      }
    } else {
      if (b.isPositive()) {
        return a.multiply(bigInt(-1));
      }
    }
    return a;
  };

  makePositive = function(a) {
    if (a.isNegative()) {
      return a.multiply(bigInt(-1));
    }
    return a;
  };


  /*
  mnew = (n) ->
  	if (n < MP_MIN_SIZE)
  		n = MP_MIN_SIZE
  	if (n == MP_MIN_SIZE && mfreecount)
  		p = free_stack[--mfreecount]
  	else
  		p = [] #(unsigned int *) malloc((n + 3) * sizeof (int))
  		#if (p == 0)
  		 *	stop("malloc failure")
  	p[0] = n
  	mtotal += n
  	return p[3]
   */


  /*
  mfree = (array, p) ->
  	p -= 3
  	mtotal -= array[p]
  	if (array[p] == MP_MIN_SIZE && mfreecount < MP_MAX_FREE)
  		free_stack[mfreecount++] = p
  	else
  		free(p)
   */


  /*
  mint = (n) ->
  	p = mnew(1)
  	if (n < 0)
  		 * !!! this is FU
  		 * MSIGN(p) = -1
  		fu = true
  	else
  		 * !!! this is FU
  		#MSIGN(p) = 1
  		fu = true
  	 * !!! this is FU
  	#MLENGTH(p) = 1
  	p[0] = Math.abs(n)
  	return p
   */


  /*
  mcopy = (a) ->
  	#unsigned int *b
  
  	b = mnew(MLENGTH(a))
  
  	 * !!! fu
  	#MSIGN(b) = MSIGN(a)
  	#MLENGTH(b) = MLENGTH(a)
  
  	for i in [0...MLENGTH(a)]
  		b[i] = a[i]
  
  	return b
   */


  /*
   * 
   * ge not invoked from anywhere - is you need ge
   * just use the bigNum's ge implementation
   * leaving it here just in case I decide to backport to C
   *
   * a >= b ?
   * and and b arrays of ints, len is an int
  ge = (a, b, len) ->
  	i = 0
  	for i in [0...len]
  		if (a[i] == b[i])
  			continue
  		else
  			break
  	if (a[i] >= b[i])
  		return 1
  	else
  		return 0
   */

  add_numbers = function() {
    var a, b, theResult;
    a = 1.0;
    b = 1.0;
    if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
      qadd();
      return;
    }
    save();
    p2 = pop();
    p1 = pop();
    if (isdouble(p1)) {
      a = p1.d;
    } else {
      a = convert_rational_to_double(p1);
    }
    if (isdouble(p2)) {
      b = p2.d;
    } else {
      b = convert_rational_to_double(p2);
    }
    theResult = a + b;
    push_double(theResult);
    return restore();
  };

  subtract_numbers = function() {
    var a, b;
    a = 0.0;
    b = 0.0;
    if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
      qsub();
      return;
    }
    save();
    p2 = pop();
    p1 = pop();
    if (isdouble(p1)) {
      a = p1.d;
    } else {
      a = convert_rational_to_double(p1);
    }
    if (isdouble(p2)) {
      b = p2.d;
    } else {
      b = convert_rational_to_double(p2);
    }
    push_double(a - b);
    return restore();
  };

  multiply_numbers = function() {
    var a, b;
    a = 0.0;
    b = 0.0;
    if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
      qmul();
      return;
    }
    save();
    p2 = pop();
    p1 = pop();
    if (isdouble(p1)) {
      a = p1.d;
    } else {
      a = convert_rational_to_double(p1);
    }
    if (isdouble(p2)) {
      b = p2.d;
    } else {
      b = convert_rational_to_double(p2);
    }
    push_double(a * b);
    return restore();
  };

  divide_numbers = function() {
    var a, b;
    a = 0.0;
    b = 0.0;
    if (isrational(stack[tos - 1]) && isrational(stack[tos - 2])) {
      qdiv();
      return;
    }
    save();
    p2 = pop();
    p1 = pop();
    if (iszero(p2)) {
      stop("divide by zero");
    }
    if (isdouble(p1)) {
      a = p1.d;
    } else {
      a = convert_rational_to_double(p1);
    }
    if (isdouble(p2)) {
      b = p2.d;
    } else {
      b = convert_rational_to_double(p2);
    }
    push_double(a / b);
    return restore();
  };

  invert_number = function() {
    var a, b;
    save();
    p1 = pop();
    if (iszero(p1)) {
      stop("divide by zero");
    }
    if (isdouble(p1)) {
      push_double(1 / p1.d);
      restore();
      return;
    }
    a = bigInt(p1.q.a);
    b = bigInt(p1.q.b);
    b = makeSignSameAs(b, a);
    a = setSignTo(a, 1);
    p1 = new U();
    p1.k = NUM;
    p1.q.a = b;
    p1.q.b = a;
    push(p1);
    return restore();
  };

  compare_rationals = function(a, b) {
    var ab, ba, t;
    t = 0;
    ab = mmul(a.q.a, b.q.b);
    ba = mmul(a.q.b, b.q.a);
    t = mcmp(ab, ba);
    return t;
  };

  compare_numbers = function(a, b) {
    var x, y;
    x = 0.0;
    y = 0.0;
    if (isrational(a) && isrational(b)) {
      return compare_rationals(a, b);
    }
    if (isdouble(a)) {
      x = a.d;
    } else {
      x = convert_rational_to_double(a);
    }
    if (isdouble(b)) {
      y = b.d;
    } else {
      y = convert_rational_to_double(b);
    }
    if (x < y) {
      return -1;
    }
    if (x > y) {
      return 1;
    }
    return 0;
  };

  negate_number = function() {
    save();
    p1 = pop();
    if (iszero(p1)) {
      push(p1);
      restore();
      return;
    }
    switch (p1.k) {
      case NUM:
        p2 = new U();
        p2.k = NUM;
        p2.q.a = bigInt(p1.q.a.multiply(bigInt.minusOne));
        p2.q.b = bigInt(p1.q.b);
        push(p2);
        break;
      case DOUBLE:
        push_double(-p1.d);
        break;
      default:
        stop("bug caught in mp_negate_number");
    }
    return restore();
  };

  bignum_truncate = function() {
    var a;
    save();
    p1 = pop();
    a = mdiv(p1.q.a, p1.q.b);
    p1 = new U();
    p1.k = NUM;
    p1.q.a = a;
    p1.q.b = bigInt(1);
    push(p1);
    return restore();
  };

  mp_numerator = function() {
    save();
    p1 = pop();
    if (p1.k !== NUM) {
      push(one);
      restore();
      return;
    }
    p2 = new U();
    p2.k = NUM;
    p2.q.a = bigInt(p1.q.a);
    p2.q.b = bigInt(1);
    push(p2);
    return restore();
  };

  mp_denominator = function() {
    save();
    p1 = pop();
    if (p1.k !== NUM) {
      push(one);
      restore();
      return;
    }
    p2 = new U();
    p2.k = NUM;
    p2.q.a = bigInt(p1.q.b);
    p2.q.b = bigInt(1);
    push(p2);
    return restore();
  };

  bignum_power_number = function(expo) {
    var a, b, t;
    save();
    p1 = pop();
    a = mpow(p1.q.a, Math.abs(expo));
    b = mpow(p1.q.b, Math.abs(expo));
    if (expo < 0) {
      t = a;
      a = b;
      b = t;
      a = makeSignSameAs(a, b);
      b = setSignTo(b, 1);
    }
    p1 = new U();
    p1.k = NUM;
    p1.q.a = a;
    p1.q.b = b;
    push(p1);
    return restore();
  };

  convert_bignum_to_double = function(p) {
    return p.toJSNumber();
  };

  convert_rational_to_double = function(p) {
    var quotientAndRemainder, result;
    if (p.q == null) {
      debugger;
    }
    quotientAndRemainder = p.q.a.divmod(p.q.b);
    result = quotientAndRemainder.quotient + quotientAndRemainder.remainder / p.q.b.toJSNumber();
    return result;
  };

  push_integer = function(n) {
    if (DEBUG) {
      console.log("pushing integer " + n);
    }
    save();
    p1 = new U();
    p1.k = NUM;
    p1.q.a = bigInt(n);
    p1.q.b = bigInt(1);
    push(p1);
    return restore();
  };

  push_double = function(d) {
    save();
    p1 = new U();
    p1.k = DOUBLE;
    p1.d = d;
    push(p1);
    return restore();
  };

  push_rational = function(a, b) {

    /*
    	save()
    	p1 = new U()
    	p1.k = NUM
    	p1.q.a = bigInt(a)
    	p1.q.b = bigInt(b)
    	## FIXME -- normalize ##
    	push(p1)
    	restore()
     */
    var p;
    p = new U();
    p.k = NUM;
    p.q.a = bigInt(a);
    p.q.b = bigInt(b);
    return push(p);
  };

  pop_integer = function() {
    var n;
    n = 0;
    save();
    p1 = pop();
    switch (p1.k) {
      case NUM:
        if (isinteger(p1) && p1.q.a.isSmall) {
          n = p1.q.a.toJSNumber();
        } else {
          n = 0x80000000;
        }
        break;
      case DOUBLE:
        n = Math.floor(p1.q.a);
        break;
      default:
        n = 0x80000000;
    }
    restore();
    return n;
  };

  print_double = function(p, flag) {
    var buf;
    buf = "";
    buf = "" + doubleToReasonableString(p.d);
    if (flag === 1 && buf === '-') {
      return print_str(buf + 1);
    } else {
      return print_str(buf);
    }
  };

  bignum_scan_integer = function(s) {
    var a, scounter, sign_;
    save();
    scounter = 0;
    sign_ = s[scounter];
    if (sign_ === '+' || sign_ === '-') {
      scounter++;
    }
    a = bigInt(s.substring(scounter));
    p1 = new U();
    p1.k = NUM;
    p1.q.a = a;
    p1.q.b = bigInt(1);
    push(p1);
    if (sign_ === '-') {
      negate();
    }
    return restore();
  };

  bignum_scan_float = function(s) {
    return push_double(parseFloat(s));
  };

  print_number = function(p, accumulator) {
    var aAsString, buf, denominatorString, topLevelCall;
    topLevelCall = false;
    if (accumulator == null) {
      topLevelCall = true;
      accumulator = "";
    }
    denominatorString = "";
    buf = "";
    switch (p.k) {
      case NUM:
        aAsString = p.q.a.toString();
        if (aAsString[0] === "-") {
          aAsString = aAsString.substring(1);
        }
        accumulator += aAsString;
        stringToBePrinted += aAsString;
        if (isfraction(p)) {
          accumulator += "/";
          stringToBePrinted += "/";
          denominatorString = p.q.b.toString();
          accumulator += denominatorString;
          stringToBePrinted += denominatorString;
        }
        break;
      case DOUBLE:
        aAsString = "" + doubleToReasonableString(p.d);
        if (aAsString[0] === "-") {
          aAsString = aAsString.substring(1);
        }
        accumulator += aAsString;
        stringToBePrinted += aAsString;
    }
    return accumulator;
  };

  gcd_numbers = function() {
    save();
    p2 = pop();
    p1 = pop();
    p3 = new U();
    p3.k = NUM;
    p3.q.a = mgcd(p1.q.a, p2.q.a);
    p3.q.b = mgcd(p1.q.b, p2.q.b);
    p3.q.a = setSignTo(p3.q.a, 1);
    push(p3);
    return restore();
  };

  pop_double = function() {
    var d;
    d = 0.0;
    save();
    p1 = pop();
    switch (p1.k) {
      case NUM:
        d = convert_rational_to_double(p1);
        break;
      case DOUBLE:
        d = p1.d;
        break;
      default:
        d = 0.0;
    }
    restore();
    return d;
  };

  bignum_float = function() {
    var d;
    d = 0.0;
    d = convert_rational_to_double(pop());
    return push_double(d);
  };

  bignum_factorial = function(n) {
    save();
    p1 = new U();
    p1.k = NUM;
    p1.q.a = __factorial(n);
    p1.q.b = bigInt(1);
    push(p1);
    return restore();
  };

  __factorial = function(n) {
    var a, b, i, o, ref, t;
    i = 0;
    if (n === 0 || n === 1) {
      a = bigInt(1);
      return a;
    }
    a = bigInt(2);
    b = bigInt(0);
    if (3 <= n) {
      for (i = o = 3, ref = n; 3 <= ref ? o <= ref : o >= ref; i = 3 <= ref ? ++o : --o) {
        b = bigInt(i);
        t = mmul(a, b);
        a = t;
      }
    }
    return a;
  };

  mask = [0x00000001, 0x00000002, 0x00000004, 0x00000008, 0x00000010, 0x00000020, 0x00000040, 0x00000080, 0x00000100, 0x00000200, 0x00000400, 0x00000800, 0x00001000, 0x00002000, 0x00004000, 0x00008000, 0x00010000, 0x00020000, 0x00040000, 0x00080000, 0x00100000, 0x00200000, 0x00400000, 0x00800000, 0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000, 0x20000000, 0x40000000, 0x80000000];

  mp_set_bit = function(x, k) {
    console.log("not implemented yet");
    debugger;
    return x[k / 32] |= mask[k % 32];
  };

  mp_clr_bit = function(x, k) {
    console.log("not implemented yet");
    debugger;
    return x[k / 32] &= ~mask[k % 32];
  };

  mshiftright = function(a) {
    return a = a.shiftRight();
  };

  Eval_binomial = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    return binomial();
  };

  binomial = function() {
    save();
    ybinomial();
    return restore();
  };

  ybinomial = function() {
    p2 = pop();
    p1 = pop();
    if (BINOM_check_args() === 0) {
      push(zero);
      return;
    }
    push(p1);
    factorial();
    push(p2);
    factorial();
    divide();
    push(p1);
    push(p2);
    subtract();
    factorial();
    return divide();
  };

  BINOM_check_args = function() {
    if (isnum(p1) && lessp(p1, zero)) {
      return 0;
    } else if (isnum(p2) && lessp(p2, zero)) {
      return 0;
    } else if (isnum(p1) && isnum(p2) && lessp(p1, p2)) {
      return 0;
    } else {
      return 1;
    }
  };

  Eval_ceiling = function() {
    push(cadr(p1));
    Eval();
    return ceiling();
  };

  ceiling = function() {
    save();
    yyceiling();
    return restore();
  };

  yyceiling = function() {
    var d, doNothing;
    d = 0.0;
    p1 = pop();
    if (!isnum(p1)) {
      push_symbol(CEILING);
      push(p1);
      list(2);
      return;
    }
    if (isdouble(p1)) {
      d = Math.ceil(p1.d);
      push_double(d);
      return;
    }
    if (isinteger(p1)) {
      push(p1);
      return;
    }
    p3 = new U();
    p3.k = NUM;
    p3.q.a = mdiv(p1.q.a, p1.q.b);
    p3.q.b = mint(1);
    push(p3);
    if (isnegativenumber(p1)) {
      return doNothing = 1;
    } else {
      push_integer(1);
      return add();
    }
  };

  Eval_choose = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    return choose();
  };

  choose = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (choose_check_args() === 0) {
      push_integer(0);
      restore();
      return;
    }
    push(p1);
    factorial();
    push(p2);
    factorial();
    divide();
    push(p1);
    push(p2);
    subtract();
    factorial();
    divide();
    return restore();
  };

  choose_check_args = function() {
    if (isnum(p1) && lessp(p1, zero)) {
      return 0;
    } else if (isnum(p2) && lessp(p2, zero)) {
      return 0;
    } else if (isnum(p1) && isnum(p2) && lessp(p1, p2)) {
      return 0;
    } else {
      return 1;
    }
  };

  Eval_circexp = function() {
    push(cadr(p1));
    Eval();
    circexp();
    return Eval();
  };

  circexp = function() {
    var h, i, o, ref;
    i = 0;
    h = 0;
    save();
    p1 = pop();
    if (car(p1) === symbol(COS)) {
      push(cadr(p1));
      expcos();
      restore();
      return;
    }
    if (car(p1) === symbol(SIN)) {
      push(cadr(p1));
      expsin();
      restore();
      return;
    }
    if (car(p1) === symbol(TAN)) {
      p1 = cadr(p1);
      push(imaginaryunit);
      push(p1);
      multiply();
      exponential();
      p2 = pop();
      push(imaginaryunit);
      push(p1);
      multiply();
      negate();
      exponential();
      p3 = pop();
      push(p3);
      push(p2);
      subtract();
      push(imaginaryunit);
      multiply();
      push(p2);
      push(p3);
      add();
      divide();
      restore();
      return;
    }
    if (car(p1) === symbol(COSH)) {
      p1 = cadr(p1);
      push(p1);
      exponential();
      push(p1);
      negate();
      exponential();
      add();
      push_rational(1, 2);
      multiply();
      restore();
      return;
    }
    if (car(p1) === symbol(SINH)) {
      p1 = cadr(p1);
      push(p1);
      exponential();
      push(p1);
      negate();
      exponential();
      subtract();
      push_rational(1, 2);
      multiply();
      restore();
      return;
    }
    if (car(p1) === symbol(TANH)) {
      p1 = cadr(p1);
      push(p1);
      push_integer(2);
      multiply();
      exponential();
      p1 = pop();
      push(p1);
      push_integer(1);
      subtract();
      push(p1);
      push_integer(1);
      add();
      divide();
      restore();
      return;
    }
    if (iscons(p1)) {
      h = tos;
      while (iscons(p1)) {
        push(car(p1));
        circexp();
        p1 = cdr(p1);
      }
      list(tos - h);
      restore();
      return;
    }
    if (p1.k === TENSOR) {
      push(p1);
      copy_tensor();
      p1 = pop();
      for (i = o = 0, ref = p1.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
        push(p1.tensor.elem[i]);
        circexp();
        p1.tensor.elem[i] = pop();
      }
      push(p1);
      restore();
      return;
    }
    push(p1);
    return restore();
  };

  Eval_clear = function() {
    if (test_flag === 0) {
      clear_term();
    }
    clear_symbols();
    defn();
    return push(symbol(NIL));
  };

  clear = function() {
    return run("clear");
  };


  /*
   Convert complex z to clock form
  
  	Input:		push	z
  
  	Output:		Result on stack
  
  	clock(z) = mag(z) * (-1) ^ (arg(z) / pi)
  
  	For example, clock(exp(i pi/3)) gives the result (-1)^(1/3)
   */

  Eval_clock = function() {
    push(cadr(p1));
    Eval();
    return clockform();
  };

  clockform = function() {
    save();
    p1 = pop();
    push(p1);
    mag();
    push_integer(-1);
    push(p1);
    arg();
    push(symbol(PI));
    divide();
    power();
    multiply();

    /*
    	p1 = pop()
    	push(p1)
    	mag()
    	push(symbol(E))
    	push(p1)
    	arg()
    	push(imaginaryunit)
    	multiply()
    	power()
    	multiply()
     */
    return restore();
  };

  Eval_coeff = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    push(cadddr(p1));
    Eval();
    p3 = pop();
    p2 = pop();
    p1 = pop();
    if (p3 === symbol(NIL)) {
      p3 = p2;
      p2 = symbol(SYMBOL_X);
    }
    push(p1);
    push(p2);
    push(p3);
    power();
    divide();
    push(p2);
    return filter();
  };

  coeff = function() {
    var h, n;
    save();
    p2 = pop();
    p1 = pop();
    h = tos;
    while (1) {
      push(p1);
      push(p2);
      push(zero);
      subst();
      Eval();
      p3 = pop();
      push(p3);
      push(p1);
      push(p3);
      subtract();
      p1 = pop();
      if (equal(p1, zero)) {
        n = tos - h;
        restore();
        return n;
      }
      push(p1);
      push(p2);
      divide();
      p1 = pop();
    }
  };

  Eval_cofactor = function() {
    var doNothing, i, j, n;
    i = 0;
    j = 0;
    n = 0;
    push(cadr(p1));
    Eval();
    p2 = pop();
    if (istensor(p2) && p2.tensor.ndim === 2 && p2.tensor.dim[0] === p2.tensor.dim[1]) {
      doNothing = 1;
    } else {
      stop("cofactor: 1st arg: square matrix expected");
    }
    n = p2.tensor.dim[0];
    push(caddr(p1));
    Eval();
    i = pop_integer();
    if (i < 1 || i > n) {
      stop("cofactor: 2nd arg: row index expected");
    }
    push(cadddr(p1));
    Eval();
    j = pop_integer();
    if (j < 1 || j > n) {
      stop("cofactor: 3rd arg: column index expected");
    }
    return cofactor(p2, n, i - 1, j - 1);
  };

  cofactor = function(p, n, row, col) {
    var ac, i, j, o, ref, ref1;
    i = 0;
    j = 0;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      for (j = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
        if (i !== row && j !== col) {
          push(p.tensor.elem[n * i + j]);
        }
      }
    }
    determinant(n - 1);
    if ((row + col) % 2) {
      return negate();
    }
  };

  Eval_condense = function() {
    push(cadr(p1));
    Eval();
    return Condense();
  };

  Condense = function() {
    var tmp;
    tmp = 0;
    tmp = expanding;
    save();
    yycondense();
    restore();
    return expanding = tmp;
  };

  yycondense = function() {
    expanding = 0;
    p1 = pop();
    if (car(p1) !== symbol(ADD)) {
      push(p1);
      return;
    }
    p3 = cdr(p1);
    push(car(p3));
    p3 = cdr(p3);
    while (iscons(p3)) {
      push(car(p3));
      gcd();
      p3 = cdr(p3);
    }
    inverse();
    p2 = pop();
    push(zero);
    p3 = cdr(p1);
    while (iscons(p3)) {
      push(p2);
      push(car(p3));
      multiply();
      add();
      p3 = cdr(p3);
    }
    yyexpand();
    push(p2);
    return divide();
  };

  Eval_conj = function() {
    push(cadr(p1));
    Eval();
    p1 = pop();
    push(p1);
    if (!Find(p1, imaginaryunit)) {
      polar();
      conjugate();
      return clockform();
    } else {
      return conjugate();
    }
  };

  conjugate = function() {
    push(imaginaryunit);
    push(imaginaryunit);
    negate();
    subst();
    return Eval();
  };

  consCount = 0;

  cons = function() {
    var p;
    consCount++;
    if (DEBUG) {
      console.log("cons tos: " + tos + " # " + consCount);
    }
    p = new U();
    p.k = CONS;
    p.cons.cdr = pop();
    if (p === p.cons.cdr) {
      debugger;
      console.log("something wrong p == its cdr");
    }
    p.cons.car = pop();

    /*
    	console.log "cons new cdr.k = " + p.cons.cdr.k + "\nor more in detail:"
    	print1 p.cons.cdr
    	console.log "cons new car.k = " + p.cons.car.k + "\nor more in detail:"
    	print1 p.cons.car
     */
    return push(p);
  };

  Eval_contract = function() {
    push(cadr(p1));
    Eval();
    if (cddr(p1) === symbol(NIL)) {
      push_integer(1);
      push_integer(2);
    } else {
      push(caddr(p1));
      Eval();
      push(cadddr(p1));
      Eval();
    }
    return contract();
  };

  contract = function() {
    save();
    yycontract();
    return restore();
  };

  yycontract = function() {
    var a, ac, ad, ae, af, ag, ah, ai, an, b, h, i, j, k, l, m, n, ndim, nelem, o, ref, ref1, ref2, ref3, ref4, ref5, ref6;
    h = 0;
    i = 0;
    j = 0;
    k = 0;
    l = 0;
    m = 0;
    n = 0;
    ndim = 0;
    nelem = 0;
    ai = [];
    an = [];
    p3 = pop();
    p2 = pop();
    p1 = pop();
    if (!istensor(p1)) {
      if (!iszero(p1)) {
        stop("contract: tensor expected, 1st arg is not a tensor");
      }
      push(zero);
      return;
    }
    push(p2);
    l = pop_integer();
    push(p3);
    m = pop_integer();
    ndim = p1.tensor.ndim;
    if (l < 1 || l > ndim || m < 1 || m > ndim || l === m || p1.tensor.dim[l - 1] !== p1.tensor.dim[m - 1]) {
      stop("contract: index out of range");
    }
    l--;
    m--;
    n = p1.tensor.dim[l];
    nelem = 1;
    for (i = o = 0, ref = ndim; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      if (i !== l && i !== m) {
        nelem *= p1.tensor.dim[i];
      }
    }
    p2 = alloc_tensor(nelem);
    p2.tensor.ndim = ndim - 2;
    j = 0;
    for (i = ac = 0, ref1 = ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      if (i !== l && i !== m) {
        p2.tensor.dim[j++] = p1.tensor.dim[i];
      }
    }
    a = p1.tensor.elem;
    b = p2.tensor.elem;
    for (i = ad = 0, ref2 = ndim; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      ai[i] = 0;
      an[i] = p1.tensor.dim[i];
    }
    for (i = ae = 0, ref3 = nelem; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
      push(zero);
      for (j = af = 0, ref4 = n; 0 <= ref4 ? af < ref4 : af > ref4; j = 0 <= ref4 ? ++af : --af) {
        ai[l] = j;
        ai[m] = j;
        h = 0;
        for (k = ag = 0, ref5 = ndim; 0 <= ref5 ? ag < ref5 : ag > ref5; k = 0 <= ref5 ? ++ag : --ag) {
          h = (h * an[k]) + ai[k];
        }
        push(a[h]);
        add();
      }
      b[i] = pop();
      for (j = ah = ref6 = ndim - 1; ref6 <= 0 ? ah <= 0 : ah >= 0; j = ref6 <= 0 ? ++ah : --ah) {
        if (j === l || j === m) {
          continue;
        }
        if (++ai[j] < an[j]) {
          break;
        }
        ai[j] = 0;
      }
    }
    if (nelem === 1) {
      return push(b[0]);
    } else {
      return push(p2);
    }
  };

  Eval_cos = function() {
    push(cadr(p1));
    Eval();
    return cosine();
  };

  cosine = function() {
    save();
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      cosine_of_angle_sum();
    } else {
      cosine_of_angle();
    }
    return restore();
  };

  cosine_of_angle_sum = function() {
    p2 = cdr(p1);
    while (iscons(p2)) {
      p4 = car(p2);
      if (isnpi(p4)) {
        push(p1);
        push(p4);
        subtract();
        p3 = pop();
        push(p3);
        cosine();
        push(p4);
        cosine();
        multiply();
        push(p3);
        sine();
        push(p4);
        sine();
        multiply();
        subtract();
        return;
      }
      p2 = cdr(p2);
    }
    return cosine_of_angle();
  };

  cosine_of_angle = function() {
    var d, n;
    if (car(p1) === symbol(ARCCOS)) {
      push(cadr(p1));
      return;
    }
    if (isdouble(p1)) {
      d = Math.cos(p1.d);
      if (Math.abs(d) < 1e-10) {
        d = 0.0;
      }
      push_double(d);
      return;
    }
    if (isnegative(p1)) {
      push(p1);
      negate();
      p1 = pop();
    }
    if (car(p1) === symbol(ARCTAN)) {
      push_integer(1);
      push(cadr(p1));
      push_integer(2);
      power();
      add();
      push_rational(-1, 2);
      power();
      return;
    }
    push(p1);
    push_integer(180);
    multiply();
    push_symbol(PI);
    divide();
    n = pop_integer();
    if (n < 0 || n === 0x80000000) {
      push(symbol(COS));
      push(p1);
      list(2);
      return;
    }
    switch (n % 360) {
      case 90:
      case 270:
        return push_integer(0);
      case 60:
      case 300:
        return push_rational(1, 2);
      case 120:
      case 240:
        return push_rational(-1, 2);
      case 45:
      case 315:
        push_rational(1, 2);
        push_integer(2);
        push_rational(1, 2);
        power();
        return multiply();
      case 135:
      case 225:
        push_rational(-1, 2);
        push_integer(2);
        push_rational(1, 2);
        power();
        return multiply();
      case 30:
      case 330:
        push_rational(1, 2);
        push_integer(3);
        push_rational(1, 2);
        power();
        return multiply();
      case 150:
      case 210:
        push_rational(-1, 2);
        push_integer(3);
        push_rational(1, 2);
        power();
        return multiply();
      case 0:
        return push_integer(1);
      case 180:
        return push_integer(-1);
      default:
        push(symbol(COS));
        push(p1);
        return list(2);
    }
  };

  Eval_cosh = function() {
    push(cadr(p1));
    Eval();
    return ycosh();
  };

  ycosh = function() {
    save();
    yycosh();
    return restore();
  };

  yycosh = function() {
    var d;
    d = 0.0;
    p1 = pop();
    if (car(p1) === symbol(ARCCOSH)) {
      push(cadr(p1));
      return;
    }
    if (isdouble(p1)) {
      d = Math.cosh(p1.d);
      if (Math.abs(d) < 1e-10) {
        d = 0.0;
      }
      push_double(d);
      return;
    }
    if (iszero(p1)) {
      push(one);
      return;
    }
    push_symbol(COSH);
    push(p1);
    return list(2);
  };

  Eval_decomp = function() {
    var h;
    h = tos;
    push(symbol(NIL));
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    p1 = pop();
    if (p1 === symbol(NIL)) {
      guess();
    } else {
      push(p1);
    }
    decomp();
    return list(tos - h);
  };

  decomp = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (Find(p1, p2) === 0) {
      push(p1);
      restore();
      return;
    }
    if (isadd(p1)) {
      decomp_sum();
      restore();
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      decomp_product();
      restore();
      return;
    }
    p3 = cdr(p1);
    while (iscons(p3)) {
      push(car(p3));
      push(p2);
      decomp();
      p3 = cdr(p3);
    }
    return restore();
  };

  decomp_sum = function() {
    var h;
    h = 0;
    p3 = cdr(p1);
    while (iscons(p3)) {
      if (Find(car(p3), p2)) {
        push(car(p3));
        push(p2);
        decomp();
      }
      p3 = cdr(p3);
    }
    h = tos;
    p3 = cdr(p1);
    while (iscons(p3)) {
      if (Find(car(p3), p2) === 0) {
        push(car(p3));
      }
      p3 = cdr(p3);
    }
    if (tos - h) {
      add_all(tos - h);
      p3 = pop();
      push(p3);
      push(p3);
      return negate();
    }
  };

  decomp_product = function() {
    var h;
    h = 0;
    p3 = cdr(p1);
    while (iscons(p3)) {
      if (Find(car(p3), p2)) {
        push(car(p3));
        push(p2);
        decomp();
      }
      p3 = cdr(p3);
    }
    h = tos;
    p3 = cdr(p1);
    while (iscons(p3)) {
      if (Find(car(p3), p2) === 0) {
        push(car(p3));
      }
      p3 = cdr(p3);
    }
    if (tos - h) {
      return multiply_all(tos - h);
    }
  };

  define_user_function = function() {
    p3 = caadr(p1);
    p4 = cdadr(p1);
    p5 = caddr(p1);
    if (!issymbol(p3)) {
      stop("function name?");
    }
    if (car(p5) === symbol(EVAL)) {
      push(cadr(p5));
      Eval();
      p5 = pop();
    }
    set_binding_and_arglist(p3, p5, p4);
    return push_symbol(NIL);
  };

  Eval_defint = function() {
    push(cadr(p1));
    Eval();
    p2 = pop();
    p1 = cddr(p1);
    while (iscons(p1)) {
      push(car(p1));
      p1 = cdr(p1);
      Eval();
      p3 = pop();
      push(car(p1));
      p1 = cdr(p1);
      Eval();
      p4 = pop();
      push(car(p1));
      p1 = cdr(p1);
      Eval();
      p5 = pop();
      push(p2);
      push(p3);
      integral();
      p2 = pop();
      push(p2);
      push(p3);
      push(p5);
      subst();
      Eval();
      push(p2);
      push(p3);
      push(p4);
      subst();
      Eval();
      subtract();
      p2 = pop();
    }
    return push(p2);
  };

  Eval_degree = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    p1 = pop();
    if (p1 === symbol(NIL)) {
      guess();
    } else {
      push(p1);
    }
    return degree();
  };

  degree = function() {
    save();
    p2 = pop();
    p1 = pop();
    p3 = zero;
    yydegree(p1);
    push(p3);
    return restore();
  };

  yydegree = function(p) {
    var results;
    if (equal(p, p2)) {
      if (iszero(p3)) {
        return p3 = one;
      }
    } else if (car(p) === symbol(POWER)) {
      if (equal(cadr(p), p2) && isnum(caddr(p)) && lessp(p3, caddr(p))) {
        return p3 = caddr(p);
      }
    } else if (iscons(p)) {
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        yydegree(car(p));
        results.push(p = cdr(p));
      }
      return results;
    }
  };

  Eval_denominator = function() {
    push(cadr(p1));
    Eval();
    return denominator();
  };

  denominator = function() {
    var h;
    h = 0;
    save();
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      push(p1);
      rationalize();
      p1 = pop();
    }
    if (car(p1) === symbol(MULTIPLY)) {
      h = tos;
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        denominator();
        p1 = cdr(p1);
      }
      multiply_all(tos - h);
    } else if (isrational(p1)) {
      push(p1);
      mp_denominator();
    } else if (car(p1) === symbol(POWER) && isnegativeterm(caddr(p1))) {
      push(p1);
      reciprocate();
    } else {
      push(one);
    }
    return restore();
  };

  Eval_derivative = function() {
    var ac, doNothing, i, n, o, ref, ref1;
    i = 0;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      guess();
      push(symbol(NIL));
    } else if (isnum(p2)) {
      guess();
      push(p2);
    } else {
      push(p2);
      p1 = cdr(p1);
      push(car(p1));
      Eval();
    }
    p5 = pop();
    p4 = pop();
    p3 = pop();
    while (1.) {
      if (isnum(p5)) {
        push(p5);
        n = pop_integer();
        if (n === 0x80000000) {
          stop("nth derivative: check n");
        }
      } else {
        n = 1;
      }
      push(p3);
      if (n >= 0) {
        for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
          push(p4);
          derivative();
        }
      } else {
        n = -n;
        for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
          push(p4);
          integral();
        }
      }
      p3 = pop();
      if (p5 === symbol(NIL)) {
        break;
      }
      if (isnum(p5)) {
        p1 = cdr(p1);
        push(car(p1));
        Eval();
        p5 = pop();
        if (p5 === symbol(NIL)) {
          break;
        }
        if (isnum(p5)) {
          doNothing = 1;
        } else {
          p4 = p5;
          p1 = cdr(p1);
          push(car(p1));
          Eval();
          p5 = pop();
        }
      } else {
        p4 = p5;
        p1 = cdr(p1);
        push(car(p1));
        Eval();
        p5 = pop();
      }
    }
    return push(p3);
  };

  derivative = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (isnum(p2)) {
      stop("undefined function");
    }
    if (istensor(p1)) {
      if (istensor(p2)) {
        d_tensor_tensor();
      } else {
        d_tensor_scalar();
      }
    } else {
      if (istensor(p2)) {
        d_scalar_tensor();
      } else {
        d_scalar_scalar();
      }
    }
    return restore();
  };

  d_scalar_scalar = function() {
    if (issymbol(p2)) {
      return d_scalar_scalar_1();
    } else {
      push(p1);
      push(p2);
      push(symbol(SECRETX));
      subst();
      push(symbol(SECRETX));
      derivative();
      push(symbol(SECRETX));
      push(p2);
      return subst();
    }
  };

  d_scalar_scalar_1 = function() {
    if (equal(p1, p2)) {
      push(one);
      return;
    }
    if (!iscons(p1)) {
      push(zero);
      return;
    }
    if (isadd(p1)) {
      dsum();
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      dproduct();
      return;
    }
    if (car(p1) === symbol(POWER)) {
      dpower();
      return;
    }
    if (car(p1) === symbol(DERIVATIVE)) {
      dd();
      return;
    }
    if (car(p1) === symbol(LOG)) {
      dlog();
      return;
    }
    if (car(p1) === symbol(SIN)) {
      dsin();
      return;
    }
    if (car(p1) === symbol(COS)) {
      dcos();
      return;
    }
    if (car(p1) === symbol(TAN)) {
      dtan();
      return;
    }
    if (car(p1) === symbol(ARCSIN)) {
      darcsin();
      return;
    }
    if (car(p1) === symbol(ARCCOS)) {
      darccos();
      return;
    }
    if (car(p1) === symbol(ARCTAN)) {
      darctan();
      return;
    }
    if (car(p1) === symbol(SINH)) {
      dsinh();
      return;
    }
    if (car(p1) === symbol(COSH)) {
      dcosh();
      return;
    }
    if (car(p1) === symbol(TANH)) {
      dtanh();
      return;
    }
    if (car(p1) === symbol(ARCSINH)) {
      darcsinh();
      return;
    }
    if (car(p1) === symbol(ARCCOSH)) {
      darccosh();
      return;
    }
    if (car(p1) === symbol(ARCTANH)) {
      darctanh();
      return;
    }
    if (car(p1) === symbol(ABS)) {
      dabs();
      return;
    }
    if (car(p1) === symbol(SGN)) {
      dsgn();
      return;
    }
    if (car(p1) === symbol(HERMITE)) {
      dhermite();
      return;
    }
    if (car(p1) === symbol(ERF)) {
      derf();
      return;
    }
    if (car(p1) === symbol(ERFC)) {
      derfc();
      return;
    }
    if (car(p1) === symbol(BESSELJ)) {
      if (iszero(caddr(p1))) {
        dbesselj0();
      } else {
        dbesseljn();
      }
      return;
    }
    if (car(p1) === symbol(BESSELY)) {
      if (iszero(caddr(p1))) {
        dbessely0();
      } else {
        dbesselyn();
      }
      return;
    }
    if (car(p1) === symbol(INTEGRAL) && caddr(p1) === p2) {
      derivative_of_integral();
      return;
    }
    return dfunction();
  };

  dsum = function() {
    var h;
    h = tos;
    p1 = cdr(p1);
    while (iscons(p1)) {
      push(car(p1));
      push(p2);
      derivative();
      p1 = cdr(p1);
    }
    return add_all(tos - h);
  };

  dproduct = function() {
    var ac, i, j, n, o, ref, ref1;
    i = 0;
    j = 0;
    n = 0;
    n = length(p1) - 1;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p3 = cdr(p1);
      for (j = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
        push(car(p3));
        if (i === j) {
          push(p2);
          derivative();
        }
        p3 = cdr(p3);
      }
      multiply_all(n);
    }
    return add_all(n);
  };

  dpower = function() {
    push(caddr(p1));
    push(cadr(p1));
    divide();
    push(cadr(p1));
    push(p2);
    derivative();
    multiply();
    push(cadr(p1));
    logarithm();
    push(caddr(p1));
    push(p2);
    derivative();
    multiply();
    add();
    push(p1);
    return multiply();
  };

  dlog = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    return divide();
  };

  dd = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    p3 = pop();
    if (car(p3) === symbol(DERIVATIVE)) {
      push_symbol(DERIVATIVE);
      push_symbol(DERIVATIVE);
      push(cadr(p3));
      if (lessp(caddr(p3), caddr(p1))) {
        push(caddr(p3));
        list(3);
        push(caddr(p1));
      } else {
        push(caddr(p1));
        list(3);
        push(caddr(p3));
      }
      return list(3);
    } else {
      push(p3);
      push(caddr(p1));
      return derivative();
    }
  };

  dfunction = function() {
    p3 = cdr(p1);
    if (p3 === symbol(NIL) || Find(p3, p2)) {
      push_symbol(DERIVATIVE);
      push(p1);
      push(p2);
      return list(3);
    } else {
      return push(zero);
    }
  };

  dsin = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    cosine();
    return multiply();
  };

  dcos = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    sine();
    multiply();
    return negate();
  };

  dtan = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    cosine();
    push_integer(-2);
    power();
    return multiply();
  };

  darcsin = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(1);
    push(cadr(p1));
    push_integer(2);
    power();
    subtract();
    push_rational(-1, 2);
    power();
    return multiply();
  };

  darccos = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(1);
    push(cadr(p1));
    push_integer(2);
    power();
    subtract();
    push_rational(-1, 2);
    power();
    multiply();
    return negate();
  };

  darctan = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(1);
    push(cadr(p1));
    push_integer(2);
    power();
    add();
    inverse();
    multiply();
    return simplify();
  };

  dsinh = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    ycosh();
    return multiply();
  };

  dcosh = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    ysinh();
    return multiply();
  };

  dtanh = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    ycosh();
    push_integer(-2);
    power();
    return multiply();
  };

  darcsinh = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    push_integer(2);
    power();
    push_integer(1);
    add();
    push_rational(-1, 2);
    power();
    return multiply();
  };

  darccosh = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    push_integer(2);
    power();
    push_integer(-1);
    add();
    push_rational(-1, 2);
    power();
    return multiply();
  };

  darctanh = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(1);
    push(cadr(p1));
    push_integer(2);
    power();
    subtract();
    inverse();
    return multiply();
  };

  dabs = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    sgn();
    return multiply();
  };

  dsgn = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    dirac();
    multiply();
    push_integer(2);
    return multiply();
  };

  dhermite = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push_integer(2);
    push(caddr(p1));
    multiply();
    multiply();
    push(cadr(p1));
    push(caddr(p1));
    push_integer(-1);
    add();
    hermite();
    return multiply();
  };

  derf = function() {
    push(cadr(p1));
    push_integer(2);
    power();
    push_integer(-1);
    multiply();
    exponential();
    push_symbol(PI);
    push_rational(-1, 2);
    power();
    multiply();
    push_integer(2);
    multiply();
    push(cadr(p1));
    push(p2);
    derivative();
    return multiply();
  };

  derfc = function() {
    push(cadr(p1));
    push_integer(2);
    power();
    push_integer(-1);
    multiply();
    exponential();
    push_symbol(PI);
    push_rational(-1, 2);
    power();
    multiply();
    push_integer(-2);
    multiply();
    push(cadr(p1));
    push(p2);
    derivative();
    return multiply();
  };

  dbesselj0 = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    push_integer(1);
    besselj();
    multiply();
    push_integer(-1);
    return multiply();
  };

  dbesseljn = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    push(caddr(p1));
    push_integer(-1);
    add();
    besselj();
    push(caddr(p1));
    push_integer(-1);
    multiply();
    push(cadr(p1));
    divide();
    push(cadr(p1));
    push(caddr(p1));
    besselj();
    multiply();
    add();
    return multiply();
  };

  dbessely0 = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    push_integer(1);
    besselj();
    multiply();
    push_integer(-1);
    return multiply();
  };

  dbesselyn = function() {
    push(cadr(p1));
    push(p2);
    derivative();
    push(cadr(p1));
    push(caddr(p1));
    push_integer(-1);
    add();
    bessely();
    push(caddr(p1));
    push_integer(-1);
    multiply();
    push(cadr(p1));
    divide();
    push(cadr(p1));
    push(caddr(p1));
    bessely();
    multiply();
    add();
    return multiply();
  };

  derivative_of_integral = function() {
    return push(cadr(p1));
  };

  DET_check_arg = function() {
    if (!istensor(p1)) {
      return 0;
    } else if (p1.tensor.ndim !== 2) {
      return 0;
    } else if (p1.tensor.dim[0] !== p1.tensor.dim[1]) {
      return 0;
    } else {
      return 1;
    }
  };

  det = function() {
    var a, ac, i, n, o, ref, ref1;
    i = 0;
    n = 0;
    save();
    p1 = pop();
    if (DET_check_arg() === 0) {
      push_symbol(DET);
      push(p1);
      list(2);
      restore();
      return;
    }
    n = p1.tensor.nelem;
    a = p1.tensor.elem;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      if (!isnum(a[i])) {
        break;
      }
    }
    if (i === n) {
      yydetg();
    } else {
      for (i = ac = 0, ref1 = p1.tensor.nelem; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
        push(p1.tensor.elem[i]);
      }
      determinant(p1.tensor.dim[0]);
    }
    return restore();
  };

  determinant = function(n) {
    var a, ac, breakFromOutherWhile, h, i, j, k, o, q, ref, ref1, s, sign_, t;
    h = 0;
    i = 0;
    j = 0;
    k = 0;
    q = 0;
    s = 0;
    sign_ = 0;
    t = 0;
    a = [];
    h = tos - n * n;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      a[i] = i;
      a[i + n] = 0;
      a[i + n + n] = 1;
    }
    sign_ = 1;
    push(zero);
    while (1) {
      if (sign_ === 1) {
        push_integer(1);
      } else {
        push_integer(-1);
      }
      for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
        k = n * a[i] + i;
        push(stack[h + k]);
        multiply();
      }
      add();
      j = n - 1;
      s = 0;
      breakFromOutherWhile = false;
      while (1) {
        q = a[n + j] + a[n + n + j];
        if (q < 0) {
          a[n + n + j] = -a[n + n + j];
          j--;
          continue;
        }
        if (q === j + 1) {
          if (j === 0) {
            breakFromOutherWhile = true;
            break;
          }
          s++;
          a[n + n + j] = -a[n + n + j];
          j--;
          continue;
        }
        break;
      }
      if (breakFromOutherWhile) {
        break;
      }
      t = a[j - a[n + j] + s];
      a[j - a[n + j] + s] = a[j - q + s];
      a[j - q + s] = t;
      a[n + j] = q;
      sign_ = -sign_;
    }
    stack[h] = stack[tos - 1];
    return tos = h + 1;
  };

  detg = function() {
    save();
    p1 = pop();
    if (DET_check_arg() === 0) {
      push_symbol(DET);
      push(p1);
      list(2);
      restore();
      return;
    }
    yydetg();
    return restore();
  };

  yydetg = function() {
    var i, n, o, ref;
    i = 0;
    n = 0;
    n = p1.tensor.dim[0];
    for (i = o = 0, ref = n * n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      push(p1.tensor.elem[i]);
    }
    lu_decomp(n);
    tos -= n * n;
    return push(p1);
  };

  M = function(h, n, i, j) {
    return stack[h + n * i + j];
  };

  setM = function(h, n, i, j, value) {
    return stack[h + n * i + j] = value;
  };

  lu_decomp = function(n) {
    var ac, ad, ae, af, d, h, i, j, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, ref7, ref8;
    d = 0;
    h = 0;
    i = 0;
    j = 0;
    h = tos - n * n;
    p1 = one;
    for (d = o = 0, ref = n - 1; 0 <= ref ? o < ref : o > ref; d = 0 <= ref ? ++o : --o) {
      if (equal(M(h, n, d, d), zero)) {
        for (i = ac = ref1 = d + 1, ref2 = n; ref1 <= ref2 ? ac < ref2 : ac > ref2; i = ref1 <= ref2 ? ++ac : --ac) {
          if (!equal(M(h, n, i, d), zero)) {
            break;
          }
        }
        if (i === n) {
          p1 = zero;
          break;
        }
        for (j = ad = ref3 = d, ref4 = n; ref3 <= ref4 ? ad < ref4 : ad > ref4; j = ref3 <= ref4 ? ++ad : --ad) {
          p2 = M(h, n, d, j);
          setM(h, n, d, j, M(h, n, i, j));
          setM(h, n, i, j, p2);
        }
        push(p1);
        negate();
        p1 = pop();
      }
      push(p1);
      push(M(h, n, d, d));
      multiply();
      p1 = pop();
      for (i = ae = ref5 = d + 1, ref6 = n; ref5 <= ref6 ? ae < ref6 : ae > ref6; i = ref5 <= ref6 ? ++ae : --ae) {
        push(M(h, n, i, d));
        push(M(h, n, d, d));
        divide();
        negate();
        p2 = pop();
        setM(h, n, i, d, zero);
        for (j = af = ref7 = d + 1, ref8 = n; ref7 <= ref8 ? af < ref8 : af > ref8; j = ref7 <= ref8 ? ++af : --af) {
          push(M(h, n, d, j));
          push(p2);
          multiply();
          push(M(h, n, i, j));
          add();
          setM(h, n, i, j, pop());
        }
      }
    }
    push(p1);
    push(M(h, n, n - 1, n - 1));
    multiply();
    return p1 = pop();
  };

  Eval_dirac = function() {
    push(cadr(p1));
    Eval();
    return dirac();
  };

  dirac = function() {
    save();
    ydirac();
    return restore();
  };

  ydirac = function() {
    p1 = pop();
    if (isdouble(p1)) {
      if (p1.d === 0) {
        push_integer(1);
        return;
      } else {
        push_integer(0);
        return;
      }
    }
    if (isrational(p1)) {
      if (MZERO(mmul(p1.q.a, p1.q.b))) {
        push_integer(1);
        return;
      } else {
        push_integer(0);
        return;
      }
    }
    if (car(p1) === symbol(POWER)) {
      push_symbol(DIRAC);
      push(cadr(p1));
      list(2);
      return;
    }
    if (isnegativeterm(p1)) {
      push_symbol(DIRAC);
      push(p1);
      negate();
      list(2);
      return;
    }
    if (isnegativeterm(p1) || (car(p1) === symbol(ADD) && isnegativeterm(cadr(p1)))) {
      push(p1);
      negate();
      p1 = pop();
    }
    push_symbol(DIRAC);
    push(p1);
    return list(2);
  };

  divisors = function() {
    var h, i, n, o, ref, subsetOfStack;
    i = 0;
    h = 0;
    n = 0;
    save();
    h = tos - 1;
    divisors_onstack();
    n = tos - h;
    subsetOfStack = stack.slice(h, h + n);
    subsetOfStack.sort(cmp_expr);
    stack = stack.slice(0, h).concat(subsetOfStack).concat(stack.slice(h + n));
    p1 = alloc_tensor(n);
    p1.tensor.ndim = 1;
    p1.tensor.dim[0] = n;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p1.tensor.elem[i] = stack[h + i];
    }
    tos = h;
    push(p1);
    return restore();
  };

  divisors_onstack = function() {
    var h, i, k, n, o, ref;
    h = 0;
    i = 0;
    k = 0;
    n = 0;
    save();
    p1 = pop();
    h = tos;
    if (isnum(p1)) {
      push(p1);
      factor_small_number();
    } else if (car(p1) === symbol(ADD)) {
      push(p1);
      __factor_add();
    } else if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
      if (isnum(car(p1))) {
        push(car(p1));
        factor_small_number();
        p1 = cdr(p1);
      }
      while (iscons(p1)) {
        p2 = car(p1);
        if (car(p2) === symbol(POWER)) {
          push(cadr(p2));
          push(caddr(p2));
        } else {
          push(p2);
          push(one);
        }
        p1 = cdr(p1);
      }
    } else if (car(p1) === symbol(POWER)) {
      push(cadr(p1));
      push(caddr(p1));
    } else {
      push(p1);
      push(one);
    }
    k = tos;
    push(one);
    gen(h, k);
    n = tos - k;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      stack[h + i] = stack[k + i];
    }
    tos = h + n;
    return restore();
  };

  gen = function(h, k) {
    var expo, i, o, ref;
    expo = 0;
    i = 0;
    save();
    p1 = pop();
    if (h === k) {
      push(p1);
      restore();
      return;
    }
    p2 = stack[h + 0];
    p3 = stack[h + 1];
    push(p3);
    expo = pop_integer();
    if (expo !== 0x80000000) {
      for (i = o = 0, ref = Math.abs(expo); 0 <= ref ? o <= ref : o >= ref; i = 0 <= ref ? ++o : --o) {
        push(p1);
        push(p2);
        push_integer(sign(expo) * i);
        power();
        multiply();
        gen(h + 2, k);
      }
    }
    return restore();
  };

  __factor_add = function() {
    save();
    p1 = pop();
    p3 = cdr(p1);
    push(car(p3));
    p3 = cdr(p3);
    while (iscons(p3)) {
      push(car(p3));
      gcd();
      p3 = cdr(p3);
    }
    p2 = pop();
    if (isplusone(p2)) {
      push(p1);
      push(one);
      restore();
      return;
    }
    if (isnum(p2)) {
      push(p2);
      factor_small_number();
    } else if (car(p2) === symbol(MULTIPLY)) {
      p3 = cdr(p2);
      if (isnum(car(p3))) {
        push(car(p3));
        factor_small_number();
      } else {
        push(car(p3));
        push(one);
      }
      p3 = cdr(p3);
      while (iscons(p3)) {
        push(car(p3));
        push(one);
        p3 = cdr(p3);
      }
    } else {
      push(p2);
      push(one);
    }
    push(p2);
    inverse();
    p2 = pop();
    push(zero);
    p3 = cdr(p1);
    while (iscons(p3)) {
      push(p2);
      push(car(p3));
      multiply();
      add();
      p3 = cdr(p3);
    }
    push(one);
    return restore();
  };

  dpow = function() {
    var a, b, base, expo, result, theta;
    a = 0.0;
    b = 0.0;
    base = 0.0;
    expo = 0.0;
    result = 0.0;
    theta = 0.0;
    expo = pop_double();
    base = pop_double();
    if (base === 0.0 && expo < 0.0) {
      stop("divide by zero");
    }
    if (base >= 0.0 || (expo % 1.0) === 0.0) {
      result = Math.pow(base, expo);
      push_double(result);
      return;
    }
    result = Math.pow(Math.abs(base), expo);
    theta = Math.PI * expo;
    if ((expo % 0.5) === 0.0) {
      a = 0.0;
      b = Math.sin(theta);
    } else {
      a = Math.cos(theta);
      b = Math.sin(theta);
    }
    push_double(a * result);
    push_double(b * result);
    push(imaginaryunit);
    multiply();
    return add();
  };

  EIG_N = 0;

  EIG_yydd = [];

  EIG_yyqq = [];

  Eval_eigen = function() {
    if (EIG_check_arg() === 0) {
      stop("eigen: argument is not a square matrix");
    }
    eigen(EIGEN);
    p1 = usr_symbol("D");
    set_binding(p1, p2);
    p1 = usr_symbol("Q");
    set_binding(p1, p3);
    return push(symbol(NIL));
  };

  Eval_eigenval = function() {
    if (EIG_check_arg() === 0) {
      push_symbol(EIGENVAL);
      push(p1);
      list(2);
      return;
    }
    eigen(EIGENVAL);
    return push(p2);
  };

  Eval_eigenvec = function() {
    if (EIG_check_arg() === 0) {
      push_symbol(EIGENVEC);
      push(p1);
      list(2);
      return;
    }
    eigen(EIGENVEC);
    return push(p3);
  };

  EIG_check_arg = function() {
    var ac, ad, ae, i, j, o, ref, ref1, ref2, ref3, ref4;
    i = 0;
    j = 0;
    push(cadr(p1));
    Eval();
    yyfloat();
    Eval();
    p1 = pop();
    if (!istensor(p1)) {
      return 0;
    }
    if (p1.tensor.ndim !== 2 || p1.tensor.dim[0] !== p1.tensor.dim[1]) {
      stop("eigen: argument is not a square matrix");
    }
    EIG_N = p1.tensor.dim[0];
    for (i = o = 0, ref = EIG_N; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      for (j = ac = 0, ref1 = EIG_N; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
        if (!isdouble(p1.tensor.elem[EIG_N * i + j])) {
          stop("eigen: matrix is not numerical");
        }
      }
    }
    for (i = ad = 0, ref2 = EIG_N - 1; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      for (j = ae = ref3 = i + 1, ref4 = EIG_N; ref3 <= ref4 ? ae < ref4 : ae > ref4; j = ref3 <= ref4 ? ++ae : --ae) {
        if (Math.abs(p1.tensor.elem[EIG_N * i + j].d - p1.tensor.elem[EIG_N * j + i].d) > 1e-10) {
          stop("eigen: matrix is not symmetrical");
        }
      }
    }
    return 1;
  };

  eigen = function(op) {
    var ac, ad, ae, af, ag, ah, aj, al, am, i, j, o, ref, ref1, ref10, ref2, ref3, ref4, ref5, ref6, ref7, ref8, ref9, results;
    i = 0;
    j = 0;
    for (i = o = 0, ref = EIG_N * EIG_N; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      EIG_yydd[i] = 0.0;
    }
    for (i = ac = 0, ref1 = EIG_N * EIG_N; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      EIG_yyqq[i] = 0.0;
    }
    for (i = ad = 0, ref2 = EIG_N; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      EIG_yydd[EIG_N * i + i] = p1.tensor.elem[EIG_N * i + i].d;
      for (j = ae = ref3 = i + 1, ref4 = EIG_N; ref3 <= ref4 ? ae < ref4 : ae > ref4; j = ref3 <= ref4 ? ++ae : --ae) {
        EIG_yydd[EIG_N * i + j] = p1.tensor.elem[EIG_N * i + j].d;
        EIG_yydd[EIG_N * j + i] = p1.tensor.elem[EIG_N * i + j].d;
      }
    }
    for (i = af = 0, ref5 = EIG_N; 0 <= ref5 ? af < ref5 : af > ref5; i = 0 <= ref5 ? ++af : --af) {
      EIG_yyqq[EIG_N * i + i] = 1.0;
      for (j = ag = ref6 = i + 1, ref7 = EIG_N; ref6 <= ref7 ? ag < ref7 : ag > ref7; j = ref6 <= ref7 ? ++ag : --ag) {
        EIG_yyqq[EIG_N * i + j] = 0.0;
        EIG_yyqq[EIG_N * j + i] = 0.0;
      }
    }
    for (i = ah = 0; ah < 100; i = ++ah) {
      if (step() === 0) {
        break;
      }
    }
    if (i === 100) {
      printstr("\nnote: eigen did not converge\n");
    }
    if (op === EIGEN || op === EIGENVAL) {
      push(p1);
      copy_tensor();
      p2 = pop();
      for (i = aj = 0, ref8 = EIG_N; 0 <= ref8 ? aj < ref8 : aj > ref8; i = 0 <= ref8 ? ++aj : --aj) {
        for (j = al = 0, ref9 = EIG_N; 0 <= ref9 ? al < ref9 : al > ref9; j = 0 <= ref9 ? ++al : --al) {
          push_double(EIG_yydd[EIG_N * i + j]);
          p2.tensor.elem[EIG_N * i + j] = pop();
        }
      }
    }
    if (op === EIGEN || op === EIGENVEC) {
      push(p1);
      copy_tensor();
      p3 = pop();
      results = [];
      for (i = am = 0, ref10 = EIG_N; 0 <= ref10 ? am < ref10 : am > ref10; i = 0 <= ref10 ? ++am : --am) {
        results.push((function() {
          var ao, ref11, results1;
          results1 = [];
          for (j = ao = 0, ref11 = EIG_N; 0 <= ref11 ? ao < ref11 : ao > ref11; j = 0 <= ref11 ? ++ao : --ao) {
            push_double(EIG_yyqq[EIG_N * i + j]);
            results1.push(p3.tensor.elem[EIG_N * i + j] = pop());
          }
          return results1;
        })());
      }
      return results;
    }
  };

  step = function() {
    var ac, count, i, j, o, ref, ref1, ref2;
    i = 0;
    j = 0;
    count = 0;
    for (i = o = 0, ref = EIG_N - 1; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      for (j = ac = ref1 = i + 1, ref2 = EIG_N; ref1 <= ref2 ? ac < ref2 : ac > ref2; j = ref1 <= ref2 ? ++ac : --ac) {
        if (EIG_yydd[EIG_N * i + j] !== 0.0) {
          step2(i, j);
          count++;
        }
      }
    }
    return count;
  };

  step2 = function(p, q) {
    var ac, ad, c, cc, k, o, ref, ref1, ref2, s, ss, t, theta;
    k = 0;
    t = 0.0;
    theta = 0.0;
    c = 0.0;
    cc = 0.0;
    s = 0.0;
    ss = 0.0;
    theta = 0.5 * (EIG_yydd[EIG_N * p + p] - EIG_yydd[EIG_N * q + q]) / EIG_yydd[EIG_N * p + q];
    t = 1.0 / (Math.abs(theta) + Math.sqrt(theta * theta + 1.0));
    if (theta < 0.0) {
      t = -t;
    }
    c = 1.0 / Math.sqrt(t * t + 1.0);
    s = t * c;
    for (k = o = 0, ref = EIG_N; 0 <= ref ? o < ref : o > ref; k = 0 <= ref ? ++o : --o) {
      cc = EIG_yydd[EIG_N * p + k];
      ss = EIG_yydd[EIG_N * q + k];
      EIG_yydd[EIG_N * p + k] = c * cc + s * ss;
      EIG_yydd[EIG_N * q + k] = c * ss - s * cc;
    }
    for (k = ac = 0, ref1 = EIG_N; 0 <= ref1 ? ac < ref1 : ac > ref1; k = 0 <= ref1 ? ++ac : --ac) {
      cc = EIG_yydd[EIG_N * k + p];
      ss = EIG_yydd[EIG_N * k + q];
      EIG_yydd[EIG_N * k + p] = c * cc + s * ss;
      EIG_yydd[EIG_N * k + q] = c * ss - s * cc;
    }
    for (k = ad = 0, ref2 = EIG_N; 0 <= ref2 ? ad < ref2 : ad > ref2; k = 0 <= ref2 ? ++ad : --ad) {
      cc = EIG_yyqq[EIG_N * p + k];
      ss = EIG_yyqq[EIG_N * q + k];
      EIG_yyqq[EIG_N * p + k] = c * cc + s * ss;
      EIG_yyqq[EIG_N * q + k] = c * ss - s * cc;
    }
    EIG_yydd[EIG_N * p + q] = 0.0;
    return EIG_yydd[EIG_N * q + p] = 0.0;
  };

  Eval_erf = function() {
    push(cadr(p1));
    Eval();
    return yerf();
  };

  yerf = function() {
    save();
    yyerf();
    return restore();
  };

  yyerf = function() {
    var d;
    d = 0.0;
    p1 = pop();
    if (isdouble(p1)) {
      d = 1.0 - erfc(p1.d);
      push_double(d);
      return;
    }
    if (isnegativeterm(p1)) {
      push_symbol(ERF);
      push(p1);
      negate();
      list(2);
      negate();
      return;
    }
    push_symbol(ERF);
    push(p1);
    list(2);
  };

  Eval_erfc = function() {
    push(cadr(p1));
    Eval();
    return yerfc();
  };

  yerfc = function() {
    save();
    yyerfc();
    return restore();
  };

  yyerfc = function() {
    var d;
    d = 0.0;
    p1 = pop();
    if (isdouble(p1)) {
      d = erfc(p1.d);
      push_double(d);
      return;
    }
    push_symbol(ERFC);
    push(p1);
    list(2);
  };

  erfc = function(x) {
    var ans, t, z;
    t = 0.0;
    z = 0.0;
    ans = 0.0;
    z = Math.abs(x);
    t = 1.0 / (1.0 + 0.5 * z);
    ans = t * Math.exp(-z * z - 1.26551223 + t * (1.00002368 + t * (0.37409196 + t * (0.09678418 + t * (-0.18628806 + t * (0.27886807 + t * (-1.13520398 + t * (1.48851587 + t * (-0.82215223 + t * 0.17087277)))))))));
    if (x >= 0.0) {
      return ans;
    } else {
      return 2.0 - ans;
    }
  };


  /*
  	 * commented-out test
  	"float(erfc(1))",
  	"0.157299",
   */

  Eval = function() {
    check_esc_flag();
    save();
    p1 = pop();
    if (p1 == null) {
      debugger;
    }
    switch (p1.k) {
      case CONS:
        Eval_cons();
        break;
      case NUM:
        push(p1);
        break;
      case DOUBLE:
        push(p1);
        break;
      case STR:
        push(p1);
        break;
      case TENSOR:
        Eval_tensor();
        break;
      case SYM:
        Eval_sym();
        break;
      default:
        stop("atom?");
    }
    return restore();
  };

  Eval_sym = function() {
    if (iskeyword(p1)) {
      push(p1);
      push(symbol(LAST));
      list(2);
      Eval();
      return;
    }
    p2 = get_binding(p1);
    push(p2);
    if (p1 !== p2) {
      return Eval();
    }
  };

  Eval_cons = function() {
    if (!issymbol(car(p1))) {
      stop("cons?");
    }
    switch (symnum(car(p1))) {
      case ABS:
        return Eval_abs();
      case ADD:
        return Eval_add();
      case ADJ:
        return Eval_adj();
      case AND:
        return Eval_and();
      case ARCCOS:
        return Eval_arccos();
      case ARCCOSH:
        return Eval_arccosh();
      case ARCSIN:
        return Eval_arcsin();
      case ARCSINH:
        return Eval_arcsinh();
      case ARCTAN:
        return Eval_arctan();
      case ARCTANH:
        return Eval_arctanh();
      case ARG:
        return Eval_arg();
      case ATOMIZE:
        return Eval_atomize();
      case BESSELJ:
        return Eval_besselj();
      case BESSELY:
        return Eval_bessely();
      case BINDING:
        return Eval_binding();
      case BINOMIAL:
        return Eval_binomial();
      case CEILING:
        return Eval_ceiling();
      case CHECK:
        return Eval_check();
      case CHOOSE:
        return Eval_choose();
      case CIRCEXP:
        return Eval_circexp();
      case CLEAR:
        return Eval_clear();
      case CLOCK:
        return Eval_clock();
      case COEFF:
        return Eval_coeff();
      case COFACTOR:
        return Eval_cofactor();
      case CONDENSE:
        return Eval_condense();
      case CONJ:
        return Eval_conj();
      case CONTRACT:
        return Eval_contract();
      case COS:
        return Eval_cos();
      case COSH:
        return Eval_cosh();
      case DECOMP:
        return Eval_decomp();
      case DEGREE:
        return Eval_degree();
      case DEFINT:
        return Eval_defint();
      case DENOMINATOR:
        return Eval_denominator();
      case DERIVATIVE:
        return Eval_derivative();
      case DET:
        return Eval_det();
      case DIM:
        return Eval_dim();
      case DIRAC:
        return Eval_dirac();
      case DISPLAY:
        return Eval_display();
      case DIVISORS:
        return Eval_divisors();
      case DO:
        return Eval_do();
      case DOT:
        return Eval_inner();
      case DRAW:
        return Eval_draw();
      case DSOLVE:
        return Eval_dsolve();
      case EIGEN:
        return Eval_eigen();
      case EIGENVAL:
        return Eval_eigenval();
      case EIGENVEC:
        return Eval_eigenvec();
      case ERF:
        return Eval_erf();
      case ERFC:
        return Eval_erfc();
      case EVAL:
        return Eval_Eval();
      case EXP:
        return Eval_exp();
      case EXPAND:
        return Eval_expand();
      case EXPCOS:
        return Eval_expcos();
      case EXPSIN:
        return Eval_expsin();
      case FACTOR:
        return Eval_factor();
      case FACTORIAL:
        return Eval_factorial();
      case FACTORPOLY:
        return Eval_factorpoly();
      case FILTER:
        return Eval_filter();
      case FLOATF:
        return Eval_float();
      case FLOOR:
        return Eval_floor();
      case FOR:
        return Eval_for();
      case GAMMA:
        return Eval_gamma();
      case GCD:
        return Eval_gcd();
      case HERMITE:
        return Eval_hermite();
      case HILBERT:
        return Eval_hilbert();
      case IMAG:
        return Eval_imag();
      case INDEX:
        return Eval_index();
      case INNER:
        return Eval_inner();
      case INTEGRAL:
        return Eval_integral();
      case INV:
        return Eval_inv();
      case INVG:
        return Eval_invg();
      case ISINTEGER:
        return Eval_isinteger();
      case ISPRIME:
        return Eval_isprime();
      case LAGUERRE:
        return Eval_laguerre();
      case LCM:
        return Eval_lcm();
      case LEADING:
        return Eval_leading();
      case LEGENDRE:
        return Eval_legendre();
      case LOG:
        return Eval_log();
      case MAG:
        return Eval_mag();
      case MOD:
        return Eval_mod();
      case MULTIPLY:
        return Eval_multiply();
      case NOT:
        return Eval_not();
      case NROOTS:
        return Eval_nroots();
      case NUMBER:
        return Eval_number();
      case NUMERATOR:
        return Eval_numerator();
      case OPERATOR:
        return Eval_operator();
      case OR:
        return Eval_or();
      case OUTER:
        return Eval_outer();
      case POLAR:
        return Eval_polar();
      case POWER:
        return Eval_power();
      case PRIME:
        return Eval_prime();
      case PRINT:
        return Eval_display();
      case PRODUCT:
        return Eval_product();
      case QUOTE:
        return Eval_quote();
      case QUOTIENT:
        return Eval_quotient();
      case RANK:
        return Eval_rank();
      case RATIONALIZE:
        return Eval_rationalize();
      case REAL:
        return Eval_real();
      case YYRECT:
        return Eval_rect();
      case ROOTS:
        return Eval_roots();
      case SETQ:
        return Eval_setq();
      case SGN:
        return Eval_sgn();
      case SIMPLIFY:
        return Eval_simplify();
      case SIN:
        return Eval_sin();
      case SINH:
        return Eval_sinh();
      case SHAPE:
        return Eval_shape();
      case SQRT:
        return Eval_sqrt();
      case STOP:
        return Eval_stop();
      case SUBST:
        return Eval_subst();
      case SUM:
        return Eval_sum();
      case TAN:
        return Eval_tan();
      case TANH:
        return Eval_tanh();
      case TAYLOR:
        return Eval_taylor();
      case TEST:
        return Eval_test();
      case TESTEQ:
        return Eval_testeq();
      case TESTGE:
        return Eval_testge();
      case TESTGT:
        return Eval_testgt();
      case TESTLE:
        return Eval_testle();
      case TESTLT:
        return Eval_testlt();
      case TRANSPOSE:
        return Eval_transpose();
      case UNIT:
        return Eval_unit();
      case ZERO:
        return Eval_zero();
      default:
        return Eval_user_function();
    }
  };

  Eval_binding = function() {
    return push(get_binding(cadr(p1)));
  };

  Eval_check = function() {
    push(cadr(p1));
    Eval_predicate();
    p1 = pop();
    if (iszero(p1)) {
      stop("check(arg): arg is zero");
    }
    return push(symbol(NIL));
  };

  Eval_det = function() {
    push(cadr(p1));
    Eval();
    return det();
  };

  Eval_dim = function() {
    var n;
    push(cadr(p1));
    Eval();
    p2 = pop();
    if (iscons(cddr(p1))) {
      push(caddr(p1));
      Eval();
      n = pop_integer();
    } else {
      n = 1;
    }
    if (!istensor(p2)) {
      return push_integer(1);
    } else if (n < 1 || n > p2.tensor.ndim) {
      return push(p1);
    } else {
      return push_integer(p2.tensor.dim[n - 1]);
    }
  };

  Eval_divisors = function() {
    push(cadr(p1));
    Eval();
    return divisors();
  };

  Eval_do = function() {
    var results;
    push(car(p1));
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      pop();
      push(car(p1));
      Eval();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  Eval_dsolve = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    push(cadddr(p1));
    Eval();
    return dsolve();
  };

  Eval_Eval = function() {
    push(cadr(p1));
    Eval();
    p1 = cddr(p1);
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      push(cadr(p1));
      Eval();
      subst();
      p1 = cddr(p1);
    }
    return Eval();
  };

  Eval_exp = function() {
    push(cadr(p1));
    Eval();
    return exponential();
  };

  Eval_factorial = function() {
    push(cadr(p1));
    Eval();
    return factorial();
  };

  Eval_factorpoly = function() {
    var results;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    factorpoly();
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      factorpoly();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  Eval_hermite = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    return hermite();
  };

  Eval_hilbert = function() {
    push(cadr(p1));
    Eval();
    return hilbert();
  };

  Eval_index = function() {
    var h;
    h = tos;
    p1 = cdr(p1);
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      p1 = cdr(p1);
    }
    return index_function(tos - h);
  };

  Eval_inv = function() {
    push(cadr(p1));
    Eval();
    return inv();
  };

  Eval_invg = function() {
    push(cadr(p1));
    Eval();
    return invg();
  };

  Eval_isinteger = function() {
    var n;
    push(cadr(p1));
    Eval();
    p1 = pop();
    if (isrational(p1)) {
      if (isinteger(p1)) {
        push(one);
      } else {
        push(zero);
      }
      return;
    }
    if (isdouble(p1)) {
      n = Math.floor(p1.d);
      if (n === p1.d) {
        push(one);
      } else {
        push(zero);
      }
      return;
    }
    push_symbol(ISINTEGER);
    push(p1);
    return list(2);
  };

  Eval_multiply = function() {
    var results;
    push(cadr(p1));
    Eval();
    p1 = cddr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      multiply();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  Eval_number = function() {
    push(cadr(p1));
    Eval();
    p1 = pop();
    if (p1.k === NUM || p1.k === DOUBLE) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };

  Eval_operator = function() {
    var h;
    h = tos;
    push_symbol(OPERATOR);
    p1 = cdr(p1);
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      p1 = cdr(p1);
    }
    return list(tos - h);
  };

  Eval_print = function() {
    p1 = cdr(p1);
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      if (equaln(get_binding(symbol(TTY)), 1)) {
        printline(pop());
      } else {
        display(pop());
      }
      p1 = cdr(p1);
    }
    return push(symbol(NIL));
  };

  Eval_quote = function() {
    return push(cadr(p1));
  };

  Eval_rank = function() {
    push(cadr(p1));
    Eval();
    p1 = pop();
    if (istensor(p1)) {
      return push_integer(p1.tensor.ndim);
    } else {
      return push(zero);
    }
  };

  setq_indexed = function() {
    var h;
    p4 = cadadr(p1);
    if (!issymbol(p4)) {
      stop("indexed assignment: error in symbol");
    }
    h = tos;
    push(caddr(p1));
    Eval();
    p2 = cdadr(p1);
    while (iscons(p2)) {
      push(car(p2));
      Eval();
      p2 = cdr(p2);
    }
    set_component(tos - h);
    p3 = pop();
    set_binding(p4, p3);
    return push(symbol(NIL));
  };

  Eval_setq = function() {
    if (caadr(p1) === symbol(INDEX)) {
      setq_indexed();
      return;
    }
    if (iscons(cadr(p1))) {
      define_user_function();
      return;
    }
    if (!issymbol(cadr(p1))) {
      stop("symbol assignment: error in symbol");
    }
    push(caddr(p1));
    Eval();
    p2 = pop();
    set_binding(cadr(p1), p2);
    return push(symbol(NIL));
  };

  Eval_sqrt = function() {
    push(cadr(p1));
    Eval();
    push_rational(1, 2);
    return power();
  };

  Eval_stop = function() {
    return stop("user stop");
  };

  Eval_subst = function() {
    push(cadddr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    push(cadr(p1));
    Eval();
    subst();
    return Eval();
  };

  Eval_unit = function() {
    var i, n, o, ref;
    i = 0;
    n = 0;
    push(cadr(p1));
    Eval();
    n = pop_integer();
    if (n < 2) {
      push(p1);
      return;
    }
    p1 = alloc_tensor(n * n);
    p1.tensor.ndim = 2;
    p1.tensor.dim[0] = n;
    p1.tensor.dim[1] = n;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p1.tensor.elem[n * i + i] = one;
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    return push(p1);
  };

  Eval_noexpand = function() {
    var x;
    x = expanding;
    expanding = 0;
    Eval();
    return expanding = x;
  };

  Eval_predicate = function() {
    save();
    p1 = pop();
    if (car(p1) === symbol(SETQ)) {
      Eval_testeq();
    } else {
      push(p1);
      Eval();
    }
    return restore();
  };

  Eval_expand = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      guess();
    } else {
      push(p2);
    }
    return expand();
  };

  expand = function() {
    save();
    p9 = pop();
    p5 = pop();
    if (istensor(p5)) {
      expand_tensor();
      restore();
      return;
    }
    if (car(p5) === symbol(ADD)) {
      push_integer(0);
      p1 = cdr(p5);
      while (iscons(p1)) {
        push(car(p1));
        push(p9);
        expand();
        add();
        p1 = cdr(p1);
      }
      restore();
      return;
    }
    push(p5);
    numerator();
    p3 = pop();
    push(p5);
    denominator();
    p2 = pop();
    remove_negative_exponents();
    push(p3);
    push(p2);
    push(p9);
    if (isone(p3) || isone(p2)) {
      if (!ispoly(p2, p9) || isone(p2)) {
        pop();
        pop();
        pop();
        push(p5);
        restore();
        return;
      }
    }
    divpoly();
    p7 = pop();
    push(p3);
    push(p2);
    push(p7);
    multiply();
    subtract();
    p3 = pop();
    if (iszero(p3)) {
      push(p7);
      restore();
      return;
    }
    push(p2);
    push(p9);
    factorpoly();
    p2 = pop();
    expand_get_C();
    expand_get_B();
    expand_get_A();
    if (istensor(p4)) {
      push(p4);
      inv();
      push(p3);
      inner();
      push(p2);
      inner();
    } else {
      push(p3);
      push(p4);
      divide();
      push(p2);
      multiply();
    }
    push(p7);
    add();
    return restore();
  };

  expand_tensor = function() {
    var i, o, ref;
    i = 0;
    push(p5);
    copy_tensor();
    p5 = pop();
    for (i = o = 0, ref = p5.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      push(p5.tensor.elem[i]);
      push(p9);
      expand();
      p5.tensor.elem[i] = pop();
    }
    return push(p5);
  };

  remove_negative_exponents = function() {
    var h, i, j, k, n, o, ref;
    h = 0;
    i = 0;
    j = 0;
    k = 0;
    n = 0;
    h = tos;
    factors(p2);
    factors(p3);
    n = tos - h;
    j = 0;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p1 = stack[h + i];
      if (car(p1) !== symbol(POWER)) {
        continue;
      }
      if (cadr(p1) !== p9) {
        continue;
      }
      push(caddr(p1));
      k = pop_integer();
      if (k === 0x80000000) {
        continue;
      }
      if (k < j) {
        j = k;
      }
    }
    tos = h;
    if (j === 0) {
      return;
    }
    push(p2);
    push(p9);
    push_integer(-j);
    power();
    multiply();
    p2 = pop();
    push(p3);
    push(p9);
    push_integer(-j);
    power();
    multiply();
    return p3 = pop();
  };

  expand_get_C = function() {
    var a, ac, h, i, j, n, o, ref, ref1;
    h = 0;
    i = 0;
    j = 0;
    n = 0;
    h = tos;
    if (car(p2) === symbol(MULTIPLY)) {
      p1 = cdr(p2);
      while (iscons(p1)) {
        p5 = car(p1);
        expand_get_CF();
        p1 = cdr(p1);
      }
    } else {
      p5 = p2;
      expand_get_CF();
    }
    n = tos - h;
    if (n === 1) {
      p4 = pop();
      return;
    }
    p4 = alloc_tensor(n * n);
    p4.tensor.ndim = 2;
    p4.tensor.dim[0] = n;
    p4.tensor.dim[1] = n;
    a = h;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      for (j = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
        push(stack[a + j]);
        push(p9);
        push_integer(i);
        power();
        divide();
        push(p9);
        filter();
        p4.tensor.elem[n * i + j] = pop();
      }
    }
    return tos -= n;
  };

  expand_get_CF = function() {
    var d, i, j, n, o, ref, results;
    d = 0;
    i = 0;
    j = 0;
    n = 0;
    if (!Find(p5, p9)) {
      return;
    }
    trivial_divide();
    if (car(p5) === symbol(POWER)) {
      push(caddr(p5));
      n = pop_integer();
      p6 = cadr(p5);
    } else {
      n = 1;
      p6 = p5;
    }
    push(p6);
    push(p9);
    degree();
    d = pop_integer();
    results = [];
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      results.push((function() {
        var ac, ref1, results1;
        results1 = [];
        for (j = ac = 0, ref1 = d; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
          push(p8);
          push(p6);
          push_integer(i);
          power();
          multiply();
          push(p9);
          push_integer(j);
          power();
          results1.push(multiply());
        }
        return results1;
      })());
    }
    return results;
  };

  trivial_divide = function() {
    var h;
    h = 0;
    if (car(p2) === symbol(MULTIPLY)) {
      h = tos;
      p0 = cdr(p2);
      while (iscons(p0)) {
        if (!equal(car(p0), p5)) {
          push(car(p0));
          Eval();
        }
        p0 = cdr(p0);
      }
      multiply_all(tos - h);
    } else {
      push_integer(1);
    }
    return p8 = pop();
  };

  expand_get_B = function() {
    var i, n, o, ref;
    i = 0;
    n = 0;
    if (!istensor(p4)) {
      return;
    }
    n = p4.tensor.dim[0];
    p8 = alloc_tensor(n);
    p8.tensor.ndim = 1;
    p8.tensor.dim[0] = n;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      push(p3);
      push(p9);
      push_integer(i);
      power();
      divide();
      push(p9);
      filter();
      p8.tensor.elem[i] = pop();
    }
    return p3 = p8;
  };

  expand_get_A = function() {
    var h, i, n, o, ref;
    h = 0;
    i = 0;
    n = 0;
    if (!istensor(p4)) {
      push(p2);
      reciprocate();
      p2 = pop();
      return;
    }
    h = tos;
    if (car(p2) === symbol(MULTIPLY)) {
      p8 = cdr(p2);
      while (iscons(p8)) {
        p5 = car(p8);
        expand_get_AF();
        p8 = cdr(p8);
      }
    } else {
      p5 = p2;
      expand_get_AF();
    }
    n = tos - h;
    p8 = alloc_tensor(n);
    p8.tensor.ndim = 1;
    p8.tensor.dim[0] = n;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p8.tensor.elem[i] = stack[h + i];
    }
    tos = h;
    return p2 = p8;
  };

  expand_get_AF = function() {
    var d, i, j, n, o, ref, results;
    d = 0;
    i = 0;
    j = 0;
    n = 1;
    if (!Find(p5, p9)) {
      return;
    }
    if (car(p5) === symbol(POWER)) {
      push(caddr(p5));
      n = pop_integer();
      p5 = cadr(p5);
    }
    push(p5);
    push(p9);
    degree();
    d = pop_integer();
    results = [];
    for (i = o = ref = n; ref <= 0 ? o < 0 : o > 0; i = ref <= 0 ? ++o : --o) {
      results.push((function() {
        var ac, ref1, results1;
        results1 = [];
        for (j = ac = 0, ref1 = d; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
          push(p5);
          push_integer(i);
          power();
          reciprocate();
          push(p9);
          push_integer(j);
          power();
          results1.push(multiply());
        }
        return results1;
      })());
    }
    return results;
  };

  Eval_expcos = function() {
    push(cadr(p1));
    Eval();
    return expcos();
  };

  expcos = function() {
    save();
    p1 = pop();
    push(imaginaryunit);
    push(p1);
    multiply();
    exponential();
    push_rational(1, 2);
    multiply();
    push(imaginaryunit);
    negate();
    push(p1);
    multiply();
    exponential();
    push_rational(1, 2);
    multiply();
    add();
    return restore();
  };

  Eval_expsin = function() {
    push(cadr(p1));
    Eval();
    return expsin();
  };

  expsin = function() {
    save();
    p1 = pop();
    push(imaginaryunit);
    push(p1);
    multiply();
    exponential();
    push(imaginaryunit);
    divide();
    push_rational(1, 2);
    multiply();
    push(imaginaryunit);
    negate();
    push(p1);
    multiply();
    exponential();
    push(imaginaryunit);
    divide();
    push_rational(1, 2);
    multiply();
    subtract();
    return restore();
  };

  Eval_factor = function() {
    var results;
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      guess();
    } else {
      push(p2);
    }
    factor();
    p1 = cdddr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      factor_again();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  factor_again = function() {
    var h, n;
    save();
    p2 = pop();
    p1 = pop();
    h = tos;
    if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        push(p2);
        factor_term();
        p1 = cdr(p1);
      }
    } else {
      push(p1);
      push(p2);
      factor_term();
    }
    n = tos - h;
    if (n > 1) {
      multiply_all_noexpand(n);
    }
    return restore();
  };

  factor_term = function() {
    save();
    factorpoly();
    p1 = pop();
    if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        p1 = cdr(p1);
      }
    } else {
      push(p1);
    }
    return restore();
  };

  factor = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (isinteger(p1)) {
      push(p1);
      factor_number();
    } else {
      push(p1);
      push(p2);
      factorpoly();
    }
    return restore();
  };

  factor_small_number = function() {
    var d, expo, i, n, o, ref;
    i = 0;
    save();
    n = pop_integer();
    if (n === 0x80000000) {
      stop("number too big to factor");
    }
    if (n < 0) {
      n = -n;
    }
    for (i = o = 0, ref = MAXPRIMETAB; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      d = primetab[i];
      if (d > n / d) {
        break;
      }
      expo = 0;
      while (n % d === 0) {
        n /= d;
        expo++;
      }
      if (expo) {
        push_integer(d);
        push_integer(expo);
      }
    }
    if (n > 1) {
      push_integer(n);
      push_integer(1);
    }
    return restore();
  };

  factorial = function() {
    var n;
    n = 0;
    save();
    p1 = pop();
    push(p1);
    n = pop_integer();
    if (n < 0 || n === 0x80000000) {
      push_symbol(FACTORIAL);
      push(p1);
      list(2);
      restore();
      return;
    }
    bignum_factorial(n);
    return restore();
  };

  simplifyfactorials = function() {
    var x;
    x = 0;
    save();
    x = expanding;
    expanding = 0;
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      push(zero);
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        simplifyfactorials();
        add();
        p1 = cdr(p1);
      }
      expanding = x;
      restore();
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      sfac_product();
      expanding = x;
      restore();
      return;
    }
    push(p1);
    expanding = x;
    return restore();
  };

  sfac_product = function() {
    var ac, ad, i, j, n, o, ref, ref1, ref2, ref3, s;
    i = 0;
    j = 0;
    n = 0;
    s = tos;
    p1 = cdr(p1);
    n = 0;
    while (iscons(p1)) {
      push(car(p1));
      p1 = cdr(p1);
      n++;
    }
    for (i = o = 0, ref = n - 1; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      if (stack[s + i] === symbol(NIL)) {
        continue;
      }
      for (j = ac = ref1 = i + 1, ref2 = n; ref1 <= ref2 ? ac < ref2 : ac > ref2; j = ref1 <= ref2 ? ++ac : --ac) {
        if (stack[s + j] === symbol(NIL)) {
          continue;
        }
        sfac_product_f(s, i, j);
      }
    }
    push(one);
    for (i = ad = 0, ref3 = n; 0 <= ref3 ? ad < ref3 : ad > ref3; i = 0 <= ref3 ? ++ad : --ad) {
      if (stack[s + i] === symbol(NIL)) {
        continue;
      }
      push(stack[s + i]);
      multiply();
    }
    p1 = pop();
    tos -= n;
    return push(p1);
  };

  sfac_product_f = function(s, a, b) {
    var i, n, o, ref;
    i = 0;
    n = 0;
    p1 = stack[s + a];
    p2 = stack[s + b];
    if (ispower(p1)) {
      p3 = caddr(p1);
      p1 = cadr(p1);
    } else {
      p3 = one;
    }
    if (ispower(p2)) {
      p4 = caddr(p2);
      p2 = cadr(p2);
    } else {
      p4 = one;
    }
    if (isfactorial(p1) && isfactorial(p2)) {
      push(p3);
      push(p4);
      add();
      yyexpand();
      n = pop_integer();
      if (n !== 0) {
        return;
      }
      push(cadr(p1));
      push(cadr(p2));
      subtract();
      yyexpand();
      n = pop_integer();
      if (n === 0 || n === 0x80000000) {
        return;
      }
      if (n < 0) {
        n = -n;
        p5 = p1;
        p1 = p2;
        p2 = p5;
        p5 = p3;
        p3 = p4;
        p4 = p5;
      }
      push(one);
      for (i = o = 1, ref = n; 1 <= ref ? o <= ref : o >= ref; i = 1 <= ref ? ++o : --o) {
        push(cadr(p2));
        push_integer(i);
        add();
        push(p3);
        power();
        multiply();
      }
      stack[s + a] = pop();
      return stack[s + b] = symbol(NIL);
    }
  };

  polycoeff = 0;

  factpoly_expo = 0;

  factorpoly = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (!Find(p1, p2)) {
      push(p1);
      restore();
      return;
    }
    if (!ispoly(p1, p2)) {
      push(p1);
      restore();
      return;
    }
    if (!issymbol(p2)) {
      push(p1);
      restore();
      return;
    }
    push(p1);
    push(p2);
    yyfactorpoly();
    return restore();
  };

  yyfactorpoly = function() {
    var h, i, o, ref;
    h = 0;
    i = 0;
    save();
    p2 = pop();
    p1 = pop();
    h = tos;
    if (isfloating(p1)) {
      stop("floating point numbers in polynomial");
    }
    polycoeff = tos;
    push(p1);
    push(p2);
    factpoly_expo = coeff() - 1;
    rationalize_coefficients(h);
    while (factpoly_expo > 0) {
      if (iszero(stack[polycoeff + 0])) {
        push_integer(1);
        p4 = pop();
        push_integer(0);
        p5 = pop();
      } else if (get_factor() === 0) {
        if (verbosing) {
          printf("no factor found\n");
        }
        break;
      }
      push(p4);
      push(p2);
      multiply();
      push(p5);
      add();
      p8 = pop();
      if (verbosing) {
        printf("success\nFACTOR=");
        print(p8);
        printf("\n");
      }

      /*
      		if (isnegativeterm(p4))
      			push(p8)
      			negate()
      			p8 = pop()
      			push(p7)
      			negate_noexpand()
      			p7 = pop()
       */
      push(p7);
      push(p8);
      multiply_noexpand();
      p7 = pop();
      yydivpoly();
      while (factpoly_expo && iszero(stack[polycoeff + factpoly_expo])) {
        factpoly_expo--;
      }
    }
    push(zero);
    for (i = o = 0, ref = factpoly_expo; 0 <= ref ? o <= ref : o >= ref; i = 0 <= ref ? ++o : --o) {
      push(stack[polycoeff + i]);
      push(p2);
      push_integer(i);
      power();
      multiply();
      add();
    }
    p1 = pop();
    if (verbosing) {
      printf("POLY=");
      print(p1);
      printf("\n");
    }
    if (factpoly_expo > 0 && isnegativeterm(stack[polycoeff + factpoly_expo])) {
      push(p1);
      negate();
      p1 = pop();
      push(p7);
      negate_noexpand();
      p7 = pop();
    }
    push(p7);
    push(p1);
    multiply_noexpand();
    p7 = pop();
    if (verbosing) {
      printf("RESULT=");
      print(p7);
      printf("\n");
    }
    stack[h] = p7;
    tos = h + 1;
    return restore();
  };

  rationalize_coefficients = function(h) {
    var ac, i, o, ref, ref1, ref2, ref3;
    i = 0;
    p7 = one;
    for (i = o = ref = h, ref1 = tos; ref <= ref1 ? o < ref1 : o > ref1; i = ref <= ref1 ? ++o : --o) {
      push(stack[i]);
      denominator();
      push(p7);
      lcm();
      p7 = pop();
    }
    for (i = ac = ref2 = h, ref3 = tos; ref2 <= ref3 ? ac < ref3 : ac > ref3; i = ref2 <= ref3 ? ++ac : --ac) {
      push(p7);
      push(stack[i]);
      multiply();
      stack[i] = pop();
    }
    push(p7);
    reciprocate();
    p7 = pop();
    if (DEBUG) {
      return console.log("rationalize_coefficients result");
    }
  };

  get_factor = function() {
    var a0, ac, ad, ae, af, an, h, i, j, na0, nan, o, ref, ref1, ref2, ref3, ref4, rootsTries_i, rootsTries_j;
    i = 0;
    j = 0;
    h = 0;
    a0 = 0;
    an = 0;
    na0 = 0;
    nan = 0;
    if (verbosing) {
      push(zero);
      for (i = o = 0, ref = factpoly_expo; 0 <= ref ? o <= ref : o >= ref; i = 0 <= ref ? ++o : --o) {
        push(stack[polycoeff + i]);
        push(p2);
        push_integer(i);
        power();
        multiply();
        add();
      }
      p1 = pop();
      printf("POLY=");
      print(p1);
      printf("\n");
    }
    h = tos;
    an = tos;
    push(stack[polycoeff + factpoly_expo]);
    divisors_onstack();
    nan = tos - an;
    a0 = tos;
    push(stack[polycoeff + 0]);
    divisors_onstack();
    na0 = tos - a0;
    if (verbosing) {
      printf("divisors of base term");
      for (i = ac = 0, ref1 = na0; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
        printf(", ");
        print(stack[a0 + i]);
      }
      printf("\n");
      printf("divisors of leading term");
      for (i = ad = 0, ref2 = nan; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
        printf(", ");
        print(stack[an + i]);
      }
      printf("\n");
    }
    for (rootsTries_i = ae = 0, ref3 = nan; 0 <= ref3 ? ae < ref3 : ae > ref3; rootsTries_i = 0 <= ref3 ? ++ae : --ae) {
      for (rootsTries_j = af = 0, ref4 = na0; 0 <= ref4 ? af < ref4 : af > ref4; rootsTries_j = 0 <= ref4 ? ++af : --af) {
        p4 = stack[an + rootsTries_i];
        p5 = stack[a0 + rootsTries_j];
        push(p5);
        push(p4);
        divide();
        negate();
        p3 = pop();
        Evalpoly();
        if (verbosing) {
          printf("try A=");
          print(p4);
          printf(", B=");
          print(p5);
          printf(", root ");
          print(p2);
          printf("=-B/A=");
          print(p3);
          printf(", POLY(");
          print(p3);
          printf(")=");
          print(p6);
          printf("\n");
        }
        if (iszero(p6)) {
          tos = h;
          if (DEBUG) {
            console.log("get_factor returning 1");
          }
          return 1;
        }
        push(p5);
        negate();
        p5 = pop();
        push(p3);
        negate();
        p3 = pop();
        Evalpoly();
        if (verbosing) {
          printf("try A=");
          print(p4);
          printf(", B=");
          print(p5);
          printf(", root ");
          print(p2);
          printf("=-B/A=");
          print(p3);
          printf(", POLY(");
          print(p3);
          printf(")=");
          print(p6);
          printf("\n");
        }
        if (iszero(p6)) {
          tos = h;
          if (DEBUG) {
            console.log("get_factor returning 1");
          }
          return 1;
        }
      }
    }
    tos = h;
    if (DEBUG) {
      console.log("get_factor returning 0");
    }
    return 0;
  };

  yydivpoly = function() {
    var i, o, ref;
    i = 0;
    p6 = zero;
    for (i = o = ref = factpoly_expo; ref <= 0 ? o < 0 : o > 0; i = ref <= 0 ? ++o : --o) {
      push(stack[polycoeff + i]);
      stack[polycoeff + i] = p6;
      push(p4);
      divide();
      p6 = pop();
      push(stack[polycoeff + i - 1]);
      push(p6);
      push(p5);
      multiply();
      subtract();
      stack[polycoeff + i - 1] = pop();
    }
    stack[polycoeff + 0] = p6;
    if (DEBUG) {
      return console.log("yydivpoly Q:");
    }
  };

  Evalpoly = function() {
    var i, o, ref;
    i = 0;
    push(zero);
    for (i = o = ref = factpoly_expo; ref <= 0 ? o <= 0 : o >= 0; i = ref <= 0 ? ++o : --o) {
      push(p3);
      multiply();
      push(stack[polycoeff + i]);
      if (DEBUG) {
        console.log("Evalpoly top of stack:");
        print1(stack[tos - i]);
      }
      add();
    }
    return p6 = pop();
  };

  factors = function(p) {
    var h;
    h = tos;
    if (car(p) === symbol(ADD)) {
      p = cdr(p);
      while (iscons(p)) {
        push_term_factors(car(p));
        p = cdr(p);
      }
    } else {
      push_term_factors(p);
    }
    return tos - h;
  };

  push_term_factors = function(p) {
    var results;
    if (car(p) === symbol(MULTIPLY)) {
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        push(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else {
      return push(p);
    }
  };


  /*
  Remove terms that involve a given symbol or expression. For example...
  
  	filter(x^2 + x + 1, x)		=>	1
  
  	filter(x^2 + x + 1, x^2)	=>	x + 1
   */

  Eval_filter = function() {
    var results;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      filter();
      results.push(p1 = cdr(p1));
    }
    return results;
  };


  /*
   For example...
  
  	push(F)
  	push(X)
  	filter()
  	F = pop()
   */

  filter = function() {
    save();
    p2 = pop();
    p1 = pop();
    filter_main();
    return restore();
  };

  filter_main = function() {
    if (car(p1) === symbol(ADD)) {
      return filter_sum();
    } else if (istensor(p1)) {
      return filter_tensor();
    } else if (Find(p1, p2)) {
      return push_integer(0);
    } else {
      return push(p1);
    }
  };

  filter_sum = function() {
    var results;
    push_integer(0);
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      push(p2);
      filter();
      add();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  filter_tensor = function() {
    var ac, i, n, o, ref, ref1;
    i = 0;
    n = 0;
    n = p1.tensor.nelem;
    p3 = alloc_tensor(n);
    p3.tensor.ndim = p1.tensor.ndim;
    for (i = o = 0, ref = p1.tensor.ndim; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      push(p1.tensor.elem[i]);
      push(p2);
      filter();
      p3.tensor.elem[i] = pop();
    }
    return push(p3);
  };

  Eval_float = function() {
    push(cadr(p1));
    Eval();
    yyfloat();
    return Eval();
  };

  yyfloat = function() {
    var h, i, o, ref;
    i = 0;
    h = 0;
    save();
    p1 = pop();
    if (iscons(p1)) {
      h = tos;
      while (iscons(p1)) {
        push(car(p1));
        yyfloat();
        p1 = cdr(p1);
      }
      list(tos - h);
    } else if (p1.k === TENSOR) {
      push(p1);
      copy_tensor();
      p1 = pop();
      for (i = o = 0, ref = p1.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
        push(p1.tensor.elem[i]);
        yyfloat();
        p1.tensor.elem[i] = pop();
      }
      push(p1);
    } else if (p1.k === NUM) {
      push(p1);
      bignum_float();
    } else if (p1 === symbol(PI)) {
      push_double(Math.PI);
    } else if (p1 === symbol(E)) {
      push_double(Math.E);
    } else {
      push(p1);
    }
    return restore();
  };

  Eval_floor = function() {
    push(cadr(p1));
    Eval();
    return yfloor();
  };

  yfloor = function() {
    save();
    yyfloor();
    return restore();
  };

  yyfloor = function() {
    var d;
    d = 0.0;
    p1 = pop();
    if (!isnum(p1)) {
      push_symbol(FLOOR);
      push(p1);
      list(2);
      return;
    }
    if (isdouble(p1)) {
      d = Math.floor(p1.d);
      push_double(d);
      return;
    }
    if (isinteger(p1)) {
      push(p1);
      return;
    }
    p3 = new U();
    p3.k = NUM;
    p3.q.a = mdiv(p1.q.a, p1.q.b);
    p3.q.b = mint(1);
    push(p3);
    if (isnegativenumber(p1)) {
      push_integer(-1);
      return add();
    }
  };

  Eval_for = function() {
    var i, j, k, o, ref, ref1;
    i = 0;
    j = 0;
    k = 0;
    p6 = cadr(p1);
    if (!issymbol(p6)) {
      stop("for: 1st arg?");
    }
    push(caddr(p1));
    Eval();
    j = pop_integer();
    if (j === 0x80000000) {
      stop("for: 2nd arg?");
    }
    push(cadddr(p1));
    Eval();
    k = pop_integer();
    if (k === 0x80000000) {
      stop("for: 3rd arg?");
    }
    p1 = cddddr(p1);
    p4 = get_binding(p6);
    p3 = get_arglist(p6);
    for (i = o = ref = j, ref1 = k; ref <= ref1 ? o <= ref1 : o >= ref1; i = ref <= ref1 ? ++o : --o) {
      push_integer(i);
      p5 = pop();
      set_binding(p6, p5);
      p2 = p1;
      while (iscons(p2)) {
        push(car(p2));
        Eval();
        pop();
        p2 = cdr(p2);
      }
    }
    set_binding_and_arglist(p6, p4, p3);
    return push_symbol(NIL);
  };

  Eval_gamma = function() {
    push(cadr(p1));
    Eval();
    return gamma();
  };

  gamma = function() {
    save();
    gammaf();
    return restore();
  };

  gammaf = function() {
    p1 = pop();
    if (isrational(p1) && MEQUAL(p1.q.a, 1) && MEQUAL(p1.q.b, 2)) {
      push_symbol(PI);
      push_rational(1, 2);
      power();
      return;
    }
    if (isrational(p1) && MEQUAL(p1.q.a, 3) && MEQUAL(p1.q.b, 2)) {
      push_symbol(PI);
      push_rational(1, 2);
      power();
      push_rational(1, 2);
      multiply();
      return;
    }
    if (isnegativeterm(p1)) {
      push_symbol(PI);
      push_integer(-1);
      multiply();
      push_symbol(PI);
      push(p1);
      multiply();
      sine();
      push(p1);
      multiply();
      push(p1);
      negate();
      gamma();
      multiply();
      divide();
      return;
    }
    if (car(p1) === symbol(ADD)) {
      gamma_of_sum();
      return;
    }
    push_symbol(GAMMA);
    push(p1);
    list(2);
  };

  gamma_of_sum = function() {
    p3 = cdr(p1);
    if (isrational(car(p3)) && MEQUAL(car(p3).q.a, 1) && MEQUAL(car(p3).q.b, 1)) {
      push(cadr(p3));
      push(cadr(p3));
      gamma();
      return multiply();
    } else {
      if (isrational(car(p3)) && MEQUAL(car(p3).q.a, -1) && MEQUAL(car(p3).q.b, 1)) {
        push(cadr(p3));
        gamma();
        push(cadr(p3));
        push_integer(-1);
        add();
        return divide();
      } else {
        push_symbol(GAMMA);
        push(p1);
        list(2);
      }
    }
  };

  Eval_gcd = function() {
    var results;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      gcd();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  gcd = function() {
    var x;
    x = expanding;
    save();
    gcd_main();
    restore();
    return expanding = x;
  };

  gcd_main = function() {
    expanding = 1;
    p2 = pop();
    p1 = pop();
    if (equal(p1, p2)) {
      push(p1);
      return;
    }
    if (isrational(p1) && isrational(p2)) {
      push(p1);
      push(p2);
      gcd_numbers();
      return;
    }
    if (car(p1) === symbol(ADD) && car(p2) === symbol(ADD)) {
      gcd_expr_expr();
      return;
    }
    if (car(p1) === symbol(ADD)) {
      gcd_expr(p1);
      p1 = pop();
    }
    if (car(p2) === symbol(ADD)) {
      gcd_expr(p2);
      p2 = pop();
    }
    if (car(p1) === symbol(MULTIPLY) && car(p2) === symbol(MULTIPLY)) {
      gcd_term_term();
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      gcd_term_factor();
      return;
    }
    if (car(p2) === symbol(MULTIPLY)) {
      gcd_factor_term();
      return;
    }
    if (car(p1) === symbol(POWER)) {
      p3 = caddr(p1);
      p1 = cadr(p1);
    } else {
      p3 = one;
    }
    if (car(p2) === symbol(POWER)) {
      p4 = caddr(p2);
      p2 = cadr(p2);
    } else {
      p4 = one;
    }
    if (!equal(p1, p2)) {
      push(one);
      return;
    }
    if (isnum(p3) && isnum(p4)) {
      push(p1);
      if (lessp(p3, p4)) {
        push(p3);
      } else {
        push(p4);
      }
      power();
      return;
    }
    push(p3);
    push(p4);
    divide();
    p5 = pop();
    if (isnum(p5)) {
      push(p1);
      if (car(p3) === symbol(MULTIPLY) && isnum(cadr(p3))) {
        p5 = cadr(p3);
      } else {
        p5 = one;
      }
      if (car(p4) === symbol(MULTIPLY) && isnum(cadr(p4))) {
        p6 = cadr(p4);
      } else {
        p6 = one;
      }
      if (lessp(p5, p6)) {
        push(p3);
      } else {
        push(p4);
      }
      power();
      return;
    }
    push(p3);
    push(p4);
    subtract();
    p5 = pop();
    if (!isnum(p5)) {
      push(one);
      return;
    }
    push(p1);
    if (isnegativenumber(p5)) {
      push(p3);
    } else {
      push(p4);
    }
    return power();
  };

  gcd_expr_expr = function() {
    if (length(p1) !== length(p2)) {
      push(one);
      return;
    }
    p3 = cdr(p1);
    push(car(p3));
    p3 = cdr(p3);
    while (iscons(p3)) {
      push(car(p3));
      gcd();
      p3 = cdr(p3);
    }
    p3 = pop();
    p4 = cdr(p2);
    push(car(p4));
    p4 = cdr(p4);
    while (iscons(p4)) {
      push(car(p4));
      gcd();
      p4 = cdr(p4);
    }
    p4 = pop();
    push(p1);
    push(p3);
    divide();
    p5 = pop();
    push(p2);
    push(p4);
    divide();
    p6 = pop();
    if (equal(p5, p6)) {
      push(p5);
      push(p3);
      push(p4);
      gcd();
      return multiply();
    } else {
      return push(one);
    }
  };

  gcd_expr = function(p) {
    var results;
    p = cdr(p);
    push(car(p));
    p = cdr(p);
    results = [];
    while (iscons(p)) {
      push(car(p));
      gcd();
      results.push(p = cdr(p));
    }
    return results;
  };

  gcd_term_term = function() {
    var results;
    push(one);
    p3 = cdr(p1);
    results = [];
    while (iscons(p3)) {
      p4 = cdr(p2);
      while (iscons(p4)) {
        push(car(p3));
        push(car(p4));
        gcd();
        multiply();
        p4 = cdr(p4);
      }
      results.push(p3 = cdr(p3));
    }
    return results;
  };

  gcd_term_factor = function() {
    var results;
    push(one);
    p3 = cdr(p1);
    results = [];
    while (iscons(p3)) {
      push(car(p3));
      push(p2);
      gcd();
      multiply();
      results.push(p3 = cdr(p3));
    }
    return results;
  };

  gcd_factor_term = function() {
    var results;
    push(one);
    p4 = cdr(p2);
    results = [];
    while (iscons(p4)) {
      push(p1);
      push(car(p4));
      gcd();
      multiply();
      results.push(p4 = cdr(p4));
    }
    return results;
  };

  guess = function() {
    var p;
    p = pop();
    push(p);
    if (Find(p, symbol(SYMBOL_X))) {
      return push_symbol(SYMBOL_X);
    } else if (Find(p, symbol(SYMBOL_Y))) {
      return push_symbol(SYMBOL_Y);
    } else if (Find(p, symbol(SYMBOL_Z))) {
      return push_symbol(SYMBOL_Z);
    } else if (Find(p, symbol(SYMBOL_T))) {
      return push_symbol(SYMBOL_T);
    } else if (Find(p, symbol(SYMBOL_S))) {
      return push_symbol(SYMBOL_S);
    } else {
      return push_symbol(SYMBOL_X);
    }
  };

  hermite = function() {
    save();
    yyhermite();
    return restore();
  };

  yyhermite = function() {
    var n;
    n = 0;
    p2 = pop();
    p1 = pop();
    push(p2);
    n = pop_integer();
    if (n < 0 || n === 0x80000000) {
      push_symbol(HERMITE);
      push(p1);
      push(p2);
      list(3);
      return;
    }
    if (issymbol(p1)) {
      return yyhermite2(n);
    } else {
      p3 = p1;
      p1 = symbol(SECRETX);
      yyhermite2(n);
      p1 = p3;
      push(symbol(SECRETX));
      push(p1);
      subst();
      return Eval();
    }
  };

  yyhermite2 = function(n) {
    var i, o, ref, results;
    i = 0;
    push_integer(1);
    push_integer(0);
    p4 = pop();
    results = [];
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p5 = p4;
      p4 = pop();
      push(p1);
      push(p4);
      multiply();
      push_integer(i);
      push(p5);
      multiply();
      subtract();
      push_integer(2);
      results.push(multiply());
    }
    return results;
  };

  hilbert = function() {
    var ac, i, j, n, o, ref, ref1;
    i = 0;
    j = 0;
    n = 0;
    save();
    p2 = pop();
    push(p2);
    n = pop_integer();
    if (n < 2) {
      push_symbol(HILBERT);
      push(p2);
      list(2);
      restore();
      return;
    }
    push_zero_matrix(n, n);
    p1 = pop();
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      for (j = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
        push_integer(i + j + 1);
        inverse();
        p1.tensor.elem[i * n + j] = pop();
      }
    }
    push(p1);
    return restore();
  };


  /*
   Returns the coefficient of the imaginary part of complex z
  
  	z		imag(z)
  	-		-------
  
  	a + i b		b
  
  	exp(i a)	sin(a)
   */

  Eval_imag = function() {
    push(cadr(p1));
    Eval();
    return imag();
  };

  imag = function() {
    save();
    rect();
    p1 = pop();
    push(p1);
    push(p1);
    conjugate();
    subtract();
    push_integer(2);
    divide();
    push(imaginaryunit);
    divide();
    return restore();
  };

  index_function = function(n) {
    var ac, ad, ae, af, i, k, m, ndim, nelem, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, ref7, s, t;
    i = 0;
    k = 0;
    m = 0;
    ndim = 0;
    nelem = 0;
    t = 0;
    save();
    s = tos - n;
    p1 = stack[s];
    if (!istensor(p1)) {
      tos -= n;
      push(p1);
      restore();
      return;
    }
    ndim = p1.tensor.ndim;
    m = n - 1;
    if (m > ndim) {
      stop("too many indices for tensor");
    }
    k = 0;
    for (i = o = 0, ref = m; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      push(stack[s + i + 1]);
      t = pop_integer();
      if (t < 1 || t > p1.tensor.dim[i]) {
        stop("index out of range");
      }
      k = k * p1.tensor.dim[i] + t - 1;
    }
    if (ndim === m) {
      tos -= n;
      push(p1.tensor.elem[k]);
      restore();
      return;
    }
    for (i = ac = ref1 = m, ref2 = ndim; ref1 <= ref2 ? ac < ref2 : ac > ref2; i = ref1 <= ref2 ? ++ac : --ac) {
      k = k * p1.tensor.dim[i] + 0;
    }
    nelem = 1;
    for (i = ad = ref3 = m, ref4 = ndim; ref3 <= ref4 ? ad < ref4 : ad > ref4; i = ref3 <= ref4 ? ++ad : --ad) {
      nelem *= p1.tensor.dim[i];
    }
    p2 = alloc_tensor(nelem);
    p2.tensor.ndim = ndim - m;
    for (i = ae = ref5 = m, ref6 = ndim; ref5 <= ref6 ? ae < ref6 : ae > ref6; i = ref5 <= ref6 ? ++ae : --ae) {
      p2.tensor.dim[i - m] = p1.tensor.dim[i];
    }
    for (i = af = 0, ref7 = nelem; 0 <= ref7 ? af < ref7 : af > ref7; i = 0 <= ref7 ? ++af : --af) {
      p2.tensor.elem[i] = p1.tensor.elem[k + i];
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    tos -= n;
    push(p2);
    return restore();
  };

  set_component = function(n) {
    var ac, ad, ae, af, ag, i, k, m, ndim, o, ref, ref1, ref2, ref3, ref4, ref5, ref6, s, t;
    i = 0;
    k = 0;
    m = 0;
    ndim = 0;
    t = 0;
    save();
    if (n < 3) {
      stop("error in indexed assign");
    }
    s = tos - n;
    p2 = stack[s];
    p1 = stack[s + 1];
    if (!istensor(p1)) {
      stop("error in indexed assign");
    }
    ndim = p1.tensor.ndim;
    m = n - 2;
    if (m > ndim) {
      stop("error in indexed assign");
    }
    k = 0;
    for (i = o = 0, ref = m; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      push(stack[s + i + 2]);
      t = pop_integer();
      if (t < 1 || t > p1.tensor.dim[i]) {
        stop("error in indexed assign\n");
      }
      k = k * p1.tensor.dim[i] + t - 1;
    }
    for (i = ac = ref1 = m, ref2 = ndim; ref1 <= ref2 ? ac < ref2 : ac > ref2; i = ref1 <= ref2 ? ++ac : --ac) {
      k = k * p1.tensor.dim[i] + 0;
    }
    p3 = alloc_tensor(p1.tensor.nelem);
    p3.tensor.ndim = p1.tensor.ndim;
    for (i = ad = 0, ref3 = p1.tensor.ndim; 0 <= ref3 ? ad < ref3 : ad > ref3; i = 0 <= ref3 ? ++ad : --ad) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    for (i = ae = 0, ref4 = p1.tensor.nelem; 0 <= ref4 ? ae < ref4 : ae > ref4; i = 0 <= ref4 ? ++ae : --ae) {
      p3.tensor.elem[i] = p1.tensor.elem[i];
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    if (p3.tensor.nelem !== p3.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    p1 = p3;
    if (ndim === m) {
      if (istensor(p2)) {
        stop("error in indexed assign");
      }
      p1.tensor.elem[k] = p2;
      if (p1.tensor.nelem !== p1.tensor.elem.length) {
        console.log("something wrong in tensor dimensions");
        debugger;
      }
      tos -= n;
      push(p1);
      restore();
      return;
    }
    if (!istensor(p2)) {
      stop("error in indexed assign");
    }
    if (ndim - m !== p2.tensor.ndim) {
      stop("error in indexed assign");
    }
    for (i = af = 0, ref5 = p2.tensor.ndim; 0 <= ref5 ? af < ref5 : af > ref5; i = 0 <= ref5 ? ++af : --af) {
      if (p1.tensor.dim[m + i] !== p2.tensor.dim[i]) {
        stop("error in indexed assign");
      }
    }
    for (i = ag = 0, ref6 = p2.tensor.nelem; 0 <= ref6 ? ag < ref6 : ag > ref6; i = 0 <= ref6 ? ++ag : --ag) {
      p1.tensor.elem[k + i] = p2.tensor.elem[i];
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    tos -= n;
    push(p1);
    return restore();
  };

  Eval_inner = function() {
    var results;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      inner();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  inner = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (istensor(p1) && istensor(p2)) {
      inner_f();
    } else {
      push(p1);
      push(p2);
      if (istensor(p1)) {
        tensor_times_scalar();
      } else if (istensor(p2)) {
        scalar_times_tensor();
      } else {
        multiply();
      }
    }
    return restore();
  };

  inner_f = function() {
    var a, ac, ad, ae, af, ag, ah, ak, b, bk, c, i, j, k, n, ndim, o, ref, ref1, ref2, ref3, ref4, ref5, ref6;
    i = 0;
    n = p1.tensor.dim[p1.tensor.ndim - 1];
    if (n !== p2.tensor.dim[0]) {
      debugger;
      stop("inner: tensor dimension check");
    }
    ndim = p1.tensor.ndim + p2.tensor.ndim - 2;
    if (ndim > MAXDIM) {
      stop("inner: rank of result exceeds maximum");
    }
    a = p1.tensor.elem;
    b = p2.tensor.elem;
    ak = 1;
    for (i = o = 0, ref = p1.tensor.ndim - 1; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      ak *= p1.tensor.dim[i];
    }
    bk = 1;
    for (i = ac = 1, ref1 = p2.tensor.ndim; 1 <= ref1 ? ac < ref1 : ac > ref1; i = 1 <= ref1 ? ++ac : --ac) {
      bk *= p2.tensor.dim[i];
    }
    p3 = alloc_tensor(ak * bk);
    c = p3.tensor.elem;
    for (i = ad = 0, ref2 = ak; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      for (j = ae = 0, ref3 = n; 0 <= ref3 ? ae < ref3 : ae > ref3; j = 0 <= ref3 ? ++ae : --ae) {
        if (iszero(a[i * n + j])) {
          continue;
        }
        for (k = af = 0, ref4 = bk; 0 <= ref4 ? af < ref4 : af > ref4; k = 0 <= ref4 ? ++af : --af) {
          push(a[i * n + j]);
          push(b[j * bk + k]);
          multiply();
          push(c[i * bk + k]);
          add();
          c[i * bk + k] = pop();
        }
      }
    }
    if (ndim === 0) {
      return push(p3.tensor.elem[0]);
    } else {
      p3.tensor.ndim = ndim;
      j = 0;
      for (i = ag = 0, ref5 = p1.tensor.ndim - 1; 0 <= ref5 ? ag < ref5 : ag > ref5; i = 0 <= ref5 ? ++ag : --ag) {
        p3.tensor.dim[i] = p1.tensor.dim[i];
      }
      j = p1.tensor.ndim - 1;
      for (i = ah = 0, ref6 = p2.tensor.ndim - 1; 0 <= ref6 ? ah < ref6 : ah > ref6; i = 0 <= ref6 ? ++ah : --ah) {
        p3.tensor.dim[j + i] = p2.tensor.dim[i + 1];
      }
      return push(p3);
    }
  };


  /*
   Table of integrals
  
  The symbol f is just a dummy symbol for creating a list f(A,B,C,C,...) where
  
  	A	is the template expression
  
  	B	is the result expression
  
  	C	is an optional list of conditional expressions
   */

  itab = ["f(a,a*x)", "f(1/x,log(x))", "f(x^a,x^(a+1)/(a+1))", "f(exp(a*x),1/a*exp(a*x))", "f(exp(a*x+b),1/a*exp(a*x+b))", "f(x*exp(a*x^2),exp(a*x^2)/(2*a))", "f(x*exp(a*x^2+b),exp(a*x^2+b)/(2*a))", "f(log(a*x),x*log(a*x)-x)", "f(a^x,a^x/log(a),or(not(number(a)),a>0))", "f(1/(a+x^2),1/sqrt(a)*arctan(x/sqrt(a)),or(not(number(a)),a>0))", "f(1/(a-x^2),1/sqrt(a)*arctanh(x/sqrt(a)))", "f(1/sqrt(a-x^2),arcsin(x/(sqrt(a))))", "f(1/sqrt(a+x^2),log(x+sqrt(a+x^2)))", "f(1/(a+b*x),1/b*log(a+b*x))", "f(1/(a+b*x)^2,-1/(b*(a+b*x)))", "f(1/(a+b*x)^3,-1/(2*b)*1/(a+b*x)^2)", "f(x/(a+b*x),x/b-a*log(a+b*x)/b/b)", "f(x/(a+b*x)^2,1/b^2*(log(a+b*x)+a/(a+b*x)))", "f(x^2/(a+b*x),1/b^2*(1/2*(a+b*x)^2-2*a*(a+b*x)+a^2*log(a+b*x)))", "f(x^2/(a+b*x)^2,1/b^3*(a+b*x-2*a*log(a+b*x)-a^2/(a+b*x)))", "f(x^2/(a+b*x)^3,1/b^3*(log(a+b*x)+2*a/(a+b*x)-1/2*a^2/(a+b*x)^2))", "f(1/x*1/(a+b*x),-1/a*log((a+b*x)/x))", "f(1/x*1/(a+b*x)^2,1/a*1/(a+b*x)-1/a^2*log((a+b*x)/x))", "f(1/x*1/(a+b*x)^3,1/a^3*(1/2*((2*a+b*x)/(a+b*x))^2+log(x/(a+b*x))))", "f(1/x^2*1/(a+b*x),-1/(a*x)+b/a^2*log((a+b*x)/x))", "f(1/x^3*1/(a+b*x),(2*b*x-a)/(2*a^2*x^2)+b^2/a^3*log(x/(a+b*x)))", "f(1/x^2*1/(a+b*x)^2,-(a+2*b*x)/(a^2*x*(a+b*x))+2*b/a^3*log((a+b*x)/x))", "f(1/(a+b*x^2),1/sqrt(a*b)*arctan(x*sqrt(a*b)/a),or(not(number(a*b)),a*b>0))", "f(1/(a+b*x^2),1/(2*sqrt(-a*b))*log((a+x*sqrt(-a*b))/(a-x*sqrt(-a*b))),or(not(number(a*b)),a*b<0))", "f(x/(a+b*x^2),1/2*1/b*log(a+b*x^2))", "f(x^2/(a+b*x^2),x/b-a/b*integral(1/(a+b*x^2),x))", "f(1/(a+b*x^2)^2,x/(2*a*(a+b*x^2))+1/2*1/a*integral(1/(a+b*x^2),x))", "f(1/x*1/(a+b*x^2),1/2*1/a*log(x^2/(a+b*x^2)))", "f(1/x^2*1/(a+b*x^2),-1/(a*x)-b/a*integral(1/(a+b*x^2),x))", "f(1/(a+b*x^3),1/3*1/a*(a/b)^(1/3)*(1/2*log(((a/b)^(1/3)+x)^3/(a+b*x^3))+sqrt(3)*arctan((2*x-(a/b)^(1/3))*(a/b)^(-1/3)/sqrt(3))))", "f(x^2/(a+b*x^3),1/3*1/b*log(a+b*x^3))", "f(1/(a+b*x^4),1/2*1/a*(a/b/4)^(1/4)*(1/2*log((x^2+2*(a/b/4)^(1/4)*x+2*(a/b/4)^(1/2))/(x^2-2*(a/b/4)^(1/4)*x+2*(a/b/4)^(1/2)))+arctan(2*(a/b/4)^(1/4)*x/(2*(a/b/4)^(1/2)-x^2))),or(not(number(a*b)),a*b>0))", "f(1/(a+b*x^4),1/2*(-a/b)^(1/4)/a*(1/2*log((x+(-a/b)^(1/4))/(x-(-a/b)^(1/4)))+arctan(x*(-a/b)^(-1/4))),or(not(number(a*b)),a*b<0))", "f(x/(a+b*x^4),1/2*sqrt(b/a)/b*arctan(x^2*sqrt(b/a)),or(not(number(a*b)),a*b>0))", "f(x/(a+b*x^4),1/4*sqrt(-b/a)/b*log((x^2-sqrt(-a/b))/(x^2+sqrt(-a/b))),or(not(number(a*b)),a*b<0))", "f(x^2/(a+b*x^4),1/4*1/b*(a/b/4)^(-1/4)*(1/2*log((x^2-2*(a/b/4)^(1/4)*x+2*sqrt(a/b/4))/(x^2+2*(a/b/4)^(1/4)*x+2*sqrt(a/b/4)))+arctan(2*(a/b/4)^(1/4)*x/(2*sqrt(a/b/4)-x^2))),or(not(number(a*b)),a*b>0))", "f(x^2/(a+b*x^4),1/4*1/b*(-a/b)^(-1/4)*(log((x-(-a/b)^(1/4))/(x+(-a/b)^(1/4)))+2*arctan(x*(-a/b)^(-1/4))),or(not(number(a*b)),a*b<0))", "f(x^3/(a+b*x^4),1/4*1/b*log(a+b*x^4))", "f(sqrt(a+b*x),2/3*1/b*sqrt((a+b*x)^3))", "f(x*sqrt(a+b*x),-2*(2*a-3*b*x)*sqrt((a+b*x)^3)/15/b^2)", "f(x^2*sqrt(a+b*x),2*(8*a^2-12*a*b*x+15*b^2*x^2)*sqrt((a+b*x)^3)/105/b^3)", "f(sqrt(a+b*x)/x,2*sqrt(a+b*x)+a*integral(1/x*1/sqrt(a+b*x),x))", "f(sqrt(a+b*x)/x^2,-sqrt(a+b*x)/x+b/2*integral(1/x*1/sqrt(a+b*x),x))", "f(1/sqrt(a+b*x),2*sqrt(a+b*x)/b)", "f(x/sqrt(a+b*x),-2/3*(2*a-b*x)*sqrt(a+b*x)/b^2)", "f(x^2/sqrt(a+b*x),2/15*(8*a^2-4*a*b*x+3*b^2*x^2)*sqrt(a+b*x)/b^3)", "f(1/x*1/sqrt(a+b*x),1/sqrt(a)*log((sqrt(a+b*x)-sqrt(a))/(sqrt(a+b*x)+sqrt(a))),or(not(number(a)),a>0))", "f(1/x*1/sqrt(a+b*x),2/sqrt(-a)*arctan(sqrt(-(a+b*x)/a)),or(not(number(a)),a<0))", "f(1/x^2*1/sqrt(a+b*x),-sqrt(a+b*x)/a/x-1/2*b/a*integral(1/x*1/sqrt(a+b*x),x))", "f(sqrt(x^2+a),1/2*(x*sqrt(x^2+a)+a*log(x+sqrt(x^2+a))))", "f(1/sqrt(x^2+a),log(x+sqrt(x^2+a)))", "f(1/x*1/sqrt(x^2+a),arcsec(x/sqrt(-a))/sqrt(-a),or(not(number(a)),a<0))", "f(1/x*1/sqrt(x^2+a),-1/sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))", "f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(a)*log((sqrt(a)+sqrt(x^2+a))/x),or(not(number(a)),a>0))", "f(sqrt(x^2+a)/x,sqrt(x^2+a)-sqrt(-a)*arcsec(x/sqrt(-a)),or(not(number(a)),a<0))", "f(x/sqrt(x^2+a),sqrt(x^2+a))", "f(x*sqrt(x^2+a),1/3*sqrt((x^2+a)^3))", "f(sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/4*(x*sqrt((x^2+a^(1/3))^3)+3/2*a^(1/3)*x*sqrt(x^2+a^(1/3))+3/2*a^(2/3)*log(x+sqrt(x^2+a^(1/3)))))", "f(sqrt(-a+x^6-3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/4*(x*sqrt((x^2-a^(1/3))^3)-3/2*a^(1/3)*x*sqrt(x^2-a^(1/3))+3/2*a^(2/3)*log(x+sqrt(x^2-a^(1/3)))))", "f(1/sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),x/a^(1/3)/sqrt(x^2+a^(1/3)))", "f(x/sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),-1/sqrt(x^2+a^(1/3)))", "f(x*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/5*sqrt((x^2+a^(1/3))^5))", "f(x^2*sqrt(x^2+a),1/4*x*sqrt((x^2+a)^3)-1/8*a*x*sqrt(x^2+a)-1/8*a^2*log(x+sqrt(x^2+a)))", "f(x^3*sqrt(x^2+a),(1/5*x^2-2/15*a)*sqrt((x^2+a)^3),and(number(a),a>0))", "f(x^3*sqrt(x^2+a),sqrt((x^2+a)^5)/5-a*sqrt((x^2+a)^3)/3,and(number(a),a<0))", "f(x^2/sqrt(x^2+a),1/2*x*sqrt(x^2+a)-1/2*a*log(x+sqrt(x^2+a)))", "f(x^3/sqrt(x^2+a),1/3*sqrt((x^2+a)^3)-a*sqrt(x^2+a))", "f(1/x^2*1/sqrt(x^2+a),-sqrt(x^2+a)/a/x)", "f(1/x^3*1/sqrt(x^2+a),-1/2*sqrt(x^2+a)/a/x^2+1/2*log((sqrt(a)+sqrt(x^2+a))/x)/a^(3/2),or(not(number(a)),a>0))", "f(1/x^3*1/sqrt(x^2-a),1/2*sqrt(x^2-a)/a/x^2+1/2*1/(a^(3/2))*arcsec(x/(a^(1/2))),or(not(number(a)),a>0))", "f(x^2*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/6*x*sqrt((x^2+a^(1/3))^5)-1/24*a^(1/3)*x*sqrt((x^2+a^(1/3))^3)-1/16*a^(2/3)*x*sqrt(x^2+a^(1/3))-1/16*a*log(x+sqrt(x^2+a^(1/3))),or(not(number(a)),a>0))", "f(x^2*sqrt(-a-3*a^(1/3)*x^4+3*a^(2/3)*x^2+x^6),1/6*x*sqrt((x^2-a^(1/3))^5)+1/24*a^(1/3)*x*sqrt((x^2-a^(1/3))^3)-1/16*a^(2/3)*x*sqrt(x^2-a^(1/3))+1/16*a*log(x+sqrt(x^2-a^(1/3))),or(not(number(a)),a>0))", "f(x^3*sqrt(a+x^6+3*a^(1/3)*x^4+3*a^(2/3)*x^2),1/7*sqrt((x^2+a^(1/3))^7)-1/5*a^(1/3)*sqrt((x^2+a^(1/3))^5),or(not(number(a)),a>0))", "f(x^3*sqrt(-a-3*a^(1/3)*x^4+3*a^(2/3)*x^2+x^6),1/7*sqrt((x^2-a^(1/3))^7)+1/5*a^(1/3)*sqrt((x^2-a^(1/3))^5),or(not(number(a)),a>0))", "f(1/(x-a)/sqrt(x^2-a^2),-sqrt(x^2-a^2)/a/(x-a))", "f(1/(x+a)/sqrt(x^2-a^2),sqrt(x^2-a^2)/a/(x+a))", "f(sqrt(a-x^2),1/2*(x*sqrt(a-x^2)+a*arcsin(x/sqrt(abs(a)))))", "f(1/x*1/sqrt(a-x^2),-1/sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x,sqrt(a-x^2)-sqrt(a)*log((sqrt(a)+sqrt(a-x^2))/x),or(not(number(a)),a>0))", "f(x/sqrt(a-x^2),-sqrt(a-x^2))", "f(x*sqrt(a-x^2),-1/3*sqrt((a-x^2)^3))", "f(x^2*sqrt(a-x^2),-x/4*sqrt((a-x^2)^3)+1/8*a*(x*sqrt(a-x^2)+a*arcsin(x/sqrt(a))),or(not(number(a)),a>0))", "f(x^3*sqrt(a-x^2),(-1/5*x^2-2/15*a)*sqrt((a-x^2)^3),or(not(number(a)),a>0))", "f(x^2/sqrt(a-x^2),-x/2*sqrt(a-x^2)+a/2*arcsin(x/sqrt(a)),or(not(number(a)),a>0))", "f(1/x^2*1/sqrt(a-x^2),-sqrt(a-x^2)/a/x,or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x^2,-sqrt(a-x^2)/x-arcsin(x/sqrt(a)),or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x^3,-1/2*sqrt(a-x^2)/x^2+1/2*log((sqrt(a)+sqrt(a-x^2))/x)/sqrt(a),or(not(number(a)),a>0))", "f(sqrt(a-x^2)/x^4,-1/3*sqrt((a-x^2)^3)/a/x^3,or(not(number(a)),a>0))", "f(sqrt(a*x^2+b),x*sqrt(a*x^2+b)/2+b*log(x*sqrt(a)+sqrt(a*x^2+b))/2/sqrt(a),and(number(a),a>0))", "f(sqrt(a*x^2+b),x*sqrt(a*x^2+b)/2+b*arcsin(x*sqrt(-a/b))/2/sqrt(-a),and(number(a),a<0))", "f(sin(a*x),-cos(a*x)/a)", "f(cos(a*x),sin(a*x)/a)", "f(tan(a*x),-log(cos(a*x))/a)", "f(1/tan(a*x),log(sin(a*x))/a)", "f(1/cos(a*x),log(tan(pi/4+a*x/2))/a)", "f(1/sin(a*x),log(tan(a*x/2))/a)", "f(sin(a*x)^2,x/2-sin(2*a*x)/(4*a))", "f(sin(a*x)^3,-cos(a*x)*(sin(a*x)^2+2)/(3*a))", "f(sin(a*x)^4,3/8*x-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a))", "f(cos(a*x)^2,x/2+sin(2*a*x)/(4*a))", "f(cos(a*x)^3,sin(a*x)*(cos(a*x)^2+2)/(3*a))", "f(cos(a*x)^4,3/8*x+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a))", "f(1/sin(a*x)^2,-1/(a*tan(a*x)))", "f(1/cos(a*x)^2,tan(a*x)/a)", "f(sin(a*x)*cos(a*x),sin(a*x)^2/(2*a))", "f(sin(a*x)^2*cos(a*x)^2,-sin(4*a*x)/(32*a)+x/8)", "f(sin(a*x)/cos(a*x)^2,1/(a*cos(a*x)))", "f(sin(a*x)^2/cos(a*x),(log(tan(pi/4+a*x/2))-sin(a*x))/a)", "f(cos(a*x)/sin(a*x)^2,-1/(a*sin(a*x)))", "f(1/(sin(a*x)*cos(a*x)),log(tan(a*x))/a)", "f(1/(sin(a*x)*cos(a*x)^2),(1/cos(a*x)+log(tan(a*x/2)))/a)", "f(1/(sin(a*x)^2*cos(a*x)),(log(tan(pi/4+a*x/2))-1/sin(a*x))/a)", "f(1/(sin(a*x)^2*cos(a*x)^2),-2/(a*tan(2*a*x)))", "f(sin(a+b*x),-cos(a+b*x)/b)", "f(cos(a+b*x),sin(a+b*x)/b)", "f(1/(b+b*sin(a*x)),-tan(pi/4-a*x/2)/a/b)", "f(1/(b-b*sin(a*x)),tan(pi/4+a*x/2)/a/b)", "f(1/(b+b*cos(a*x)),tan(a*x/2)/a/b)", "f(1/(b-b*cos(a*x)),-1/tan(a*x/2)/a/b)", "f(1/(a+b*sin(x)),1/sqrt(b^2-a^2)*log((a*tan(x/2)+b-sqrt(b^2-a^2))/(a*tan(x/2)+b+sqrt(b^2-a^2))),b^2-a^2)", "f(1/(a+b*cos(x)),1/sqrt(b^2-a^2)*log((sqrt(b^2-a^2)*tan(x/2)+a+b)/(sqrt(b^2-a^2)*tan(x/2)-a-b)),b^2-a^2)", "f(x*sin(a*x),sin(a*x)/a^2-x*cos(a*x)/a)", "f(x^2*sin(a*x),2*x*sin(a*x)/a^2-(a^2*x^2-2)*cos(a*x)/a^3)", "f(x*cos(a*x),cos(a*x)/a^2+x*sin(a*x)/a)", "f(x^2*cos(a*x),2*x*cos(a*x)/a^2+(a^2*x^2-2)*sin(a*x)/a^3)", "f(arcsin(a*x),x*arcsin(a*x)+sqrt(1-a^2*x^2)/a)", "f(arccos(a*x),x*arccos(a*x)-sqrt(1-a^2*x^2)/a)", "f(arctan(a*x),x*arctan(a*x)-1/2*log(1+a^2*x^2)/a)", "f(log(a*x),x*log(a*x)-x)", "f(x*log(a*x),x^2*log(a*x)/2-x^2/4)", "f(x^2*log(a*x),x^3*log(a*x)/3-1/9*x^3)", "f(log(x)^2,x*log(x)^2-2*x*log(x)+2*x)", "f(1/x*1/(a+log(x)),log(a+log(x)))", "f(log(a*x+b),(a*x+b)*log(a*x+b)/a-x)", "f(log(a*x+b)/x^2,a/b*log(x)-(a*x+b)*log(a*x+b)/b/x)", "f(sinh(x),cosh(x))", "f(cosh(x),sinh(x))", "f(tanh(x),log(cosh(x)))", "f(x*sinh(x),x*cosh(x)-sinh(x))", "f(x*cosh(x),x*sinh(x)-cosh(x))", "f(sinh(x)^2,sinh(2*x)/4-x/2)", "f(tanh(x)^2,x-tanh(x))", "f(cosh(x)^2,sinh(2*x)/4+x/2)", "f(x^3*exp(a*x^2),exp(a*x^2)*(x^2/a-1/(a^2))/2)", "f(x^3*exp(a*x^2+b),exp(a*x^2)*exp(b)*(x^2/a-1/(a^2))/2)", "f(exp(a*x^2),-i*sqrt(pi)*erf(i*sqrt(a)*x)/sqrt(a)/2)", "f(erf(a*x),x*erf(a*x)+exp(-a^2*x^2)/a/sqrt(pi))", "f(x^2*(1-x^2)^(3/2),(x*sqrt(1-x^2)*(-8*x^4+14*x^2-3)+3*arcsin(x))/48)", "f(x^2*(1-x^2)^(5/2),(x*sqrt(1-x^2)*(48*x^6-136*x^4+118*x^2-15)+15*arcsin(x))/384)", "f(x^4*(1-x^2)^(3/2),(-x*sqrt(1-x^2)*(16*x^6-24*x^4+2*x^2+3)+3*arcsin(x))/128)", "f(x*exp(a*x),exp(a*x)*(a*x-1)/(a^2))", "f(x*exp(a*x+b),exp(a*x+b)*(a*x-1)/(a^2))", "f(x^2*exp(a*x),exp(a*x)*(a^2*x^2-2*a*x+2)/(a^3))", "f(x^2*exp(a*x+b),exp(a*x+b)*(a^2*x^2-2*a*x+2)/(a^3))", "f(x^3*exp(a*x),exp(a*x)*x^3/a-3/a*integral(x^2*exp(a*x),x))", "f(x^3*exp(a*x+b),exp(a*x+b)*x^3/a-3/a*integral(x^2*exp(a*x+b),x))", 0];

  Eval_integral = function() {
    var ac, doNothing, i, n, o, ref, ref1;
    i = 0;
    n = 0;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      guess();
      push(symbol(NIL));
    } else if (isnum(p2)) {
      guess();
      push(p2);
    } else {
      push(p2);
      p1 = cdr(p1);
      push(car(p1));
      Eval();
    }
    p5 = pop();
    p4 = pop();
    p3 = pop();
    while (1.) {
      if (isnum(p5)) {
        push(p5);
        n = pop_integer();
        if (n === 0x80000000) {
          stop("nth integral: check n");
        }
      } else {
        n = 1;
      }
      push(p3);
      if (n >= 0) {
        for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
          push(p4);
          integral();
        }
      } else {
        n = -n;
        for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
          push(p4);
          derivative();
        }
      }
      p3 = pop();
      if (p5 === symbol(NIL)) {
        break;
      }
      if (isnum(p5)) {
        p1 = cdr(p1);
        push(car(p1));
        Eval();
        p5 = pop();
        if (p5 === symbol(NIL)) {
          break;
        }
        if (isnum(p5)) {
          doNothing = 1;
        } else {
          p4 = p5;
          p1 = cdr(p1);
          push(car(p1));
          Eval();
          p5 = pop();
        }
      } else {
        p4 = p5;
        p1 = cdr(p1);
        push(car(p1));
        Eval();
        p5 = pop();
      }
    }
    return push(p3);
  };

  integral = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      integral_of_sum();
    } else if (car(p1) === symbol(MULTIPLY)) {
      integral_of_product();
    } else {
      integral_of_form();
    }
    p1 = pop();
    if (Find(p1, symbol(INTEGRAL))) {
      stop("integral: sorry, could not find a solution");
    }
    push(p1);
    simplify();
    Eval();
    return restore();
  };

  integral_of_sum = function() {
    var results;
    p1 = cdr(p1);
    push(car(p1));
    push(p2);
    integral();
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      push(p2);
      integral();
      add();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  integral_of_product = function() {
    push(p1);
    push(p2);
    partition();
    p1 = pop();
    integral_of_form();
    return multiply();
  };

  integral_of_form = function() {
    push(p1);
    push(p2);
    transform(itab);
    p3 = pop();
    if (p3 === symbol(NIL)) {
      push_symbol(INTEGRAL);
      push(p1);
      push(p2);
      return list(3);
    } else {
      return push(p3);
    }
  };

  INV_check_arg = function() {
    if (!istensor(p1)) {
      return 0;
    } else if (p1.tensor.ndim !== 2) {
      return 0;
    } else if (p1.tensor.dim[0] !== p1.tensor.dim[1]) {
      return 0;
    } else {
      return 1;
    }
  };

  inv = function() {
    var a, i, n, o, ref;
    i = 0;
    n = 0;
    save();
    p1 = pop();
    if (INV_check_arg() === 0) {
      push_symbol(INV);
      push(p1);
      list(2);
      restore();
      return;
    }
    n = p1.tensor.nelem;
    a = p1.tensor.elem;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      if (!isnum(a[i])) {
        break;
      }
    }
    if (i === n) {
      yyinvg();
    } else {
      push(p1);
      adj();
      push(p1);
      det();
      p2 = pop();
      if (iszero(p2)) {
        stop("inverse of singular matrix");
      }
      push(p2);
      divide();
    }
    return restore();
  };

  invg = function() {
    save();
    p1 = pop();
    if (INV_check_arg() === 0) {
      push_symbol(INVG);
      push(p1);
      list(2);
      restore();
      return;
    }
    yyinvg();
    return restore();
  };

  yyinvg = function() {
    var ac, ad, ae, h, i, j, n, o, ref, ref1, ref2, ref3;
    h = 0;
    i = 0;
    j = 0;
    n = 0;
    n = p1.tensor.dim[0];
    h = tos;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      for (j = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; j = 0 <= ref1 ? ++ac : --ac) {
        if (i === j) {
          push(one);
        } else {
          push(zero);
        }
      }
    }
    for (i = ad = 0, ref2 = n * n; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      push(p1.tensor.elem[i]);
    }
    INV_decomp(n);
    p1 = alloc_tensor(n * n);
    p1.tensor.ndim = 2;
    p1.tensor.dim[0] = n;
    p1.tensor.dim[1] = n;
    for (i = ae = 0, ref3 = n * n; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
      p1.tensor.elem[i] = stack[h + i];
    }
    tos -= 2 * n * n;
    return push(p1);
  };

  INV_decomp = function(n) {
    var a, ac, ad, ae, d, i, j, o, ref, ref1, ref2, ref3, ref4, results, u;
    a = 0;
    d = 0;
    i = 0;
    j = 0;
    u = 0;
    a = tos - n * n;
    u = a - n * n;
    results = [];
    for (d = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; d = 0 <= ref ? ++o : --o) {
      if (equal(stack[a + n * d + d], zero)) {
        for (i = ac = ref1 = d + 1, ref2 = n; ref1 <= ref2 ? ac < ref2 : ac > ref2; i = ref1 <= ref2 ? ++ac : --ac) {
          if (!equal(stack[a + n * i + d], zero)) {
            break;
          }
        }
        if (i === n) {
          stop("inverse of singular matrix");
        }
        for (j = ad = 0, ref3 = n; 0 <= ref3 ? ad < ref3 : ad > ref3; j = 0 <= ref3 ? ++ad : --ad) {
          p2 = stack[a + n * d + j];
          stack[a + n * d + j] = stack[a + n * i + j];
          stack[a + n * i + j] = p2;
          p2 = stack[u + n * d + j];
          stack[u + n * d + j] = stack[u + n * i + j];
          stack[u + n * i + j] = p2;
        }
      }
      p2 = stack[a + n * d + d];
      for (j = ae = 0, ref4 = n; 0 <= ref4 ? ae < ref4 : ae > ref4; j = 0 <= ref4 ? ++ae : --ae) {
        if (j > d) {
          push(stack[a + n * d + j]);
          push(p2);
          divide();
          stack[a + n * d + j] = pop();
        }
        push(stack[u + n * d + j]);
        push(p2);
        divide();
        stack[u + n * d + j] = pop();
      }
      results.push((function() {
        var af, ref5, results1;
        results1 = [];
        for (i = af = 0, ref5 = n; 0 <= ref5 ? af < ref5 : af > ref5; i = 0 <= ref5 ? ++af : --af) {
          if (i === d) {
            continue;
          }
          p2 = stack[a + n * i + d];
          results1.push((function() {
            var ag, ref6, results2;
            results2 = [];
            for (j = ag = 0, ref6 = n; 0 <= ref6 ? ag < ref6 : ag > ref6; j = 0 <= ref6 ? ++ag : --ag) {
              if (j > d) {
                push(stack[a + n * i + j]);
                push(stack[a + n * d + j]);
                push(p2);
                multiply();
                subtract();
                stack[a + n * i + j] = pop();
              }
              push(stack[u + n * i + j]);
              push(stack[u + n * d + j]);
              push(p2);
              multiply();
              subtract();
              results2.push(stack[u + n * i + j] = pop());
            }
            return results2;
          })());
        }
        return results1;
      })());
    }
    return results;
  };

  iszero = function(p) {
    var i, o, ref;
    i = 0;
    switch (p.k) {
      case NUM:
        if (MZERO(p.q.a)) {
          return 1;
        }
        break;
      case DOUBLE:
        if (p.d === 0.0) {
          return 1;
        }
        break;
      case TENSOR:
        for (i = o = 0, ref = p.tensor.nelem; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
          if (!iszero(p.tensor.elem[i])) {
            return 0;
          }
        }
        return 1;
    }
    return 0;
  };

  isnegativenumber = function(p) {
    switch (p.k) {
      case NUM:
        if (MSIGN(p.q.a) === -1) {
          return 1;
        }
        break;
      case DOUBLE:
        if (p.d < 0.0) {
          return 1;
        }
    }
    return 0;
  };

  isplusone = function(p) {
    switch (p.k) {
      case NUM:
        if (MEQUAL(p.q.a, 1) && MEQUAL(p.q.b, 1)) {
          return 1;
        }
        break;
      case DOUBLE:
        if (p.d === 1.0) {
          return 1;
        }
    }
    return 0;
  };

  isminusone = function(p) {
    switch (p.k) {
      case NUM:
        if (MEQUAL(p.q.a, -1) && MEQUAL(p.q.b, 1)) {
          return 1;
        }
        break;
      case DOUBLE:
        if (p.d === -1.0) {
          return 1;
        }
    }
    return 0;
  };

  isinteger = function(p) {
    if (p.k === NUM && MEQUAL(p.q.b, 1)) {
      return 1;
    } else {
      return 0;
    }
  };

  isnonnegativeinteger = function(p) {
    if (isrational(p) && MEQUAL(p.q.b, 1) && MSIGN(p.q.a) === 1) {
      return 1;
    } else {
      return 0;
    }
  };

  isposint = function(p) {
    if (isinteger(p) && MSIGN(p.q.a) === 1) {
      return 1;
    } else {
      return 0;
    }
  };

  ispoly = function(p, x) {
    if (Find(p, x)) {
      return ispoly_expr(p, x);
    } else {
      return 0;
    }
  };

  ispoly_expr = function(p, x) {
    if (car(p) === symbol(ADD)) {
      p = cdr(p);
      while (iscons(p)) {
        if (!ispoly_term(car(p), x)) {
          return 0;
        }
        p = cdr(p);
      }
      return 1;
    } else {
      return ispoly_term(p, x);
    }
  };

  ispoly_term = function(p, x) {
    if (car(p) === symbol(MULTIPLY)) {
      p = cdr(p);
      while (iscons(p)) {
        if (!ispoly_factor(car(p), x)) {
          return 0;
        }
        p = cdr(p);
      }
      return 1;
    } else {
      return ispoly_factor(p, x);
    }
  };

  ispoly_factor = function(p, x) {
    if (equal(p, x)) {
      return 1;
    }
    if (car(p) === symbol(POWER) && equal(cadr(p), x)) {
      if (isposint(caddr(p))) {
        return 1;
      } else {
        return 0;
      }
    }
    if (Find(p, x)) {
      return 0;
    } else {
      return 1;
    }
  };

  isnegativeterm = function(p) {
    if (isnegativenumber(p)) {
      return 1;
    } else if (car(p) === symbol(MULTIPLY) && isnegativenumber(cadr(p))) {
      return 1;
    } else {
      return 0;
    }
  };

  isimaginarynumber = function(p) {
    if ((car(p) === symbol(MULTIPLY) && length(p) === 3 && isnum(cadr(p)) && equal(caddr(p), imaginaryunit)) || equal(p, imaginaryunit)) {
      return 1;
    } else {
      return 0;
    }
  };

  iscomplexnumber = function(p) {
    if ((car(p) === symbol(ADD) && length(p) === 3 && isnum(cadr(p)) && isimaginarynumber(caddr(p))) || isimaginarynumber(p)) {
      return 1;
    } else {
      return 0;
    }
  };

  iseveninteger = function(p) {
    if (isinteger(p) && p.q.a.isEven()) {
      return 1;
    } else {
      return 0;
    }
  };

  isnegative = function(p) {
    if (car(p) === symbol(ADD) && isnegativeterm(cadr(p))) {
      return 1;
    } else if (isnegativeterm(p)) {
      return 1;
    } else {
      return 0;
    }
  };

  issymbolic = function(p) {
    if (issymbol(p)) {
      return 1;
    } else {
      while (iscons(p)) {
        if (issymbolic(car(p))) {
          return 1;
        }
        p = cdr(p);
      }
      return 0;
    }
  };

  isintegerfactor = function(p) {
    if (isinteger(p) || car(p) === symbol(POWER) && isinteger(cadr(p)) && isinteger(caddr(p))) {
      return 1;
    } else {
      return 0;
    }
  };

  isoneover = function(p) {
    if (car(p) === symbol(POWER) && isminusone(caddr(p))) {
      return 1;
    } else {
      return 0;
    }
  };

  isfraction = function(p) {
    if (p.k === NUM && !MEQUAL(p.q.b, 1)) {
      return 1;
    } else {
      return 0;
    }
  };

  equaln = function(p, n) {
    switch (p.k) {
      case NUM:
        if (MEQUAL(p.q.a, n) && MEQUAL(p.q.b, 1)) {
          return 1;
        }
        break;
      case DOUBLE:
        if (p.d === n) {
          return 1;
        }
    }
    return 0;
  };

  equalq = function(p, a, b) {
    switch (p.k) {
      case NUM:
        if (MEQUAL(p.q.a, a) && MEQUAL(p.q.b, b)) {
          return 1;
        }
        break;
      case DOUBLE:
        if (p.d === a / b) {
          return 1;
        }
    }
    return 0;
  };

  isoneoversqrttwo = function(p) {
    if (car(p) === symbol(POWER) && equaln(cadr(p), 2) && equalq(caddr(p), -1, 2)) {
      return 1;
    } else {
      return 0;
    }
  };

  isminusoneoversqrttwo = function(p) {
    if (car(p) === symbol(MULTIPLY) && equaln(cadr(p), -1) && isoneoversqrttwo(caddr(p)) && length(p) === 3) {
      return 1;
    } else {
      return 0;
    }
  };

  isfloating = function(p) {
    if (p.k === DOUBLE) {
      return 1;
    }
    while (iscons(p)) {
      if (isfloating(car(p))) {
        return 1;
      }
      p = cdr(p);
    }
    return 0;
  };

  isimaginaryunit = function(p) {
    if (equal(p, imaginaryunit)) {
      return 1;
    } else {
      return 0;
    }
  };

  isquarterturn = function(p) {
    var minussign, n;
    n = 0;
    minussign = 0;
    if (car(p) !== symbol(MULTIPLY)) {
      return 0;
    }
    if (equal(cadr(p), imaginaryunit)) {
      if (caddr(p) !== symbol(PI)) {
        return 0;
      }
      if (length(p) !== 3) {
        return 0;
      }
      return 2;
    }
    if (!isnum(cadr(p))) {
      return 0;
    }
    if (!equal(caddr(p), imaginaryunit)) {
      return 0;
    }
    if (cadddr(p) !== symbol(PI)) {
      return 0;
    }
    if (length(p) !== 4) {
      return 0;
    }
    push(cadr(p));
    push_integer(2);
    multiply();
    n = pop_integer();
    if (n === 0x80000000) {
      return 0;
    }
    if (n < 1) {
      minussign = 1;
      n = -n;
    }
    switch (n % 4) {
      case 0:
        n = 1;
        break;
      case 1:
        if (minussign) {
          n = 4;
        } else {
          n = 3;
        }
        break;
      case 2:
        n = 2;
        break;
      case 3:
        if (minussign) {
          n = 3;
        } else {
          n = 4;
        }
    }
    return n;
  };

  isnpi = function(p) {
    var doNothing, n;
    n = 0;
    if (p === symbol(PI)) {
      return 2;
    }
    if (car(p) === symbol(MULTIPLY) && isnum(cadr(p)) && caddr(p) === symbol(PI) && length(p) === 3) {
      doNothing = 0;
    } else {
      return 0;
    }
    push(cadr(p));
    push_integer(2);
    multiply();
    n = pop_integer();
    if (n === 0x80000000) {
      return 0;
    }
    if (n < 0) {
      n = 4 - (-n) % 4;
    } else {
      n = 1 + (n - 1) % 4;
    }
    return n;
  };

  $.iszero = iszero;

  $.isnegativenumber = isnegativenumber;

  $.isplusone = isplusone;

  $.isminusone = isminusone;

  $.isinteger = isinteger;

  $.isnonnegativeinteger = isnonnegativeinteger;

  $.isposint = isposint;

  $.isnegativeterm = isnegativeterm;

  $.isimaginarynumber = isimaginarynumber;

  $.iscomplexnumber = iscomplexnumber;

  $.iseveninteger = iseveninteger;

  $.isnegative = isnegative;

  $.issymbolic = issymbolic;

  $.isintegerfactor = isintegerfactor;

  $.isoneover = isoneover;

  $.isfraction = isfraction;

  $.isoneoversqrttwo = isoneoversqrttwo;

  $.isminusoneoversqrttwo = isminusoneoversqrttwo;

  $.isfloating = isfloating;

  $.isimaginaryunit = isimaginaryunit;

  $.isquarterturn = isquarterturn;

  $.isnpi = isnpi;

  Eval_isprime = function() {
    push(cadr(p1));
    Eval();
    p1 = pop();
    if (isnonnegativeinteger(p1) && mprime(p1.q.a)) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };


  /*
   Laguerre function
  
  Example
  
  	laguerre(x,3)
  
  Result
  
  	   1   3    3   2
  	- --- x  + --- x  - 3 x + 1
  	   6        2
  
  The computation uses the following recurrence relation.
  
  	L(x,0,k) = 1
  
  	L(x,1,k) = -x + k + 1
  
  	n*L(x,n,k) = (2*(n-1)+1-x+k)*L(x,n-1,k) - (n-1+k)*L(x,n-2,k)
  
  In the "for" loop i = n-1 so the recurrence relation becomes
  
  	(i+1)*L(x,n,k) = (2*i+1-x+k)*L(x,n-1,k) - (i+k)*L(x,n-2,k)
   */

  Eval_laguerre = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    push(cadddr(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      push_integer(0);
    } else {
      push(p2);
    }
    return laguerre();
  };

  laguerre = function() {
    var n;
    n = 0;
    save();
    p3 = pop();
    p2 = pop();
    p1 = pop();
    push(p2);
    n = pop_integer();
    if (n < 0 || n === 0x80000000) {
      push_symbol(LAGUERRE);
      push(p1);
      push(p2);
      push(p3);
      list(4);
      restore();
      return;
    }
    if (issymbol(p1)) {
      laguerre2(n);
    } else {
      p4 = p1;
      p1 = symbol(SECRETX);
      laguerre2(n);
      p1 = p4;
      push(symbol(SECRETX));
      push(p1);
      subst();
      Eval();
    }
    return restore();
  };

  laguerre2 = function(n) {
    var i, o, ref, results;
    i = 0;
    push_integer(1);
    push_integer(0);
    p6 = pop();
    results = [];
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p5 = p6;
      p6 = pop();
      push_integer(2 * i + 1);
      push(p1);
      subtract();
      push(p3);
      add();
      push(p6);
      multiply();
      push_integer(i);
      push(p3);
      add();
      push(p5);
      multiply();
      subtract();
      push_integer(i + 1);
      results.push(divide());
    }
    return results;
  };

  Eval_lcm = function() {
    var results;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      lcm();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  lcm = function() {
    var x;
    x = 0;
    x = expanding;
    save();
    yylcm();
    restore();
    return expanding = x;
  };

  yylcm = function() {
    expanding = 1;
    p2 = pop();
    p1 = pop();
    push(p1);
    push(p2);
    gcd();
    push(p1);
    divide();
    push(p2);
    divide();
    return inverse();
  };


  /*
   Return the leading coefficient of a polynomial.
  
  Example
  
  	leading(5x^2+x+1,x)
  
  Result
  
  	5
  
  The result is undefined if P is not a polynomial.
   */

  Eval_leading = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    p1 = pop();
    if (p1 === symbol(NIL)) {
      guess();
    } else {
      push(p1);
    }
    return leading();
  };

  leading = function() {
    save();
    p2 = pop();
    p1 = pop();
    push(p1);
    push(p2);
    degree();
    p3 = pop();
    push(p1);
    push(p2);
    push(p3);
    power();
    divide();
    push(p2);
    filter();
    return restore();
  };


  /*
   Legendre function
  
  Example
  
  	legendre(x,3,0)
  
  Result
  
  	 5   3    3
  	--- x  - --- x
  	 2        2
  
  The computation uses the following recurrence relation.
  
  	P(x,0) = 1
  
  	P(x,1) = x
  
  	n*P(x,n) = (2*(n-1)+1)*x*P(x,n-1) - (n-1)*P(x,n-2)
  
  In the "for" loop we have i = n-1 so the recurrence relation becomes
  
  	(i+1)*P(x,n) = (2*i+1)*x*P(x,n-1) - i*P(x,n-2)
  
  For m > 0
  
  	P(x,n,m) = (-1)^m * (1-x^2)^(m/2) * d^m/dx^m P(x,n)
   */

  Eval_legendre = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    push(cadddr(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      push_integer(0);
    } else {
      push(p2);
    }
    return legendre();
  };

  legendre = function() {
    save();
    __legendre();
    return restore();
  };

  __legendre = function() {
    var m, n;
    m = 0;
    n = 0;
    p3 = pop();
    p2 = pop();
    p1 = pop();
    push(p2);
    n = pop_integer();
    push(p3);
    m = pop_integer();
    if (n < 0 || n === 0x80000000 || m < 0 || m === 0x80000000) {
      push_symbol(LEGENDRE);
      push(p1);
      push(p2);
      push(p3);
      list(4);
      return;
    }
    if (issymbol(p1)) {
      __legendre2(n, m);
    } else {
      p4 = p1;
      p1 = symbol(SECRETX);
      __legendre2(n, m);
      p1 = p4;
      push(symbol(SECRETX));
      push(p1);
      subst();
      Eval();
    }
    return __legendre3(m);
  };

  __legendre2 = function(n, m) {
    var ac, i, o, ref, ref1, results;
    i = 0;
    push_integer(1);
    push_integer(0);
    p6 = pop();
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      p5 = p6;
      p6 = pop();
      push_integer(2 * i + 1);
      push(p1);
      multiply();
      push(p6);
      multiply();
      push_integer(i);
      push(p5);
      multiply();
      subtract();
      push_integer(i + 1);
      divide();
    }
    results = [];
    for (i = ac = 0, ref1 = m; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      push(p1);
      results.push(derivative());
    }
    return results;
  };

  __legendre3 = function(m) {
    if (m === 0) {
      return;
    }
    if (car(p1) === symbol(COS)) {
      push(cadr(p1));
      sine();
      square();
    } else if (car(p1) === symbol(SIN)) {
      push(cadr(p1));
      cosine();
      square();
    } else {
      push_integer(1);
      push(p1);
      square();
      subtract();
    }
    push_integer(m);
    push_rational(1, 2);
    multiply();
    power();
    multiply();
    if (m % 2) {
      return negate();
    }
  };

  list = function(n) {
    var listIterator, o, ref, results;
    listIterator = 0;
    push(symbol(NIL));
    results = [];
    for (listIterator = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; listIterator = 0 <= ref ? ++o : --o) {
      results.push(cons());
    }
    return results;
  };

  Eval_log = function() {
    push(cadr(p1));
    Eval();
    return logarithm();
  };

  logarithm = function() {
    save();
    yylog();
    return restore();
  };

  yylog = function() {
    var d;
    d = 0.0;
    p1 = pop();
    if (p1 === symbol(E)) {
      push_integer(1);
      return;
    }
    if (equaln(p1, 1)) {
      push_integer(0);
      return;
    }
    if (isnegativenumber(p1)) {
      push(p1);
      negate();
      logarithm();
      push(imaginaryunit);
      push_symbol(PI);
      multiply();
      add();
      return;
    }
    if (isdouble(p1)) {
      d = Math.log(p1.d);
      push_double(d);
      return;
    }
    if (isfraction(p1)) {
      push(p1);
      numerator();
      logarithm();
      push(p1);
      denominator();
      logarithm();
      subtract();
      return;
    }
    if (car(p1) === symbol(POWER)) {
      push(caddr(p1));
      push(cadr(p1));
      logarithm();
      multiply();
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      push_integer(0);
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        logarithm();
        add();
        p1 = cdr(p1);
      }
      return;
    }
    push_symbol(LOG);
    push(p1);
    return list(2);
  };

  madd = function(a, b) {
    return a.add(b);
  };

  msub = function(a, b) {
    return a.subtract(b);
  };

  addf = function(a, b) {
    return a.add(b);
  };

  subf = function(a, b) {
    return a.subtract(b);
  };

  ucmp = function(a, b) {
    return a.compareAbs(b);
  };


  /*
   Magnitude of complex z
  
  	z		mag(z)
  	-		------
  
  	a		a
  
  	-a		a
  
  	(-1)^a		1
  
  	exp(a + i b)	exp(a)
  
  	a b		mag(a) mag(b)
  
  	a + i b		sqrt(a^2 + b^2)
  
  Notes
  
  	1. Handles mixed polar and rectangular forms, e.g. 1 + exp(i pi/3)
  
  	2. jean-francois.debroux reports that when z=(a+i*b)/(c+i*d) then
  
  		mag(numerator(z)) / mag(denominator(z))
  
  	   must be used to get the correct answer. Now the operation is
  	   automatic.
   */

  Eval_mag = function() {
    push(cadr(p1));
    Eval();
    return mag();
  };

  mag = function() {
    save();
    p1 = pop();
    push(p1);
    numerator();
    yymag();
    push(p1);
    denominator();
    yymag();
    divide();
    return restore();
  };

  yymag = function() {
    save();
    p1 = pop();
    if (isnegativenumber(p1)) {
      push(p1);
      negate();
    } else if (car(p1) === symbol(POWER) && equaln(cadr(p1), -1)) {
      push_integer(1);
    } else if (car(p1) === symbol(POWER) && cadr(p1) === symbol(E)) {
      push(caddr(p1));
      real();
      exponential();
    } else if (car(p1) === symbol(MULTIPLY)) {
      push_integer(1);
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        mag();
        multiply();
        p1 = cdr(p1);
      }
    } else if (car(p1) === symbol(ADD)) {
      push(p1);
      rect();
      p1 = pop();
      push(p1);
      real();
      push_integer(2);
      power();
      push(p1);
      imag();
      push_integer(2);
      power();
      add();
      push_rational(1, 2);
      power();
      simplify_trig();
    } else {
      push(p1);
    }
    return restore();
  };

  mgcd = function(u, v) {
    return bigInt.gcd(u, v);
  };

  new_string = function(s) {
    save();
    p1 = new U();
    p1.k = STR;
    p1.str = s;
    push(p1);
    return restore();
  };

  out_of_memory = function() {
    return stop("out of memory");
  };

  push_zero_matrix = function(i, j) {
    push(alloc_tensor(i * j));
    stack[tos - 1].tensor.ndim = 2;
    stack[tos - 1].tensor.dim[0] = i;
    return stack[tos - 1].tensor.dim[1] = j;
  };

  push_identity_matrix = function(n) {
    var i, o, ref;
    push_zero_matrix(n, n);
    i = 0;
    for (i = o = 0, ref = n; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      stack[tos - 1].tensor.elem[i * n + i] = one;
    }
    if (stack[tos - 1].tensor.nelem !== stack[tos - 1].tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
  };

  push_cars = function(p) {
    var results;
    results = [];
    while (iscons(p)) {
      push(car(p));
      results.push(p = cdr(p));
    }
    return results;
  };

  peek = function() {
    save();
    p1 = pop();
    push(p1);
    printline(p1);
    return restore();
  };

  peek2 = function() {
    print_lisp(stack[tos - 2]);
    return print_lisp(stack[tos - 1]);
  };

  equal = function(p1, p2) {
    if (cmp_expr(p1, p2) === 0) {
      return 1;
    } else {
      return 0;
    }
  };

  lessp = function(p1, p2) {
    if (cmp_expr(p1, p2) < 0) {
      return 1;
    } else {
      return 0;
    }
  };

  sign = function(n) {
    if (n < 0) {
      return -1;
    } else if (n > 0) {
      return 1;
    } else {
      return 0;
    }
  };

  cmp_expr = function(p1, p2) {
    var n;
    n = 0;
    if (p1 === p2) {
      return 0;
    }
    if (p1 === symbol(NIL)) {
      return -1;
    }
    if (p2 === symbol(NIL)) {
      return 1;
    }
    if (isnum(p1) && isnum(p2)) {
      return sign(compare_numbers(p1, p2));
    }
    if (isnum(p1)) {
      return -1;
    }
    if (isnum(p2)) {
      return 1;
    }
    if (isstr(p1) && isstr(p2)) {
      return sign(strcmp(p1.str, p2.str));
    }
    if (isstr(p1)) {
      return -1;
    }
    if (isstr(p2)) {
      return 1;
    }
    if (issymbol(p1) && issymbol(p2)) {
      return sign(strcmp(get_printname(p1), get_printname(p2)));
    }
    if (issymbol(p1)) {
      return -1;
    }
    if (issymbol(p2)) {
      return 1;
    }
    if (istensor(p1) && istensor(p2)) {
      return compare_tensors(p1, p2);
    }
    if (istensor(p1)) {
      return -1;
    }
    if (istensor(p2)) {
      return 1;
    }
    while (iscons(p1) && iscons(p2)) {
      n = cmp_expr(car(p1), car(p2));
      if (n !== 0) {
        return n;
      }
      p1 = cdr(p1);
      p2 = cdr(p2);
    }
    if (iscons(p2)) {
      return -1;
    }
    if (iscons(p1)) {
      return 1;
    }
    return 0;
  };

  length = function(p) {
    var n;
    n = 0;
    while (iscons(p)) {
      p = cdr(p);
      n++;
    }
    return n;
  };

  unique = function(p) {
    save();
    p1 = symbol(NIL);
    p2 = symbol(NIL);
    unique_f(p);
    if (p2 !== symbol(NIL)) {
      p1 = symbol(NIL);
    }
    p = p1;
    restore();
    return p;
  };

  unique_f = function(p) {
    if (isstr(p)) {
      if (p1 === symbol(NIL)) {
        p1 = p;
      } else if (p !== p1) {
        p2 = p;
      }
      return;
    }
    while (iscons(p)) {
      unique_f(car(p));
      if (p2 !== symbol(NIL)) {
        return;
      }
      p = cdr(p);
    }
  };

  ssqrt = function() {
    push_rational(1, 2);
    return power();
  };

  yyexpand = function() {
    var x;
    x = expanding;
    expanding = 1;
    Eval();
    return expanding = x;
  };

  exponential = function() {
    push_symbol(E);
    swap();
    return power();
  };

  square = function() {
    push_integer(2);
    return power();
  };

  sort_stack = function(n) {
    var h, subsetOfStack;
    h = tos - n;
    subsetOfStack = stack.slice(h, h + n);
    subsetOfStack.sort(cmp_expr);
    return stack = stack.slice(0, h).concat(subsetOfStack).concat(stack.slice(h + n));
  };

  $.equal = equal;

  $.length = length;

  mmul = function(a, b) {
    return a.multiply(b);
  };

  mdiv = function(a, b) {
    return a.divide(b);
  };


  /*
  static void
  addf(unsigned int *a, unsigned int *b, int len)
  {
  	int i
  	long long t = 0; # can be signed or unsigned 
  	for (i = 0; i < len; i++) {
  		t += (long long) a[i] + b[i]
  		a[i] = (unsigned int) t
  		t >>= 32
  	}
  }
  
  // a = a - b
  
  static void
  subf(unsigned int *a, unsigned int *b, int len)
  {
  	int i
  	long long t = 0; # must be signed
  	for (i = 0; i < len; i++) {
  		t += (long long) a[i] - b[i]
  		a[i] = (unsigned int) t
  		t >>= 32
  	}
  }
  
  // a = b * c
  
  // 0xffffffff + 0xffffffff * 0xffffffff == 0xffffffff00000000
  
  static void
  mulf(unsigned int *a, unsigned int *b, int len, unsigned int c)
  {
  	int i
  	unsigned long long t = 0; # must be unsigned
  	for (i = 0; i < len; i++) {
  		t += (unsigned long long) b[i] * c
  		a[i] = (unsigned int) t
  		t >>= 32
  	}
  	a[i] = (unsigned int) t
  }
   */

  mmod = function(a, b) {
    return a.mod(b);
  };

  mdivrem = function(a, b) {
    var toReturn;
    toReturn = a.divmod(b);
    return [toReturn.quotient, toReturn.remainder];
  };

  Eval_mod = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    return mod();
  };

  mod = function() {
    var n;
    n = 0;
    save();
    p2 = pop();
    p1 = pop();
    if (iszero(p2)) {
      stop("mod function: divide by zero");
    }
    if (!isnum(p1) || !isnum(p2)) {
      push_symbol(MOD);
      push(p1);
      push(p2);
      list(3);
      restore();
      return;
    }
    if (isdouble(p1)) {
      push(p1);
      n = pop_integer();
      if (n === 0x80000000) {
        stop("mod function: cannot convert float value to integer");
      }
      push_integer(n);
      p1 = pop();
    }
    if (isdouble(p2)) {
      push(p2);
      n = pop_integer();
      if (n === 0x80000000) {
        stop("mod function: cannot convert float value to integer");
      }
      push_integer(n);
      p2 = pop();
    }
    if (!isinteger(p1) || !isinteger(p2)) {
      stop("mod function: integer arguments expected");
    }
    p3 = new U();
    p3.k = NUM;
    p3.q.a = mmod(p1.q.a, p2.q.a);
    p3.q.b = mint(1);
    push(p3);
    return restore();
  };

  mpow = function(a, n) {
    return a.pow(n);
  };

  mprime = function(n) {
    return n.isProbablePrime();
  };

  mroot = function(n, index) {
    var i, j, k, o, ref, x, y;
    n = n.abs();
    i = 0;
    j = 0;
    k = 0;
    if (index === 0) {
      stop("root index is zero");
    }
    k = 0;
    while (n.shiftRight(k) > 0) {
      k++;
    }
    if (k === 0) {
      return mint(0);
    }
    k = Math.floor((k - 1) / index);
    j = Math.floor(k / 32 + 1);
    x = bigInt(j);
    for (i = o = 0, ref = j; 0 <= ref ? o < ref : o > ref; i = 0 <= ref ? ++o : --o) {
      x = x.and(bigInt(1).shiftLeft(i).not());
    }
    while (k >= 0) {
      x = x.or(bigInt(1).shiftLeft(k));
      y = mpow(x, index);
      switch (mcmp(y, n)) {
        case 0:
          return x;
        case 1:
          x = x.and(bigInt(1).shiftLeft(k).not());
      }
      k--;
    }
    return 0;
  };

  multiply = function() {
    if (esc_flag) {
      stop("escape key stop");
    }
    if (isnum(stack[tos - 2]) && isnum(stack[tos - 1])) {
      return multiply_numbers();
    } else {
      save();
      yymultiply();
      return restore();
    }
  };

  yymultiply = function() {
    var h, i, n, o, ref, ref1;
    h = 0;
    i = 0;
    n = 0;
    p2 = pop();
    p1 = pop();
    h = tos;
    if (iszero(p1) || iszero(p2)) {
      push(zero);
      return;
    }
    if (expanding && isadd(p1)) {
      p1 = cdr(p1);
      push(zero);
      while (iscons(p1)) {
        push(car(p1));
        push(p2);
        multiply();
        add();
        p1 = cdr(p1);
      }
      return;
    }
    if (expanding && isadd(p2)) {
      p2 = cdr(p2);
      push(zero);
      while (iscons(p2)) {
        push(p1);
        push(car(p2));
        multiply();
        add();
        p2 = cdr(p2);
      }
      return;
    }
    if (!istensor(p1) && istensor(p2)) {
      push(p1);
      push(p2);
      scalar_times_tensor();
      return;
    }
    if (istensor(p1) && !istensor(p2)) {
      push(p1);
      push(p2);
      tensor_times_scalar();
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
    } else {
      push(p1);
      list(1);
      p1 = pop();
    }
    if (car(p2) === symbol(MULTIPLY)) {
      p2 = cdr(p2);
    } else {
      push(p2);
      list(1);
      p2 = pop();
    }
    if (isnum(car(p1)) && isnum(car(p2))) {
      push(car(p1));
      push(car(p2));
      multiply_numbers();
      p1 = cdr(p1);
      p2 = cdr(p2);
    } else if (isnum(car(p1))) {
      push(car(p1));
      p1 = cdr(p1);
    } else if (isnum(car(p2))) {
      push(car(p2));
      p2 = cdr(p2);
    } else {
      push(one);
    }
    parse_p1();
    parse_p2();
    while (iscons(p1) && iscons(p2)) {
      if (caar(p1) === symbol(OPERATOR) && caar(p2) === symbol(OPERATOR)) {
        push_symbol(OPERATOR);
        push(cdar(p1));
        push(cdar(p2));
        append();
        cons();
        p1 = cdr(p1);
        p2 = cdr(p2);
        parse_p1();
        parse_p2();
        continue;
      }
      switch (cmp_expr(p3, p4)) {
        case -1:
          push(car(p1));
          p1 = cdr(p1);
          parse_p1();
          break;
        case 1:
          push(car(p2));
          p2 = cdr(p2);
          parse_p2();
          break;
        case 0:
          combine_factors(h);
          p1 = cdr(p1);
          p2 = cdr(p2);
          parse_p1();
          parse_p2();
          break;
        default:
          stop("internal error 2");
      }
    }
    while (iscons(p1)) {
      push(car(p1));
      p1 = cdr(p1);
    }
    while (iscons(p2)) {
      push(car(p2));
      p2 = cdr(p2);
    }
    __normalize_radical_factors(h);
    if (expanding) {
      for (i = o = ref = h, ref1 = tos; ref <= ref1 ? o < ref1 : o > ref1; i = ref <= ref1 ? ++o : --o) {
        if (isadd(stack[i])) {
          multiply_all(tos - h);
          return;
        }
      }
    }
    n = tos - h;
    if (n === 1) {
      return;
    }
    if (isrational(stack[h]) && equaln(stack[h], 1)) {
      if (n === 2) {
        p7 = pop();
        pop();
        push(p7);
      } else {
        stack[h] = symbol(MULTIPLY);
        list(n);
      }
      return;
    }
    list(n);
    p7 = pop();
    push_symbol(MULTIPLY);
    push(p7);
    return cons();
  };

  parse_p1 = function() {
    p3 = car(p1);
    p5 = one;
    if (car(p3) === symbol(POWER)) {
      p5 = caddr(p3);
      return p3 = cadr(p3);
    }
  };

  parse_p2 = function() {
    p4 = car(p2);
    p6 = one;
    if (car(p4) === symbol(POWER)) {
      p6 = caddr(p4);
      return p4 = cadr(p4);
    }
  };

  combine_factors = function(h) {
    push(p4);
    push(p5);
    push(p6);
    add();
    power();
    p7 = pop();
    if (isnum(p7)) {
      push(stack[h]);
      push(p7);
      multiply_numbers();
      return stack[h] = pop();
    } else if (car(p7) === symbol(MULTIPLY)) {
      if (isnum(cadr(p7)) && cdddr(p7) === symbol(NIL)) {
        push(stack[h]);
        push(cadr(p7));
        multiply_numbers();
        stack[h] = pop();
        return push(caddr(p7));
      } else {
        return push(p7);
      }
    } else {
      return push(p7);
    }
  };

  gp = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, -6, -7, -8, -3, -4, -5, 13, 14, 15, -16, 9, 10, 11, -12], [0, 0, 6, -1, -11, 10, -2, -15, 14, 12, -5, 4, -9, 16, -8, 7, -13], [0, 0, 7, 11, -1, -9, 15, -2, -13, 5, 12, -3, -10, 8, 16, -6, -14], [0, 0, 8, -10, 9, -1, -14, 13, -2, -4, 3, 12, -11, -7, 6, 16, -15], [0, 0, 3, 2, 15, -14, 1, 11, -10, 16, -8, 7, 13, 12, -5, 4, 9], [0, 0, 4, -15, 2, 13, -11, 1, 9, 8, 16, -6, 14, 5, 12, -3, 10], [0, 0, 5, 14, -13, 2, 10, -9, 1, -7, 6, 16, 15, -4, 3, 12, 11], [0, 0, 13, 12, -5, 4, 16, -8, 7, -1, -11, 10, -3, -2, -15, 14, -6], [0, 0, 14, 5, 12, -3, 8, 16, -6, 11, -1, -9, -4, 15, -2, -13, -7], [0, 0, 15, -4, 3, 12, -7, 6, 16, -10, 9, -1, -5, -14, 13, -2, -8], [0, 0, 16, -9, -10, -11, -13, -14, -15, -3, -4, -5, 1, -6, -7, -8, 2], [0, 0, 9, -16, 8, -7, -12, 5, -4, -2, -15, 14, 6, -1, -11, 10, 3], [0, 0, 10, -8, -16, 6, -5, -12, 3, 15, -2, -13, 7, 11, -1, -9, 4], [0, 0, 11, 7, -6, -16, 4, -3, -12, -14, 13, -2, 8, -10, 9, -1, 5], [0, 0, 12, 13, 14, 15, 9, 10, 11, -6, -7, -8, -2, -3, -4, -5, -1]];

  combine_gammas = function(h) {
    var n;
    n = gp[Math.floor(p1.gamma)][Math.floor(p2.gamma)];
    if (n < 0) {
      n = -n;
      push(stack[h]);
      negate();
      stack[h] = pop();
    }
    if (n > 1) {
      return push(_gamma[n]);
    }
  };

  multiply_noexpand = function() {
    var x;
    x = expanding;
    expanding = 0;
    multiply();
    return expanding = x;
  };

  multiply_all = function(n) {
    var h, i, o, ref;
    i = 0;
    if (n === 1) {
      return;
    }
    if (n === 0) {
      push(one);
      return;
    }
    h = tos - n;
    push(stack[h]);
    for (i = o = 1, ref = n; 1 <= ref ? o < ref : o > ref; i = 1 <= ref ? ++o : --o) {
      push(stack[h + i]);
      multiply();
    }
    stack[h] = pop();
    return tos = h + 1;
  };

  multiply_all_noexpand = function(n) {
    var x;
    x = expanding;
    expanding = 0;
    multiply_all(n);
    return expanding = x;
  };

  divide = function() {
    if (isnum(stack[tos - 2]) && isnum(stack[tos - 1])) {
      return divide_numbers();
    } else {
      inverse();
      return multiply();
    }
  };

  inverse = function() {
    if (isnum(stack[tos - 1])) {
      return invert_number();
    } else {
      push_integer(-1);
      return power();
    }
  };

  reciprocate = function() {
    if (isnum(stack[tos - 1])) {
      return invert_number();
    } else {
      push_integer(-1);
      return power();
    }
  };

  negate = function() {
    if (isnum(stack[tos - 1])) {
      return negate_number();
    } else {
      push_integer(-1);
      return multiply();
    }
  };

  negate_expand = function() {
    var x;
    x = expanding;
    expanding = 1;
    negate();
    return expanding = x;
  };

  negate_noexpand = function() {
    var x;
    x = expanding;
    expanding = 0;
    negate();
    return expanding = x;
  };

  __normalize_radical_factors = function(h) {
    var ac, ad, i, o, ref, ref1, ref2, ref3, ref4, ref5;
    i = 0;
    if (isplusone(stack[h]) || isminusone(stack[h]) || isdouble(stack[h])) {
      return;
    }
    for (i = o = ref = h + 1, ref1 = tos; ref <= ref1 ? o < ref1 : o > ref1; i = ref <= ref1 ? ++o : --o) {
      if (__is_radical_number(stack[i])) {
        break;
      }
    }
    if (i === tos) {
      return;
    }
    save();
    push(stack[h]);
    mp_numerator();
    p1 = pop();
    for (i = ac = ref2 = h + 1, ref3 = tos; ref2 <= ref3 ? ac < ref3 : ac > ref3; i = ref2 <= ref3 ? ++ac : --ac) {
      if (isplusone(p1) || isminusone(p1)) {
        break;
      }
      if (!__is_radical_number(stack[i])) {
        continue;
      }
      p3 = cadr(stack[i]);
      p4 = caddr(stack[i]);
      if (!isnegativenumber(p4)) {
        continue;
      }
      push(p1);
      push(p3);
      divide();
      p5 = pop();
      if (!isinteger(p5)) {
        continue;
      }
      p1 = p5;
      push_symbol(POWER);
      push(p3);
      push(one);
      push(p4);
      add();
      list(3);
      stack[i] = pop();
    }
    push(stack[h]);
    mp_denominator();
    p2 = pop();
    for (i = ad = ref4 = h + 1, ref5 = tos; ref4 <= ref5 ? ad < ref5 : ad > ref5; i = ref4 <= ref5 ? ++ad : --ad) {
      if (isplusone(p2)) {
        break;
      }
      if (!__is_radical_number(stack[i])) {
        continue;
      }
      p3 = cadr(stack[i]);
      p4 = caddr(stack[i]);
      if (isnegativenumber(p4)) {
        continue;
      }
      push(p2);
      push(p3);
      divide();
      p5 = pop();
      if (!isinteger(p5)) {
        continue;
      }
      p2 = p5;
      push_symbol(POWER);
      push(p3);
      push(p4);
      push(one);
      subtract();
      list(3);
      stack[i] = pop();
    }
    push(p1);
    push(p2);
    divide();
    stack[h] = pop();
    return restore();
  };

  __is_radical_number = function(p) {
    if (car(p) === symbol(POWER) && isnum(cadr(p)) && isnum(caddr(p)) && !isminusone(cadr(p))) {
      return 1;
    } else {
      return 0;
    }
  };

  NROOTS_YMAX = 101;

  NROOTS_DELTA = 1.0e-6;

  NROOTS_EPSILON = 1.0e-9;

  NROOTS_ABS = function(z) {
    return Math.sqrt(z.r * z.r + z.i * z.i);
  };

  theRandom = 0.0;

  NROOTS_RANDOM = function() {
    return 4.0 * Math.random() - 2.0;
  };

  numericRootOfPolynomial = (function() {
    function numericRootOfPolynomial() {}

    numericRootOfPolynomial.prototype.r = 0.0;

    numericRootOfPolynomial.prototype.i = 0.0;

    return numericRootOfPolynomial;

  })();

  nroots_a = new numericRootOfPolynomial();

  nroots_b = new numericRootOfPolynomial();

  nroots_x = new numericRootOfPolynomial();

  nroots_y = new numericRootOfPolynomial();

  nroots_fa = new numericRootOfPolynomial();

  nroots_fb = new numericRootOfPolynomial();

  nroots_dx = new numericRootOfPolynomial();

  nroots_df = new numericRootOfPolynomial();

  nroots_c = [];

  for (initNRoots = o = 0, ref = NROOTS_YMAX; 0 <= ref ? o < ref : o > ref; initNRoots = 0 <= ref ? ++o : --o) {
    nroots_c[initNRoots] = new numericRootOfPolynomial();
  }

  Eval_nroots = function() {
    var ac, ad, ae, h, i, k, n, ref1, ref2, ref3;
    h = 0;
    i = 0;
    k = 0;
    n = 0;
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      guess();
    } else {
      push(p2);
    }
    p2 = pop();
    p1 = pop();
    if (!ispoly(p1, p2)) {
      stop("nroots: polynomial?");
    }
    h = tos;
    push(p1);
    push(p2);
    n = coeff();
    if (n > NROOTS_YMAX) {
      stop("nroots: degree?");
    }
    for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      push(stack[h + i]);
      real();
      yyfloat();
      Eval();
      p1 = pop();
      push(stack[h + i]);
      imag();
      yyfloat();
      Eval();
      p2 = pop();
      if (!isdouble(p1) || !isdouble(p2)) {
        stop("nroots: coefficients?");
      }
      nroots_c[i].r = p1.d;
      nroots_c[i].i = p2.d;
    }
    tos = h;
    monic(n);
    for (k = ad = ref2 = n; ad > 1; k = ad += -1) {
      findroot(k);
      if (Math.abs(nroots_a.r) < NROOTS_DELTA) {
        nroots_a.r = 0.0;
      }
      if (Math.abs(nroots_a.i) < NROOTS_DELTA) {
        nroots_a.i = 0.0;
      }
      push_double(nroots_a.r);
      push_double(nroots_a.i);
      push(imaginaryunit);
      multiply();
      add();
      NROOTS_divpoly(k);
    }
    n = tos - h;
    if (n > 1) {
      sort_stack(n);
      p1 = alloc_tensor(n);
      p1.tensor.ndim = 1;
      p1.tensor.dim[0] = n;
      for (i = ae = 0, ref3 = n; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
        p1.tensor.elem[i] = stack[h + i];
      }
      tos = h;
      return push(p1);
    }
  };

  monic = function(n) {
    var ac, k, ref1, t;
    k = 0;
    t = 0.0;
    nroots_y.r = nroots_c[n - 1].r;
    nroots_y.i = nroots_c[n - 1].i;
    t = nroots_y.r * nroots_y.r + nroots_y.i * nroots_y.i;
    for (k = ac = 0, ref1 = n - 1; 0 <= ref1 ? ac < ref1 : ac > ref1; k = 0 <= ref1 ? ++ac : --ac) {
      nroots_c[k].r = (nroots_c[k].r * nroots_y.r + nroots_c[k].i * nroots_y.i) / t;
      nroots_c[k].i = (nroots_c[k].i * nroots_y.r - nroots_c[k].r * nroots_y.i) / t;
    }
    nroots_c[n - 1].r = 1.0;
    return nroots_c[n - 1].i = 0.0;
  };

  findroot = function(n) {
    var ac, ad, j, k, nrabs, t;
    j = 0;
    k = 0;
    t = 0.0;
    if (NROOTS_ABS(nroots_c[0]) < NROOTS_DELTA) {
      nroots_a.r = 0.0;
      nroots_a.i = 0.0;
      return;
    }
    for (j = ac = 0; ac < 100; j = ++ac) {
      nroots_a.r = NROOTS_RANDOM();
      nroots_a.i = NROOTS_RANDOM();
      compute_fa(n);
      nroots_b.r = nroots_a.r;
      nroots_b.i = nroots_a.i;
      nroots_fb.r = nroots_fa.r;
      nroots_fb.i = nroots_fa.i;
      nroots_a.r = NROOTS_RANDOM();
      nroots_a.i = NROOTS_RANDOM();
      for (k = ad = 0; ad < 1000; k = ++ad) {
        compute_fa(n);
        nrabs = NROOTS_ABS(nroots_fa);
        if (DEBUG) {
          console.log("nrabs: " + nrabs);
        }
        if (nrabs < NROOTS_EPSILON) {
          return;
        }
        if (NROOTS_ABS(nroots_fa) < NROOTS_ABS(nroots_fb)) {
          nroots_x.r = nroots_a.r;
          nroots_x.i = nroots_a.i;
          nroots_a.r = nroots_b.r;
          nroots_a.i = nroots_b.i;
          nroots_b.r = nroots_x.r;
          nroots_b.i = nroots_x.i;
          nroots_x.r = nroots_fa.r;
          nroots_x.i = nroots_fa.i;
          nroots_fa.r = nroots_fb.r;
          nroots_fa.i = nroots_fb.i;
          nroots_fb.r = nroots_x.r;
          nroots_fb.i = nroots_x.i;
        }
        nroots_dx.r = nroots_b.r - nroots_a.r;
        nroots_dx.i = nroots_b.i - nroots_a.i;
        nroots_df.r = nroots_fb.r - nroots_fa.r;
        nroots_df.i = nroots_fb.i - nroots_fa.i;
        t = nroots_df.r * nroots_df.r + nroots_df.i * nroots_df.i;
        if (t === 0.0) {
          break;
        }
        nroots_y.r = (nroots_dx.r * nroots_df.r + nroots_dx.i * nroots_df.i) / t;
        nroots_y.i = (nroots_dx.i * nroots_df.r - nroots_dx.r * nroots_df.i) / t;
        nroots_a.r = nroots_b.r - (nroots_y.r * nroots_fb.r - nroots_y.i * nroots_fb.i);
        nroots_a.i = nroots_b.i - (nroots_y.r * nroots_fb.i + nroots_y.i * nroots_fb.r);
      }
    }
    return stop("nroots: convergence error");
  };

  compute_fa = function(n) {
    var ac, k, ref1, results, t;
    k = 0;
    t = 0.0;
    nroots_x.r = nroots_a.r;
    nroots_x.i = nroots_a.i;
    nroots_fa.r = nroots_c[0].r + nroots_c[1].r * nroots_x.r - nroots_c[1].i * nroots_x.i;
    nroots_fa.i = nroots_c[0].i + nroots_c[1].r * nroots_x.i + nroots_c[1].i * nroots_x.r;
    results = [];
    for (k = ac = 2, ref1 = n; 2 <= ref1 ? ac < ref1 : ac > ref1; k = 2 <= ref1 ? ++ac : --ac) {
      t = nroots_a.r * nroots_x.r - nroots_a.i * nroots_x.i;
      nroots_x.i = nroots_a.r * nroots_x.i + nroots_a.i * nroots_x.r;
      nroots_x.r = t;
      nroots_fa.r += nroots_c[k].r * nroots_x.r - nroots_c[k].i * nroots_x.i;
      results.push(nroots_fa.i += nroots_c[k].r * nroots_x.i + nroots_c[k].i * nroots_x.r);
    }
    return results;
  };

  NROOTS_divpoly = function(n) {
    var ac, ad, k, ref1, ref2, results;
    k = 0;
    for (k = ac = ref1 = n - 1; ref1 <= 0 ? ac < 0 : ac > 0; k = ref1 <= 0 ? ++ac : --ac) {
      nroots_c[k - 1].r += nroots_c[k].r * nroots_a.r - nroots_c[k].i * nroots_a.i;
      nroots_c[k - 1].i += nroots_c[k].i * nroots_a.r + nroots_c[k].r * nroots_a.i;
    }
    if (NROOTS_ABS(nroots_c[0]) > NROOTS_DELTA) {
      stop("nroots: residual error");
    }
    results = [];
    for (k = ad = 0, ref2 = n - 1; 0 <= ref2 ? ad < ref2 : ad > ref2; k = 0 <= ref2 ? ++ad : --ad) {
      nroots_c[k].r = nroots_c[k + 1].r;
      results.push(nroots_c[k].i = nroots_c[k + 1].i);
    }
    return results;
  };

  Eval_numerator = function() {
    push(cadr(p1));
    Eval();
    return numerator();
  };

  numerator = function() {
    var h;
    h = 0;
    save();
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      push(p1);
      rationalize();
      p1 = pop();
    }
    if (car(p1) === symbol(MULTIPLY)) {
      h = tos;
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        numerator();
        p1 = cdr(p1);
      }
      multiply_all(tos - h);
    } else if (isrational(p1)) {
      push(p1);
      mp_numerator();
    } else if (car(p1) === symbol(POWER) && isnegativeterm(caddr(p1))) {
      push(one);
    } else {
      push(p1);
    }
    return restore();
  };

  Eval_outer = function() {
    var results;
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    results = [];
    while (iscons(p1)) {
      push(car(p1));
      Eval();
      outer();
      results.push(p1 = cdr(p1));
    }
    return results;
  };

  outer = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (istensor(p1) && istensor(p2)) {
      yyouter();
    } else {
      push(p1);
      push(p2);
      if (istensor(p1)) {
        tensor_times_scalar();
      } else if (istensor(p2)) {
        scalar_times_tensor();
      } else {
        multiply();
      }
    }
    return restore();
  };

  yyouter = function() {
    var ac, ad, ae, af, i, j, k, ndim, nelem, ref1, ref2, ref3, ref4;
    i = 0;
    j = 0;
    k = 0;
    ndim = 0;
    nelem = 0;
    ndim = p1.tensor.ndim + p2.tensor.ndim;
    if (ndim > MAXDIM) {
      stop("outer: rank of result exceeds maximum");
    }
    nelem = p1.tensor.nelem * p2.tensor.nelem;
    p3 = alloc_tensor(nelem);
    p3.tensor.ndim = ndim;
    for (i = ac = 0, ref1 = p1.tensor.ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    j = i;
    for (i = ad = 0, ref2 = p2.tensor.ndim; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      p3.tensor.dim[j + i] = p2.tensor.dim[i];
    }
    k = 0;
    for (i = ae = 0, ref3 = p1.tensor.nelem; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
      for (j = af = 0, ref4 = p2.tensor.nelem; 0 <= ref4 ? af < ref4 : af > ref4; j = 0 <= ref4 ? ++af : --af) {
        push(p1.tensor.elem[i]);
        push(p2.tensor.elem[j]);
        multiply();
        p3.tensor.elem[k++] = pop();
      }
    }
    return push(p3);
  };


  /*
   Partition a term
  
  	Input stack:
  
  		term (factor or product of factors)
  
  		free variable
  
  	Output stack:
  
  		constant expression
  
  		variable expression
   */

  partition = function() {
    save();
    p2 = pop();
    p1 = pop();
    push_integer(1);
    p3 = pop();
    p4 = p3;
    p1 = cdr(p1);
    while (iscons(p1)) {
      if (Find(car(p1), p2)) {
        push(p4);
        push(car(p1));
        multiply();
        p4 = pop();
      } else {
        push(p3);
        push(car(p1));
        multiply();
        p3 = pop();
      }
      p1 = cdr(p1);
    }
    push(p3);
    push(p4);
    return restore();
  };


  /*
  Convert complex z to polar form
  
  	Input:		push	z
  
  	Output:		Result on stack
  
  	polar(z) = mag(z) * exp(i * arg(z))
   */

  Eval_polar = function() {
    push(cadr(p1));
    Eval();
    return polar();
  };

  polar = function() {
    save();
    p1 = pop();
    push(p1);
    mag();
    push(imaginaryunit);
    push(p1);
    arg();
    multiply();
    exponential();
    multiply();
    return restore();
  };

  n_factor_number = 0;

  factor_number = function() {
    var h;
    h = 0;
    save();
    p1 = pop();
    if (equaln(p1, 0) || equaln(p1, 1) || equaln(p1, -1)) {
      push(p1);
      restore();
      return;
    }
    n_factor_number = p1.q.a;
    h = tos;
    factor_a();
    if (tos - h > 1) {
      list(tos - h);
      push_symbol(MULTIPLY);
      swap();
      cons();
    }
    return restore();
  };

  factor_a = function() {
    var ac, k;
    k = 0;
    if (n_factor_number.isNegative()) {
      n_factor_number = setSignTo(n_factor_number, 1);
      push_integer(-1);
    }
    for (k = ac = 0; ac < 10000; k = ++ac) {
      try_kth_prime(k);
      if (n_factor_number.compare(1) === 0) {
        return;
      }
    }
    return factor_b();
  };

  try_kth_prime = function(k) {
    var count, d, q, r, ref1;
    count = 0;
    d = mint(primetab[k]);
    count = 0;
    while (1.) {
      if (n_factor_number.compare(1) === 0) {
        if (count) {
          push_factor(d, count);
        }
        return;
      }
      ref1 = mdivrem(n_factor_number, d), q = ref1[0], r = ref1[1];
      if (r.isZero()) {
        count++;
        n_factor_number = q;
      } else {
        break;
      }
    }
    if (count) {
      push_factor(d, count);
    }
    if (mcmp(q, d) === -1) {
      push_factor(n_factor_number, 1);
      return n_factor_number = mint(1);
    }
  };

  factor_b = function() {
    var bigint_one, g, k, l, t, x, xprime;
    k = 0;
    l = 0;
    bigint_one = mint(1);
    x = mint(5);
    xprime = mint(2);
    k = 1;
    l = 1;
    while (1.) {
      if (mprime(n_factor_number)) {
        push_factor(n_factor_number, 1);
        return 0;
      }
      while (1.) {
        if (esc_flag) {
          stop("esc");
        }
        t = msub(xprime, x);
        t = setSignTo(t, 1);
        g = mgcd(t, n_factor_number);
        if (MEQUAL(g, 1)) {
          if (--k === 0) {
            xprime = x;
            l *= 2;
            k = l;
          }
          t = mmul(x, x);
          x = madd(t, bigint_one);
          t = mmod(x, n_factor_number);
          x = t;
          continue;
        }
        push_factor(g, 1);
        if (mcmp(g, n_factor_number) === 0) {
          return -1;
        }
        t = mdiv(n_factor_number, g);
        n_factor_number = t;
        t = mmod(x, n_factor_number);
        x = t;
        t = mmod(xprime, n_factor_number);
        xprime = t;
        break;
      }
    }
  };

  push_factor = function(d, count) {
    p1 = new U();
    p1.k = NUM;
    p1.q.a = d;
    p1.q.b = mint(1);
    push(p1);
    if (count > 1) {
      push_symbol(POWER);
      swap();
      p1 = new U();
      p1.k = NUM;
      p1.q.a = mint(count);
      p1.q.b = mint(1);
      push(p1);
      return list(3);
    }
  };


  /* Power function
  
  	Input:		push	Base
  
  			push	Exponent
  
  	Output:		Result on stack
   */

  Eval_power = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    return power();
  };

  power = function() {
    save();
    yypower();
    return restore();
  };

  yypower = function() {
    var n;
    n = 0;
    p2 = pop();
    p1 = pop();
    if (isrational(p1) && isrational(p2)) {
      push(p1);
      push(p2);
      qpow();
      return;
    }
    if (isnum(p1) && isnum(p2)) {
      push(p1);
      push(p2);
      dpow();
      return;
    }
    if (istensor(p1)) {
      power_tensor();
      return;
    }
    if (p1 === symbol(E) && car(p2) === symbol(LOG)) {
      push(cadr(p2));
      return;
    }
    if (p1 === symbol(E) && isdouble(p2)) {
      push_double(Math.exp(p2.d));
      return;
    }
    if (equal(p1, one) || iszero(p2)) {
      push(one);
      return;
    }
    if (equal(p2, one)) {
      push(p1);
      return;
    }
    if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
      push(car(p1));
      push(p2);
      power();
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        push(p2);
        power();
        multiply();
        p1 = cdr(p1);
      }
      return;
    }
    if (car(p1) === symbol(POWER)) {
      push(cadr(p1));
      push(caddr(p1));
      push(p2);
      multiply();
      power();
      return;
    }
    if (expanding && isadd(p1) && isnum(p2)) {
      push(p2);
      n = pop_integer();
      if (n > 1 && n !== 0x80000000) {
        power_sum(n);
        return;
      }
    }
    if (trigmode === 1 && car(p1) === symbol(SIN) && iseveninteger(p2)) {
      push_integer(1);
      push(cadr(p1));
      cosine();
      push_integer(2);
      power();
      subtract();
      push(p2);
      push_rational(1, 2);
      multiply();
      power();
      return;
    }
    if (trigmode === 2 && car(p1) === symbol(COS) && iseveninteger(p2)) {
      push_integer(1);
      push(cadr(p1));
      sine();
      push_integer(2);
      power();
      subtract();
      push(p2);
      push_rational(1, 2);
      multiply();
      power();
      return;
    }
    if (iscomplexnumber(p1)) {
      if (isinteger(p2)) {
        push(p1);
        conjugate();
        p3 = pop();
        push(p3);
        push(p3);
        push(p1);
        multiply();
        divide();
        push(p2);
        negate();
        power();
        return;
      }
      if (isnum(p2)) {
        push(p1);
        mag();
        push(p2);
        power();
        push_integer(-1);
        push(p1);
        arg();
        push(p2);
        multiply();
        push(symbol(PI));
        divide();
        power();
        multiply();
        return;

        /*
        			push(p1)
        			mag()
        			push(p2)
        			power()
        			push(symbol(E))
        			push(p1)
        			arg()
        			push(p2)
        			multiply()
        			push(imaginaryunit)
        			multiply()
        			power()
        			multiply()
         */
      }
    }
    if (simplify_polar()) {
      return;
    }
    push_symbol(POWER);
    push(p1);
    push(p2);
    return list(3);
  };

  power_sum = function(n) {
    var a, ac, ad, ae, i, j, k, ref1, ref2, ref3;
    a = [];
    i = 0;
    j = 0;
    k = 0;
    k = length(p1) - 1;
    push_frame(k * (n + 1));
    p1 = cdr(p1);
    for (i = ac = 0, ref1 = k; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      for (j = ad = 0, ref2 = n; 0 <= ref2 ? ad <= ref2 : ad >= ref2; j = 0 <= ref2 ? ++ad : --ad) {
        push(car(p1));
        push_integer(j);
        power();
        stack[frame + i * (n + 1) + j] = pop();
      }
      p1 = cdr(p1);
    }
    push_integer(n);
    factorial();
    p1 = pop();
    for (i = ae = 0, ref3 = k; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
      a[i] = 0;
    }
    push(zero);
    multinomial_sum(k, n, a, 0, n);
    return pop_frame(k * (n + 1));
  };

  multinomial_sum = function(k, n, a, i, m) {
    var ac, ad, ae, j, ref1, ref2, ref3;
    j = 0;
    if (i < k - 1) {
      for (j = ac = 0, ref1 = m; 0 <= ref1 ? ac <= ref1 : ac >= ref1; j = 0 <= ref1 ? ++ac : --ac) {
        a[i] = j;
        multinomial_sum(k, n, a, i + 1, m - j);
      }
      return;
    }
    a[i] = m;
    push(p1);
    for (j = ad = 0, ref2 = k; 0 <= ref2 ? ad < ref2 : ad > ref2; j = 0 <= ref2 ? ++ad : --ad) {
      push_integer(a[j]);
      factorial();
      divide();
    }
    for (j = ae = 0, ref3 = k; 0 <= ref3 ? ae < ref3 : ae > ref3; j = 0 <= ref3 ? ++ae : --ae) {
      push(stack[frame + j * (n + 1) + a[j]]);
      multiply();
    }
    return add();
  };

  simplify_polar = function() {
    var doNothing, n;
    n = 0;
    n = isquarterturn(p2);
    switch (n) {
      case 0:
        doNothing = 1;
        break;
      case 1:
        push_integer(1);
        return 1;
      case 2:
        push_integer(-1);
        return 1;
      case 3:
        push(imaginaryunit);
        return 1;
      case 4:
        push(imaginaryunit);
        negate();
        return 1;
    }
    if (car(p2) === symbol(ADD)) {
      p3 = cdr(p2);
      while (iscons(p3)) {
        n = isquarterturn(car(p3));
        if (n) {
          break;
        }
        p3 = cdr(p3);
      }
      switch (n) {
        case 0:
          return 0;
        case 1:
          push_integer(1);
          break;
        case 2:
          push_integer(-1);
          break;
        case 3:
          push(imaginaryunit);
          break;
        case 4:
          push(imaginaryunit);
          negate();
      }
      push(p2);
      push(car(p3));
      subtract();
      exponential();
      multiply();
      return 1;
    }
    return 0;
  };

  Eval_prime = function() {
    push(cadr(p1));
    Eval();
    return prime();
  };

  prime = function() {
    var n;
    n = 0;
    n = pop_integer();
    if (n < 1 || n > MAXPRIMETAB) {
      stop("prime: Argument out of range.");
    }
    n = primetab[n - 1];
    return push_integer(n);
  };

  power_str = "^";

  stringToBePrinted = "";

  print_str = function(s) {
    return stringToBePrinted += s;
  };

  print_char = function(c) {
    return stringToBePrinted += c;
  };

  collectResultLine = function(p) {
    stringToBePrinted = "";
    print_expr(p);
    return stringToBePrinted;
  };

  printline = function(p) {
    stringToBePrinted = "";
    print_expr(p);
    return console.log(stringToBePrinted);
  };

  print_denom = function(p, d) {
    save();
    p1 = cadr(p);
    p2 = caddr(p);
    if (d === 1 && !isminusone(p2)) {
      print_char('(');
    }
    if (isfraction(p1) || car(p1) === symbol(ADD) || car(p1) === symbol(MULTIPLY) || car(p1) === symbol(POWER) || lessp(p1, zero)) {
      print_char('(');
      print_expr(p1);
      print_char(')');
    } else {
      print_expr(p1);
    }
    if (isminusone(p2)) {
      restore();
      return;
    }
    if (test_flag === 0) {
      print_str(power_str);
    } else {
      print_char('^');
    }
    push(p2);
    negate();
    p2 = pop();
    if (isfraction(p2) || car(p2) === symbol(ADD) || car(p2) === symbol(MULTIPLY) || car(p2) === symbol(POWER)) {
      print_char('(');
      print_expr(p2);
      print_char(')');
    } else {
      print_expr(p2);
    }
    if (d === 1) {
      print_char(')');
    }
    return restore();
  };

  print_a_over_b = function(p) {
    var d, doNothing, n;
    flag = 0;
    n = 0;
    d = 0;
    save();
    n = 0;
    d = 0;
    p1 = cdr(p);
    p2 = car(p1);
    if (isrational(p2)) {
      push(p2);
      mp_numerator();
      absval();
      p3 = pop();
      push(p2);
      mp_denominator();
      p4 = pop();
      if (!isplusone(p3)) {
        n++;
      }
      if (!isplusone(p4)) {
        d++;
      }
      p1 = cdr(p1);
    } else {
      p3 = one;
      p4 = one;
    }
    while (iscons(p1)) {
      p2 = car(p1);
      if (is_denominator(p2)) {
        d++;
      } else {
        n++;
      }
      p1 = cdr(p1);
    }
    if (n === 0) {
      print_char('1');
    } else {
      flag = 0;
      p1 = cdr(p);
      if (isrational(car(p1))) {
        p1 = cdr(p1);
      }
      if (!isplusone(p3)) {
        print_factor(p3);
        flag = 1;
      }
      while (iscons(p1)) {
        p2 = car(p1);
        if (is_denominator(p2)) {
          doNothing = 1;
        } else {
          if (flag) {
            print_multiply_sign();
          }
          print_factor(p2);
          flag = 1;
        }
        p1 = cdr(p1);
      }
    }
    if (test_flag === 0) {
      print_str(" / ");
    } else {
      print_str("/");
    }
    if (d > 1) {
      print_char('(');
    }
    flag = 0;
    p1 = cdr(p);
    if (isrational(car(p1))) {
      p1 = cdr(p1);
    }
    if (!isplusone(p4)) {
      print_factor(p4);
      flag = 1;
    }
    while (iscons(p1)) {
      p2 = car(p1);
      if (is_denominator(p2)) {
        if (flag) {
          print_multiply_sign();
        }
        print_denom(p2, d);
        flag = 1;
      }
      p1 = cdr(p1);
    }
    if (d > 1) {
      print_char(')');
    }
    return restore();
  };

  print_expr = function(p) {
    var results;
    if (isadd(p)) {
      p = cdr(p);
      if (sign_of_term(car(p)) === '-') {
        print_str("-");
      }
      print_term(car(p));
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        if (sign_of_term(car(p)) === '+') {
          if (test_flag === 0) {
            print_str(" + ");
          } else {
            print_str("+");
          }
        } else {
          if (test_flag === 0) {
            print_str(" - ");
          } else {
            print_str("-");
          }
        }
        print_term(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else {
      if (sign_of_term(p) === '-') {
        print_str("-");
      }
      return print_term(p);
    }
  };

  sign_of_term = function(p) {
    if (car(p) === symbol(MULTIPLY) && isnum(cadr(p)) && lessp(cadr(p), zero)) {
      return '-';
    } else if (isnum(p) && lessp(p, zero)) {
      return '-';
    } else {
      return '+';
    }
  };

  print_term = function(p) {
    var results;
    if (car(p) === symbol(MULTIPLY) && any_denominators(p)) {
      print_a_over_b(p);
      return;
    }
    if (car(p) === symbol(MULTIPLY)) {
      p = cdr(p);
      if (isminusone(car(p))) {
        p = cdr(p);
      }
      print_factor(car(p));
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        print_multiply_sign();
        print_factor(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else {
      return print_factor(p);
    }
  };

  print_subexpr = function(p) {
    print_char('(');
    print_expr(p);
    return print_char(')');
  };

  print_factorial_function = function(p) {
    p = cadr(p);
    if (car(p) === symbol(ADD) || car(p) === symbol(MULTIPLY) || car(p) === symbol(POWER) || car(p) === symbol(FACTORIAL)) {
      print_subexpr(p);
    } else {
      print_expr(p);
    }
    return print_char('!');
  };

  print_tensor = function(p) {
    return print_tensor_inner(p, 0, 0);
  };

  print_tensor_inner = function(p, j, k) {
    var ac, i, ref1;
    i = 0;
    print_str("(");
    for (i = ac = 0, ref1 = p.tensor.dim[j]; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      if (j + 1 === p.tensor.ndim) {
        print_expr(p.tensor.elem[k]);
        k++;
      } else {
        k = print_tensor_inner(p, j + 1, k);
      }
      if (i + 1 < p.tensor.dim[j]) {
        if (test_flag === 0) {
          print_str(",");
        } else {
          print_str(",");
        }
      }
    }
    print_str(")");
    return k;
  };

  print_factor = function(p) {
    if (isnum(p)) {
      print_number(p);
      return;
    }
    if (isstr(p)) {
      print_str("\"");
      print_str(p.str);
      print_str("\"");
      return;
    }
    if (istensor(p)) {
      print_tensor(p);
      return;
    }
    if (isadd(p) || car(p) === symbol(MULTIPLY)) {
      print_str("(");
      print_expr(p);
      print_str(")");
      return;
    }
    if (car(p) === symbol(POWER)) {
      if (cadr(p) === symbol(E)) {
        print_str("exp(");
        print_expr(caddr(p));
        print_str(")");
        return;
      }
      if (isminusone(caddr(p))) {
        if (test_flag === 0) {
          print_str("1 / ");
        } else {
          print_str("1/");
        }
        if (iscons(cadr(p))) {
          print_str("(");
          print_expr(cadr(p));
          print_str(")");
        } else {
          print_expr(cadr(p));
        }
        return;
      }
      if (isadd(cadr(p)) || caadr(p) === symbol(MULTIPLY) || caadr(p) === symbol(POWER) || isnegativenumber(cadr(p))) {
        print_str("(");
        print_expr(cadr(p));
        print_str(")");
      } else if (isnum(cadr(p)) && (lessp(cadr(p), zero) || isfraction(cadr(p)))) {
        print_str("(");
        print_factor(cadr(p));
        print_str(")");
      } else {
        print_factor(cadr(p));
      }
      if (test_flag === 0) {
        print_str(power_str);
      } else {
        print_str("^");
      }
      if (iscons(caddr(p)) || isfraction(caddr(p)) || (isnum(caddr(p)) && lessp(caddr(p), zero))) {
        print_str("(");
        print_expr(caddr(p));
        print_str(")");
      } else {
        print_factor(caddr(p));
      }
      return;
    }
    if (car(p) === symbol(INDEX) && issymbol(cadr(p))) {
      print_index_function(p);
      return;
    }
    if (car(p) === symbol(FACTORIAL)) {
      print_factorial_function(p);
      return;
    }
    if (iscons(p)) {
      print_factor(car(p));
      p = cdr(p);
      print_str("(");
      if (iscons(p)) {
        print_expr(car(p));
        p = cdr(p);
        while (iscons(p)) {
          if (test_flag === 0) {
            print_str(",");
          } else {
            print_str(",");
          }
          print_expr(car(p));
          p = cdr(p);
        }
      }
      print_str(")");
      return;
    }
    if (p === symbol(DERIVATIVE)) {
      return print_char('d');
    } else if (p === symbol(E)) {
      return print_str("exp(1)");
    } else if (p === symbol(PI)) {
      return print_str("pi");
    } else {
      return print_str(get_printname(p));
    }
  };

  print1 = function(p, accumulator) {
    var topLevelCall;
    topLevelCall = false;
    if (accumulator == null) {
      topLevelCall = true;
      accumulator = "";
    }
    switch (p.k) {
      case CONS:
        accumulator += "(";
        accumulator = print1(car(p), accumulator);
        if (p === cdr(p)) {
          console.log("oh no recursive!");
          debugger;
        }
        p = cdr(p);
        while (iscons(p)) {
          accumulator += " ";
          accumulator = print1(car(p), accumulator);
          p = cdr(p);
          if (p === cdr(p)) {
            console.log("oh no recursive!");
            debugger;
          }
        }
        if (p !== symbol(NIL)) {
          accumulator += " . ";
          accumulator = print1(p, accumulator);
        }
        accumulator += ")";
        break;
      case STR:
        accumulator += p.str;
        break;
      case NUM:
      case DOUBLE:
        accumulator = print_number(p, accumulator);
        break;
      case SYM:
        accumulator += get_printname(p);
        break;
      default:
        accumulator += "<tensor>";
    }
    if (topLevelCall) {
      return console.log(accumulator);
    } else {
      return accumulator;
    }
  };

  print_multiply_sign = function() {
    if (test_flag === 0) {
      return print_str(" ");
    } else {
      return print_str("*");
    }
  };

  is_denominator = function(p) {
    if (car(p) === symbol(POWER) && cadr(p) !== symbol(E) && isnegativeterm(caddr(p))) {
      return 1;
    } else {
      return 0;
    }
  };

  any_denominators = function(p) {
    var q;
    p = cdr(p);
    while (iscons(p)) {
      q = car(p);
      if (is_denominator(q)) {
        return 1;
      }
      p = cdr(p);
    }
    return 0;
  };

  Eval_product = function() {
    var ac, i, j, k, ref1, ref2;
    i = 0;
    j = 0;
    k = 0;
    p6 = cadr(p1);
    if (!issymbol(p6)) {
      stop("product: 1st arg?");
    }
    push(caddr(p1));
    Eval();
    j = pop_integer();
    if (j === 0x80000000) {
      stop("product: 2nd arg?");
    }
    push(cadddr(p1));
    Eval();
    k = pop_integer();
    if (k === 0x80000000) {
      stop("product: 3rd arg?");
    }
    p1 = caddddr(p1);
    p4 = get_binding(p6);
    p3 = get_arglist(p6);
    push_integer(1);
    for (i = ac = ref1 = j, ref2 = k; ref1 <= ref2 ? ac <= ref2 : ac >= ref2; i = ref1 <= ref2 ? ++ac : --ac) {
      push_integer(i);
      p5 = pop();
      set_binding(p6, p5);
      push(p1);
      Eval();
      multiply();
    }
    return set_binding_and_arglist(p6, p4, p3);
  };

  qadd = function() {
    var a, ab, b, ba, c;
    save();
    p2 = pop();
    p1 = pop();
    ab = mmul(p1.q.a, p2.q.b);
    ba = mmul(p1.q.b, p2.q.a);
    a = madd(ab, ba);
    if (MZERO(a)) {
      push(zero);
      restore();
      return;
    }
    b = mmul(p1.q.b, p2.q.b);
    c = mgcd(a, b);
    c = makeSignSameAs(c, b);
    p1 = new U();
    p1.k = NUM;
    p1.q.a = mdiv(a, c);
    p1.q.b = mdiv(b, c);
    push(p1);
    return restore();
  };

  qdiv = function() {
    var aa, bb, c;
    save();
    p2 = pop();
    p1 = pop();
    if (MZERO(p2.q.a)) {
      stop("divide by zero");
    }
    if (MZERO(p1.q.a)) {
      push(zero);
      restore();
      return;
    }
    aa = mmul(p1.q.a, p2.q.b);
    bb = mmul(p1.q.b, p2.q.a);
    c = mgcd(aa, bb);
    c = makeSignSameAs(c, bb);
    p1 = new U();
    p1.k = NUM;
    p1.q.a = mdiv(aa, c);
    p1.q.b = mdiv(bb, c);
    push(p1);
    return restore();
  };

  qmul = function() {
    var aa, bb, c;
    save();
    p2 = pop();
    p1 = pop();
    if (MZERO(p1.q.a) || MZERO(p2.q.a)) {
      push(zero);
      restore();
      return;
    }
    aa = mmul(p1.q.a, p2.q.a);
    bb = mmul(p1.q.b, p2.q.b);
    c = mgcd(aa, bb);
    c = makeSignSameAs(c, bb);
    p1 = new U();
    p1.k = NUM;
    p1.q.a = mdiv(aa, c);
    p1.q.b = mdiv(bb, c);
    push(p1);
    return restore();
  };

  qpow = function() {
    save();
    qpowf();
    return restore();
  };

  qpowf = function() {
    var a, b, expo, t, x, y;
    expo = 0;
    p2 = pop();
    p1 = pop();
    if (isplusone(p1) || iszero(p2)) {
      push_integer(1);
      return;
    }
    if (iszero(p1)) {
      if (isnegativenumber(p2)) {
        stop("divide by zero");
      }
      push(zero);
      return;
    }
    if (isplusone(p2)) {
      push(p1);
      return;
    }
    if (isinteger(p2)) {
      push(p2);
      expo = pop_integer();
      if (expo === 0x80000000) {
        push_symbol(POWER);
        push(p1);
        push(p2);
        list(3);
        return;
      }
      x = mpow(p1.q.a, Math.abs(expo));
      y = mpow(p1.q.b, Math.abs(expo));
      if (expo < 0) {
        t = x;
        x = y;
        y = t;
        x = makeSignSameAs(x, y);
        y = makePositive(y);
      }
      p3 = new U();
      p3.k = NUM;
      p3.q.a = x;
      p3.q.b = y;
      push(p3);
      return;
    }
    if (isminusone(p1)) {
      push(p2);
      normalize_angle();
      return;
    }
    if (isnegativenumber(p1)) {
      push(p1);
      negate();
      push(p2);
      qpow();
      push_integer(-1);
      push(p2);
      qpow();
      multiply();
      return;
    }
    if (!isinteger(p1)) {
      push(p1);
      mp_numerator();
      push(p2);
      qpow();
      push(p1);
      mp_denominator();
      push(p2);
      negate();
      qpow();
      multiply();
      return;
    }
    if (is_small_integer(p1)) {
      push(p1);
      push(p2);
      quickfactor();
      return;
    }
    if (!p2.q.a.isSmall || !p2.q.b.isSmall) {
      push_symbol(POWER);
      push(p1);
      push(p2);
      list(3);
      return;
    }
    a = p2.q.a;
    b = p2.q.b;
    x = mroot(p1.q.a, b);
    if (x === 0) {
      push_symbol(POWER);
      push(p1);
      push(p2);
      list(3);
      return;
    }
    y = mpow(x, a);
    p3 = new U();
    p3.k = NUM;
    if (p2.q.a.isNegative()) {
      p3.q.a = bigInt(1);
      p3.q.b = y;
    } else {
      p3.q.a = y;
      p3.q.b = bigInt(1);
    }
    return push(p3);
  };

  normalize_angle = function() {
    save();
    p1 = pop();
    if (isinteger(p1)) {
      if (p1.q.a.isOdd()) {
        push_integer(-1);
      } else {
        push_integer(1);
      }
      restore();
      return;
    }
    push(p1);
    bignum_truncate();
    p2 = pop();
    if (isnegativenumber(p1)) {
      push(p2);
      push_integer(-1);
      add();
      p2 = pop();
    }
    push(p1);
    push(p2);
    subtract();
    p3 = pop();
    push_symbol(POWER);
    push_integer(-1);
    push(p3);
    list(3);
    if (p2.q.a.isOdd()) {
      negate();
    }
    return restore();
  };

  is_small_integer = function(p) {
    return p.q.a.isSmall;
  };

  quickfactor = function() {
    var ac, h, i, n, ref1, stackIndex;
    i = 0;
    save();
    p2 = pop();
    p1 = pop();
    h = tos;
    push(p1);
    factor_small_number();
    n = tos - h;
    stackIndex = h;
    for (i = ac = 0, ref1 = n; ac < ref1; i = ac += 2) {
      push(stack[stackIndex + i]);
      push(stack[stackIndex + i + 1]);
      push(p2);
      multiply();
      quickpower();
    }
    multiply_all(tos - h - n);
    p1 = pop();
    tos = h;
    push(p1);
    return restore();
  };

  quickpower = function() {
    var expo;
    expo = 0;
    save();
    p2 = pop();
    p1 = pop();
    push(p2);
    bignum_truncate();
    p3 = pop();
    push(p2);
    push(p3);
    subtract();
    p4 = pop();
    if (!iszero(p4)) {
      push_symbol(POWER);
      push(p1);
      push(p4);
      list(3);
    }
    push(p3);
    expo = pop_integer();
    if (expo === 0x80000000) {
      push_symbol(POWER);
      push(p1);
      push(p3);
      list(3);
      restore();
      return;
    }
    if (expo === 0) {
      restore();
      return;
    }
    push(p1);
    bignum_power_number(expo);
    return restore();
  };

  Eval_quotient = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    push(cadddr(p1));
    Eval();
    p1 = pop();
    if (p1 === symbol(NIL)) {
      p1 = symbol(SYMBOL_X);
    }
    push(p1);
    return divpoly();
  };

  divpoly = function() {
    var ac, dividend, divisor, h, i, m, n, ref1, x;
    h = 0;
    i = 0;
    m = 0;
    n = 0;
    x = 0;
    save();
    p3 = pop();
    p2 = pop();
    p1 = pop();
    h = tos;
    dividend = tos;
    push(p1);
    push(p3);
    m = coeff() - 1;
    divisor = tos;
    push(p2);
    push(p3);
    n = coeff() - 1;
    x = m - n;
    push_integer(0);
    p5 = pop();
    while (x >= 0) {
      push(stack[dividend + m]);
      push(stack[divisor + n]);
      divide();
      p4 = pop();
      for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac <= ref1 : ac >= ref1; i = 0 <= ref1 ? ++ac : --ac) {
        push(stack[dividend + x + i]);
        push(stack[divisor + i]);
        push(p4);
        multiply();
        subtract();
        stack[dividend + x + i] = pop();
      }
      push(p5);
      push(p4);
      push(p3);
      push_integer(x);
      power();
      multiply();
      add();
      p5 = pop();
      m--;
      x--;
    }
    tos = h;
    push(p5);
    return restore();
  };

  DEBUG = 0;

  Eval_rationalize = function() {
    push(cadr(p1));
    Eval();
    return rationalize();
  };

  rationalize = function() {
    var x;
    x = expanding;
    save();
    yyrationalize();
    restore();
    return expanding = x;
  };

  yyrationalize = function() {
    p1 = pop();
    if (istensor(p1)) {
      __rationalize_tensor();
      return;
    }
    expanding = 0;
    if (car(p1) !== symbol(ADD)) {
      push(p1);
      return;
    }
    if (DEBUG) {
      printf("rationalize: this is the input expr:\n");
      printline(p1);
    }
    push(one);
    multiply_denominators(p1);
    p2 = pop();
    if (DEBUG) {
      printf("rationalize: this is the common denominator:\n");
      printline(p2);
    }
    push(zero);
    p3 = cdr(p1);
    while (iscons(p3)) {
      push(p2);
      push(car(p3));
      multiply();
      add();
      p3 = cdr(p3);
    }
    if (DEBUG) {
      printf("rationalize: original expr times common denominator:\n");
      printline(stack[tos - 1]);
    }
    Condense();
    if (DEBUG) {
      printf("rationalize: after factoring:\n");
      printline(stack[tos - 1]);
    }
    push(p2);
    divide();
    if (DEBUG) {
      printf("rationalize: after dividing by common denom. (and we're done):\n");
      return printline(stack[tos - 1]);
    }
  };

  multiply_denominators = function(p) {
    var results;
    if (car(p) === symbol(ADD)) {
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        multiply_denominators_term(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else {
      return multiply_denominators_term(p);
    }
  };

  multiply_denominators_term = function(p) {
    var results;
    if (car(p) === symbol(MULTIPLY)) {
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        multiply_denominators_factor(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else {
      return multiply_denominators_factor(p);
    }
  };

  multiply_denominators_factor = function(p) {
    if (car(p) !== symbol(POWER)) {
      return;
    }
    push(p);
    p = caddr(p);
    if (isnegativenumber(p)) {
      inverse();
      __lcm();
      return;
    }
    if (car(p) === symbol(MULTIPLY) && isnegativenumber(cadr(p))) {
      inverse();
      __lcm();
      return;
    }
    return pop();
  };

  __rationalize_tensor = function() {
    var ac, i, n, ref1;
    i = 0;
    push(p1);
    Eval();
    p1 = pop();
    if (!istensor(p1)) {
      push(p1);
      return;
    }
    n = p1.tensor.nelem;
    for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      push(p1.tensor.elem[i]);
      rationalize();
      p1.tensor.elem[i] = pop();
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    return push(p1);
  };

  __lcm = function() {
    save();
    p1 = pop();
    p2 = pop();
    push(p1);
    push(p2);
    multiply();
    push(p1);
    push(p2);
    gcd();
    divide();
    return restore();
  };


  /*
   Returns the real part of complex z
  
  	z		real(z)
  	-		-------
  
  	a + i b		a
  
  	exp(i a)	cos(a)
   */

  Eval_real = function() {
    push(cadr(p1));
    Eval();
    return real();
  };

  real = function() {
    save();
    rect();
    p1 = pop();
    push(p1);
    push(p1);
    conjugate();
    add();
    push_integer(2);
    divide();
    return restore();
  };


  /*
  Convert complex z to rectangular form
  
  	Input:		push	z
  
  	Output:		Result on stack
   */

  Eval_rect = function() {
    push(cadr(p1));
    Eval();
    return rect();
  };

  rect = function() {
    save();
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      push_integer(0);
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        rect();
        add();
        p1 = cdr(p1);
      }
    } else {
      push(p1);
      mag();
      push(p1);
      arg();
      p1 = pop();
      push(p1);
      cosine();
      push(imaginaryunit);
      push(p1);
      sine();
      multiply();
      add();
      multiply();
    }
    return restore();
  };

  Eval_roots = function() {
    p2 = cadr(p1);
    if (car(p2) === symbol(SETQ) || car(p2) === symbol(TESTEQ)) {
      push(cadr(p2));
      Eval();
      push(caddr(p2));
      Eval();
      subtract();
    } else {
      push(p2);
      Eval();
      p2 = pop();
      if (car(p2) === symbol(SETQ) || car(p2) === symbol(TESTEQ)) {
        push(cadr(p2));
        Eval();
        push(caddr(p2));
        Eval();
        subtract();
      } else {
        push(p2);
      }
    }
    push(caddr(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      guess();
    } else {
      push(p2);
    }
    p2 = pop();
    p1 = pop();
    if (!ispoly(p1, p2)) {
      stop("roots: 1st argument is not a polynomial");
    }
    push(p1);
    push(p2);
    return roots();
  };

  hasImaginaryCoeff = function() {
    var ac, h, i, imaginaryCoefficients, k, ref1;
    polycoeff = tos;
    push(p1);
    push(p2);
    k = coeff();
    imaginaryCoefficients = false;
    h = tos;
    for (i = ac = ref1 = k; ac > 0; i = ac += -1) {
      if (iscomplexnumber(stack[tos - i])) {
        imaginaryCoefficients = true;
        break;
      }
    }
    tos -= k;
    return imaginaryCoefficients;
  };

  roots = function() {
    var ac, h, i, n, ref1;
    h = 0;
    i = 0;
    n = 0;
    h = tos - 2;
    roots2();
    n = tos - h;
    if (n === 0) {
      stop("roots: the polynomial is not factorable, try nroots");
    }
    if (n === 1) {
      return;
    }
    sort_stack(n);
    save();
    p1 = alloc_tensor(n);
    p1.tensor.ndim = 1;
    p1.tensor.dim[0] = n;
    for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p1.tensor.elem[i] = stack[h + i];
    }
    tos = h;
    push(p1);
    return restore();
  };

  roots2 = function() {
    save();
    p2 = pop();
    p1 = pop();
    push(p1);
    push(p2);
    if (!hasImaginaryCoeff()) {
      factorpoly();
      p1 = pop();
    } else {
      pop();
      pop();
    }
    if (car(p1) === symbol(MULTIPLY)) {
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        push(p2);
        roots3();
        p1 = cdr(p1);
      }
    } else {
      push(p1);
      push(p2);
      roots3();
    }
    return restore();
  };

  roots3 = function() {
    save();
    p2 = pop();
    p1 = pop();
    if (car(p1) === symbol(POWER) && ispoly(cadr(p1), p2) && isposint(caddr(p1))) {
      push(cadr(p1));
      push(p2);
      mini_solve();
    } else if (ispoly(p1, p2)) {
      push(p1);
      push(p2);
      mini_solve();
    }
    return restore();
  };

  mini_solve = function() {
    var C_CHECKED_AS_NOT_ZERO, R_18_a_b_c_d, R_27_a2_d, R_2_b3, R_3_a, R_3_a_C, R_3_a_c, R_4_DELTA03, R_6_a, R_6_a_C, R_C, R_C_over_3a, R_C_simplified_toCheckIfZero, R_DELTA0, R_DELTA0_toBeCheckedIfZero, R_DELTA1, R_Q, R_a_b_c, R_a_c, R_b2, R_b2_c2, R_b3, R_c2, R_c3, R_determinant, R_m27_a2_d2, R_m4_a_c3, R_m4_b3_d, R_m9_a_b_c, R_m_b_over_3a, flipSignOFQSoCIsNotZero, i_sqrt3, n, one_minus_i_sqrt3, one_plus_i_sqrt3, root_solution;
    n = 0;
    save();
    p2 = pop();
    p1 = pop();
    push(p1);
    push(p2);
    n = coeff();
    if (n === 2) {
      p3 = pop();
      p4 = pop();
      push(p4);
      push(p3);
      divide();
      negate();
      restore();
      return;
    }
    if (n === 3) {
      p3 = pop();
      p4 = pop();
      p5 = pop();
      push(p4);
      push(p4);
      multiply();
      push_integer(4);
      push(p3);
      multiply();
      push(p5);
      multiply();
      subtract();
      push_rational(1, 2);
      power();
      p6 = pop();
      push(p6);
      push(p4);
      subtract();
      push(p3);
      divide();
      push_rational(1, 2);
      multiply();
      push(p6);
      push(p4);
      add();
      negate();
      push(p3);
      divide();
      push_rational(1, 2);
      multiply();
      restore();
      return;
    }
    if (n === 4) {
      p3 = pop();
      p4 = pop();
      p5 = pop();
      p6 = pop();
      push(p5);
      push(p5);
      multiply();
      R_c2 = pop();
      push(R_c2);
      push(p5);
      multiply();
      R_c3 = pop();
      push(p4);
      push(p4);
      multiply();
      R_b2 = pop();
      push(R_b2);
      push(p4);
      multiply();
      R_b3 = pop();
      push(R_b3);
      push(p6);
      push_integer(-4);
      multiply();
      multiply();
      R_m4_b3_d = pop();
      push(R_b3);
      push_integer(2);
      multiply();
      R_2_b3 = pop();
      push_integer(3);
      push(p3);
      multiply();
      R_3_a = pop();
      push(R_3_a);
      push_integer(9);
      multiply();
      push(p3);
      multiply();
      push(p6);
      multiply();
      R_27_a2_d = pop();
      push(R_27_a2_d);
      push(p6);
      multiply();
      negate();
      R_m27_a2_d2 = pop();
      push(R_3_a);
      push_integer(2);
      multiply();
      R_6_a = pop();
      push(p3);
      push(p5);
      multiply();
      R_a_c = pop();
      push(R_a_c);
      push(p4);
      multiply();
      R_a_b_c = pop();
      push(R_a_c);
      push_integer(3);
      multiply();
      R_3_a_c = pop();
      push_integer(-4);
      push(p3);
      push(R_c3);
      multiply();
      multiply();
      R_m4_a_c3 = pop();
      push(R_a_b_c);
      push_integer(9);
      multiply();
      negate();
      R_m9_a_b_c = pop();
      push(R_m9_a_b_c);
      push(p6);
      push_integer(-2);
      multiply();
      multiply();
      R_18_a_b_c_d = pop();
      push(R_b2);
      push(R_3_a_c);
      subtract();
      R_DELTA0 = pop();
      push(R_b2);
      push(R_c2);
      multiply();
      R_b2_c2 = pop();
      push(R_DELTA0);
      push_integer(3);
      power();
      push_integer(4);
      multiply();
      R_4_DELTA03 = pop();
      push(R_DELTA0);
      simplify();
      Eval();
      yyfloat();
      Eval();
      absval();
      R_DELTA0_toBeCheckedIfZero = pop();
      push(R_18_a_b_c_d);
      push(R_m4_b3_d);
      push(R_b2_c2);
      push(R_m4_a_c3);
      push(R_m27_a2_d2);
      add();
      add();
      add();
      add();
      simplify();
      Eval();
      yyfloat();
      Eval();
      absval();
      R_determinant = pop();
      push(R_2_b3);
      push(R_m9_a_b_c);
      push(R_27_a2_d);
      add();
      add();
      R_DELTA1 = pop();
      push(R_DELTA1);
      push_integer(2);
      power();
      push(R_4_DELTA03);
      subtract();
      push_rational(1, 2);
      power();
      R_Q = pop();
      push(p4);
      negate();
      push(R_3_a);
      divide();
      R_m_b_over_3a = pop();
      if (iszero(R_determinant)) {
        if (iszero(R_DELTA0_toBeCheckedIfZero)) {
          push(R_m_b_over_3a);
          restore();
          return;
        } else {
          push(p3);
          push(p6);
          push_integer(9);
          multiply();
          multiply();
          push(p4);
          push(p5);
          multiply();
          subtract();
          push(R_DELTA0);
          push_integer(2);
          multiply();
          divide();
          root_solution = pop();
          push(root_solution);
          push(root_solution);
          push(R_a_b_c);
          push_integer(4);
          multiply();
          push(p3);
          push(p3);
          push(p6);
          push_integer(9);
          multiply();
          multiply();
          multiply();
          negate();
          push(R_b3);
          negate();
          add();
          add();
          push(p3);
          push(R_DELTA0);
          multiply();
          divide();
          restore();
          return;
        }
      }
      C_CHECKED_AS_NOT_ZERO = false;
      flipSignOFQSoCIsNotZero = false;
      while (!C_CHECKED_AS_NOT_ZERO) {
        push(R_Q);
        if (flipSignOFQSoCIsNotZero) {
          negate();
        }
        push(R_DELTA1);
        add();
        push_rational(1, 2);
        multiply();
        push_rational(1, 3);
        power();
        R_C = pop();
        push(R_C);
        simplify();
        Eval();
        yyfloat();
        Eval();
        absval();
        R_C_simplified_toCheckIfZero = pop();
        if (iszero(R_C_simplified_toCheckIfZero)) {
          flipSignOFQSoCIsNotZero = true;
        } else {
          C_CHECKED_AS_NOT_ZERO = true;
        }
      }
      push(R_C);
      push(R_3_a);
      multiply();
      R_3_a_C = pop();
      push(R_3_a_C);
      push_integer(2);
      multiply();
      R_6_a_C = pop();
      push(imaginaryunit);
      push_integer(3);
      push_rational(1, 2);
      power();
      multiply();
      i_sqrt3 = pop();
      push_integer(1);
      push(i_sqrt3);
      add();
      one_plus_i_sqrt3 = pop();
      push_integer(1);
      push(i_sqrt3);
      subtract();
      one_minus_i_sqrt3 = pop();
      push(R_C);
      push(R_3_a);
      divide();
      R_C_over_3a = pop();
      push(R_m_b_over_3a);
      push(R_C_over_3a);
      negate();
      push(R_DELTA0);
      push(R_3_a_C);
      divide();
      negate();
      add();
      add();
      simplify();
      push(R_m_b_over_3a);
      push(R_C_over_3a);
      push(one_plus_i_sqrt3);
      multiply();
      push_integer(2);
      divide();
      push(one_minus_i_sqrt3);
      push(R_DELTA0);
      multiply();
      push(R_6_a_C);
      divide();
      add();
      add();
      simplify();
      push(R_m_b_over_3a);
      push(R_C_over_3a);
      push(one_minus_i_sqrt3);
      multiply();
      push_integer(2);
      divide();
      push(one_plus_i_sqrt3);
      push(R_DELTA0);
      multiply();
      push(R_6_a_C);
      divide();
      add();
      add();
      simplify();
      restore();
      return;
    }
    tos -= n;
    return restore();
  };

  T_INTEGER = 1001;

  T_DOUBLE = 1002;

  T_SYMBOL = 1003;

  T_FUNCTION = 1004;

  T_NEWLINE = 1006;

  T_STRING = 1007;

  T_GTEQ = 1008;

  T_LTEQ = 1009;

  T_EQ = 1010;

  token = "";

  newline_flag = 0;

  meta_mode = 0;

  input_str = 0;

  scan_str = 0;

  token_str = 0;

  token_buf = 0;

  scanned = "";

  scan = function(s) {
    if (DEBUG) {
      console.log("#### scanning " + s);
    }
    scanned = s;
    meta_mode = 0;
    expanding++;
    input_str = 0;
    scan_str = 0;
    get_next_token();
    if (token === "") {
      push(symbol(NIL));
      expanding--;
      return 0;
    }
    scan_stmt();
    expanding--;
    return token_str - input_str;
  };

  scan_meta = function(s) {
    scanned = s;
    meta_mode = 1;
    expanding++;
    input_str = 0;
    scan_str = 0;
    get_next_token();
    if (token === "") {
      push(symbol(NIL));
      expanding--;
      return 0;
    }
    scan_stmt();
    expanding--;
    return token_str - input_str;
  };

  scan_stmt = function() {
    scan_relation();
    if (token === '=') {
      get_next_token();
      push_symbol(SETQ);
      swap();
      scan_relation();
      return list(3);
    }
  };

  scan_relation = function() {
    scan_expression();
    switch (token) {
      case T_EQ:
        push_symbol(TESTEQ);
        swap();
        get_next_token();
        scan_expression();
        return list(3);
      case T_LTEQ:
        push_symbol(TESTLE);
        swap();
        get_next_token();
        scan_expression();
        return list(3);
      case T_GTEQ:
        push_symbol(TESTGE);
        swap();
        get_next_token();
        scan_expression();
        return list(3);
      case '<':
        push_symbol(TESTLT);
        swap();
        get_next_token();
        scan_expression();
        return list(3);
      case '>':
        push_symbol(TESTGT);
        swap();
        get_next_token();
        scan_expression();
        return list(3);
    }
  };

  scan_expression = function() {
    var h;
    h = tos;
    switch (token) {
      case '+':
        get_next_token();
        scan_term();
        break;
      case '-':
        get_next_token();
        scan_term();
        negate();
        break;
      default:
        scan_term();
    }
    while (newline_flag === 0 && (token === '+' || token === '-')) {
      if (token === '+') {
        get_next_token();
        scan_term();
      } else {
        get_next_token();
        scan_term();
        negate();
      }
    }
    if (tos - h > 1) {
      list(tos - h);
      push_symbol(ADD);
      swap();
      return cons();
    }
  };

  is_factor = function() {
    switch (token) {
      case '*':
      case '/':
        return 1;
      case '(':
      case T_SYMBOL:
      case T_FUNCTION:
      case T_INTEGER:
      case T_DOUBLE:
      case T_STRING:
        if (newline_flag) {
          scan_str = token_str;
          return 0;
        } else {
          return 1;
        }
    }
    return 0;
  };

  scan_term = function() {
    var h;
    h = tos;
    scan_power();
    if (tos > h && isrational(stack[tos - 1]) && equaln(stack[tos - 1], 1)) {
      pop();
    }
    while (is_factor()) {
      if (token === '*') {
        get_next_token();
        scan_power();
      } else if (token === '/') {
        get_next_token();
        scan_power();
        inverse();
      } else {
        scan_power();
      }
      if (tos > h + 1 && isnum(stack[tos - 2]) && isnum(stack[tos - 1])) {
        multiply();
      }
      if (tos > h && isrational(stack[tos - 1]) && equaln(stack[tos - 1], 1)) {
        pop();
      }
    }
    if (h === tos) {
      return push_integer(1);
    } else if (tos - h > 1) {
      list(tos - h);
      push_symbol(MULTIPLY);
      swap();
      return cons();
    }
  };

  scan_power = function() {
    scan_factor();
    if (token === '^') {
      get_next_token();
      push_symbol(POWER);
      swap();
      scan_power();
      return list(3);
    }
  };

  scan_factor = function() {
    var h, results;
    h = tos;
    if (token === '(') {
      scan_subexpr();
    } else if (token === T_SYMBOL) {
      scan_symbol();
    } else if (token === T_FUNCTION) {
      scan_function_call();
    } else if (token === T_INTEGER) {
      bignum_scan_integer(token_buf);
      get_next_token();
    } else if (token === T_DOUBLE) {
      bignum_scan_float(token_buf);
      get_next_token();
    } else if (token === T_STRING) {
      scan_string();
    } else {
      scan_error("syntax error");
    }
    if (token === '[') {
      get_next_token();
      push_symbol(INDEX);
      swap();
      scan_expression();
      while (token === ',') {
        get_next_token();
        scan_expression();
      }
      if (token !== ']') {
        scan_error("] expected");
      }
      get_next_token();
      list(tos - h);
    }
    results = [];
    while (token === '!') {
      get_next_token();
      push_symbol(FACTORIAL);
      swap();
      results.push(list(2));
    }
    return results;
  };

  scan_symbol = function() {
    if (token !== T_SYMBOL) {
      scan_error("symbol expected");
    }
    if (meta_mode && token_buf.length === 1) {
      switch (token_buf[0]) {
        case 'a':
          push(symbol(METAA));
          break;
        case 'b':
          push(symbol(METAB));
          break;
        case 'x':
          push(symbol(METAX));
          break;
        default:
          push(usr_symbol(token_buf));
      }
    } else {
      push(usr_symbol(token_buf));
    }
    return get_next_token();
  };

  scan_string = function() {
    new_string(token_buf);
    return get_next_token();
  };

  scan_function_call = function() {
    var n, p;
    n = 1;
    p = new U();
    p = usr_symbol(token_buf);
    push(p);
    get_next_token();
    get_next_token();
    if (token !== ')') {
      scan_stmt();
      n++;
      while (token === ',') {
        get_next_token();
        scan_stmt();
        n++;
      }
    }
    if (token !== ')') {
      scan_error(") expected");
    }
    get_next_token();
    return list(n);
  };

  scan_subexpr = function() {
    var n;
    n = 0;
    if (token !== '(') {
      scan_error("( expected");
    }
    get_next_token();
    scan_stmt();
    if (token === ',') {
      n = 1;
      while (token === ',') {
        get_next_token();
        scan_stmt();
        n++;
      }
      build_tensor(n);
    }
    if (token !== ')') {
      scan_error(") expected");
    }
    return get_next_token();
  };

  scan_error = function(errmsg) {
    errorMessage = "";
    while (input_str !== scan_str) {
      if ((scanned[input_str] === '\n' || scanned[input_str] === '\r') && input_str + 1 === scan_str) {
        break;
      }
      errorMessage += scanned[input_str++];
    }
    errorMessage += " ? ";
    while (scanned[input_str] && (scanned[input_str] !== '\n' && scanned[input_str] !== '\r')) {
      errorMessage += scanned[input_str++];
    }
    errorMessage += '\n';
    return stop(errmsg);
  };

  build_tensor = function(n) {
    var ac, i, ref1;
    i = 0;
    save();
    p2 = alloc_tensor(n);
    p2.tensor.ndim = 1;
    p2.tensor.dim[0] = n;
    for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p2.tensor.elem[i] = stack[tos - n + i];
    }
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    tos -= n;
    push(p2);
    return restore();
  };

  get_next_token = function() {
    newline_flag = 0;
    while (1.) {
      get_token();
      if (token !== T_NEWLINE) {
        break;
      }
      newline_flag = 1;
    }
    if (DEBUG) {
      return console.log("get_next_token token: " + token);
    }
  };

  get_token = function() {
    while (isspace(scanned[scan_str])) {
      if (scanned[scan_str] === '\n' || scanned[scan_str] === '\r') {
        token = T_NEWLINE;
        scan_str++;
        return;
      }
      scan_str++;
    }
    token_str = scan_str;
    if (scan_str === scanned.length) {
      token = "";
      return;
    }
    if (isdigit(scanned[scan_str]) || scanned[scan_str] === '.') {
      while (isdigit(scanned[scan_str])) {
        scan_str++;
      }
      if (scanned[scan_str] === '.') {
        scan_str++;
        while (isdigit(scanned[scan_str])) {
          scan_str++;
        }
        if (scanned[scan_str] === 'e' && (scanned[scan_str + 1] === '+' || scanned[scan_str + 1] === '-' || isdigit(scanned[scan_str + 1]))) {
          scan_str += 2;
          while (isdigit(scanned[scan_str])) {
            scan_str++;
          }
        }
        token = T_DOUBLE;
      } else {
        token = T_INTEGER;
      }
      update_token_buf(token_str, scan_str);
      return;
    }
    if (isalpha(scanned[scan_str])) {
      while (isalnum(scanned[scan_str])) {
        scan_str++;
      }
      if (scanned[scan_str] === '(') {
        token = T_FUNCTION;
      } else {
        token = T_SYMBOL;
      }
      update_token_buf(token_str, scan_str);
      return;
    }
    if (scanned[scan_str] === '"') {
      scan_str++;
      while (scanned[scan_str] !== '"') {
        if (scan_str === scanned.length || scanned[scan_str] === '\n' || scanned[scan_str] === '\r') {
          scan_error("runaway string");
        }
        scan_str++;
      }
      scan_str++;
      token = T_STRING;
      update_token_buf(token_str + 1, scan_str - 1);
      return;
    }
    if (scanned[scan_str] === '#' || scanned[scan_str] === '-' && scanned[scan_str + 1] === '-') {
      while (scanned[scan_str] && scanned[scan_str] !== '\n' && scanned[scan_str] !== '\r') {
        scan_str++;
      }
      if (scanned[scan_str]) {
        scan_str++;
      }
      token = T_NEWLINE;
      return;
    }
    if (scanned[scan_str] === '=' && scanned[scan_str + 1] === '=') {
      scan_str += 2;
      token = T_EQ;
      return;
    }
    if (scanned[scan_str] === '<' && scanned[scan_str + 1] === '=') {
      scan_str += 2;
      token = T_LTEQ;
      return;
    }
    if (scanned[scan_str] === '>' && scanned[scan_str + 1] === '=') {
      scan_str += 2;
      token = T_GTEQ;
      return;
    }
    return token = scanned[scan_str++];
  };

  update_token_buf = function(a, b) {
    return token_buf = scanned.substring(a, b);
  };

  $.scan = scan;

  Eval_sgn = function() {
    push(cadr(p1));
    Eval();
    return sgn();
  };

  sgn = function() {
    save();
    yysgn();
    return restore();
  };

  yysgn = function() {
    p1 = pop();
    if (isdouble(p1)) {
      if (p1.d > 0) {
        push_integer(1);
        return;
      } else {
        if (p1.d === 0) {
          push_integer(1);
          return;
        } else {
          push_integer(-1);
          return;
        }
      }
    }
    if (isrational(p1)) {
      if (MSIGN(mmul(p1.q.a, p1.q.b)) === -1) {
        push_integer(-1);
        return;
      } else {
        if (MZERO(mmul(p1.q.a, p1.q.b))) {
          push_integer(0);
          return;
        } else {
          push_integer(1);
          return;
        }
      }
    }
    if (iscomplexnumber(p1)) {
      push_integer(-1);
      push(p1);
      absval();
      power();
      push(p1);
      multiply();
      return;
    }
    if (isnegativeterm(p1)) {
      push_symbol(SGN);
      push(p1);
      negate();
      list(2);
      push_integer(-1);
      multiply();
      return;
    }

    /*
    	push_integer(2)
    	push(p1)
    	heaviside()
    	multiply()
    	push_integer(-1)
    	add()
     */
    push_symbol(SGN);
    push(p1);
    return list(2);
  };

  Eval_shape = function() {
    push(cadr(p1));
    Eval();
    return shape();
  };

  shape = function() {
    var ac, ad, ai, an, i, ndim, ref1, ref2, t;
    i = 0;
    ndim = 0;
    t = 0;
    ai = [];
    an = [];
    for (i = ac = 0, ref1 = MAXDIM; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      ai[i] = 0;
      an[i] = 0;
    }
    save();
    p1 = pop();
    if (!istensor(p1)) {
      if (!iszero(p1)) {
        stop("transpose: tensor expected, 1st arg is not a tensor");
      }
      push(zero);
      restore();
      return;
    }
    ndim = p1.tensor.ndim;
    p2 = alloc_tensor(ndim);
    p2.tensor.ndim = 1;
    p2.tensor.dim[0] = ndim;
    for (i = ad = 0, ref2 = ndim; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      push_integer(p1.tensor.dim[i]);
      p2.tensor.elem[i] = pop();
    }
    push(p2);
    return restore();
  };


  /*
   Simplify factorials
  
  The following script
  
  	F(n,k) = k binomial(n,k)
  	(F(n,k) + F(n,k-1)) / F(n+1,k)
  
  generates
  
         k! n!             n! (1 - k + n)!              k! n!
   -------------------- + -------------------- - ----------------------
   (-1 + k)! (1 + n)!     (1 + n)! (-k + n)!     k (-1 + k)! (1 + n)!
  
  Simplify each term to get
  
     k       1 - k + n       1
  ------- + ----------- - -------
   1 + n       1 + n       1 + n
  
  Then simplify the sum to get
  
     n
  -------
   1 + n
   */

  Eval_simfac = function() {
    push(cadr(p1));
    Eval();
    return simfac();
  };

  simfac = function() {
    var h;
    h = 0;
    save();
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      h = tos;
      p1 = cdr(p1);
      while (p1 !== symbol(NIL)) {
        push(car(p1));
        simfac_term();
        p1 = cdr(p1);
      }
      add_all(tos - h);
    } else {
      push(p1);
      simfac_term();
    }
    return restore();
  };


  /*
  void
  simfac(void)
  {
  	int h
  	save()
  	p1 = pop()
  	if (car(p1) == symbol(ADD)) {
  		h = tos
  		p1 = cdr(p1)
  		while (p1 != symbol(NIL)) {
  			push(car(p1))
  			simfac_term()
  			p1 = cdr(p1)
  		}
  		addk(tos - h)
  		p1 = pop()
  		if (find(p1, symbol(FACTORIAL))) {
  			push(p1)
  			if (car(p1) == symbol(ADD)) {
  				Condense()
  				simfac_term()
  			}
  		}
  	} else {
  		push(p1)
  		simfac_term()
  	}
  	restore()
  }
  
  #endif
   */

  simfac_term = function() {
    var doNothing, h;
    h = 0;
    save();
    p1 = pop();
    if (car(p1) !== symbol(MULTIPLY)) {
      push(p1);
      restore();
      return;
    }
    h = tos;
    p1 = cdr(p1);
    while (p1 !== symbol(NIL)) {
      push(car(p1));
      p1 = cdr(p1);
    }
    while (yysimfac(h)) {
      doNothing = 1;
    }
    multiply_all_noexpand(tos - h);
    return restore();
  };

  yysimfac = function(h) {
    var ac, ad, i, j, ref1, ref2, ref3, ref4;
    i = 0;
    j = 0;
    for (i = ac = ref1 = h, ref2 = tos; ref1 <= ref2 ? ac < ref2 : ac > ref2; i = ref1 <= ref2 ? ++ac : --ac) {
      p1 = stack[i];
      for (j = ad = ref3 = h, ref4 = tos; ref3 <= ref4 ? ad < ref4 : ad > ref4; j = ref3 <= ref4 ? ++ad : --ad) {
        if (i === j) {
          continue;
        }
        p2 = stack[j];
        if (car(p1) === symbol(FACTORIAL) && car(p2) === symbol(POWER) && isminusone(caddr(p2)) && equal(cadr(p1), cadr(p2))) {
          push(cadr(p1));
          push(one);
          subtract();
          factorial();
          stack[i] = pop();
          stack[j] = one;
          return 1;
        }
        if (car(p2) === symbol(POWER) && isminusone(caddr(p2)) && caadr(p2) === symbol(FACTORIAL) && equal(p1, cadadr(p2))) {
          push(p1);
          push_integer(-1);
          add();
          factorial();
          reciprocate();
          stack[i] = pop();
          stack[j] = one;
          return 1;
        }
        if (car(p2) === symbol(FACTORIAL)) {
          push(p1);
          push(cadr(p2));
          subtract();
          p3 = pop();
          if (isplusone(p3)) {
            push(p1);
            factorial();
            stack[i] = pop();
            stack[j] = one;
            return 1;
          }
        }
        if (car(p1) === symbol(POWER) && isminusone(caddr(p1)) && car(p2) === symbol(POWER) && isminusone(caddr(p2)) && caadr(p2) === symbol(FACTORIAL)) {
          push(cadr(p1));
          push(cadr(cadr(p2)));
          subtract();
          p3 = pop();
          if (isplusone(p3)) {
            push(cadr(p1));
            factorial();
            reciprocate();
            stack[i] = pop();
            stack[j] = one;
            return 1;
          }
        }
        if (car(p1) === symbol(FACTORIAL) && car(p2) === symbol(POWER) && isminusone(caddr(p2)) && caadr(p2) === symbol(FACTORIAL)) {
          push(cadr(p1));
          push(cadr(cadr(p2)));
          subtract();
          p3 = pop();
          if (isplusone(p3)) {
            stack[i] = cadr(p1);
            stack[j] = one;
            return 1;
          }
          if (isminusone(p3)) {
            push(cadr(cadr(p2)));
            reciprocate();
            stack[i] = pop();
            stack[j] = one;
            return 1;
          }
          if (equaln(p3, 2)) {
            stack[i] = cadr(p1);
            push(cadr(p1));
            push_integer(-1);
            add();
            stack[j] = pop();
            return 1;
          }
          if (equaln(p3, -2)) {
            push(cadr(cadr(p2)));
            reciprocate();
            stack[i] = pop();
            push(cadr(cadr(p2)));
            push_integer(-1);
            add();
            reciprocate();
            stack[j] = pop();
            return 1;
          }
        }
      }
    }
    return 0;
  };

  Eval_simplify = function() {
    push(cadr(p1));
    Eval();
    return simplify();
  };

  simplify = function() {
    save();
    simplify_main();
    return restore();
  };

  simplify_main = function() {
    p1 = pop();
    if (istensor(p1)) {
      simplify_tensor();
      return;
    }
    if (Find(p1, symbol(FACTORIAL))) {
      push(p1);
      simfac();
      p2 = pop();
      push(p1);
      rationalize();
      simfac();
      p3 = pop();
      if (count(p2) < count(p3)) {
        p1 = p2;
      } else {
        p1 = p3;
      }
    }
    f1();
    f2();
    f3();
    f4();
    f5();
    f9();
    return push(p1);
  };

  simplify_tensor = function() {
    var ac, ad, i, ref1, ref2;
    i = 0;
    p2 = alloc_tensor(p1.tensor.nelem);
    p2.tensor.ndim = p1.tensor.ndim;
    for (i = ac = 0, ref1 = p1.tensor.ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p2.tensor.dim[i] = p1.tensor.dim[i];
    }
    for (i = ad = 0, ref2 = p1.tensor.nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      push(p1.tensor.elem[i]);
      simplify();
      p2.tensor.elem[i] = pop();
    }
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    if (iszero(p2)) {
      p2 = zero;
    }
    return push(p2);
  };

  count = function(p) {
    var n;
    if (iscons(p)) {
      n = 0;
      while (iscons(p)) {
        n += count(car(p)) + 1;
        p = cdr(p);
      }
    } else {
      n = 1;
    }
    return n;
  };

  f1 = function() {
    if (car(p1) !== symbol(ADD)) {
      return;
    }
    push(p1);
    rationalize();
    p2 = pop();
    if (count(p2) < count(p1)) {
      return p1 = p2;
    }
  };

  f2 = function() {
    if (car(p1) !== symbol(ADD)) {
      return;
    }
    push(p1);
    Condense();
    p2 = pop();
    if (count(p2) <= count(p1)) {
      return p1 = p2;
    }
  };

  f3 = function() {
    push(p1);
    rationalize();
    negate();
    rationalize();
    negate();
    rationalize();
    p2 = pop();
    if (count(p2) < count(p1)) {
      return p1 = p2;
    }
  };

  f4 = function() {
    if (iszero(p1)) {
      return;
    }
    push(p1);
    rationalize();
    inverse();
    rationalize();
    inverse();
    rationalize();
    p2 = pop();
    if (count(p2) < count(p1)) {
      return p1 = p2;
    }
  };

  simplify_trig = function() {
    save();
    p1 = pop();
    f5();
    push(p1);
    return restore();
  };

  f5 = function() {
    if (Find(p1, symbol(SIN)) === 0 && Find(p1, symbol(COS)) === 0) {
      return;
    }
    p2 = p1;
    trigmode = 1;
    push(p2);
    Eval();
    p3 = pop();
    trigmode = 2;
    push(p2);
    Eval();
    p4 = pop();
    trigmode = 0;
    if (count(p4) < count(p3) || nterms(p4) < nterms(p3)) {
      p3 = p4;
    }
    if (count(p3) < count(p1) || nterms(p3) < nterms(p1)) {
      return p1 = p3;
    }
  };

  f9 = function() {
    if (car(p1) !== symbol(ADD)) {
      return;
    }
    push_integer(0);
    p2 = cdr(p1);
    while (iscons(p2)) {
      push(car(p2));
      simplify();
      add();
      p2 = cdr(p2);
    }
    p2 = pop();
    if (count(p2) < count(p1)) {
      return p1 = p2;
    }
  };

  nterms = function(p) {
    if (car(p) !== symbol(ADD)) {
      return 1;
    } else {
      return length(p) - 1;
    }
  };

  Eval_sin = function() {
    push(cadr(p1));
    Eval();
    return sine();
  };

  sine = function() {
    save();
    p1 = pop();
    if (car(p1) === symbol(ADD)) {
      sine_of_angle_sum();
    } else {
      sine_of_angle();
    }
    return restore();
  };

  sine_of_angle_sum = function() {
    p2 = cdr(p1);
    while (iscons(p2)) {
      p4 = car(p2);
      if (isnpi(p4)) {
        push(p1);
        push(p4);
        subtract();
        p3 = pop();
        push(p3);
        sine();
        push(p4);
        cosine();
        multiply();
        push(p3);
        cosine();
        push(p4);
        sine();
        multiply();
        add();
        return;
      }
      p2 = cdr(p2);
    }
    return sine_of_angle();
  };

  sine_of_angle = function() {
    var d, n;
    if (car(p1) === symbol(ARCSIN)) {
      push(cadr(p1));
      return;
    }
    if (isdouble(p1)) {
      d = Math.sin(p1.d);
      if (Math.abs(d) < 1e-10) {
        d = 0.0;
      }
      push_double(d);
      return;
    }
    if (isnegative(p1)) {
      push(p1);
      negate();
      sine();
      negate();
      return;
    }
    if (car(p1) === symbol(ARCTAN)) {
      push(cadr(p1));
      push_integer(1);
      push(cadr(p1));
      push_integer(2);
      power();
      add();
      push_rational(-1, 2);
      power();
      multiply();
      return;
    }
    push(p1);
    push_integer(180);
    multiply();
    push_symbol(PI);
    divide();
    n = pop_integer();
    if (n < 0 || n === 0x80000000) {
      push(symbol(SIN));
      push(p1);
      list(2);
      return;
    }
    switch (n % 360) {
      case 0:
      case 180:
        return push_integer(0);
      case 30:
      case 150:
        return push_rational(1, 2);
      case 210:
      case 330:
        return push_rational(-1, 2);
      case 45:
      case 135:
        push_rational(1, 2);
        push_integer(2);
        push_rational(1, 2);
        power();
        return multiply();
      case 225:
      case 315:
        push_rational(-1, 2);
        push_integer(2);
        push_rational(1, 2);
        power();
        return multiply();
      case 60:
      case 120:
        push_rational(1, 2);
        push_integer(3);
        push_rational(1, 2);
        power();
        return multiply();
      case 240:
      case 300:
        push_rational(-1, 2);
        push_integer(3);
        push_rational(1, 2);
        power();
        return multiply();
      case 90:
        return push_integer(1);
      case 270:
        return push_integer(-1);
      default:
        push(symbol(SIN));
        push(p1);
        return list(2);
    }
  };

  Eval_sinh = function() {
    push(cadr(p1));
    Eval();
    return ysinh();
  };

  ysinh = function() {
    save();
    yysinh();
    return restore();
  };

  yysinh = function() {
    var d;
    d = 0.0;
    p1 = pop();
    if (car(p1) === symbol(ARCSINH)) {
      push(cadr(p1));
      return;
    }
    if (isdouble(p1)) {
      d = Math.sinh(p1.d);
      if (Math.abs(d) < 1e-10) {
        d = 0.0;
      }
      push_double(d);
      return;
    }
    if (iszero(p1)) {
      push(zero);
      return;
    }
    push_symbol(SINH);
    push(p1);
    return list(2);
  };


  /*
  	Substitute new expr for old expr in expr.
  
  	Input:	push	expr
  
  		push	old expr
  
  		push	new expr
  
  	Output:	Result on stack
   */

  subst = function() {
    var ac, ad, i, ref1, ref2;
    i = 0;
    save();
    p3 = pop();
    p2 = pop();
    if (p2 === symbol(NIL) || p3 === symbol(NIL)) {
      restore();
      return;
    }
    p1 = pop();
    if (istensor(p1)) {
      p4 = alloc_tensor(p1.tensor.nelem);
      p4.tensor.ndim = p1.tensor.ndim;
      for (i = ac = 0, ref1 = p1.tensor.ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
        p4.tensor.dim[i] = p1.tensor.dim[i];
      }
      for (i = ad = 0, ref2 = p1.tensor.nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
        push(p1.tensor.elem[i]);
        push(p2);
        push(p3);
        subst();
        p4.tensor.elem[i] = pop();
        if (p4.tensor.nelem !== p4.tensor.elem.length) {
          console.log("something wrong in tensor dimensions");
          debugger;
        }
      }
      push(p4);
    } else if (equal(p1, p2)) {
      push(p3);
    } else if (iscons(p1)) {
      push(car(p1));
      push(p2);
      push(p3);
      subst();
      push(cdr(p1));
      push(p2);
      push(p3);
      subst();
      cons();
    } else {
      push(p1);
    }
    return restore();
  };

  Eval_tan = function() {
    push(cadr(p1));
    Eval();
    return tangent();
  };

  tangent = function() {
    save();
    yytangent();
    return restore();
  };

  yytangent = function() {
    var d, n;
    n = 0;
    d = 0.0;
    p1 = pop();
    if (car(p1) === symbol(ARCTAN)) {
      push(cadr(p1));
      return;
    }
    if (isdouble(p1)) {
      d = Math.tan(p1.d);
      if (Math.abs(d) < 1e-10) {
        d = 0.0;
      }
      push_double(d);
      return;
    }
    if (isnegative(p1)) {
      push(p1);
      negate();
      tangent();
      negate();
      return;
    }
    push(p1);
    push_integer(180);
    multiply();
    push_symbol(PI);
    divide();
    n = pop_integer();
    if (n < 0 || n === 0x80000000) {
      push(symbol(TAN));
      push(p1);
      list(2);
      return;
    }
    switch (n % 360) {
      case 0:
      case 180:
        return push_integer(0);
      case 30:
      case 210:
        push_rational(1, 3);
        push_integer(3);
        push_rational(1, 2);
        power();
        return multiply();
      case 150:
      case 330:
        push_rational(-1, 3);
        push_integer(3);
        push_rational(1, 2);
        power();
        return multiply();
      case 45:
      case 225:
        return push_integer(1);
      case 135:
      case 315:
        return push_integer(-1);
      case 60:
      case 240:
        push_integer(3);
        push_rational(1, 2);
        return power();
      case 120:
      case 300:
        push_integer(3);
        push_rational(1, 2);
        power();
        return negate();
      default:
        push(symbol(TAN));
        push(p1);
        return list(2);
    }
  };

  Eval_tanh = function() {
    var d;
    d = 0.0;
    push(cadr(p1));
    Eval();
    p1 = pop();
    if (car(p1) === symbol(ARCTANH)) {
      push(cadr(p1));
      return;
    }
    if (isdouble(p1)) {
      d = Math.tanh(p1.d);
      if (Math.abs(d) < 1e-10) {
        d = 0.0;
      }
      push_double(d);
      return;
    }
    if (iszero(p1)) {
      push(zero);
      return;
    }
    push_symbol(TANH);
    push(p1);
    return list(2);
  };


  /*
  Taylor expansion of a function
  
  	push(F)
  	push(X)
  	push(N)
  	push(A)
  	taylor()
   */

  Eval_taylor = function() {
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      guess();
    } else {
      push(p2);
    }
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      push_integer(24);
    } else {
      push(p2);
    }
    p1 = cdr(p1);
    push(car(p1));
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      push_integer(0);
    } else {
      push(p2);
    }
    return taylor();
  };

  taylor = function() {
    var ac, i, k, ref1;
    i = 0;
    k = 0;
    save();
    p4 = pop();
    p3 = pop();
    p2 = pop();
    p1 = pop();
    push(p3);
    k = pop_integer();
    if (k === 0x80000000) {
      push_symbol(TAYLOR);
      push(p1);
      push(p2);
      push(p3);
      push(p4);
      list(5);
      restore();
      return;
    }
    push(p1);
    push(p2);
    push(p4);
    subst();
    Eval();
    push_integer(1);
    p5 = pop();
    for (i = ac = 1, ref1 = k; 1 <= ref1 ? ac <= ref1 : ac >= ref1; i = 1 <= ref1 ? ++ac : --ac) {
      push(p1);
      push(p2);
      derivative();
      p1 = pop();
      if (iszero(p1)) {
        break;
      }
      push(p5);
      push(p2);
      push(p4);
      subtract();
      multiply();
      p5 = pop();
      push(p1);
      push(p2);
      push(p4);
      subst();
      Eval();
      push(p5);
      multiply();
      push_integer(i);
      factorial();
      divide();
      add();
    }
    return restore();
  };

  Eval_tensor = function() {
    var a, ac, ad, b, i, ndim, nelem, ref1, ref2;
    i = 0;
    ndim = 0;
    nelem = 0;
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    nelem = p1.tensor.nelem;
    ndim = p1.tensor.ndim;
    p2 = alloc_tensor(nelem);
    p2.tensor.ndim = ndim;
    for (i = ac = 0, ref1 = ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p2.tensor.dim[i] = p1.tensor.dim[i];
    }
    a = p1.tensor.elem;
    b = p2.tensor.elem;
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    for (i = ad = 0, ref2 = nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      push(a[i]);
      Eval();
      b[i] = pop();
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    push(p2);
    return promote_tensor();
  };

  tensor_plus_tensor = function() {
    var a, ac, ad, ae, b, c, i, ndim, nelem, ref1, ref2, ref3;
    i = 0;
    ndim = 0;
    nelem = 0;
    save();
    p2 = pop();
    p1 = pop();
    ndim = p1.tensor.ndim;
    if (ndim !== p2.tensor.ndim) {
      push(symbol(NIL));
      restore();
      return;
    }
    for (i = ac = 0, ref1 = ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      if (p1.tensor.dim[i] !== p2.tensor.dim[i]) {
        push(symbol(NIL));
        restore();
        return;
      }
    }
    nelem = p1.tensor.nelem;
    p3 = alloc_tensor(nelem);
    p3.tensor.ndim = ndim;
    for (i = ad = 0, ref2 = ndim; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    a = p1.tensor.elem;
    b = p2.tensor.elem;
    c = p3.tensor.elem;
    for (i = ae = 0, ref3 = nelem; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
      push(a[i]);
      push(b[i]);
      add();
      c[i] = pop();
    }
    push(p3);
    return restore();
  };

  tensor_times_scalar = function() {
    var a, ac, ad, b, i, ndim, nelem, ref1, ref2;
    i = 0;
    ndim = 0;
    nelem = 0;
    save();
    p2 = pop();
    p1 = pop();
    ndim = p1.tensor.ndim;
    nelem = p1.tensor.nelem;
    p3 = alloc_tensor(nelem);
    p3.tensor.ndim = ndim;
    for (i = ac = 0, ref1 = ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    a = p1.tensor.elem;
    b = p3.tensor.elem;
    for (i = ad = 0, ref2 = nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      push(a[i]);
      push(p2);
      multiply();
      b[i] = pop();
    }
    push(p3);
    return restore();
  };

  scalar_times_tensor = function() {
    var a, ac, ad, b, i, ndim, nelem, ref1, ref2;
    i = 0;
    ndim = 0;
    nelem = 0;
    save();
    p2 = pop();
    p1 = pop();
    ndim = p2.tensor.ndim;
    nelem = p2.tensor.nelem;
    p3 = alloc_tensor(nelem);
    p3.tensor.ndim = ndim;
    for (i = ac = 0, ref1 = ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p3.tensor.dim[i] = p2.tensor.dim[i];
    }
    a = p2.tensor.elem;
    b = p3.tensor.elem;
    for (i = ad = 0, ref2 = nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      push(p1);
      push(a[i]);
      multiply();
      b[i] = pop();
    }
    push(p3);
    return restore();
  };

  is_square_matrix = function(p) {
    if (istensor(p) && p.tensor.ndim === 2 && p.tensor.dim[0] === p.tensor.dim[1]) {
      return 1;
    } else {
      return 0;
    }
  };

  d_tensor_tensor = function() {
    var a, ac, ad, ae, b, c, i, j, ndim, nelem, ref1, ref2, ref3;
    i = 0;
    j = 0;
    ndim = 0;
    nelem = 0;
    ndim = p1.tensor.ndim;
    nelem = p1.tensor.nelem;
    if (ndim + 1 >= MAXDIM) {
      push_symbol(DERIVATIVE);
      push(p1);
      push(p2);
      list(3);
      return;
    }
    p3 = alloc_tensor(nelem * p2.tensor.nelem);
    p3.tensor.ndim = ndim + 1;
    for (i = ac = 0, ref1 = ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    p3.tensor.dim[ndim] = p2.tensor.dim[0];
    a = p1.tensor.elem;
    b = p2.tensor.elem;
    c = p3.tensor.elem;
    for (i = ad = 0, ref2 = nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      for (j = ae = 0, ref3 = p2.tensor.nelem; 0 <= ref3 ? ae < ref3 : ae > ref3; j = 0 <= ref3 ? ++ae : --ae) {
        push(a[i]);
        push(b[j]);
        derivative();
        c[i * p2.tensor.nelem + j] = pop();
      }
    }
    return push(p3);
  };

  d_scalar_tensor = function() {
    var a, ac, b, i, ref1;
    p3 = alloc_tensor(p2.tensor.nelem);
    p3.tensor.ndim = 1;
    p3.tensor.dim[0] = p2.tensor.dim[0];
    a = p2.tensor.elem;
    b = p3.tensor.elem;
    for (i = ac = 0, ref1 = p2.tensor.nelem; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      push(p1);
      push(a[i]);
      derivative();
      b[i] = pop();
    }
    return push(p3);
  };

  d_tensor_scalar = function() {
    var a, ac, ad, b, i, ref1, ref2;
    i = 0;
    p3 = alloc_tensor(p1.tensor.nelem);
    p3.tensor.ndim = p1.tensor.ndim;
    for (i = ac = 0, ref1 = p1.tensor.ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    a = p1.tensor.elem;
    b = p3.tensor.elem;
    for (i = ad = 0, ref2 = p1.tensor.nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      push(a[i]);
      push(p2);
      derivative();
      b[i] = pop();
    }
    return push(p3);
  };

  compare_tensors = function(p1, p2) {
    var ac, ad, i, ref1, ref2;
    i = 0;
    if (p1.tensor.ndim < p2.tensor.ndim) {
      return -1;
    }
    if (p1.tensor.ndim > p2.tensor.ndim) {
      return 1;
    }
    for (i = ac = 0, ref1 = p1.tensor.ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      if (p1.tensor.dim[i] < p2.tensor.dim[i]) {
        return -1;
      }
      if (p1.tensor.dim[i] > p2.tensor.dim[i]) {
        return 1;
      }
    }
    for (i = ad = 0, ref2 = p1.tensor.nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      if (equal(p1.tensor.elem[i], p2.tensor.elem[i])) {
        continue;
      }
      if (lessp(p1.tensor.elem[i], p2.tensor.elem[i])) {
        return -1;
      } else {
        return 1;
      }
    }
    return 0;
  };

  power_tensor = function() {
    var ac, ad, i, k, n, ref1, ref2, results;
    i = 0;
    k = 0;
    n = 0;
    k = p1.tensor.ndim - 1;
    if (p1.tensor.dim[0] !== p1.tensor.dim[k]) {
      push_symbol(POWER);
      push(p1);
      push(p2);
      list(3);
      return;
    }
    push(p2);
    n = pop_integer();
    if (n === 0x80000000) {
      push_symbol(POWER);
      push(p1);
      push(p2);
      list(3);
      return;
    }
    if (n === 0) {
      if (p1.tensor.ndim !== 2) {
        stop("power(tensor,0) with tensor rank not equal to 2");
      }
      n = p1.tensor.dim[0];
      p1 = alloc_tensor(n * n);
      p1.tensor.ndim = 2;
      p1.tensor.dim[0] = n;
      p1.tensor.dim[1] = n;
      for (i = ac = 0, ref1 = n; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
        p1.tensor.elem[n * i + i] = one;
      }
      if (p1.tensor.nelem !== p1.tensor.elem.length) {
        console.log("something wrong in tensor dimensions");
        debugger;
      }
      push(p1);
      return;
    }
    if (n < 0) {
      n = -n;
      push(p1);
      inv();
      p1 = pop();
    }
    push(p1);
    results = [];
    for (i = ad = 1, ref2 = n; 1 <= ref2 ? ad < ref2 : ad > ref2; i = 1 <= ref2 ? ++ad : --ad) {
      push(p1);
      inner();
      if (iszero(stack[tos - 1])) {
        break;
      } else {
        results.push(void 0);
      }
    }
    return results;
  };

  copy_tensor = function() {
    var ac, ad, i, ref1, ref2;
    i = 0;
    save();
    p1 = pop();
    p2 = alloc_tensor(p1.tensor.nelem);
    p2.tensor.ndim = p1.tensor.ndim;
    for (i = ac = 0, ref1 = p1.tensor.ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p2.tensor.dim[i] = p1.tensor.dim[i];
    }
    for (i = ad = 0, ref2 = p1.tensor.nelem; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      p2.tensor.elem[i] = p1.tensor.elem[i];
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    push(p2);
    return restore();
  };

  promote_tensor = function() {
    var ac, ad, ae, af, ag, i, j, k, ndim, nelem, ref1, ref2, ref3, ref4, ref5;
    i = 0;
    j = 0;
    k = 0;
    nelem = 0;
    ndim = 0;
    save();
    p1 = pop();
    if (!istensor(p1)) {
      push(p1);
      restore();
      return;
    }
    p2 = p1.tensor.elem[0];
    for (i = ac = 1, ref1 = p1.tensor.nelem; 1 <= ref1 ? ac < ref1 : ac > ref1; i = 1 <= ref1 ? ++ac : --ac) {
      if (!compatible(p2, p1.tensor.elem[i])) {
        stop("Cannot promote tensor due to inconsistent tensor components.");
      }
    }
    if (!istensor(p2)) {
      push(p1);
      restore();
      return;
    }
    ndim = p1.tensor.ndim + p2.tensor.ndim;
    if (ndim > MAXDIM) {
      stop("tensor rank > 24");
    }
    nelem = p1.tensor.nelem * p2.tensor.nelem;
    p3 = alloc_tensor(nelem);
    p3.tensor.ndim = ndim;
    for (i = ad = 0, ref2 = p1.tensor.ndim; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      p3.tensor.dim[i] = p1.tensor.dim[i];
    }
    for (j = ae = 0, ref3 = p2.tensor.ndim; 0 <= ref3 ? ae < ref3 : ae > ref3; j = 0 <= ref3 ? ++ae : --ae) {
      p3.tensor.dim[i + j] = p2.tensor.dim[j];
    }
    k = 0;
    for (i = af = 0, ref4 = p1.tensor.nelem; 0 <= ref4 ? af < ref4 : af > ref4; i = 0 <= ref4 ? ++af : --af) {
      p2 = p1.tensor.elem[i];
      for (j = ag = 0, ref5 = p2.tensor.nelem; 0 <= ref5 ? ag < ref5 : ag > ref5; j = 0 <= ref5 ? ++ag : --ag) {
        p3.tensor.elem[k++] = p2.tensor.elem[j];
      }
    }
    if (p2.tensor.nelem !== p2.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    if (p3.tensor.nelem !== p3.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    push(p3);
    return restore();
  };

  compatible = function(p, q) {
    var ac, i, ref1;
    if (!istensor(p) && !istensor(q)) {
      return 1;
    }
    if (!istensor(p) || !istensor(q)) {
      return 0;
    }
    if (p.tensor.ndim !== q.tensor.ndim) {
      return 0;
    }
    for (i = ac = 0, ref1 = p.tensor.ndim; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      if (p.tensor.dim[i] !== q.tensor.dim[i]) {
        return 0;
      }
    }
    return 1;
  };

  Eval_test = function() {
    p1 = cdr(p1);
    while (iscons(p1)) {
      if (cdr(p1) === symbol(NIL)) {
        push(car(p1));
        Eval();
        return;
      }
      push(car(p1));
      Eval_predicate();
      p2 = pop();
      if (!iszero(p2)) {
        push(cadr(p1));
        Eval();
        return;
      }
      p1 = cddr(p1);
    }
    return push_integer(0);
  };

  Eval_testeq = function() {
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    subtract();
    p1 = pop();
    if (iszero(p1)) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };

  Eval_testge = function() {
    if (cmp_args() >= 0) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };

  Eval_testgt = function() {
    if (cmp_args() > 0) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };

  Eval_testle = function() {
    if (cmp_args() <= 0) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };

  Eval_testlt = function() {
    if (cmp_args() < 0) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };

  Eval_not = function() {
    push(cadr(p1));
    Eval_predicate();
    p1 = pop();
    if (iszero(p1)) {
      return push_integer(1);
    } else {
      return push_integer(0);
    }
  };

  Eval_and = function() {
    p1 = cdr(p1);
    while (iscons(p1)) {
      push(car(p1));
      Eval_predicate();
      p2 = pop();
      if (iszero(p2)) {
        push_integer(0);
        return;
      }
      p1 = cdr(p1);
    }
    return push_integer(1);
  };

  Eval_or = function() {
    p1 = cdr(p1);
    while (iscons(p1)) {
      push(car(p1));
      Eval_predicate();
      p2 = pop();
      if (!iszero(p2)) {
        push_integer(1);
        return;
      }
      p1 = cdr(p1);
    }
    return push_integer(0);
  };

  cmp_args = function() {
    var t;
    t = 0;
    push(cadr(p1));
    Eval();
    push(caddr(p1));
    Eval();
    subtract();
    p1 = pop();
    if (p1.k !== NUM && p1.k !== DOUBLE) {
      push(p1);
      yyfloat();
      Eval();
      p1 = pop();
    }
    if (iszero(p1)) {
      return 0;
    }
    switch (p1.k) {
      case NUM:
        if (MSIGN(p1.q.a) === -1) {
          t = -1;
        } else {
          t = 1;
        }
        break;
      case DOUBLE:
        if (p1.d < 0.0) {
          t = -1;
        } else {
          t = 1;
        }
        break;
      default:
        stop("relational operator: cannot determine due to non-numerical comparison");
        t = 0;
    }
    return t;
  };


  /*
  Transform an expression using table look-up
  
  The expression and free variable are on the stack.
  
  The argument s is a null terminated list of transform rules.
  
  For example, see itab.cpp
  
  Internally, the following symbols are used:
  
  	F	input expression
  
  	X	free variable, i.e. F of X
  
  	A	template expression
  
  	B	result expression
  
  	C	list of conditional expressions
   */

  transform = function(s) {
    var ac, eachEntry, h, len;
    h = 0;
    save();
    p4 = pop();
    p3 = pop();
    push(get_binding(symbol(METAA)));
    push(get_binding(symbol(METAB)));
    push(get_binding(symbol(METAX)));
    set_binding(symbol(METAX), p4);
    h = tos;
    push_integer(1);
    push(p3);
    push(p4);
    polyform();
    push(p4);
    decomp();
    for (ac = 0, len = s.length; ac < len; ac++) {
      eachEntry = s[ac];
      if (DEBUG) {
        console.log("scanning table entry " + eachEntry);
      }
      if (eachEntry) {
        scan_meta(eachEntry);
        p1 = pop();
        p5 = cadr(p1);
        p6 = caddr(p1);
        p7 = cdddr(p1);
        if (f_equals_a(h)) {
          break;
        }
      }
    }
    tos = h;
    if (eachEntry) {
      push(p6);
      Eval();
      p1 = pop();
    } else {
      p1 = symbol(NIL);
    }
    set_binding(symbol(METAX), pop());
    set_binding(symbol(METAB), pop());
    set_binding(symbol(METAA), pop());
    push(p1);
    return restore();
  };

  f_equals_a = function(h) {
    var ac, ad, i, j, ref1, ref2, ref3, ref4;
    i = 0;
    j = 0;
    for (i = ac = ref1 = h, ref2 = tos; ref1 <= ref2 ? ac < ref2 : ac > ref2; i = ref1 <= ref2 ? ++ac : --ac) {
      set_binding(symbol(METAA), stack[i]);
      for (j = ad = ref3 = h, ref4 = tos; ref3 <= ref4 ? ad < ref4 : ad > ref4; j = ref3 <= ref4 ? ++ad : --ad) {
        set_binding(symbol(METAB), stack[j]);
        p1 = p7;
        while (iscons(p1)) {
          push(car(p1));
          Eval();
          p2 = pop();
          if (iszero(p2)) {
            break;
          }
          p1 = cdr(p1);
        }
        if (iscons(p1)) {
          continue;
        }
        push(p3);
        push(p5);
        Eval();
        subtract();
        p1 = pop();
        if (iszero(p1)) {
          return 1;
        }
      }
    }
    return 0;
  };

  Eval_transpose = function() {
    push(cadr(p1));
    Eval();
    if (cddr(p1) === symbol(NIL)) {
      push_integer(1);
      push_integer(2);
    } else {
      push(caddr(p1));
      Eval();
      push(cadddr(p1));
      Eval();
    }
    return transpose();
  };

  transpose = function() {
    var a, ac, ad, ae, af, ag, ah, ai, an, b, i, j, k, l, m, ndim, nelem, ref1, ref2, ref3, ref4, ref5, ref6, t;
    i = 0;
    j = 0;
    k = 0;
    l = 0;
    m = 0;
    ndim = 0;
    nelem = 0;
    t = 0;
    ai = [];
    an = [];
    for (i = ac = 0, ref1 = MAXDIM; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      ai[i] = 0;
      an[i] = 0;
    }
    save();
    p3 = pop();
    p2 = pop();
    p1 = pop();
    if (!istensor(p1)) {
      if (!iszero(p1)) {
        stop("transpose: tensor expected, 1st arg is not a tensor");
      }
      push(zero);
      restore();
      return;
    }
    ndim = p1.tensor.ndim;
    nelem = p1.tensor.nelem;
    if (ndim === 1) {
      push(p1);
      restore();
      return;
    }
    push(p2);
    l = pop_integer();
    push(p3);
    m = pop_integer();
    if (l < 1 || l > ndim || m < 1 || m > ndim) {
      stop("transpose: index out of range");
    }
    l--;
    m--;
    p2 = alloc_tensor(nelem);
    p2.tensor.ndim = ndim;
    for (i = ad = 0, ref2 = ndim; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      p2.tensor.dim[i] = p1.tensor.dim[i];
    }
    p2.tensor.dim[l] = p1.tensor.dim[m];
    p2.tensor.dim[m] = p1.tensor.dim[l];
    a = p1.tensor.elem;
    b = p2.tensor.elem;
    for (i = ae = 0, ref3 = ndim; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
      ai[i] = 0;
      an[i] = p1.tensor.dim[i];
    }
    for (i = af = 0, ref4 = nelem; 0 <= ref4 ? af < ref4 : af > ref4; i = 0 <= ref4 ? ++af : --af) {
      t = ai[l];
      ai[l] = ai[m];
      ai[m] = t;
      t = an[l];
      an[l] = an[m];
      an[m] = t;
      k = 0;
      for (j = ag = 0, ref5 = ndim; 0 <= ref5 ? ag < ref5 : ag > ref5; j = 0 <= ref5 ? ++ag : --ag) {
        k = (k * an[j]) + ai[j];
      }
      t = ai[l];
      ai[l] = ai[m];
      ai[m] = t;
      t = an[l];
      an[l] = an[m];
      an[m] = t;
      b[k] = a[i];
      for (j = ah = ref6 = ndim - 1; ref6 <= 0 ? ah <= 0 : ah >= 0; j = ref6 <= 0 ? ++ah : --ah) {
        if (++ai[j] < an[j]) {
          break;
        }
        ai[j] = 0;
      }
    }
    push(p2);
    return restore();
  };

  Eval_user_function = function() {
    var h;
    if (car(p1) === symbol(SYMBOL_D) && get_arglist(symbol(SYMBOL_D)) === symbol(NIL)) {
      Eval_derivative();
      return;
    }
    p3 = get_binding(car(p1));
    p4 = get_arglist(car(p1));
    p5 = cdr(p1);
    if (p3 === car(p1)) {
      h = tos;
      push(p3);
      p1 = p5;
      while (iscons(p1)) {
        push(car(p1));
        Eval();
        p1 = cdr(p1);
      }
      list(tos - h);
      return;
    }
    p1 = p4;
    p2 = p5;
    h = tos;
    while (iscons(p1) && iscons(p2)) {
      push(car(p1));
      push(car(p2));
      Eval();
      p1 = cdr(p1);
      p2 = cdr(p2);
    }
    list(tos - h);
    p6 = pop();
    push(p3);
    if (iscons(p6)) {
      push(p6);
      rewrite_args();
    }
    return Eval();
  };

  rewrite_args = function() {
    var h, n;
    n = 0;
    save();
    p2 = pop();
    p1 = pop();
    if (istensor(p1)) {
      n = rewrite_args_tensor();
      restore();
      return n;
    }
    if (iscons(p1)) {
      h = tos;
      push(car(p1));
      p1 = cdr(p1);
      while (iscons(p1)) {
        push(car(p1));
        push(p2);
        n += rewrite_args();
        p1 = cdr(p1);
      }
      list(tos - h);
      restore();
      return n;
    }
    if (!issymbol(p1)) {
      push(p1);
      restore();
      return 0;
    }
    p3 = p2;
    while (iscons(p3)) {
      if (p1 === car(p3)) {
        push(cadr(p3));
        restore();
        return 1;
      }
      p3 = cddr(p3);
    }
    p3 = get_binding(p1);
    push(p3);
    if (p1 !== p3) {
      push(p2);
      n = rewrite_args();
      if (n === 0) {
        pop();
        push(p1);
      }
    }
    restore();
    return n;
  };

  rewrite_args_tensor = function() {
    var ac, i, n, ref1;
    n = 0;
    i = 0;
    push(p1);
    copy_tensor();
    p1 = pop();
    for (i = ac = 0, ref1 = p1.tensor.nelem; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      push(p1.tensor.elem[i]);
      push(p2);
      n += rewrite_args();
      p1.tensor.elem[i] = pop();
    }
    if (p1.tensor.nelem !== p1.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    push(p1);
    return n;
  };

  Eval_zero = function() {
    var ac, ad, i, k, m, n, ref1, ref2;
    i = 0;
    k = [];
    m = 0;
    n = 0;
    for (i = ac = 0, ref1 = MAXDIM; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      k[i] = 0;
    }
    m = 1;
    n = 0;
    p2 = cdr(p1);
    while (iscons(p2)) {
      push(car(p2));
      Eval();
      i = pop_integer();
      if (i < 2) {
        push(zero);
        return;
      }
      m *= i;
      k[n++] = i;
      p2 = cdr(p2);
    }
    if (n === 0) {
      push(zero);
      return;
    }
    p1 = alloc_tensor(m);
    p1.tensor.ndim = n;
    for (i = ad = 0, ref2 = n; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      p1.tensor.dim[i] = k[i];
    }
    return push(p1);
  };


  /*
  // up to 100 blocks of 100,000 atoms
  
  #define M 100
  #define N 100000
  
  U *mem[M]
  int mcount
  
  U *free_list
  int free_count
  
  U *
  alloc(void)
  {
  	U *p
  	if (free_count == 0) {
  		if (mcount == 0)
  			alloc_mem()
  		else {
  			gc()
  			if (free_count < N * mcount / 2)
  				alloc_mem()
  		}
  		if (free_count == 0)
  			stop("atom space exhausted")
  	}
  	p = free_list
  	free_list = free_list->u.cons.cdr
  	free_count--
  	return p
  }
   */

  allocatedId = 0;

  alloc_tensor = function(nelem) {
    var ac, i, p, ref1;
    i = 0;
    p = new U();
    p.k = TENSOR;
    p.tensor = new tensor();
    p.tensor.nelem = nelem;
    for (i = ac = 0, ref1 = nelem; 0 <= ref1 ? ac < ref1 : ac > ref1; i = 0 <= ref1 ? ++ac : --ac) {
      p.tensor.elem[i] = zero;
    }
    p.tensor.allocatedId = allocatedId;
    allocatedId++;
    if (p.tensor.nelem !== p.tensor.elem.length) {
      console.log("something wrong in tensor dimensions");
      debugger;
    }
    return p;
  };


  /*
  // garbage collector
  
  void
  gc(void)
  {
  	int i, j
  	U *p
  
  	// tag everything
  
  	for (i = 0; i < mcount; i++) {
  		p = mem[i]
  		for (j = 0; j < N; j++)
  			p[j].tag = 1
  	}
  
  	// untag what's used
  
  	untag(p0)
  	untag(p1)
  	untag(p2)
  	untag(p3)
  	untag(p4)
  	untag(p5)
  	untag(p6)
  	untag(p7)
  	untag(p8)
  	untag(p9)
  
  	untag(one)
  	untag(zero)
  	untag(imaginaryunit)
  
  	for (i = 0; i < NSYM; i++) {
  		untag(binding[i])
  		untag(arglist[i])
  	}
  
  	for (i = 0; i < tos; i++)
  		untag(stack[i])
  
  	for (i = (int) (frame - stack); i < TOS; i++)
  		untag(stack[i])
  
  	// collect everything that's still tagged
  
  	free_count = 0
  
  	for (i = 0; i < mcount; i++) {
  		p = mem[i]
  		for (j = 0; j < N; j++) {
  			if (p[j].tag == 0)
  				continue
  			// still tagged so it's unused, put on free list
  			switch (p[j].k) {
  			case TENSOR:
  				free(p[j].u.tensor)
  				break
  			case STR:
  				free(p[j].u.str)
  				break
  			case NUM:
  				mfree(p[j].u.q.a)
  				mfree(p[j].u.q.b)
  				break
  			}
  			p[j].k = CONS; // so no double free occurs above
  			p[j].u.cons.cdr = free_list
  			free_list = p + j
  			free_count++
  		}
  	}
  }
  
  void
  untag(U *p)
  {
  	int i
  
  	if (iscons(p)) {
  		do {
  			if (p->tag == 0)
  				return
  			p->tag = 0
  			untag(p->u.cons.car)
  			p = p->u.cons.cdr
  		} while (iscons(p))
  		untag(p)
  		return
  	}
  
  	if (p->tag) {
  		p->tag = 0
   		if (istensor(p)) {
  			for (i = 0; i < p->u.tensor->nelem; i++)
  				untag(p->u.tensor->elem[i])
  		}
  	}
  }
  
  // get memory for 100,000 atoms
  
  void
  alloc_mem(void)
  {
  	int i
  	U *p
  	if (mcount == M)
  		return
  	p = (U *) malloc(N * sizeof (struct U))
  	if (p == NULL)
  		return
  	mem[mcount++] = p
  	for (i = 0; i < N; i++) {
  		p[i].k = CONS; // so no free in gc
  		p[i].u.cons.cdr = p + i + 1
  	}
  	p[N - 1].u.cons.cdr = free_list
  	free_list = p
  	free_count += N
  }
  
  void
  print_mem_info(void)
  {
  	char buf[100]
  
  	sprintf(buf, "%d blocks (%d bytes/block)\n", N * mcount, (int) sizeof (U))
  	printstr(buf)
  
  	sprintf(buf, "%d free\n", free_count)
  	printstr(buf)
  
  	sprintf(buf, "%d used\n", N * mcount - free_count)
  	printstr(buf)
  }
   */

  YMAX = 10000;

  glyph = (function() {
    function glyph() {}

    glyph.prototype.c = 0;

    glyph.prototype.x = 0;

    glyph.prototype.y = 0;

    return glyph;

  })();

  chartab = [];

  for (charTabIndex = ac = 0, ref1 = YMAX; 0 <= ref1 ? ac < ref1 : ac > ref1; charTabIndex = 0 <= ref1 ? ++ac : --ac) {
    chartab[charTabIndex] = new glyph();
  }

  yindex = 0;

  level = 0;

  emit_x = 0;

  expr_level = 0;

  display_flag = 0;

  printchar_nowrap = function(character, accumulator) {
    var topLevelCall;
    if (accumulator == null) {
      topLevelCall = true;
      accumulator = "";
    }
    accumulator += character;
    return accumulator;
  };

  printchar = function(character, accumulator) {
    return printchar_nowrap(character, accumulator);
  };

  display = function(p) {
    var h, ref2, w, y;
    h = 0;
    w = 0;
    y = 0;
    save();
    yindex = 0;
    level = 0;
    emit_x = 0;
    emit_top_expr(p);
    ref2 = get_size(0, yindex), h = ref2[0], w = ref2[1], y = ref2[2];
    if (w > 100) {
      printline(p);
      restore();
      return;
    }
    print_it();
    return restore();
  };

  emit_top_expr = function(p) {
    if (car(p) === symbol(SETQ)) {
      emit_expr(cadr(p));
      __emit_str(" = ");
      emit_expr(caddr(p));
      return;
    }
    if (istensor(p)) {
      return emit_tensor(p);
    } else {
      return emit_expr(p);
    }
  };

  will_be_displayed_as_fraction = function(p) {
    if (level > 0) {
      return 0;
    }
    if (isfraction(p)) {
      return 1;
    }
    if (car(p) !== symbol(MULTIPLY)) {
      return 0;
    }
    if (isfraction(cadr(p))) {
      return 1;
    }
    while (iscons(p)) {
      if (isdenominator(car(p))) {
        return 1;
      }
      p = cdr(p);
    }
    return 0;
  };

  emit_expr = function(p) {
    expr_level++;
    if (car(p) === symbol(ADD)) {
      p = cdr(p);
      if (__is_negative(car(p))) {
        __emit_char('-');
        if (will_be_displayed_as_fraction(car(p))) {
          __emit_char(' ');
        }
      }
      emit_term(car(p));
      p = cdr(p);
      while (iscons(p)) {
        if (__is_negative(car(p))) {
          __emit_char(' ');
          __emit_char('-');
          __emit_char(' ');
        } else {
          __emit_char(' ');
          __emit_char('+');
          __emit_char(' ');
        }
        emit_term(car(p));
        p = cdr(p);
      }
    } else {
      if (__is_negative(p)) {
        __emit_char('-');
        if (will_be_displayed_as_fraction(p)) {
          __emit_char(' ');
        }
      }
      emit_term(p);
    }
    return expr_level--;
  };

  emit_unsigned_expr = function(p) {
    var results;
    if (car(p) === symbol(ADD)) {
      p = cdr(p);
      emit_term(car(p));
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        if (__is_negative(car(p))) {
          __emit_char(' ');
          __emit_char('-');
          __emit_char(' ');
        } else {
          __emit_char(' ');
          __emit_char('+');
          __emit_char(' ');
        }
        emit_term(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else {
      return emit_term(p);
    }
  };

  __is_negative = function(p) {
    if (isnegativenumber(p)) {
      return 1;
    }
    if (car(p) === symbol(MULTIPLY) && isnegativenumber(cadr(p))) {
      return 1;
    }
    return 0;
  };

  emit_term = function(p) {
    var n;
    if (car(p) === symbol(MULTIPLY)) {
      n = count_denominators(p);
      if (n && level === 0) {
        return emit_fraction(p, n);
      } else {
        return emit_multiply(p, n);
      }
    } else {
      return emit_factor(p);
    }
  };

  isdenominator = function(p) {
    if (car(p) === symbol(POWER) && cadr(p) !== symbol(E) && __is_negative(caddr(p))) {
      return 1;
    } else {
      return 0;
    }
  };

  count_denominators = function(p) {
    var q;
    count = 0;
    p = cdr(p);
    while (iscons(p)) {
      q = car(p);
      if (isdenominator(q)) {
        count++;
      }
      p = cdr(p);
    }
    return count;
  };

  emit_multiply = function(p, n) {
    var results;
    if (n === 0) {
      p = cdr(p);
      if (isplusone(car(p)) || isminusone(car(p))) {
        p = cdr(p);
      }
      emit_factor(car(p));
      p = cdr(p);
      results = [];
      while (iscons(p)) {
        __emit_char(' ');
        emit_factor(car(p));
        results.push(p = cdr(p));
      }
      return results;
    } else {
      emit_numerators(p);
      __emit_char('/');
      if (n > 1 || isfraction(cadr(p))) {
        __emit_char('(');
        emit_denominators(p);
        return __emit_char(')');
      } else {
        return emit_denominators(p);
      }
    }
  };

  emit_fraction = function(p, d) {
    var doNothing, k1, k2, n, x;
    count = 0;
    k1 = 0;
    k2 = 0;
    n = 0;
    x = 0;
    save();
    p3 = one;
    p4 = one;
    if (isrational(cadr(p))) {
      push(cadr(p));
      mp_numerator();
      absval();
      p3 = pop();
      push(cadr(p));
      mp_denominator();
      p4 = pop();
    }
    if (isdouble(cadr(p))) {
      push(cadr(p));
      absval();
      p3 = pop();
    }
    if (isplusone(p3)) {
      n = 0;
    } else {
      n = 1;
    }
    p1 = cdr(p);
    if (isnum(car(p1))) {
      p1 = cdr(p1);
    }
    while (iscons(p1)) {
      p2 = car(p1);
      if (isdenominator(p2)) {
        doNothing = 1;
      } else {
        n++;
      }
      p1 = cdr(p1);
    }
    x = emit_x;
    k1 = yindex;
    count = 0;
    if (!isplusone(p3)) {
      emit_number(p3, 0);
      count++;
    }
    p1 = cdr(p);
    if (isnum(car(p1))) {
      p1 = cdr(p1);
    }
    while (iscons(p1)) {
      p2 = car(p1);
      if (isdenominator(p2)) {
        doNothing = 1;
      } else {
        if (count > 0) {
          __emit_char(' ');
        }
        if (n === 1) {
          emit_expr(p2);
        } else {
          emit_factor(p2);
        }
        count++;
      }
      p1 = cdr(p1);
    }
    if (count === 0) {
      __emit_char('1');
    }
    k2 = yindex;
    count = 0;
    if (!isplusone(p4)) {
      emit_number(p4, 0);
      count++;
      d++;
    }
    p1 = cdr(p);
    if (isrational(car(p1))) {
      p1 = cdr(p1);
    }
    while (iscons(p1)) {
      p2 = car(p1);
      if (isdenominator(p2)) {
        if (count > 0) {
          __emit_char(' ');
        }
        emit_denominator(p2, d);
        count++;
      }
      p1 = cdr(p1);
    }
    fixup_fraction(x, k1, k2);
    return restore();
  };

  emit_numerators = function(p) {
    var doNothing, n;
    int(n);
    save();
    p1 = one;
    p = cdr(p);
    if (isrational(car(p))) {
      push(car(p));
      mp_numerator();
      absval();
      p1 = pop();
      p = cdr(p);
    } else if (isdouble(car(p))) {
      push(car(p));
      absval();
      p1 = pop();
      p = cdr(p);
    }
    n = 0;
    if (!isplusone(p1)) {
      emit_number(p1, 0);
      n++;
    }
    while (iscons(p)) {
      if (isdenominator(car(p))) {
        doNothing = 1;
      } else {
        if (n > 0) {
          __emit_char(' ');
        }
        emit_factor(car(p));
        n++;
      }
      p = cdr(p);
    }
    if (n === 0) {
      __emit_char('1');
    }
    return restore();
  };

  emit_denominators = function(p) {
    var n;
    int(n);
    save();
    n = 0;
    p = cdr(p);
    if (isfraction(car(p))) {
      push(car(p));
      mp_denominator();
      p1 = pop();
      emit_number(p1, 0);
      n++;
      p = cdr(p);
    }
    while (iscons(p)) {
      if (isdenominator(car(p))) {
        if (n > 0) {
          __emit_char(' ');
        }
        emit_denominator(car(p), 0);
        n++;
      }
      p = cdr(p);
    }
    return restore();
  };

  emit_factor = function(p) {
    if (istensor(p)) {
      if (level === 0) {
        emit_flat_tensor(p);
      } else {
        emit_flat_tensor(p);
      }
      return;
    }
    if (isdouble(p)) {
      emit_number(p, 0);
      return;
    }
    if (car(p) === symbol(ADD) || car(p) === symbol(MULTIPLY)) {
      emit_subexpr(p);
      return;
    }
    if (car(p) === symbol(POWER)) {
      emit_power(p);
      return;
    }
    if (iscons(p)) {
      emit_function(p);
      return;
    }
    if (isnum(p)) {
      if (level === 0) {
        emit_numerical_fraction(p);
      } else {
        emit_number(p, 0);
      }
      return;
    }
    if (issymbol(p)) {
      emit_symbol(p);
      return;
    }
    if (isstr(p)) {
      emit_string(p);
    }
  };

  emit_numerical_fraction = function(p) {
    var k1, k2, x;
    k1 = 0;
    k2 = 0;
    x = 0;
    save();
    push(p);
    mp_numerator();
    absval();
    p3 = pop();
    push(p);
    mp_denominator();
    p4 = pop();
    if (isplusone(p4)) {
      emit_number(p3, 0);
      restore();
      return;
    }
    x = emit_x;
    k1 = yindex;
    emit_number(p3, 0);
    k2 = yindex;
    emit_number(p4, 0);
    fixup_fraction(x, k1, k2);
    return restore();
  };

  isfactor = function(p) {
    if (iscons(p) && car(p) !== symbol(ADD) && car(p) !== symbol(MULTIPLY) && car(p) !== symbol(POWER)) {
      return 1;
    }
    if (issymbol(p)) {
      return 1;
    }
    if (isfraction(p)) {
      return 0;
    }
    if (isnegativenumber(p)) {
      return 0;
    }
    if (isnum(p)) {
      return 1;
    }
    return 0;
  };

  emit_power = function(p) {
    var k1, k2, x;
    k1 = 0;
    k2 = 0;
    x = 0;
    if (cadr(p) === symbol(E)) {
      __emit_str("exp(");
      emit_expr(caddr(p));
      __emit_char(')');
      return;
    }
    if (level > 0) {
      if (isminusone(caddr(p))) {
        __emit_char('1');
        __emit_char('/');
        if (isfactor(cadr(p))) {
          emit_factor(cadr(p));
        } else {
          emit_subexpr(cadr(p));
        }
      } else {
        if (isfactor(cadr(p))) {
          emit_factor(cadr(p));
        } else {
          emit_subexpr(cadr(p));
        }
        __emit_char('^');
        if (isfactor(caddr(p))) {
          emit_factor(caddr(p));
        } else {
          emit_subexpr(caddr(p));
        }
      }
      return;
    }
    if (__is_negative(caddr(p))) {
      x = emit_x;
      k1 = yindex;
      __emit_char('1');
      k2 = yindex;
      emit_denominator(p, 1);
      fixup_fraction(x, k1, k2);
      return;
    }
    k1 = yindex;
    if (isfactor(cadr(p))) {
      emit_factor(cadr(p));
    } else {
      emit_subexpr(cadr(p));
    }
    k2 = yindex;
    level++;
    emit_expr(caddr(p));
    level--;
    return fixup_power(k1, k2);
  };

  emit_denominator = function(p, n) {
    var k1, k2;
    k1 = 0;
    k2 = 0;
    if (isminusone(caddr(p))) {
      if (n === 1) {
        emit_expr(cadr(p));
      } else {
        emit_factor(cadr(p));
      }
      return;
    }
    k1 = yindex;
    if (isfactor(cadr(p))) {
      emit_factor(cadr(p));
    } else {
      emit_subexpr(cadr(p));
    }
    k2 = yindex;
    level++;
    emit_unsigned_expr(caddr(p));
    level--;
    return fixup_power(k1, k2);
  };

  emit_function = function(p) {
    if (car(p) === symbol(INDEX) && issymbol(cadr(p))) {
      emit_index_function(p);
      return;
    }
    if (car(p) === symbol(FACTORIAL)) {
      emit_factorial_function(p);
      return;
    }
    if (car(p) === symbol(DERIVATIVE)) {
      __emit_char('d');
    } else {
      emit_symbol(car(p));
    }
    __emit_char('(');
    p = cdr(p);
    if (iscons(p)) {
      emit_expr(car(p));
      p = cdr(p);
      while (iscons(p)) {
        __emit_char(',');
        emit_expr(car(p));
        p = cdr(p);
      }
    }
    return __emit_char(')');
  };

  emit_index_function = function(p) {
    p = cdr(p);
    if (caar(p) === symbol(ADD) || caar(p) === symbol(MULTIPLY) || caar(p) === symbol(POWER) || caar(p) === symbol(FACTORIAL)) {
      emit_subexpr(car(p));
    } else {
      emit_expr(car(p));
    }
    __emit_char('[');
    p = cdr(p);
    if (iscons(p)) {
      emit_expr(car(p));
      p = cdr(p);
      while (iscons(p)) {
        __emit_char(',');
        emit_expr(car(p));
        p = cdr(p);
      }
    }
    return __emit_char(']');
  };

  emit_factorial_function = function(p) {
    p = cadr(p);
    if (car(p) === symbol(ADD) || car(p) === symbol(MULTIPLY) || car(p) === symbol(POWER) || car(p) === symbol(FACTORIAL)) {
      emit_subexpr(p);
    } else {
      emit_expr(p);
    }
    return __emit_char('!');
  };

  emit_subexpr = function(p) {
    __emit_char('(');
    emit_expr(p);
    return __emit_char(')');
  };

  emit_symbol = function(p) {
    var ad, i, pPrintName, ref2, results;
    i = 0;
    if (p === symbol(E)) {
      __emit_str("exp(1)");
      return;
    }
    pPrintName = get_printname(p);
    results = [];
    for (i = ad = 0, ref2 = pPrintName.length; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      results.push(__emit_char(pPrintName[i]));
    }
    return results;
  };

  emit_string = function(p) {
    var ad, i, pString, ref2;
    i = 0;
    pString = p.str;
    __emit_char('"');
    for (i = ad = 0, ref2 = pString.length; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      __emit_char(pString[i]);
    }
    return __emit_char('"');
  };

  fixup_fraction = function(x, k1, k2) {
    var ad, dx, dy, h1, h2, i, ref2, ref3, ref4, results, w, w1, w2, y, y1, y2;
    dx = 0;
    dy = 0;
    i = 0;
    w = 0;
    y = 0;
    h1 = 0;
    w1 = 0;
    y1 = 0;
    h2 = 0;
    w2 = 0;
    y2 = 0;
    ref2 = get_size(k1, k2), h1 = ref2[0], w1 = ref2[1], y1 = ref2[2];
    ref3 = get_size(k2, yindex), h2 = ref3[0], w2 = ref3[1], y2 = ref3[2];
    if (w2 > w1) {
      dx = (w2 - w1) / 2;
    } else {
      dx = 0;
    }
    dx++;
    y = y1 + h1 - 1;
    dy = -y - 1;
    move(k1, k2, dx, dy);
    if (w2 > w1) {
      dx = -w1;
    } else {
      dx = -w1 + (w1 - w2) / 2;
    }
    dx++;
    dy = -y2 + 1;
    move(k2, yindex, dx, dy);
    if (w2 > w1) {
      w = w2;
    } else {
      w = w1;
    }
    w += 2;
    emit_x = x;
    results = [];
    for (i = ad = 0, ref4 = w; 0 <= ref4 ? ad < ref4 : ad > ref4; i = 0 <= ref4 ? ++ad : --ad) {
      results.push(__emit_char('-'));
    }
    return results;
  };

  fixup_power = function(k1, k2) {
    var dy, h1, h2, ref2, ref3, w1, w2, y1, y2;
    dy = 0;
    h1 = 0;
    w1 = 0;
    y1 = 0;
    h2 = 0;
    w2 = 0;
    y2 = 0;
    ref2 = get_size(k1, k2), h1 = ref2[0], w1 = ref2[1], y1 = ref2[2];
    ref3 = get_size(k2, yindex), h2 = ref3[0], w2 = ref3[1], y2 = ref3[2];
    dy = -y2 - h2 + 1;
    dy += y1 - 1;
    return move(k2, yindex, 0, dy);
  };

  move = function(j, k, dx, dy) {
    var ad, i, ref2, ref3, results;
    i = 0;
    results = [];
    for (i = ad = ref2 = j, ref3 = k; ref2 <= ref3 ? ad < ref3 : ad > ref3; i = ref2 <= ref3 ? ++ad : --ad) {
      chartab[i].x += dx;
      results.push(chartab[i].y += dy);
    }
    return results;
  };

  get_size = function(j, k) {
    var ad, h, i, max_x, max_y, min_x, min_y, ref2, ref3, w, y;
    i = 0;
    min_x = chartab[j].x;
    max_x = chartab[j].x;
    min_y = chartab[j].y;
    max_y = chartab[j].y;
    for (i = ad = ref2 = j + 1, ref3 = k; ref2 <= ref3 ? ad < ref3 : ad > ref3; i = ref2 <= ref3 ? ++ad : --ad) {
      if (chartab[i].x < min_x) {
        min_x = chartab[i].x;
      }
      if (chartab[i].x > max_x) {
        max_x = chartab[i].x;
      }
      if (chartab[i].y < min_y) {
        min_y = chartab[i].y;
      }
      if (chartab[i].y > max_y) {
        max_y = chartab[i].y;
      }
    }
    h = max_y - min_y + 1;
    w = max_x - min_x + 1;
    y = min_y;
    return [h, w, y];
  };

  displaychar = function(c) {
    return __emit_char(c);
  };

  __emit_char = function(c) {
    if (yindex === YMAX) {
      return;
    }
    if (chartab[yindex] == null) {
      debugger;
    }
    chartab[yindex].c = c;
    chartab[yindex].x = emit_x;
    chartab[yindex].y = 0;
    yindex++;
    return emit_x++;
  };

  __emit_str = function(s) {
    var ad, i, ref2, results;
    i = 0;
    results = [];
    for (i = ad = 0, ref2 = s.length; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      results.push(__emit_char(s[i]));
    }
    return results;
  };

  emit_number = function(p, emit_sign) {
    var ad, ae, af, i, ref2, ref3, ref4, results, results1, tmpString;
    tmpString = "";
    i = 0;
    switch (p.k) {
      case NUM:
        tmpString = p.q.a.toString();
        if (tmpString[0] === '-' && emit_sign === 0) {
          tmpString = tmpString.substring(1);
        }
        for (i = ad = 0, ref2 = tmpString.length; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
          __emit_char(tmpString[i]);
        }
        tmpString = p.q.b.toString();
        if (tmpString === "1") {
          break;
        }
        __emit_char('/');
        results = [];
        for (i = ae = 0, ref3 = tmpString.length; 0 <= ref3 ? ae < ref3 : ae > ref3; i = 0 <= ref3 ? ++ae : --ae) {
          results.push(__emit_char(tmpString[i]));
        }
        return results;
        break;
      case DOUBLE:
        tmpString = doubleToReasonableString(p.d);
        if (tmpString[0] === '-' && emit_sign === 0) {
          tmpString = tmpString.substring(1);
        }
        results1 = [];
        for (i = af = 0, ref4 = tmpString.length; 0 <= ref4 ? af < ref4 : af > ref4; i = 0 <= ref4 ? ++af : --af) {
          results1.push(__emit_char(tmpString[i]));
        }
        return results1;
    }
  };

  cmpGlyphs = function(a, b) {
    if (a.y < b.y) {
      return -1;
    }
    if (a.y > b.y) {
      return 1;
    }
    if (a.x < b.x) {
      return -1;
    }
    if (a.x > b.x) {
      return 1;
    }
    return 0;
  };

  print_it = function() {
    var accumulatedPrint, ad, i, ref2, subsetOfStack, x, y;
    i = 0;
    accumulatedPrint = "";
    subsetOfStack = chartab.slice(0, yindex);
    subsetOfStack.sort(cmpGlyphs);
    chartab = [].concat(subsetOfStack).concat(chartab.slice(yindex));
    x = 0;
    y = chartab[0].y;
    for (i = ad = 0, ref2 = yindex; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      while (chartab[i].y > y) {
        accumulatedPrint = printchar('\n', accumulatedPrint);
        x = 0;
        y++;
      }
      while (chartab[i].x > x) {
        accumulatedPrint = printchar_nowrap(' ', accumulatedPrint);
        x++;
      }
      accumulatedPrint = printchar_nowrap(chartab[i].c, accumulatedPrint);
      x++;
    }
    if (PRINTOUTRESULT) {
      return console.log(accumulatedPrint);
    }
  };

  buffer = "";

  getdisplaystr = function() {
    yindex = 0;
    level = 0;
    emit_x = 0;
    emit_expr(pop());
    fill_buf();
    return buffer;
  };

  fill_buf = function() {
    var ad, i, ref2, sIndex, subsetOfStack, tmpBuffer, x, y;
    tmpBuffer = buffer;
    sIndex = 0;
    i = 0;
    subsetOfStack = chartab.slice(0, yindex);
    subsetOfStack.sort(cmpGlyphs);
    chartab = [].concat(subsetOfStack).concat(chartab.slice(yindex));
    x = 0;
    y = chartab[0].y;
    for (i = ad = 0, ref2 = yindex; 0 <= ref2 ? ad < ref2 : ad > ref2; i = 0 <= ref2 ? ++ad : --ad) {
      while (chartab[i].y > y) {
        tmpBuffer[sIndex++] = '\n';
        x = 0;
        y++;
      }
      while (chartab[i].x > x) {
        tmpBuffer[sIndex++] = ' ';
        x++;
      }
      tmpBuffer[sIndex++] = chartab[i].c;
      x++;
    }
    return tmpBuffer[sIndex++] = '\n';
  };

  N = 100;

  oneElement = (function() {
    function oneElement() {}

    oneElement.prototype.x = 0;

    oneElement.prototype.y = 0;

    oneElement.prototype.h = 0;

    oneElement.prototype.w = 0;

    oneElement.prototype.index = 0;

    oneElement.prototype.count = 0;

    return oneElement;

  })();

  elem = [];

  for (elelmIndex = ad = 0; ad < 10000; elelmIndex = ++ad) {
    elem[elelmIndex] = new oneElement;
  }

  SPACE_BETWEEN_COLUMNS = 3;

  SPACE_BETWEEN_ROWS = 1;

  emit_tensor = function(p) {
    var ae, af, ag, ah, col, dx, dy, eh, ew, h, i, n, ncol, nrow, ref2, ref3, ref4, ref5, ref6, row, w, x, y;
    i = 0;
    n = 0;
    nrow = 0;
    ncol = 0;
    x = 0;
    y = 0;
    h = 0;
    w = 0;
    dx = 0;
    dy = 0;
    eh = 0;
    ew = 0;
    row = 0;
    col = 0;
    if (p.tensor.ndim > 2) {
      emit_flat_tensor(p);
      return;
    }
    nrow = p.tensor.dim[0];
    if (p.tensor.ndim === 2) {
      ncol = p.tensor.dim[1];
    } else {
      ncol = 1;
    }
    n = nrow * ncol;
    if (n > N) {
      emit_flat_tensor(p);
      return;
    }
    x = emit_x;
    for (i = ae = 0, ref2 = n; 0 <= ref2 ? ae < ref2 : ae > ref2; i = 0 <= ref2 ? ++ae : --ae) {
      elem[i].index = yindex;
      elem[i].x = emit_x;
      emit_expr(p.tensor.elem[i]);
      elem[i].count = yindex - elem[i].index;
      ref3 = get_size(elem[i].index, yindex), elem[i].h = ref3[0], elem[i].w = ref3[1], elem[i].y = ref3[2];
    }
    eh = 0;
    ew = 0;
    for (i = af = 0, ref4 = n; 0 <= ref4 ? af < ref4 : af > ref4; i = 0 <= ref4 ? ++af : --af) {
      if (elem[i].h > eh) {
        eh = elem[i].h;
      }
      if (elem[i].w > ew) {
        ew = elem[i].w;
      }
    }
    h = nrow * eh + (nrow - 1) * SPACE_BETWEEN_ROWS;
    w = ncol * ew + (ncol - 1) * SPACE_BETWEEN_COLUMNS;
    y = -(h / 2);
    for (row = ag = 0, ref5 = nrow; 0 <= ref5 ? ag < ref5 : ag > ref5; row = 0 <= ref5 ? ++ag : --ag) {
      for (col = ah = 0, ref6 = ncol; 0 <= ref6 ? ah < ref6 : ah > ref6; col = 0 <= ref6 ? ++ah : --ah) {
        i = row * ncol + col;
        dx = x - elem[i].x;
        dy = y - elem[i].y;
        move(elem[i].index, elem[i].index + elem[i].count, dx, dy);
        dx = 0;
        if (col > 0) {
          dx = col * (ew + SPACE_BETWEEN_COLUMNS);
        }
        dy = 0;
        if (row > 0) {
          dy = row * (eh + SPACE_BETWEEN_ROWS);
        }
        dx += (ew - elem[i].w) / 2;
        dy += (eh - elem[i].h) / 2;
        move(elem[i].index, elem[i].index + elem[i].count, dx, dy);
      }
    }
    return emit_x = x + w;

    /*
    	if 0
    
    		 * left brace
    
    		for (i = 0; i < h; i++) {
    			if (yindex == YMAX)
    				break
    			chartab[yindex].c = '|'
    			chartab[yindex].x = x - 2
    			chartab[yindex].y = y + i
    			yindex++
    		}
    
    		 * right brace
    
    		emit_x++
    
    		for (i = 0; i < h; i++) {
    			if (yindex == YMAX)
    				break
    			chartab[yindex].c = '|'
    			chartab[yindex].x = emit_x
    			chartab[yindex].y = y + i
    			yindex++
    		}
    
    		emit_x++
    
    	endif
     */
  };

  emit_flat_tensor = function(p) {
    return emit_tensor_inner(p, 0, 0);
  };

  emit_tensor_inner = function(p, j, k) {
    var ae, i, ref2;
    i = 0;
    __emit_char('(');
    for (i = ae = 0, ref2 = p.tensor.dim[j]; 0 <= ref2 ? ae < ref2 : ae > ref2; i = 0 <= ref2 ? ++ae : --ae) {
      if (j + 1 === p.tensor.ndim) {
        emit_expr(p.tensor.elem[k]);
        k = k + 1;
      } else {
        k = emit_tensor_inner(p, j + 1, k);
      }
      if (i + 1 < p.tensor.dim[j]) {
        __emit_char(',');
      }
    }
    __emit_char(')');
    return k;
  };


  /*
  void
  test_display(void)
  {
  	test(__FILE__, s, sizeof s / sizeof (char *))
  }
  
  #endif
   */

  Find = function(p, q) {
    var ae, i, ref2;
    i = 0;
    if (equal(p, q)) {
      return 1;
    }
    if (istensor(p)) {
      for (i = ae = 0, ref2 = p.tensor.nelem; 0 <= ref2 ? ae < ref2 : ae > ref2; i = 0 <= ref2 ? ++ae : --ae) {
        if (Find(p.tensor.elem[i], q)) {
          return 1;
        }
      }
      return 0;
    }
    while (iscons(p)) {
      if (Find(car(p), q)) {
        return 1;
      }
      p = cdr(p);
    }
    return 0;
  };

  $.Find = Find;

  init = function() {
    var ae, af, i, ref2, ref3;
    i = 0;
    flag = 0;
    tos = 0;
    esc_flag = 0;
    draw_flag = 0;
    frame = TOS;
    if (flag) {
      return;
    }
    flag = 1;
    for (i = ae = 0, ref2 = NSYM; 0 <= ref2 ? ae < ref2 : ae > ref2; i = 0 <= ref2 ? ++ae : --ae) {
      symtab[i] = new U();
    }
    for (i = af = 0, ref3 = NSYM; 0 <= ref3 ? af < ref3 : af > ref3; i = 0 <= ref3 ? ++af : --af) {
      symtab[i].k = SYM;
      binding[i] = symtab[i];
      arglist[i] = symbol(NIL);
    }
    p0 = symbol(NIL);
    p1 = symbol(NIL);
    p2 = symbol(NIL);
    p3 = symbol(NIL);
    p4 = symbol(NIL);
    p5 = symbol(NIL);
    p6 = symbol(NIL);
    p7 = symbol(NIL);
    p8 = symbol(NIL);
    p9 = symbol(NIL);
    std_symbol("abs", ABS);
    std_symbol("add", ADD);
    std_symbol("adj", ADJ);
    std_symbol("and", AND);
    std_symbol("arccos", ARCCOS);
    std_symbol("arccosh", ARCCOSH);
    std_symbol("arcsin", ARCSIN);
    std_symbol("arcsinh", ARCSINH);
    std_symbol("arctan", ARCTAN);
    std_symbol("arctanh", ARCTANH);
    std_symbol("arg", ARG);
    std_symbol("atomize", ATOMIZE);
    std_symbol("besselj", BESSELJ);
    std_symbol("bessely", BESSELY);
    std_symbol("binding", BINDING);
    std_symbol("binomial", BINOMIAL);
    std_symbol("ceiling", CEILING);
    std_symbol("check", CHECK);
    std_symbol("choose", CHOOSE);
    std_symbol("circexp", CIRCEXP);
    std_symbol("clear", CLEAR);
    std_symbol("clock", CLOCK);
    std_symbol("coeff", COEFF);
    std_symbol("cofactor", COFACTOR);
    std_symbol("condense", CONDENSE);
    std_symbol("conj", CONJ);
    std_symbol("contract", CONTRACT);
    std_symbol("cos", COS);
    std_symbol("cosh", COSH);
    std_symbol("decomp", DECOMP);
    std_symbol("defint", DEFINT);
    std_symbol("deg", DEGREE);
    std_symbol("denominator", DENOMINATOR);
    std_symbol("det", DET);
    std_symbol("derivative", DERIVATIVE);
    std_symbol("dim", DIM);
    std_symbol("dirac", DIRAC);
    std_symbol("display", DISPLAY);
    std_symbol("divisors", DIVISORS);
    std_symbol("do", DO);
    std_symbol("dot", DOT);
    std_symbol("draw", DRAW);
    std_symbol("dsolve", DSOLVE);
    std_symbol("erf", ERF);
    std_symbol("erfc", ERFC);
    std_symbol("eigen", EIGEN);
    std_symbol("eigenval", EIGENVAL);
    std_symbol("eigenvec", EIGENVEC);
    std_symbol("eval", EVAL);
    std_symbol("exp", EXP);
    std_symbol("expand", EXPAND);
    std_symbol("expcos", EXPCOS);
    std_symbol("expsin", EXPSIN);
    std_symbol("factor", FACTOR);
    std_symbol("factorial", FACTORIAL);
    std_symbol("factorpoly", FACTORPOLY);
    std_symbol("filter", FILTER);
    std_symbol("float", FLOATF);
    std_symbol("floor", FLOOR);
    std_symbol("for", FOR);
    std_symbol("Gamma", GAMMA);
    std_symbol("gcd", GCD);
    std_symbol("hermite", HERMITE);
    std_symbol("hilbert", HILBERT);
    std_symbol("imag", IMAG);
    std_symbol("component", INDEX);
    std_symbol("inner", INNER);
    std_symbol("integral", INTEGRAL);
    std_symbol("inv", INV);
    std_symbol("invg", INVG);
    std_symbol("isinteger", ISINTEGER);
    std_symbol("isprime", ISPRIME);
    std_symbol("laguerre", LAGUERRE);
    std_symbol("lcm", LCM);
    std_symbol("leading", LEADING);
    std_symbol("legendre", LEGENDRE);
    std_symbol("log", LOG);
    std_symbol("mag", MAG);
    std_symbol("mod", MOD);
    std_symbol("multiply", MULTIPLY);
    std_symbol("not", NOT);
    std_symbol("nroots", NROOTS);
    std_symbol("number", NUMBER);
    std_symbol("numerator", NUMERATOR);
    std_symbol("operator", OPERATOR);
    std_symbol("or", OR);
    std_symbol("outer", OUTER);
    std_symbol("polar", POLAR);
    std_symbol("power", POWER);
    std_symbol("prime", PRIME);
    std_symbol("print", PRINT);
    std_symbol("product", PRODUCT);
    std_symbol("quote", QUOTE);
    std_symbol("quotient", QUOTIENT);
    std_symbol("rank", RANK);
    std_symbol("rationalize", RATIONALIZE);
    std_symbol("real", REAL);
    std_symbol("rect", YYRECT);
    std_symbol("roots", ROOTS);
    std_symbol("equals", SETQ);
    std_symbol("sgn", SGN);
    std_symbol("simplify", SIMPLIFY);
    std_symbol("sin", SIN);
    std_symbol("sinh", SINH);
    std_symbol("shape", SHAPE);
    std_symbol("sqrt", SQRT);
    std_symbol("stop", STOP);
    std_symbol("subst", SUBST);
    std_symbol("sum", SUM);
    std_symbol("tan", TAN);
    std_symbol("tanh", TANH);
    std_symbol("taylor", TAYLOR);
    std_symbol("test", TEST);
    std_symbol("testeq", TESTEQ);
    std_symbol("testge", TESTGE);
    std_symbol("testgt", TESTGT);
    std_symbol("testle", TESTLE);
    std_symbol("testlt", TESTLT);
    std_symbol("transpose", TRANSPOSE);
    std_symbol("unit", UNIT);
    std_symbol("zero", ZERO);
    std_symbol("nil", NIL);
    std_symbol("autoexpand", AUTOEXPAND);
    std_symbol("bake", BAKE);
    std_symbol("last", LAST);
    std_symbol("trace", TRACE);
    std_symbol("tty", TTY);
    std_symbol("~", YYE);
    std_symbol("$DRAWX", DRAWX);
    std_symbol("$METAA", METAA);
    std_symbol("$METAB", METAB);
    std_symbol("$METAX", METAX);
    std_symbol("$SECRETX", SECRETX);
    std_symbol("pi", PI);
    std_symbol("a", SYMBOL_A);
    std_symbol("b", SYMBOL_B);
    std_symbol("c", SYMBOL_C);
    std_symbol("d", SYMBOL_D);
    std_symbol("i", SYMBOL_I);
    std_symbol("j", SYMBOL_J);
    std_symbol("n", SYMBOL_N);
    std_symbol("r", SYMBOL_R);
    std_symbol("s", SYMBOL_S);
    std_symbol("t", SYMBOL_T);
    std_symbol("x", SYMBOL_X);
    std_symbol("y", SYMBOL_Y);
    std_symbol("z", SYMBOL_Z);
    std_symbol("$C1", C1);
    std_symbol("$C2", C2);
    std_symbol("$C3", C3);
    std_symbol("$C4", C4);
    std_symbol("$C5", C5);
    std_symbol("$C6", C6);
    push_integer(0);
    zero = pop();
    push_integer(1);
    one = pop();
    push_symbol(POWER);
    if (DEBUG) {
      print1(stack[tos - 1]);
    }
    push_integer(-1);
    if (DEBUG) {
      print1(stack[tos - 1]);
    }
    push_rational(1, 2);
    if (DEBUG) {
      print1(stack[tos - 1]);
    }
    list(3);
    if (DEBUG) {
      print1(stack[tos - 1]);
    }
    imaginaryunit = pop();
    return defn();
  };

  defn_str = ["e=exp(1)", "i=sqrt(-1)", "autoexpand=1", "trange=(-pi,pi)", "xrange=(-10,10)", "yrange=(-10,10)", "last=0", "trace=0", "tty=0", "cross(u,v)=(u[2]*v[3]-u[3]*v[2],u[3]*v[1]-u[1]*v[3],u[1]*v[2]-u[2]*v[1])", "curl(v)=(d(v[3],y)-d(v[2],z),d(v[1],z)-d(v[3],x),d(v[2],x)-d(v[1],y))", "div(v)=d(v[1],x)+d(v[2],y)+d(v[3],z)", "ln(x)=log(x)"];

  defn = function() {
    var ae, definitionOfInterest, defn_i, ref2, results;
    results = [];
    for (defn_i = ae = 0, ref2 = defn_str.length; 0 <= ref2 ? ae < ref2 : ae > ref2; defn_i = 0 <= ref2 ? ++ae : --ae) {
      definitionOfInterest = defn_str[defn_i];
      scan(definitionOfInterest);
      if (DEBUG) {
        console.log("... evaling " + definitionOfInterest);
        console.log("top of stack:");
        print1(stack[tos - 1]);
      }
      Eval();
      results.push(pop());
    }
    return results;
  };

  mcmp = function(a, b) {
    return a.compare(b);
  };

  mcmpint = function(a, n) {
    var b, t;
    b = bigInt(n);
    t = mcmp(a, b);
    return t;
  };


  /*
  #if SELFTEST
  
  void
  test_mcmp(void)
  {
  	int i, j, k
  	unsigned int *x, *y
  	logout("testing mcmp\n")
  	for (i = -1000; i < 1000; i++) {
  		x = mint(i)
  		for (j = -1000; j < 1000; j++) {
  			y = mint(j)
  			k = mcmp(x, y)
  			if (i == j && k != 0) {
  				logout("failed\n")
  				errout()
  			}
  			if (i < j && k != -1) {
  				logout("failed\n")
  				errout()
  			}
  			if (i > j && k != 1) {
  				logout("failed\n")
  				errout()
  			}
  			mfree(y)
  		}
  		mfree(x)
  	}
  	logout("ok\n")
  }
  
  #endif
   */

  strcmp = function(str1, str2) {
    if (str1 === str2) {
      return 0;
    } else if (str1 > str2) {
      return 1;
    } else {
      return -1;
    }
  };

  doubleToReasonableString = function(d) {
    return parseFloat(d.toPrecision(6));
  };

  clear_term = function() {};

  isspace = function(s) {
    if (s == null) {
      return false;
    }
    return s === ' ' || s === '\t' || s === '\n' || s === '\v' || s === '\f' || s === '\r';
  };

  isdigit = function(str) {
    if (str == null) {
      return false;
    }
    return /^\d+$/.test(str);
  };

  isalpha = function(str) {
    if (str == null) {
      return false;
    }
    if (str == null) {
      debugger;
    }
    return str.search(/[^A-Za-z]/) === -1;
  };

  isalnum = function(str) {
    if (str == null) {
      return false;
    }
    return isalpha(str) || isdigit(str);
  };

  stop = function(s) {
    var message;
    errorMessage += "Stop: ";
    errorMessage += s;
    message = errorMessage;
    errorMessage = '';
    tos = 0;
    throw new Error(message);
  };

  inited = false;

  run = function(stringToBeRun) {
    var allReturnedStrings, collectedResult, error, error1, error2, i, indexOfPartRemainingToBeParsed, n;
    stringToBeRun = stringToBeRun;
    if (stringToBeRun === "selftest") {
      selftest();
      return;
    }
    if (!inited) {
      inited = true;
      init();
    }
    i = 0;
    n = 0;
    indexOfPartRemainingToBeParsed = 0;
    allReturnedStrings = "";
    while (1.) {
      try {
        errorMessage = "";
        check_stack();
        n = scan(stringToBeRun.substring(indexOfPartRemainingToBeParsed));
        p1 = pop();
        check_stack();
      } catch (error1) {
        error = error1;
        if (PRINTOUTRESULT) {
          console.log(error);
        }
        allReturnedStrings += error.message;
        init();
        break;
      }
      if (n === 0) {
        break;
      }
      indexOfPartRemainingToBeParsed += n;
      push(p1);
      try {
        top_level_eval();
        p2 = pop();
        check_stack();
        if (p2 === symbol(NIL)) {
          continue;
        }
        if (isstr(p2)) {
          console.log(p2.str);
          console.log("\n");
          continue;
        }
        collectedResult = collectResultLine(p2);
        allReturnedStrings += collectedResult;
        if (PRINTOUTRESULT) {
          console.log("printline");
          console.log(collectedResult);
        }
        if (PRINTOUTRESULT) {
          console.log("display:");
          display(p2);
        }
        allReturnedStrings += "\n";
      } catch (error2) {
        error = error2;
        collectedResult = error.message;
        if (PRINTOUTRESULT) {
          console.log(collectedResult);
        }
        allReturnedStrings += collectedResult;
        allReturnedStrings += "\n";
        init();
      }
    }
    if (allReturnedStrings[allReturnedStrings.length - 1] === "\n") {
      allReturnedStrings = allReturnedStrings.substring(0, allReturnedStrings.length - 1);
    }
    return allReturnedStrings;
  };

  check_stack = function() {
    if (tos !== 0) {
      debugger;
      stop("stack error");
    }
    if (frame !== TOS) {
      debugger;
      return stop("frame error");
    }
  };

  echo_input = function(s) {
    console.log(s);
    return console.log("\n");
  };

  top_level_eval = function() {
    var doNothing;
    if (DEBUG) {
      console.log("#### top level eval");
    }
    save();
    trigmode = 0;
    p1 = symbol(AUTOEXPAND);
    if (iszero(get_binding(p1))) {
      expanding = 0;
    } else {
      expanding = 1;
    }
    p1 = pop();
    push(p1);
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      push(p2);
      restore();
      return;
    }
    set_binding(symbol(LAST), p2);
    if (!iszero(get_binding(symbol(BAKE)))) {
      push(p2);
      bake();
      p2 = pop();
    }
    if ((p1 === symbol(SYMBOL_I) || p1 === symbol(SYMBOL_J)) && isimaginaryunit(p2)) {
      doNothing = 0;
    } else if (isimaginaryunit(get_binding(symbol(SYMBOL_J)))) {
      push(p2);
      push(imaginaryunit);
      push_symbol(SYMBOL_J);
      subst();
      p2 = pop();
    } else if (isimaginaryunit(get_binding(symbol(SYMBOL_I)))) {
      push(p2);
      push(imaginaryunit);
      push_symbol(SYMBOL_I);
      subst();
      p2 = pop();
    }
    push(p2);
    return restore();
  };

  check_esc_flag = function() {
    if (esc_flag) {
      return stop("esc key");
    }
  };

  (typeof exports !== "undefined" && exports !== null ? exports : this).run = run;

  tos = 0;

  nil_symbols = 0;

  push = function(p) {
    if (p == null) {
      debugger;
    }
    if (p.isZero != null) {
      debugger;
    }
    if (p === symbol(NIL)) {
      nil_symbols++;
      if (DEBUG) {
        console.log("pushing symbol(NIL) #" + nil_symbols);
      }
    }
    if (tos >= frame) {
      stop("stack overflow");
    }
    return stack[tos++] = p;
  };

  pop = function() {
    var elementToBeReturned;
    if (tos === 0) {
      debugger;
      stop("stack underflow");
    }
    if (stack[tos - 1] == null) {
      debugger;
    }
    elementToBeReturned = stack[--tos];
    return elementToBeReturned;
  };

  push_frame = function(n) {
    var ae, i, ref2, results;
    i = 0;
    frame -= n;
    if (frame < tos) {
      debugger;
      stop("frame overflow, circular reference?");
    }
    results = [];
    for (i = ae = 0, ref2 = n; 0 <= ref2 ? ae < ref2 : ae > ref2; i = 0 <= ref2 ? ++ae : --ae) {
      results.push(stack[frame + i] = symbol(NIL));
    }
    return results;
  };

  pop_frame = function(n) {
    frame += n;
    if (frame > TOS) {
      return stop("frame underflow");
    }
  };

  save = function() {
    frame -= 10;
    if (frame < tos) {
      debugger;
      stop("frame overflow, circular reference?");
    }
    stack[frame + 0] = p0;
    stack[frame + 1] = p1;
    stack[frame + 2] = p2;
    stack[frame + 3] = p3;
    stack[frame + 4] = p4;
    stack[frame + 5] = p5;
    stack[frame + 6] = p6;
    stack[frame + 7] = p7;
    stack[frame + 8] = p8;
    return stack[frame + 9] = p9;
  };

  restore = function() {
    if (frame > TOS - 10) {
      stop("frame underflow");
    }
    p0 = stack[frame + 0];
    p1 = stack[frame + 1];
    p2 = stack[frame + 2];
    p3 = stack[frame + 3];
    p4 = stack[frame + 4];
    p5 = stack[frame + 5];
    p6 = stack[frame + 6];
    p7 = stack[frame + 7];
    p8 = stack[frame + 8];
    p9 = stack[frame + 9];
    return frame += 10;
  };

  swap = function() {
    var p, q;
    p = pop();
    q = pop();
    push(p);
    return push(q);
  };

  dupl = function() {
    var p;
    p = pop();
    push(p);
    return push(p);
  };

  $.dupl = dupl;

  $.swap = swap;

  $.restore = restore;

  $.save = save;

  $.push = push;

  $.pop = pop;

  std_symbol = function(s, n) {
    var p;
    p = symtab[n];
    if (p == null) {
      debugger;
    }
    return p.printname = s;
  };

  usr_symbol = function(s) {
    var ae, i, p, ref2;
    i = 0;
    for (i = ae = 0, ref2 = NSYM; 0 <= ref2 ? ae < ref2 : ae > ref2; i = 0 <= ref2 ? ++ae : --ae) {
      if (symtab[i].printname === "") {
        break;
      }
      if (s === symtab[i].printname) {
        return symtab[i];
      }
    }
    if (i === NSYM) {
      stop("symbol table overflow");
    }
    p = symtab[i];
    p.printname = s;
    return p;
  };

  get_printname = function(p) {
    if (p.k !== SYM) {
      stop("symbol error");
    }
    return p.printname;
  };

  set_binding = function(p, q) {
    var indexFound;
    if (p.k !== SYM) {
      stop("symbol error");
    }
    indexFound = symtab.indexOf(p);
    if (symtab.indexOf(p, indexFound + 1) !== -1) {
      console.log("ops, more than one element!");
      debugger;
    }
    if (DEBUG) {
      console.log("lookup >> set_binding lookup " + indexFound);
    }
    binding[indexFound] = q;
    return arglist[indexFound] = symbol(NIL);
  };

  get_binding = function(p) {
    var indexFound;
    if (p.k !== SYM) {
      stop("symbol error");
    }
    indexFound = symtab.indexOf(p);
    if (symtab.indexOf(p, indexFound + 1) !== -1) {
      console.log("ops, more than one element!");
      debugger;
    }
    if (DEBUG) {
      console.log("lookup >> get_binding lookup " + indexFound);
    }
    return binding[indexFound];
  };

  set_binding_and_arglist = function(p, q, r) {
    var indexFound;
    if (p.k !== SYM) {
      stop("symbol error");
    }
    indexFound = symtab.indexOf(p);
    if (symtab.indexOf(p, indexFound + 1) !== -1) {
      console.log("ops, more than one element!");
      debugger;
    }
    if (DEBUG) {
      console.log("lookup >> set_binding_and_arglist lookup " + indexFound);
    }
    binding[indexFound] = q;
    return arglist[indexFound] = r;
  };

  get_arglist = function(p) {
    var indexFound;
    if (p.k !== SYM) {
      stop("symbol error");
    }
    indexFound = symtab.indexOf(p);
    if (symtab.indexOf(p, indexFound + 1) !== -1) {
      console.log("ops, more than one element!");
      debugger;
    }
    if (DEBUG) {
      console.log("lookup >> get_arglist lookup " + indexFound);
    }
    return arglist[indexFound];
  };

  lookupsTotal = 0;

  symnum = function(p) {
    var indexFound;
    lookupsTotal++;
    if (p.k !== SYM) {
      stop("symbol error");
    }
    indexFound = symtab.indexOf(p);
    if (symtab.indexOf(p, indexFound + 1) !== -1) {
      console.log("ops, more than one element!");
      debugger;
    }
    if (DEBUG) {
      console.log("lookup >> symnum lookup " + indexFound + " lookup # " + lookupsTotal);
    }
    return indexFound;
  };

  push_symbol = function(k) {
    return push(symtab[k]);
  };

  clear_symbols = function() {
    var ae, i, ref2, results;
    i = 0;
    results = [];
    for (i = ae = 0, ref2 = NSYM; 0 <= ref2 ? ae < ref2 : ae > ref2; i = 0 <= ref2 ? ++ae : --ae) {
      binding[i] = symtab[i];
      results.push(arglist[i] = symbol(NIL));
    }
    return results;
  };

  $.get_binding = get_binding;

  $.set_binding = set_binding;

  $.usr_symbol = usr_symbol;

  if (!inited) {
    inited = true;
    init();
  }

  $.init = init;

  parse_internal = function(argu) {
    if (typeof argu === 'string') {
      return scan(argu);
    } else if (typeof argu === 'number') {
      if (argu % 1 === 0) {
        return push_integer(argu);
      } else {
        return push_double(argu);
      }
    } else if (argu instanceof U) {
      return push(argu);
    } else {
      console.warn('unknown argument type', argu);
      return push(symbol(NIL));
    }
  };

  parse = function(argu) {
    var data, error, error1;
    try {
      parse_internal(argu);
      data = pop();
      check_stack();
    } catch (error1) {
      error = error1;
      reset_after_error();
      throw error;
    }
    return data;
  };

  exec = function() {
    var ae, argu, argus, error, error1, fn, len, name, result;
    name = arguments[0], argus = 2 <= arguments.length ? slice.call(arguments, 1) : [];
    fn = get_binding(usr_symbol(name));
    check_stack();
    push(fn);
    for (ae = 0, len = argus.length; ae < len; ae++) {
      argu = argus[ae];
      parse_internal(argu);
    }
    list(1 + argus.length);
    p1 = pop();
    push(p1);
    try {
      fixed_top_level_eval();
      result = pop();
      check_stack();
    } catch (error1) {
      error = error1;
      reset_after_error();
      throw error;
    }
    return result;
  };

  reset_after_error = function() {
    tos = 0;
    esc_flag = 0;
    draw_flag = 0;
    return frame = TOS;
  };

  fixed_top_level_eval = function() {
    save();
    trigmode = 0;
    p1 = symbol(AUTOEXPAND);
    if (iszero(get_binding(p1))) {
      expanding = 0;
    } else {
      expanding = 1;
    }
    p1 = pop();
    push(p1);
    Eval();
    p2 = pop();
    if (p2 === symbol(NIL)) {
      push(p2);
      restore();
      return;
    }
    if (!iszero(get_binding(symbol(BAKE)))) {
      push(p2);
      bake();
      p2 = pop();
    }
    push(p2);
    return restore();
  };

  $.exec = exec;

  $.parse = parse;

  (function() {
    var ae, builtin_fns, fn, len, results;
    builtin_fns = ["abs", "add", "adj", "and", "arccos", "arccosh", "arcsin", "arcsinh", "arctan", "arctanh", "arg", "atomize", "besselj", "bessely", "binding", "binomial", "ceiling", "check", "choose", "circexp", "clear", "clock", "coeff", "cofactor", "condense", "conj", "contract", "cos", "cosh", "decomp", "defint", "deg", "denominator", "det", "derivative", "dim", "dirac", "display", "divisors", "do", "dot", "draw", "dsolve", "erf", "erfc", "eigen", "eigenval", "eigenvec", "eval", "exp", "expand", "expcos", "expsin", "factor", "factorial", "factorpoly", "filter", "float", "floor", "for", "Gamma", "gcd", "hermite", "hilbert", "imag", "component", "inner", "integral", "inv", "invg", "isinteger", "isprime", "laguerre", "lcm", "leading", "legendre", "log", "mag", "mod", "multiply", "not", "nroots", "number", "numerator", "operator", "or", "outer", "polar", "power", "prime", "print", "product", "quote", "quotient", "rank", "rationalize", "real", "rect", "roots", "equals", "sgn", "simplify", "sin", "sinh", "sqrt", "stop", "subst", "sum", "tan", "tanh", "taylor", "test", "testeq", "testge", "testgt", "testle", "testlt", "transpose", "unit", "zero"];
    results = [];
    for (ae = 0, len = builtin_fns.length; ae < len; ae++) {
      fn = builtin_fns[ae];
      results.push($[fn] = exec.bind(this, fn));
    }
    return results;
  })();

}).call(this);

},{"big-integer":13}],13:[function(require,module,exports){
var bigInt = (function (undefined) {
    "use strict";

    var BASE = 1e7,
        LOG_BASE = 7,
        MAX_INT = 9007199254740992,
        MAX_INT_ARR = smallToArray(MAX_INT),
        LOG_MAX_INT = Math.log(MAX_INT);

    function Integer(v, radix) {
        if (typeof v === "undefined") return Integer[0];
        if (typeof radix !== "undefined") return +radix === 10 ? parseValue(v) : parseBase(v, radix);
        return parseValue(v);
    }

    function BigInteger(value, sign) {
        this.value = value;
        this.sign = sign;
        this.isSmall = false;
    }
    BigInteger.prototype = Object.create(Integer.prototype);

    function SmallInteger(value) {
        this.value = value;
        this.sign = value < 0;
        this.isSmall = true;
    }
    SmallInteger.prototype = Object.create(Integer.prototype);

    function isPrecise(n) {
        return -MAX_INT < n && n < MAX_INT;
    }

    function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes
        if (n < 1e7)
            return [n];
        if (n < 1e14)
            return [n % 1e7, Math.floor(n / 1e7)];
        return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)];
    }

    function arrayToSmall(arr) { // If BASE changes this function may need to change
        trim(arr);
        var length = arr.length;
        if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) {
            switch (length) {
                case 0: return 0;
                case 1: return arr[0];
                case 2: return arr[0] + arr[1] * BASE;
                default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE;
            }
        }
        return arr;
    }

    function trim(v) {
        var i = v.length;
        while (v[--i] === 0);
        v.length = i + 1;
    }

    function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger
        var x = new Array(length);
        var i = -1;
        while (++i < length) {
            x[i] = 0;
        }
        return x;
    }

    function truncate(n) {
        if (n > 0) return Math.floor(n);
        return Math.ceil(n);
    }

    function add(a, b) { // assumes a and b are arrays with a.length >= b.length
        var l_a = a.length,
            l_b = b.length,
            r = new Array(l_a),
            carry = 0,
            base = BASE,
            sum, i;
        for (i = 0; i < l_b; i++) {
            sum = a[i] + b[i] + carry;
            carry = sum >= base ? 1 : 0;
            r[i] = sum - carry * base;
        }
        while (i < l_a) {
            sum = a[i] + carry;
            carry = sum === base ? 1 : 0;
            r[i++] = sum - carry * base;
        }
        if (carry > 0) r.push(carry);
        return r;
    }

    function addAny(a, b) {
        if (a.length >= b.length) return add(a, b);
        return add(b, a);
    }

    function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT
        var l = a.length,
            r = new Array(l),
            base = BASE,
            sum, i;
        for (i = 0; i < l; i++) {
            sum = a[i] - base + carry;
            carry = Math.floor(sum / base);
            r[i] = sum - carry * base;
            carry += 1;
        }
        while (carry > 0) {
            r[i++] = carry % base;
            carry = Math.floor(carry / base);
        }
        return r;
    }

    BigInteger.prototype.add = function (v) {
        var value, n = parseValue(v);
        if (this.sign !== n.sign) {
            return this.subtract(n.negate());
        }
        var a = this.value, b = n.value;
        if (n.isSmall) {
            return new BigInteger(addSmall(a, Math.abs(b)), this.sign);
        }
        return new BigInteger(addAny(a, b), this.sign);
    };
    BigInteger.prototype.plus = BigInteger.prototype.add;

    SmallInteger.prototype.add = function (v) {
        var n = parseValue(v);
        var a = this.value;
        if (a < 0 !== n.sign) {
            return this.subtract(n.negate());
        }
        var b = n.value;
        if (n.isSmall) {
            if (isPrecise(a + b)) return new SmallInteger(a + b);
            b = smallToArray(Math.abs(b));
        }
        return new BigInteger(addSmall(b, Math.abs(a)), a < 0);
    };
    SmallInteger.prototype.plus = SmallInteger.prototype.add;

    function subtract(a, b) { // assumes a and b are arrays with a >= b
        var a_l = a.length,
            b_l = b.length,
            r = new Array(a_l),
            borrow = 0,
            base = BASE,
            i, difference;
        for (i = 0; i < b_l; i++) {
            difference = a[i] - borrow - b[i];
            if (difference < 0) {
                difference += base;
                borrow = 1;
            } else borrow = 0;
            r[i] = difference;
        }
        for (i = b_l; i < a_l; i++) {
            difference = a[i] - borrow;
            if (difference < 0) difference += base;
            else {
                r[i++] = difference;
                break;
            }
            r[i] = difference;
        }
        for (; i < a_l; i++) {
            r[i] = a[i];
        }
        trim(r);
        return r;
    }

    function subtractAny(a, b, sign) {
        var value, isSmall;
        if (compareAbs(a, b) >= 0) {
            value = subtract(a,b);
        } else {
            value = subtract(b, a);
            sign = !sign;
        }
        value = arrayToSmall(value);
        if (typeof value === "number") {
            if (sign) value = -value;
            return new SmallInteger(value);
        }
        return new BigInteger(value, sign);
    }

    function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT
        var l = a.length,
            r = new Array(l),
            carry = -b,
            base = BASE,
            i, difference;
        for (i = 0; i < l; i++) {
            difference = a[i] + carry;
            carry = Math.floor(difference / base);
            difference %= base;
            r[i] = difference < 0 ? difference + base : difference;
        }
        r = arrayToSmall(r);
        if (typeof r === "number") {
            if (sign) r = -r;
            return new SmallInteger(r);
        } return new BigInteger(r, sign);
    }

    BigInteger.prototype.subtract = function (v) {
        var n = parseValue(v);
        if (this.sign !== n.sign) {
            return this.add(n.negate());
        }
        var a = this.value, b = n.value;
        if (n.isSmall)
            return subtractSmall(a, Math.abs(b), this.sign);
        return subtractAny(a, b, this.sign);
    };
    BigInteger.prototype.minus = BigInteger.prototype.subtract;

    SmallInteger.prototype.subtract = function (v) {
        var n = parseValue(v);
        var a = this.value;
        if (a < 0 !== n.sign) {
            return this.add(n.negate());
        }
        var b = n.value;
        if (n.isSmall) {
            return new SmallInteger(a - b);
        }
        return subtractSmall(b, Math.abs(a), a >= 0);
    };
    SmallInteger.prototype.minus = SmallInteger.prototype.subtract;

    BigInteger.prototype.negate = function () {
        return new BigInteger(this.value, !this.sign);
    };
    SmallInteger.prototype.negate = function () {
        var sign = this.sign;
        var small = new SmallInteger(-this.value);
        small.sign = !sign;
        return small;
    };

    BigInteger.prototype.abs = function () {
        return new BigInteger(this.value, false);
    };
    SmallInteger.prototype.abs = function () {
        return new SmallInteger(Math.abs(this.value));
    };

    function multiplyLong(a, b) {
        var a_l = a.length,
            b_l = b.length,
            l = a_l + b_l,
            r = createArray(l),
            base = BASE,
            product, carry, i, a_i, b_j;
        for (i = 0; i < a_l; ++i) {
            a_i = a[i];
            for (var j = 0; j < b_l; ++j) {
                b_j = b[j];
                product = a_i * b_j + r[i + j];
                carry = Math.floor(product / base);
                r[i + j] = product - carry * base;
                r[i + j + 1] += carry;
            }
        }
        trim(r);
        return r;
    }

    function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE
        var l = a.length,
            r = new Array(l),
            base = BASE,
            carry = 0,
            product, i;
        for (i = 0; i < l; i++) {
            product = a[i] * b + carry;
            carry = Math.floor(product / base);
            r[i] = product - carry * base;
        }
        while (carry > 0) {
            r[i++] = carry % base;
            carry = Math.floor(carry / base);
        }
        return r;
    }

    function shiftLeft(x, n) {
        var r = [];
        while (n-- > 0) r.push(0);
        return r.concat(x);
    }

    function multiplyKaratsuba(x, y) {
        var n = Math.max(x.length, y.length);
        
        if (n <= 30) return multiplyLong(x, y);
        n = Math.ceil(n / 2);

        var b = x.slice(n),
            a = x.slice(0, n),
            d = y.slice(n),
            c = y.slice(0, n);

        var ac = multiplyKaratsuba(a, c),
            bd = multiplyKaratsuba(b, d),
            abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d));

        var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n));
        trim(product);
        return product;
    }

    // The following function is derived from a surface fit of a graph plotting the performance difference
    // between long multiplication and karatsuba multiplication versus the lengths of the two arrays.
    function useKaratsuba(l1, l2) {
        return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0;
    }

    BigInteger.prototype.multiply = function (v) {
        var value, n = parseValue(v),
            a = this.value, b = n.value,
            sign = this.sign !== n.sign,
            abs;
        if (n.isSmall) {
            if (b === 0) return Integer[0];
            if (b === 1) return this;
            if (b === -1) return this.negate();
            abs = Math.abs(b);
            if (abs < BASE) {
                return new BigInteger(multiplySmall(a, abs), sign);
            }
            b = smallToArray(abs);
        }
        if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes
            return new BigInteger(multiplyKaratsuba(a, b), sign);
        return new BigInteger(multiplyLong(a, b), sign);
    };

    BigInteger.prototype.times = BigInteger.prototype.multiply;

    function multiplySmallAndArray(a, b, sign) { // a >= 0
        if (a < BASE) {
            return new BigInteger(multiplySmall(b, a), sign);
        }
        return new BigInteger(multiplyLong(b, smallToArray(a)), sign);
    }
    SmallInteger.prototype._multiplyBySmall = function (a) {
            if (isPrecise(a.value * this.value)) {
                return new SmallInteger(a.value * this.value);
            }
            return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign);
    };
    BigInteger.prototype._multiplyBySmall = function (a) {
            if (a.value === 0) return Integer[0];
            if (a.value === 1) return this;
            if (a.value === -1) return this.negate();
            return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign);
    };
    SmallInteger.prototype.multiply = function (v) {
        return parseValue(v)._multiplyBySmall(this);
    };
    SmallInteger.prototype.times = SmallInteger.prototype.multiply;

    function square(a) {
        var l = a.length,
            r = createArray(l + l),
            base = BASE,
            product, carry, i, a_i, a_j;
        for (i = 0; i < l; i++) {
            a_i = a[i];
            for (var j = 0; j < l; j++) {
                a_j = a[j];
                product = a_i * a_j + r[i + j];
                carry = Math.floor(product / base);
                r[i + j] = product - carry * base;
                r[i + j + 1] += carry;
            }
        }
        trim(r);
        return r;
    }

    BigInteger.prototype.square = function () {
        return new BigInteger(square(this.value), false);
    };

    SmallInteger.prototype.square = function () {
        var value = this.value * this.value;
        if (isPrecise(value)) return new SmallInteger(value);
        return new BigInteger(square(smallToArray(Math.abs(this.value))), false);
    };

    function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes.
        var a_l = a.length,
            b_l = b.length,
            base = BASE,
            result = createArray(b.length),
            divisorMostSignificantDigit = b[b_l - 1],
            // normalization
            lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)),
            remainder = multiplySmall(a, lambda),
            divisor = multiplySmall(b, lambda),
            quotientDigit, shift, carry, borrow, i, l, q;
        if (remainder.length <= a_l) remainder.push(0);
        divisor.push(0);
        divisorMostSignificantDigit = divisor[b_l - 1];
        for (shift = a_l - b_l; shift >= 0; shift--) {
            quotientDigit = base - 1;
            if (remainder[shift + b_l] !== divisorMostSignificantDigit) {
              quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit);
            }
            // quotientDigit <= base - 1
            carry = 0;
            borrow = 0;
            l = divisor.length;
            for (i = 0; i < l; i++) {
                carry += quotientDigit * divisor[i];
                q = Math.floor(carry / base);
                borrow += remainder[shift + i] - (carry - q * base);
                carry = q;
                if (borrow < 0) {
                    remainder[shift + i] = borrow + base;
                    borrow = -1;
                } else {
                    remainder[shift + i] = borrow;
                    borrow = 0;
                }
            }
            while (borrow !== 0) {
                quotientDigit -= 1;
                carry = 0;
                for (i = 0; i < l; i++) {
                    carry += remainder[shift + i] - base + divisor[i];
                    if (carry < 0) {
                        remainder[shift + i] = carry + base;
                        carry = 0;
                    } else {
                        remainder[shift + i] = carry;
                        carry = 1;
                    }
                }
                borrow += carry;
            }
            result[shift] = quotientDigit;
        }
        // denormalization
        remainder = divModSmall(remainder, lambda)[0];
        return [arrayToSmall(result), arrayToSmall(remainder)];
    }

    function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/
        // Performs faster than divMod1 on larger input sizes.
        var a_l = a.length,
            b_l = b.length,
            result = [],
            part = [],
            base = BASE,
            guess, xlen, highx, highy, check;
        while (a_l) {
            part.unshift(a[--a_l]);
            if (compareAbs(part, b) < 0) {
                result.push(0);
                continue;
            }
            xlen = part.length;
            highx = part[xlen - 1] * base + part[xlen - 2];
            highy = b[b_l - 1] * base + b[b_l - 2];
            if (xlen > b_l) {
                highx = (highx + 1) * base;
            }
            guess = Math.ceil(highx / highy);
            do {
                check = multiplySmall(b, guess);
                if (compareAbs(check, part) <= 0) break;
                guess--;
            } while (guess);
            result.push(guess);
            part = subtract(part, check);
        }
        result.reverse();
        return [arrayToSmall(result), arrayToSmall(part)];
    }

    function divModSmall(value, lambda) {
        var length = value.length,
            quotient = createArray(length),
            base = BASE,
            i, q, remainder, divisor;
        remainder = 0;
        for (i = length - 1; i >= 0; --i) {
            divisor = remainder * base + value[i];
            q = truncate(divisor / lambda);
            remainder = divisor - q * lambda;
            quotient[i] = q | 0;
        }
        return [quotient, remainder | 0];
    }

    function divModAny(self, v) {
        var value, n = parseValue(v);
        var a = self.value, b = n.value;
        var quotient;
        if (b === 0) throw new Error("Cannot divide by zero");
        if (self.isSmall) {
            if (n.isSmall) {
                return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)];
            }
            return [Integer[0], self];
        }
        if (n.isSmall) {
            if (b === 1) return [self, Integer[0]];
            if (b == -1) return [self.negate(), Integer[0]];
            var abs = Math.abs(b);
            if (abs < BASE) {
                value = divModSmall(a, abs);
                quotient = arrayToSmall(value[0]);
                var remainder = value[1];
                if (self.sign) remainder = -remainder;
                if (typeof quotient === "number") {
                    if (self.sign !== n.sign) quotient = -quotient;
                    return [new SmallInteger(quotient), new SmallInteger(remainder)];
                }
                return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)];
            }
            b = smallToArray(abs);
        }
        var comparison = compareAbs(a, b);
        if (comparison === -1) return [Integer[0], self];
        if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]];

        // divMod1 is faster on smaller input sizes
        if (a.length + b.length <= 200)
            value = divMod1(a, b);
        else value = divMod2(a, b);

        quotient = value[0];
        var qSign = self.sign !== n.sign,
            mod = value[1],
            mSign = self.sign;
        if (typeof quotient === "number") {
            if (qSign) quotient = -quotient;
            quotient = new SmallInteger(quotient);
        } else quotient = new BigInteger(quotient, qSign);
        if (typeof mod === "number") {
            if (mSign) mod = -mod;
            mod = new SmallInteger(mod);
        } else mod = new BigInteger(mod, mSign);
        return [quotient, mod];
    }

    BigInteger.prototype.divmod = function (v) {
        var result = divModAny(this, v);
        return {
            quotient: result[0],
            remainder: result[1]
        };
    };
    SmallInteger.prototype.divmod = BigInteger.prototype.divmod;

    BigInteger.prototype.divide = function (v) {
        return divModAny(this, v)[0];
    };
    SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide;

    BigInteger.prototype.mod = function (v) {
        return divModAny(this, v)[1];
    };
    SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod;

    BigInteger.prototype.pow = function (v) {
        var n = parseValue(v),
            a = this.value,
            b = n.value,
            value, x, y;
        if (b === 0) return Integer[1];
        if (a === 0) return Integer[0];
        if (a === 1) return Integer[1];
        if (a === -1) return n.isEven() ? Integer[1] : Integer[-1];
        if (n.sign) {
            return Integer[0];
        }
        if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large.");
        if (this.isSmall) {
            if (isPrecise(value = Math.pow(a, b)))
                return new SmallInteger(truncate(value));
        }
        x = this;
        y = Integer[1];
        while (true) {
            if (b & 1 === 1) {
                y = y.times(x);
                --b;
            }
            if (b === 0) break;
            b /= 2;
            x = x.square();
        }
        return y;
    };
    SmallInteger.prototype.pow = BigInteger.prototype.pow;

    BigInteger.prototype.modPow = function (exp, mod) {
        exp = parseValue(exp);
        mod = parseValue(mod);
        if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0");
        var r = Integer[1],
            base = this.mod(mod);
        while (exp.isPositive()) {
            if (base.isZero()) return Integer[0];
            if (exp.isOdd()) r = r.multiply(base).mod(mod);
            exp = exp.divide(2);
            base = base.square().mod(mod);
        }
        return r;
    };
    SmallInteger.prototype.modPow = BigInteger.prototype.modPow;

    function compareAbs(a, b) {
        if (a.length !== b.length) {
            return a.length > b.length ? 1 : -1;
        }
        for (var i = a.length - 1; i >= 0; i--) {
            if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1;
        }
        return 0;
    }

    BigInteger.prototype.compareAbs = function (v) {
        var n = parseValue(v),
            a = this.value,
            b = n.value;
        if (n.isSmall) return 1;
        return compareAbs(a, b);
    };
    SmallInteger.prototype.compareAbs = function (v) {
        var n = parseValue(v),
            a = Math.abs(this.value),
            b = n.value;
        if (n.isSmall) {
            b = Math.abs(b);
            return a === b ? 0 : a > b ? 1 : -1;
        }
        return -1;
    };

    BigInteger.prototype.compare = function (v) {
        // See discussion about comparison with Infinity:
        // https://github.com/peterolson/BigInteger.js/issues/61
        if (v === Infinity) {
            return -1;
        }
        if (v === -Infinity) {
            return 1;
        }

        var n = parseValue(v),
            a = this.value,
            b = n.value;
        if (this.sign !== n.sign) {
            return n.sign ? 1 : -1;
        }
        if (n.isSmall) {
            return this.sign ? -1 : 1;
        }
        return compareAbs(a, b) * (this.sign ? -1 : 1);
    };
    BigInteger.prototype.compareTo = BigInteger.prototype.compare;

    SmallInteger.prototype.compare = function (v) {
        if (v === Infinity) {
            return -1;
        }
        if (v === -Infinity) {
            return 1;
        }

        var n = parseValue(v),
            a = this.value,
            b = n.value;
        if (n.isSmall) {
            return a == b ? 0 : a > b ? 1 : -1;
        }
        if (a < 0 !== n.sign) {
            return a < 0 ? -1 : 1;
        }
        return a < 0 ? 1 : -1;
    };
    SmallInteger.prototype.compareTo = SmallInteger.prototype.compare;

    BigInteger.prototype.equals = function (v) {
        return this.compare(v) === 0;
    };
    SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals;

    BigInteger.prototype.notEquals = function (v) {
        return this.compare(v) !== 0;
    };
    SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals;

    BigInteger.prototype.greater = function (v) {
        return this.compare(v) > 0;
    };
    SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater;

    BigInteger.prototype.lesser = function (v) {
        return this.compare(v) < 0;
    };
    SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser;

    BigInteger.prototype.greaterOrEquals = function (v) {
        return this.compare(v) >= 0;
    };
    SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals;

    BigInteger.prototype.lesserOrEquals = function (v) {
        return this.compare(v) <= 0;
    };
    SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals;

    BigInteger.prototype.isEven = function () {
        return (this.value[0] & 1) === 0;
    };
    SmallInteger.prototype.isEven = function () {
        return (this.value & 1) === 0;
    };

    BigInteger.prototype.isOdd = function () {
        return (this.value[0] & 1) === 1;
    };
    SmallInteger.prototype.isOdd = function () {
        return (this.value & 1) === 1;
    };

    BigInteger.prototype.isPositive = function () {
        return !this.sign;
    };
    SmallInteger.prototype.isPositive = function () {
        return this.value > 0;
    };

    BigInteger.prototype.isNegative = function () {
        return this.sign;
    };
    SmallInteger.prototype.isNegative = function () {
        return this.value < 0;
    };

    BigInteger.prototype.isUnit = function () {
        return false;
    };
    SmallInteger.prototype.isUnit = function () {
        return Math.abs(this.value) === 1;
    };

    BigInteger.prototype.isZero = function () {
        return false;
    };
    SmallInteger.prototype.isZero = function () {
        return this.value === 0;
    };
    BigInteger.prototype.isDivisibleBy = function (v) {
        var n = parseValue(v);
        var value = n.value;
        if (value === 0) return false;
        if (value === 1) return true;
        if (value === 2) return this.isEven();
        return this.mod(n).equals(Integer[0]);
    };
    SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy;

    function isBasicPrime(v) {
        var n = v.abs();
        if (n.isUnit()) return false;
        if (n.equals(2) || n.equals(3) || n.equals(5)) return true;
        if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false;
        if (n.lesser(25)) return true;
        // we don't know if it's prime: let the other functions figure it out
    }

    BigInteger.prototype.isPrime = function () {
        var isPrime = isBasicPrime(this);
        if (isPrime !== undefined) return isPrime;
        var n = this.abs(),
            nPrev = n.prev();
        var a = [2, 3, 5, 7, 11, 13, 17, 19],
            b = nPrev,
            d, t, i, x;
        while (b.isEven()) b = b.divide(2);
        for (i = 0; i < a.length; i++) {
            x = bigInt(a[i]).modPow(b, n);
            if (x.equals(Integer[1]) || x.equals(nPrev)) continue;
            for (t = true, d = b; t && d.lesser(nPrev) ; d = d.multiply(2)) {
                x = x.square().mod(n);
                if (x.equals(nPrev)) t = false;
            }
            if (t) return false;
        }
        return true;
    };
    SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime;

    BigInteger.prototype.isProbablePrime = function (iterations) {
        var isPrime = isBasicPrime(this);
        if (isPrime !== undefined) return isPrime;
        var n = this.abs();
        var t = iterations === undefined ? 5 : iterations;
        // use the Fermat primality test
        for (var i = 0; i < t; i++) {
            var a = bigInt.randBetween(2, n.minus(2));
            if (!a.modPow(n.prev(), n).isUnit()) return false; // definitely composite
        }
        return true; // large chance of being prime
    };
    SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime;

    BigInteger.prototype.next = function () {
        var value = this.value;
        if (this.sign) {
            return subtractSmall(value, 1, this.sign);
        }
        return new BigInteger(addSmall(value, 1), this.sign);
    };
    SmallInteger.prototype.next = function () {
        var value = this.value;
        if (value + 1 < MAX_INT) return new SmallInteger(value + 1);
        return new BigInteger(MAX_INT_ARR, false);
    };

    BigInteger.prototype.prev = function () {
        var value = this.value;
        if (this.sign) {
            return new BigInteger(addSmall(value, 1), true);
        }
        return subtractSmall(value, 1, this.sign);
    };
    SmallInteger.prototype.prev = function () {
        var value = this.value;
        if (value - 1 > -MAX_INT) return new SmallInteger(value - 1);
        return new BigInteger(MAX_INT_ARR, true);
    };

    var powersOfTwo = [1];
    while (powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]);
    var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1];

    function shift_isSmall(n) {
        return ((typeof n === "number" || typeof n === "string") && +Math.abs(n) <= BASE) ||
            (n instanceof BigInteger && n.value.length <= 1);
    }

    BigInteger.prototype.shiftLeft = function (n) {
        if (!shift_isSmall(n)) {
            throw new Error(String(n) + " is too large for shifting.");
        }
        n = +n;
        if (n < 0) return this.shiftRight(-n);
        var result = this;
        while (n >= powers2Length) {
            result = result.multiply(highestPower2);
            n -= powers2Length - 1;
        }
        return result.multiply(powersOfTwo[n]);
    };
    SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft;

    BigInteger.prototype.shiftRight = function (n) {
        var remQuo;
        if (!shift_isSmall(n)) {
            throw new Error(String(n) + " is too large for shifting.");
        }
        n = +n;
        if (n < 0) return this.shiftLeft(-n);
        var result = this;
        while (n >= powers2Length) {
            if (result.isZero()) return result;
            remQuo = divModAny(result, highestPower2);
            result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
            n -= powers2Length - 1;
        }
        remQuo = divModAny(result, powersOfTwo[n]);
        return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
    };
    SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight;

    function bitwise(x, y, fn) {
        y = parseValue(y);
        var xSign = x.isNegative(), ySign = y.isNegative();
        var xRem = xSign ? x.not() : x,
            yRem = ySign ? y.not() : y;
        var xBits = [], yBits = [];
        var xStop = false, yStop = false;
        while (!xStop || !yStop) {
            if (xRem.isZero()) { // virtual sign extension for simulating two's complement
                xStop = true;
                xBits.push(xSign ? 1 : 0);
            }
            else if (xSign) xBits.push(xRem.isEven() ? 1 : 0); // two's complement for negative numbers
            else xBits.push(xRem.isEven() ? 0 : 1);

            if (yRem.isZero()) {
                yStop = true;
                yBits.push(ySign ? 1 : 0);
            }
            else if (ySign) yBits.push(yRem.isEven() ? 1 : 0);
            else yBits.push(yRem.isEven() ? 0 : 1);

            xRem = xRem.over(2);
            yRem = yRem.over(2);
        }
        var result = [];
        for (var i = 0; i < xBits.length; i++) result.push(fn(xBits[i], yBits[i]));
        var sum = bigInt(result.pop()).negate().times(bigInt(2).pow(result.length));
        while (result.length) {
            sum = sum.add(bigInt(result.pop()).times(bigInt(2).pow(result.length)));
        }
        return sum;
    }

    BigInteger.prototype.not = function () {
        return this.negate().prev();
    };
    SmallInteger.prototype.not = BigInteger.prototype.not;

    BigInteger.prototype.and = function (n) {
        return bitwise(this, n, function (a, b) { return a & b; });
    };
    SmallInteger.prototype.and = BigInteger.prototype.and;

    BigInteger.prototype.or = function (n) {
        return bitwise(this, n, function (a, b) { return a | b; });
    };
    SmallInteger.prototype.or = BigInteger.prototype.or;

    BigInteger.prototype.xor = function (n) {
        return bitwise(this, n, function (a, b) { return a ^ b; });
    };
    SmallInteger.prototype.xor = BigInteger.prototype.xor;

    var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I;
    function roughLOB(n) { // get lowestOneBit (rough)
        // SmallInteger: return Min(lowestOneBit(n), 1 << 30)
        // BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7]
        var v = n.value, x = typeof v === "number" ? v | LOBMASK_I : v[0] + v[1] * BASE | LOBMASK_BI;
        return x & -x;
    }

    function max(a, b) {
        a = parseValue(a);
        b = parseValue(b);
        return a.greater(b) ? a : b;
    }
    function min(a,b) {
        a = parseValue(a);
        b = parseValue(b);
        return a.lesser(b) ? a : b;
    }
    function gcd(a, b) {
        a = parseValue(a).abs();
        b = parseValue(b).abs();
        if (a.equals(b)) return a;
        if (a.isZero()) return b;
        if (b.isZero()) return a;
        var c = Integer[1], d, t;
        while (a.isEven() && b.isEven()) {
            d = Math.min(roughLOB(a), roughLOB(b));
            a = a.divide(d);
            b = b.divide(d);
            c = c.multiply(d);
        }
        while (a.isEven()) {
            a = a.divide(roughLOB(a));
        }
        do {
            while (b.isEven()) {
                b = b.divide(roughLOB(b));
            }
            if (a.greater(b)) {
                t = b; b = a; a = t;
            }
            b = b.subtract(a);
        } while (!b.isZero());
        return c.isUnit() ? a : a.multiply(c);
    }
    function lcm(a, b) {
        a = parseValue(a).abs();
        b = parseValue(b).abs();
        return a.divide(gcd(a, b)).multiply(b);
    }
    function randBetween(a, b) {
        a = parseValue(a);
        b = parseValue(b);
        var low = min(a, b), high = max(a, b);
        var range = high.subtract(low);
        if (range.isSmall) return low.add(Math.round(Math.random() * range));
        var length = range.value.length - 1;
        var result = [], restricted = true;
        for (var i = length; i >= 0; i--) {
            var top = restricted ? range.value[i] : BASE;
            var digit = truncate(Math.random() * top);
            result.unshift(digit);
            if (digit < top) restricted = false;
        }
        result = arrayToSmall(result);
        return low.add(typeof result === "number" ? new SmallInteger(result) : new BigInteger(result, false));
    }
    var parseBase = function (text, base) {
        var val = Integer[0], pow = Integer[1],
            length = text.length;
        if (2 <= base && base <= 36) {
            if (length <= LOG_MAX_INT / Math.log(base)) {
                return new SmallInteger(parseInt(text, base));
            }
        }
        base = parseValue(base);
        var digits = [];
        var i;
        var isNegative = text[0] === "-";
        for (i = isNegative ? 1 : 0; i < text.length; i++) {
            var c = text[i].toLowerCase(),
                charCode = c.charCodeAt(0);
            if (48 <= charCode && charCode <= 57) digits.push(parseValue(c));
            else if (97 <= charCode && charCode <= 122) digits.push(parseValue(c.charCodeAt(0) - 87));
            else if (c === "<") {
                var start = i;
                do { i++; } while (text[i] !== ">");
                digits.push(parseValue(text.slice(start + 1, i)));
            }
            else throw new Error(c + " is not a valid character");
        }
        digits.reverse();
        for (i = 0; i < digits.length; i++) {
            val = val.add(digits[i].times(pow));
            pow = pow.times(base);
        }
        return isNegative ? val.negate() : val;
    };

    function stringify(digit) {
        var v = digit.value;
        if (typeof v === "number") v = [v];
        if (v.length === 1 && v[0] <= 35) {
            return "0123456789abcdefghijklmnopqrstuvwxyz".charAt(v[0]);
        }
        return "<" + v + ">";
    }
    function toBase(n, base) {
        base = bigInt(base);
        if (base.isZero()) {
            if (n.isZero()) return "0";
            throw new Error("Cannot convert nonzero numbers to base 0.");
        }
        if (base.equals(-1)) {
            if (n.isZero()) return "0";
            if (n.isNegative()) return new Array(1 - n).join("10");
            return "1" + new Array(+n).join("01");
        }
        var minusSign = "";
        if (n.isNegative() && base.isPositive()) {
            minusSign = "-";
            n = n.abs();
        }
        if (base.equals(1)) {
            if (n.isZero()) return "0";
            return minusSign + new Array(+n + 1).join(1);
        }
        var out = [];
        var left = n, divmod;
        while (left.isNegative() || left.compareAbs(base) >= 0) {
            divmod = left.divmod(base);
            left = divmod.quotient;
            var digit = divmod.remainder;
            if (digit.isNegative()) {
                digit = base.minus(digit).abs();
                left = left.next();
            }
            out.push(stringify(digit));
        }
        out.push(stringify(left));
        return minusSign + out.reverse().join("");
    }

    BigInteger.prototype.toString = function (radix) {
        if (radix === undefined) radix = 10;
        if (radix !== 10) return toBase(this, radix);
        var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit;
        while (--l >= 0) {
            digit = String(v[l]);
            str += zeros.slice(digit.length) + digit;
        }
        var sign = this.sign ? "-" : "";
        return sign + str;
    };
    SmallInteger.prototype.toString = function (radix) {
        if (radix === undefined) radix = 10;
        if (radix != 10) return toBase(this, radix);
        return String(this.value);
    };

    BigInteger.prototype.valueOf = function () {
        return +this.toString();
    };
    BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf;

    SmallInteger.prototype.valueOf = function () {
        return this.value;
    };
    SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf;
    
    function parseStringValue(v) {
            if (isPrecise(+v)) {
                var x = +v;
                if (x === truncate(x))
                    return new SmallInteger(x);
                throw "Invalid integer: " + v;
            }
            var sign = v[0] === "-";
            if (sign) v = v.slice(1);
            var split = v.split(/e/i);
            if (split.length > 2) throw new Error("Invalid integer: " + split.join("e"));
            if (split.length === 2) {
                var exp = split[1];
                if (exp[0] === "+") exp = exp.slice(1);
                exp = +exp;
                if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent.");
                var text = split[0];
                var decimalPlace = text.indexOf(".");
                if (decimalPlace >= 0) {
                    exp -= text.length - decimalPlace - 1;
                    text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1);
                }
                if (exp < 0) throw new Error("Cannot include negative exponent part for integers");
                text += (new Array(exp + 1)).join("0");
                v = text;
            }
            var isValid = /^([0-9][0-9]*)$/.test(v);
            if (!isValid) throw new Error("Invalid integer: " + v);
            var r = [], max = v.length, l = LOG_BASE, min = max - l;
            while (max > 0) {
                r.push(+v.slice(min, max));
                min -= l;
                if (min < 0) min = 0;
                max -= l;
            }
            trim(r);
            return new BigInteger(r, sign);
    }
    
    function parseNumberValue(v) {
        if (isPrecise(v)) {
            if (v !== truncate(v)) throw new Error(v + " is not an integer.");
            return new SmallInteger(v);
        }
        return parseStringValue(v.toString());
    }

    function parseValue(v) {
        if (typeof v === "number") {
            return parseNumberValue(v);
        }
        if (typeof v === "string") {
            return parseStringValue(v);
        }
        return v;
    }
    // Pre-define numbers in range [-999,999]
    for (var i = 0; i < 1000; i++) {
        Integer[i] = new SmallInteger(i);
        if (i > 0) Integer[-i] = new SmallInteger(-i);
    }
    // Backwards compatibility
    Integer.one = Integer[1];
    Integer.zero = Integer[0];
    Integer.minusOne = Integer[-1];
    Integer.max = max;
    Integer.min = min;
    Integer.gcd = gcd;
    Integer.lcm = lcm;
    Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger; };
    Integer.randBetween = randBetween;
    return Integer;
})();

// Node.js check
if (typeof module !== "undefined" && module.hasOwnProperty("exports")) {
    module.exports = bigInt;
}

},{}],14:[function(require,module,exports){
this.j$ = this.jStat = (function(Math, undefined) {

// For quick reference.
var concat = Array.prototype.concat;
var slice = Array.prototype.slice;
var toString = Object.prototype.toString;

// Calculate correction for IEEE error
// TODO: This calculation can be improved.
function calcRdx(n, m) {
  var val = n > m ? n : m;
  return Math.pow(10,
                  17 - ~~(Math.log(((val > 0) ? val : -val)) * Math.LOG10E));
}


var isArray = Array.isArray || function isArray(arg) {
  return toString.call(arg) === '[object Array]';
};


function isFunction(arg) {
  return toString.call(arg) === '[object Function]';
}


function isNumber(arg) {
  return typeof arg === 'number' && arg === arg;
}


// Converts the jStat matrix to vector.
function toVector(arr) {
  return concat.apply([], arr);
}


// The one and only jStat constructor.
function jStat() {
  return new jStat._init(arguments);
}


// TODO: Remove after all references in src files have been removed.
jStat.fn = jStat.prototype;


// By separating the initializer from the constructor it's easier to handle
// always returning a new instance whether "new" was used or not.
jStat._init = function _init(args) {
  var i;

  // If first argument is an array, must be vector or matrix.
  if (isArray(args[0])) {
    // Check if matrix.
    if (isArray(args[0][0])) {
      // See if a mapping function was also passed.
      if (isFunction(args[1]))
        args[0] = jStat.map(args[0], args[1]);
      // Iterate over each is faster than this.push.apply(this, args[0].
      for (i = 0; i < args[0].length; i++)
        this[i] = args[0][i];
      this.length = args[0].length;

    // Otherwise must be a vector.
    } else {
      this[0] = isFunction(args[1]) ? jStat.map(args[0], args[1]) : args[0];
      this.length = 1;
    }

  // If first argument is number, assume creation of sequence.
  } else if (isNumber(args[0])) {
    this[0] = jStat.seq.apply(null, args);
    this.length = 1;

  // Handle case when jStat object is passed to jStat.
  } else if (args[0] instanceof jStat) {
    // Duplicate the object and pass it back.
    return jStat(args[0].toArray());

  // Unexpected argument value, return empty jStat object.
  // TODO: This is strange behavior. Shouldn't this throw or some such to let
  // the user know they had bad arguments?
  } else {
    this[0] = [];
    this.length = 1;
  }

  return this;
};
jStat._init.prototype = jStat.prototype;
jStat._init.constructor = jStat;


// Utility functions.
// TODO: for internal use only?
jStat.utils = {
  calcRdx: calcRdx,
  isArray: isArray,
  isFunction: isFunction,
  isNumber: isNumber,
  toVector: toVector
};


// Easily extend the jStat object.
// TODO: is this seriously necessary?
jStat.extend = function extend(obj) {
  var i, j;

  if (arguments.length === 1) {
    for (j in obj)
      jStat[j] = obj[j];
    return this;
  }

  for (i = 1; i < arguments.length; i++) {
    for (j in arguments[i])
      obj[j] = arguments[i][j];
  }

  return obj;
};


// Returns the number of rows in the matrix.
jStat.rows = function rows(arr) {
  return arr.length || 1;
};


// Returns the number of columns in the matrix.
jStat.cols = function cols(arr) {
  return arr[0].length || 1;
};


// Returns the dimensions of the object { rows: i, cols: j }
jStat.dimensions = function dimensions(arr) {
  return {
    rows: jStat.rows(arr),
    cols: jStat.cols(arr)
  };
};


// Returns a specified row as a vector
jStat.row = function row(arr, index) {
  return arr[index];
};


// Returns the specified column as a vector
jStat.col = function cols(arr, index) {
  var column = new Array(arr.length);
  for (var i = 0; i < arr.length; i++)
    column[i] = [arr[i][index]];
  return column;
};


// Returns the diagonal of the matrix
jStat.diag = function diag(arr) {
  var nrow = jStat.rows(arr);
  var res = new Array(nrow);
  for (var row = 0; row < nrow; row++)
    res[row] = [arr[row][row]];
  return res;
};


// Returns the anti-diagonal of the matrix
jStat.antidiag = function antidiag(arr) {
  var nrow = jStat.rows(arr) - 1;
  var res = new Array(nrow);
  for (var i = 0; nrow >= 0; nrow--, i++)
    res[i] = [arr[i][nrow]];
  return res;
};

// Transpose a matrix or array.
jStat.transpose = function transpose(arr) {
  var obj = [];
  var objArr, rows, cols, j, i;

  // Make sure arr is in matrix format.
  if (!isArray(arr[0]))
    arr = [arr];

  rows = arr.length;
  cols = arr[0].length;

  for (i = 0; i < cols; i++) {
    objArr = new Array(rows);
    for (j = 0; j < rows; j++)
      objArr[j] = arr[j][i];
    obj.push(objArr);
  }

  // If obj is vector, return only single array.
  return obj.length === 1 ? obj[0] : obj;
};


// Map a function to an array or array of arrays.
// "toAlter" is an internal variable.
jStat.map = function map(arr, func, toAlter) {
  var row, nrow, ncol, res, col;

  if (!isArray(arr[0]))
    arr = [arr];

  nrow = arr.length;
  ncol = arr[0].length;
  res = toAlter ? arr : new Array(nrow);

  for (row = 0; row < nrow; row++) {
    // if the row doesn't exist, create it
    if (!res[row])
      res[row] = new Array(ncol);
    for (col = 0; col < ncol; col++)
      res[row][col] = func(arr[row][col], row, col);
  }

  return res.length === 1 ? res[0] : res;
};


// Cumulatively combine the elements of an array or array of arrays using a function.
jStat.cumreduce = function cumreduce(arr, func, toAlter) {
  var row, nrow, ncol, res, col;

  if (!isArray(arr[0]))
    arr = [arr];

  nrow = arr.length;
  ncol = arr[0].length;
  res = toAlter ? arr : new Array(nrow);

  for (row = 0; row < nrow; row++) {
    // if the row doesn't exist, create it
    if (!res[row])
      res[row] = new Array(ncol);
    if (ncol > 0)
      res[row][0] = arr[row][0];
    for (col = 1; col < ncol; col++)
      res[row][col] = func(res[row][col-1], arr[row][col]);
  }
  return res.length === 1 ? res[0] : res;
};


// Destructively alter an array.
jStat.alter = function alter(arr, func) {
  return jStat.map(arr, func, true);
};


// Generate a rows x cols matrix according to the supplied function.
jStat.create = function  create(rows, cols, func) {
  var res = new Array(rows);
  var i, j;

  if (isFunction(cols)) {
    func = cols;
    cols = rows;
  }

  for (i = 0; i < rows; i++) {
    res[i] = new Array(cols);
    for (j = 0; j < cols; j++)
      res[i][j] = func(i, j);
  }

  return res;
};


function retZero() { return 0; }


// Generate a rows x cols matrix of zeros.
jStat.zeros = function zeros(rows, cols) {
  if (!isNumber(cols))
    cols = rows;
  return jStat.create(rows, cols, retZero);
};


function retOne() { return 1; }


// Generate a rows x cols matrix of ones.
jStat.ones = function ones(rows, cols) {
  if (!isNumber(cols))
    cols = rows;
  return jStat.create(rows, cols, retOne);
};


// Generate a rows x cols matrix of uniformly random numbers.
jStat.rand = function rand(rows, cols) {
  if (!isNumber(cols))
    cols = rows;
  return jStat.create(rows, cols, Math.random);
};


function retIdent(i, j) { return i === j ? 1 : 0; }


// Generate an identity matrix of size row x cols.
jStat.identity = function identity(rows, cols) {
  if (!isNumber(cols))
    cols = rows;
  return jStat.create(rows, cols, retIdent);
};


// Tests whether a matrix is symmetric
jStat.symmetric = function symmetric(arr) {
  var issymmetric = true;
  var size = arr.length;
  var row, col;

  if (arr.length !== arr[0].length)
    return false;

  for (row = 0; row < size; row++) {
    for (col = 0; col < size; col++)
      if (arr[col][row] !== arr[row][col])
        return false;
  }

  return true;
};


// Set all values to zero.
jStat.clear = function clear(arr) {
  return jStat.alter(arr, retZero);
};


// Generate sequence.
jStat.seq = function seq(min, max, length, func) {
  if (!isFunction(func))
    func = false;

  var arr = [];
  var hival = calcRdx(min, max);
  var step = (max * hival - min * hival) / ((length - 1) * hival);
  var current = min;
  var cnt;

  // Current is assigned using a technique to compensate for IEEE error.
  // TODO: Needs better implementation.
  for (cnt = 0;
       current <= max;
       cnt++, current = (min * hival + step * hival * cnt) / hival) {
    arr.push((func ? func(current, cnt) : current));
  }

  return arr;
};


// TODO: Go over this entire implementation. Seems a tragic waste of resources
// doing all this work. Instead, and while ugly, use new Function() to generate
// a custom function for each static method.

// Quick reference.
var jProto = jStat.prototype;

// Default length.
jProto.length = 0;

// For internal use only.
// TODO: Check if they're actually used, and if they are then rename them
// to _*
jProto.push = Array.prototype.push;
jProto.sort = Array.prototype.sort;
jProto.splice = Array.prototype.splice;
jProto.slice = Array.prototype.slice;


// Return a clean array.
jProto.toArray = function toArray() {
  return this.length > 1 ? slice.call(this) : slice.call(this)[0];
};


// Map a function to a matrix or vector.
jProto.map = function map(func, toAlter) {
  return jStat(jStat.map(this, func, toAlter));
};


// Cumulatively combine the elements of a matrix or vector using a function.
jProto.cumreduce = function cumreduce(func, toAlter) {
  return jStat(jStat.cumreduce(this, func, toAlter));
};


// Destructively alter an array.
jProto.alter = function alter(func) {
  jStat.alter(this, func);
  return this;
};


// Extend prototype with methods that have no argument.
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    jProto[passfunc] = function(func) {
      var self = this,
      results;
      // Check for callback.
      if (func) {
        setTimeout(function() {
          func.call(self, jProto[passfunc].call(self));
        });
        return this;
      }
      results = jStat[passfunc](this);
      return isArray(results) ? jStat(results) : results;
    };
  })(funcs[i]);
})('transpose clear symmetric rows cols dimensions diag antidiag'.split(' '));


// Extend prototype with methods that have one argument.
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    jProto[passfunc] = function(index, func) {
      var self = this;
      // check for callback
      if (func) {
        setTimeout(function() {
          func.call(self, jProto[passfunc].call(self, index));
        });
        return this;
      }
      return jStat(jStat[passfunc](this, index));
    };
  })(funcs[i]);
})('row col'.split(' '));


// Extend prototype with simple shortcut methods.
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    jProto[passfunc] = new Function(
        'return jStat(jStat.' + passfunc + '.apply(null, arguments));');
  })(funcs[i]);
})('create zeros ones rand identity'.split(' '));


// Exposing jStat.
return jStat;

}(Math));
(function(jStat, Math) {

var isFunction = jStat.utils.isFunction;

// Ascending functions for sort
function ascNum(a, b) { return a - b; }

function clip(arg, min, max) {
  return Math.max(min, Math.min(arg, max));
}


// sum of an array
jStat.sum = function sum(arr) {
  var sum = 0;
  var i = arr.length;
  while (--i >= 0)
    sum += arr[i];
  return sum;
};


// sum squared
jStat.sumsqrd = function sumsqrd(arr) {
  var sum = 0;
  var i = arr.length;
  while (--i >= 0)
    sum += arr[i] * arr[i];
  return sum;
};


// sum of squared errors of prediction (SSE)
jStat.sumsqerr = function sumsqerr(arr) {
  var mean = jStat.mean(arr);
  var sum = 0;
  var i = arr.length;
  var tmp;
  while (--i >= 0) {
    tmp = arr[i] - mean;
    sum += tmp * tmp;
  }
  return sum;
};

// sum of an array in each row
jStat.sumrow = function sumrow(arr) {
  var sum = 0;
  var i = arr.length;
  while (--i >= 0)
    sum += arr[i];
  return sum;
};

// product of an array
jStat.product = function product(arr) {
  var prod = 1;
  var i = arr.length;
  while (--i >= 0)
    prod *= arr[i];
  return prod;
};


// minimum value of an array
jStat.min = function min(arr) {
  var low = arr[0];
  var i = 0;
  while (++i < arr.length)
    if (arr[i] < low)
      low = arr[i];
  return low;
};


// maximum value of an array
jStat.max = function max(arr) {
  var high = arr[0];
  var i = 0;
  while (++i < arr.length)
    if (arr[i] > high)
      high = arr[i];
  return high;
};


// unique values of an array
jStat.unique = function unique(arr) {
  var hash = {}, _arr = [];
  for(var i = 0; i < arr.length; i++) {
    if (!hash[arr[i]]) {
      hash[arr[i]] = true;
      _arr.push(arr[i]);
    }
  }
  return _arr;
};


// mean value of an array
jStat.mean = function mean(arr) {
  return jStat.sum(arr) / arr.length;
};


// mean squared error (MSE)
jStat.meansqerr = function meansqerr(arr) {
  return jStat.sumsqerr(arr) / arr.length;
};


// geometric mean of an array
jStat.geomean = function geomean(arr) {
  return Math.pow(jStat.product(arr), 1 / arr.length);
};


// median of an array
jStat.median = function median(arr) {
  var arrlen = arr.length;
  var _arr = arr.slice().sort(ascNum);
  // check if array is even or odd, then return the appropriate
  return !(arrlen & 1)
    ? (_arr[(arrlen / 2) - 1 ] + _arr[(arrlen / 2)]) / 2
    : _arr[(arrlen / 2) | 0 ];
};


// cumulative sum of an array
jStat.cumsum = function cumsum(arr) {
  return jStat.cumreduce(arr, function (a, b) { return a + b; });
};


// cumulative product of an array
jStat.cumprod = function cumprod(arr) {
  return jStat.cumreduce(arr, function (a, b) { return a * b; });
};


// successive differences of a sequence
jStat.diff = function diff(arr) {
  var diffs = [];
  var arrLen = arr.length;
  var i;
  for (i = 1; i < arrLen; i++)
    diffs.push(arr[i] - arr[i - 1]);
  return diffs;
};


// ranks of an array
jStat.rank = function (arr) {
  var arrlen = arr.length;
  var sorted = arr.slice().sort(ascNum);
  var ranks = new Array(arrlen);
  for (var i = 0; i < arrlen; i++) {
    var first = sorted.indexOf(arr[i]);
    var last = sorted.lastIndexOf(arr[i]);
    if (first === last) {
      var val = first;
    } else {
      var val = (first + last) / 2;
    }
    ranks[i] = val + 1;
  }
  return ranks;
};


// mode of an array
// if there are multiple modes of an array, return all of them
// is this the appropriate way of handling it?
jStat.mode = function mode(arr) {
  var arrLen = arr.length;
  var _arr = arr.slice().sort(ascNum);
  var count = 1;
  var maxCount = 0;
  var numMaxCount = 0;
  var mode_arr = [];
  var i;

  for (i = 0; i < arrLen; i++) {
    if (_arr[i] === _arr[i + 1]) {
      count++;
    } else {
      if (count > maxCount) {
        mode_arr = [_arr[i]];
        maxCount = count;
        numMaxCount = 0;
      }
      // are there multiple max counts
      else if (count === maxCount) {
        mode_arr.push(_arr[i]);
        numMaxCount++;
      }
      // resetting count for new value in array
      count = 1;
    }
  }

  return numMaxCount === 0 ? mode_arr[0] : mode_arr;
};


// range of an array
jStat.range = function range(arr) {
  return jStat.max(arr) - jStat.min(arr);
};

// variance of an array
// flag = true indicates sample instead of population
jStat.variance = function variance(arr, flag) {
  return jStat.sumsqerr(arr) / (arr.length - (flag ? 1 : 0));
};

// deviation of an array
jStat.deviation = function (arr) {
  var mean = jStat.mean(arr);
  var arrlen = arr.length;
  var dev = new Array(arrlen);
  for (var i = 0; i < arrlen; i++) {
    dev[i] = arr[i] - mean;
  }
  return dev;
};

// standard deviation of an array
// flag = true indicates sample instead of population
jStat.stdev = function stdev(arr, flag) {
  return Math.sqrt(jStat.variance(arr, flag));
};


// mean deviation (mean absolute deviation) of an array
jStat.meandev = function meandev(arr) {
  var devSum = 0;
  var mean = jStat.mean(arr);
  var i;
  for (i = arr.length - 1; i >= 0; i--)
    devSum += Math.abs(arr[i] - mean);
  return devSum / arr.length;
};


// median deviation (median absolute deviation) of an array
jStat.meddev = function meddev(arr) {
  var devSum = 0;
  var median = jStat.median(arr);
  var i;
  for (i = arr.length - 1; i >= 0; i--)
    devSum += Math.abs(arr[i] - median);
  return devSum / arr.length;
};


// coefficient of variation
jStat.coeffvar = function coeffvar(arr) {
  return jStat.stdev(arr) / jStat.mean(arr);
};


// quartiles of an array
jStat.quartiles = function quartiles(arr) {
  var arrlen = arr.length;
  var _arr = arr.slice().sort(ascNum);
  return [
    _arr[ Math.round((arrlen) / 4) - 1 ],
    _arr[ Math.round((arrlen) / 2) - 1 ],
    _arr[ Math.round((arrlen) * 3 / 4) - 1 ]
  ];
};


// Arbitary quantiles of an array. Direct port of the scipy.stats
// implementation by Pierre GF Gerard-Marchant.
jStat.quantiles = function quantiles(arr, quantilesArray, alphap, betap) {
  var sortedArray = arr.slice().sort(ascNum);
  var quantileVals = [quantilesArray.length];
  var n = arr.length;
  var i, p, m, aleph, k, gamma;

  if (typeof alphap === 'undefined')
    alphap = 3 / 8;
  if (typeof betap === 'undefined')
    betap = 3 / 8;

  for (i = 0; i < quantilesArray.length; i++) {
    p = quantilesArray[i];
    m = alphap + p * (1 - alphap - betap);
    aleph = n * p + m;
    k = Math.floor(clip(aleph, 1, n - 1));
    gamma = clip(aleph - k, 0, 1);
    quantileVals[i] = (1 - gamma) * sortedArray[k - 1] + gamma * sortedArray[k];
  }

  return quantileVals;
};

// Returns the k-th percentile of values in a range, where k is in the
// range 0..1, exclusive.
jStat.percentile = function percentile(arr, k) {
  var _arr = arr.slice().sort(ascNum);
  var realIndex = k * (_arr.length - 1);
  var index = parseInt(realIndex);
  var frac = realIndex - index;

  if (index + 1 < _arr.length) {
    return _arr[index] * (1 - frac) + _arr[index + 1] * frac;
  } else {
    return _arr[index];
  }
}


// The percentile rank of score in a given array. Returns the percentage
// of all values in the input array that are less than (kind='strict') or
// less or equal than (kind='weak') score. Default is weak.
jStat.percentileOfScore = function percentileOfScore(arr, score, kind) {
  var counter = 0;
  var len = arr.length;
  var strict = false;
  var value, i;

  if (kind === 'strict')
    strict = true;

  for (i = 0; i < len; i++) {
    value = arr[i];
    if ((strict && value < score) ||
        (!strict && value <= score)) {
      counter++;
    }
  }

  return counter / len;
};


// Histogram (bin count) data
jStat.histogram = function histogram(arr, bins) {
  var first = jStat.min(arr);
  var binCnt = bins || 4;
  var binWidth = (jStat.max(arr) - first) / binCnt;
  var len = arr.length;
  var bins = [];
  var i;

  for (i = 0; i < binCnt; i++)
    bins[i] = 0;
  for (i = 0; i < len; i++)
    bins[Math.min(Math.floor(((arr[i] - first) / binWidth)), binCnt - 1)] += 1;

  return bins;
};


// covariance of two arrays
jStat.covariance = function covariance(arr1, arr2) {
  var u = jStat.mean(arr1);
  var v = jStat.mean(arr2);
  var arr1Len = arr1.length;
  var sq_dev = new Array(arr1Len);
  var i;

  for (i = 0; i < arr1Len; i++)
    sq_dev[i] = (arr1[i] - u) * (arr2[i] - v);

  return jStat.sum(sq_dev) / (arr1Len - 1);
};


// (pearson's) population correlation coefficient, rho
jStat.corrcoeff = function corrcoeff(arr1, arr2) {
  return jStat.covariance(arr1, arr2) /
      jStat.stdev(arr1, 1) /
      jStat.stdev(arr2, 1);
};

  // (spearman's) rank correlation coefficient, sp
jStat.spearmancoeff =  function (arr1, arr2) {
  arr1 = jStat.rank(arr1);
  arr2 = jStat.rank(arr2);
  var arr1dev = jStat.deviation(arr1);
  var arr2dev = jStat.deviation(arr2);
  return jStat.sum(arr1dev.map(function (x, i) {
    return x * arr2dev[i];
  })) /
  Math.sqrt(jStat.sum(arr1dev.map(function (x) {
    return Math.pow(x, 2);
    })) * jStat.sum(arr2dev.map(function (x) {
      return Math.pow(x, 2);
  }))
  );
}


// statistical standardized moments (general form of skew/kurt)
jStat.stanMoment = function stanMoment(arr, n) {
  var mu = jStat.mean(arr);
  var sigma = jStat.stdev(arr);
  var len = arr.length;
  var skewSum = 0;

  for (i = 0; i < len; i++)
    skewSum += Math.pow((arr[i] - mu) / sigma, n);

  return skewSum / arr.length;
};

// (pearson's) moment coefficient of skewness
jStat.skewness = function skewness(arr) {
  return jStat.stanMoment(arr, 3);
};

// (pearson's) (excess) kurtosis
jStat.kurtosis = function kurtosis(arr) {
  return jStat.stanMoment(arr, 4) - 3;
};


var jProto = jStat.prototype;


// Extend jProto with method for calculating cumulative sums and products.
// This differs from the similar extension below as cumsum and cumprod should
// not be run again in the case fullbool === true.
// If a matrix is passed, automatically assume operation should be done on the
// columns.
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    // If a matrix is passed, automatically assume operation should be done on
    // the columns.
    jProto[passfunc] = function(fullbool, func) {
      var arr = [];
      var i = 0;
      var tmpthis = this;
      // Assignment reassignation depending on how parameters were passed in.
      if (isFunction(fullbool)) {
        func = fullbool;
        fullbool = false;
      }
      // Check if a callback was passed with the function.
      if (func) {
        setTimeout(function() {
          func.call(tmpthis, jProto[passfunc].call(tmpthis, fullbool));
        });
        return this;
      }
      // Check if matrix and run calculations.
      if (this.length > 1) {
        tmpthis = fullbool === true ? this : this.transpose();
        for (; i < tmpthis.length; i++)
          arr[i] = jStat[passfunc](tmpthis[i]);
        return arr;
      }
      // Pass fullbool if only vector, not a matrix. for variance and stdev.
      return jStat[passfunc](this[0], fullbool);
    };
  })(funcs[i]);
})(('cumsum cumprod').split(' '));


// Extend jProto with methods which don't require arguments and work on columns.
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    // If a matrix is passed, automatically assume operation should be done on
    // the columns.
    jProto[passfunc] = function(fullbool, func) {
      var arr = [];
      var i = 0;
      var tmpthis = this;
      // Assignment reassignation depending on how parameters were passed in.
      if (isFunction(fullbool)) {
        func = fullbool;
        fullbool = false;
      }
      // Check if a callback was passed with the function.
      if (func) {
        setTimeout(function() {
          func.call(tmpthis, jProto[passfunc].call(tmpthis, fullbool));
        });
        return this;
      }
      // Check if matrix and run calculations.
      if (this.length > 1) {
        if (passfunc !== 'sumrow')
          tmpthis = fullbool === true ? this : this.transpose();
        for (; i < tmpthis.length; i++)
          arr[i] = jStat[passfunc](tmpthis[i]);
        return fullbool === true
            ? jStat[passfunc](jStat.utils.toVector(arr))
            : arr;
      }
      // Pass fullbool if only vector, not a matrix. for variance and stdev.
      return jStat[passfunc](this[0], fullbool);
    };
  })(funcs[i]);
})(('sum sumsqrd sumsqerr sumrow product min max unique mean meansqerr ' +
    'geomean median diff rank mode range variance deviation stdev meandev ' +
    'meddev coeffvar quartiles histogram skewness kurtosis').split(' '));


// Extend jProto with functions that take arguments. Operations on matrices are
// done on columns.
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    jProto[passfunc] = function() {
      var arr = [];
      var i = 0;
      var tmpthis = this;
      var args = Array.prototype.slice.call(arguments);

      // If the last argument is a function, we assume it's a callback; we
      // strip the callback out and call the function again.
      if (isFunction(args[args.length - 1])) {
        var callbackFunction = args[args.length - 1];
        var argsToPass = args.slice(0, args.length - 1);

        setTimeout(function() {
          callbackFunction.call(tmpthis,
                                jProto[passfunc].apply(tmpthis, argsToPass));
        });
        return this;

      // Otherwise we curry the function args and call normally.
      } else {
        var callbackFunction = undefined;
        var curriedFunction = function curriedFunction(vector) {
          return jStat[passfunc].apply(tmpthis, [vector].concat(args));
        }
      }

      // If this is a matrix, run column-by-column.
      if (this.length > 1) {
        tmpthis = tmpthis.transpose();
        for (; i < tmpthis.length; i++)
          arr[i] = curriedFunction(tmpthis[i]);
        return arr;
      }

      // Otherwise run on the vector.
      return curriedFunction(this[0]);
    };
  })(funcs[i]);
})('quantiles percentileOfScore'.split(' '));

}(this.jStat, Math));
// Special functions //
(function(jStat, Math) {

// Log-gamma function
jStat.gammaln = function gammaln(x) {
  var j = 0;
  var cof = [
    76.18009172947146, -86.50532032941677, 24.01409824083091,
    -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5
  ];
  var ser = 1.000000000190015;
  var xx, y, tmp;
  tmp = (y = xx = x) + 5.5;
  tmp -= (xx + 0.5) * Math.log(tmp);
  for (; j < 6; j++)
    ser += cof[j] / ++y;
  return Math.log(2.5066282746310005 * ser / xx) - tmp;
};


// gamma of x
jStat.gammafn = function gammafn(x) {
  var p = [-1.716185138865495, 24.76565080557592, -379.80425647094563,
           629.3311553128184, 866.9662027904133, -31451.272968848367,
           -36144.413418691176, 66456.14382024054
  ];
  var q = [-30.8402300119739, 315.35062697960416, -1015.1563674902192,
           -3107.771671572311, 22538.118420980151, 4755.8462775278811,
           -134659.9598649693, -115132.2596755535];
  var fact = false;
  var n = 0;
  var xden = 0;
  var xnum = 0;
  var y = x;
  var i, z, yi, res, sum, ysq;
  if (y <= 0) {
    res = y % 1 + 3.6e-16;
    if (res) {
      fact = (!(y & 1) ? 1 : -1) * Math.PI / Math.sin(Math.PI * res);
      y = 1 - y;
    } else {
      return Infinity;
    }
  }
  yi = y;
  if (y < 1) {
    z = y++;
  } else {
    z = (y -= n = (y | 0) - 1) - 1;
  }
  for (i = 0; i < 8; ++i) {
    xnum = (xnum + p[i]) * z;
    xden = xden * z + q[i];
  }
  res = xnum / xden + 1;
  if (yi < y) {
    res /= yi;
  } else if (yi > y) {
    for (i = 0; i < n; ++i) {
      res *= y;
      y++;
    }
  }
  if (fact) {
    res = fact / res;
  }
  return res;
};


// lower incomplete gamma function, which is usually typeset with a
// lower-case greek gamma as the function symbol
jStat.gammap = function gammap(a, x) {
  return jStat.lowRegGamma(a, x) * jStat.gammafn(a);
};


// The lower regularized incomplete gamma function, usually written P(a,x)
jStat.lowRegGamma = function lowRegGamma(a, x) {
  var aln = jStat.gammaln(a);
  var ap = a;
  var sum = 1 / a;
  var del = sum;
  var b = x + 1 - a;
  var c = 1 / 1.0e-30;
  var d = 1 / b;
  var h = d;
  var i = 1;
  // calculate maximum number of itterations required for a
  var ITMAX = -~(Math.log((a >= 1) ? a : 1 / a) * 8.5 + a * 0.4 + 17);
  var an, endval;

  if (x < 0 || a <= 0) {
    return NaN;
  } else if (x < a + 1) {
    for (; i <= ITMAX; i++) {
      sum += del *= x / ++ap;
    }
    return (sum * Math.exp(-x + a * Math.log(x) - (aln)));
  }

  for (; i <= ITMAX; i++) {
    an = -i * (i - a);
    b += 2;
    d = an * d + b;
    c = b + an / c;
    d = 1 / d;
    h *= d * c;
  }

  return (1 - h * Math.exp(-x + a * Math.log(x) - (aln)));
};

// natural log factorial of n
jStat.factorialln = function factorialln(n) {
  return n < 0 ? NaN : jStat.gammaln(n + 1);
};

// factorial of n
jStat.factorial = function factorial(n) {
  return n < 0 ? NaN : jStat.gammafn(n + 1);
};

// combinations of n, m
jStat.combination = function combination(n, m) {
  // make sure n or m don't exceed the upper limit of usable values
  return (n > 170 || m > 170)
      ? Math.exp(jStat.combinationln(n, m))
      : (jStat.factorial(n) / jStat.factorial(m)) / jStat.factorial(n - m);
};


jStat.combinationln = function combinationln(n, m){
  return jStat.factorialln(n) - jStat.factorialln(m) - jStat.factorialln(n - m);
};


// permutations of n, m
jStat.permutation = function permutation(n, m) {
  return jStat.factorial(n) / jStat.factorial(n - m);
};


// beta function
jStat.betafn = function betafn(x, y) {
  // ensure arguments are positive
  if (x <= 0 || y <= 0)
    return undefined;
  // make sure x + y doesn't exceed the upper limit of usable values
  return (x + y > 170)
      ? Math.exp(jStat.betaln(x, y))
      : jStat.gammafn(x) * jStat.gammafn(y) / jStat.gammafn(x + y);
};


// natural logarithm of beta function
jStat.betaln = function betaln(x, y) {
  return jStat.gammaln(x) + jStat.gammaln(y) - jStat.gammaln(x + y);
};


// Evaluates the continued fraction for incomplete beta function by modified
// Lentz's method.
jStat.betacf = function betacf(x, a, b) {
  var fpmin = 1e-30;
  var m = 1;
  var qab = a + b;
  var qap = a + 1;
  var qam = a - 1;
  var c = 1;
  var d = 1 - qab * x / qap;
  var m2, aa, del, h;

  // These q's will be used in factors that occur in the coefficients
  if (Math.abs(d) < fpmin)
    d = fpmin;
  d = 1 / d;
  h = d;

  for (; m <= 100; m++) {
    m2 = 2 * m;
    aa = m * (b - m) * x / ((qam + m2) * (a + m2));
    // One step (the even one) of the recurrence
    d = 1 + aa * d;
    if (Math.abs(d) < fpmin)
      d = fpmin;
    c = 1 + aa / c;
    if (Math.abs(c) < fpmin)
      c = fpmin;
    d = 1 / d;
    h *= d * c;
    aa = -(a + m) * (qab + m) * x / ((a + m2) * (qap + m2));
    // Next step of the recurrence (the odd one)
    d = 1 + aa * d;
    if (Math.abs(d) < fpmin)
      d = fpmin;
    c = 1 + aa / c;
    if (Math.abs(c) < fpmin)
      c = fpmin;
    d = 1 / d;
    del = d * c;
    h *= del;
    if (Math.abs(del - 1.0) < 3e-7)
      break;
  }

  return h;
};


// Returns the inverse of the lower regularized inomplete gamma function
jStat.gammapinv = function gammapinv(p, a) {
  var j = 0;
  var a1 = a - 1;
  var EPS = 1e-8;
  var gln = jStat.gammaln(a);
  var x, err, t, u, pp, lna1, afac;

  if (p >= 1)
    return Math.max(100, a + 100 * Math.sqrt(a));
  if (p <= 0)
    return 0;
  if (a > 1) {
    lna1 = Math.log(a1);
    afac = Math.exp(a1 * (lna1 - 1) - gln);
    pp = (p < 0.5) ? p : 1 - p;
    t = Math.sqrt(-2 * Math.log(pp));
    x = (2.30753 + t * 0.27061) / (1 + t * (0.99229 + t * 0.04481)) - t;
    if (p < 0.5)
      x = -x;
    x = Math.max(1e-3,
                 a * Math.pow(1 - 1 / (9 * a) - x / (3 * Math.sqrt(a)), 3));
  } else {
    t = 1 - a * (0.253 + a * 0.12);
    if (p < t)
      x = Math.pow(p / t, 1 / a);
    else
      x = 1 - Math.log(1 - (p - t) / (1 - t));
  }

  for(; j < 12; j++) {
    if (x <= 0)
      return 0;
    err = jStat.lowRegGamma(a, x) - p;
    if (a > 1)
      t = afac * Math.exp(-(x - a1) + a1 * (Math.log(x) - lna1));
    else
      t = Math.exp(-x + a1 * Math.log(x) - gln);
    u = err / t;
    x -= (t = u / (1 - 0.5 * Math.min(1, u * ((a - 1) / x - 1))));
    if (x <= 0)
      x = 0.5 * (x + t);
    if (Math.abs(t) < EPS * x)
      break;
  }

  return x;
};


// Returns the error function erf(x)
jStat.erf = function erf(x) {
  var cof = [-1.3026537197817094, 6.4196979235649026e-1, 1.9476473204185836e-2,
             -9.561514786808631e-3, -9.46595344482036e-4, 3.66839497852761e-4,
             4.2523324806907e-5, -2.0278578112534e-5, -1.624290004647e-6,
             1.303655835580e-6, 1.5626441722e-8, -8.5238095915e-8,
             6.529054439e-9, 5.059343495e-9, -9.91364156e-10,
             -2.27365122e-10, 9.6467911e-11, 2.394038e-12,
             -6.886027e-12, 8.94487e-13, 3.13092e-13,
             -1.12708e-13, 3.81e-16, 7.106e-15,
             -1.523e-15, -9.4e-17, 1.21e-16,
             -2.8e-17];
  var j = cof.length - 1;
  var isneg = false;
  var d = 0;
  var dd = 0;
  var t, ty, tmp, res;

  if (x < 0) {
    x = -x;
    isneg = true;
  }

  t = 2 / (2 + x);
  ty = 4 * t - 2;

  for(; j > 0; j--) {
    tmp = d;
    d = ty * d - dd + cof[j];
    dd = tmp;
  }

  res = t * Math.exp(-x * x + 0.5 * (cof[0] + ty * d) - dd);
  return isneg ? res - 1 : 1 - res;
};


// Returns the complmentary error function erfc(x)
jStat.erfc = function erfc(x) {
  return 1 - jStat.erf(x);
};


// Returns the inverse of the complementary error function
jStat.erfcinv = function erfcinv(p) {
  var j = 0;
  var x, err, t, pp;
  if (p >= 2)
    return -100;
  if (p <= 0)
    return 100;
  pp = (p < 1) ? p : 2 - p;
  t = Math.sqrt(-2 * Math.log(pp / 2));
  x = -0.70711 * ((2.30753 + t * 0.27061) /
                  (1 + t * (0.99229 + t * 0.04481)) - t);
  for (; j < 2; j++) {
    err = jStat.erfc(x) - pp;
    x += err / (1.12837916709551257 * Math.exp(-x * x) - x * err);
  }
  return (p < 1) ? x : -x;
};


// Returns the inverse of the incomplete beta function
jStat.ibetainv = function ibetainv(p, a, b) {
  var EPS = 1e-8;
  var a1 = a - 1;
  var b1 = b - 1;
  var j = 0;
  var lna, lnb, pp, t, u, err, x, al, h, w, afac;
  if (p <= 0)
    return 0;
  if (p >= 1)
    return 1;
  if (a >= 1 && b >= 1) {
    pp = (p < 0.5) ? p : 1 - p;
    t = Math.sqrt(-2 * Math.log(pp));
    x = (2.30753 + t * 0.27061) / (1 + t* (0.99229 + t * 0.04481)) - t;
    if (p < 0.5)
      x = -x;
    al = (x * x - 3) / 6;
    h = 2 / (1 / (2 * a - 1)  + 1 / (2 * b - 1));
    w = (x * Math.sqrt(al + h) / h) - (1 / (2 * b - 1) - 1 / (2 * a - 1)) *
        (al + 5 / 6 - 2 / (3 * h));
    x = a / (a + b * Math.exp(2 * w));
  } else {
    lna = Math.log(a / (a + b));
    lnb = Math.log(b / (a + b));
    t = Math.exp(a * lna) / a;
    u = Math.exp(b * lnb) / b;
    w = t + u;
    if (p < t / w)
      x = Math.pow(a * w * p, 1 / a);
    else
      x = 1 - Math.pow(b * w * (1 - p), 1 / b);
  }
  afac = -jStat.gammaln(a) - jStat.gammaln(b) + jStat.gammaln(a + b);
  for(; j < 10; j++) {
    if (x === 0 || x === 1)
      return x;
    err = jStat.ibeta(x, a, b) - p;
    t = Math.exp(a1 * Math.log(x) + b1 * Math.log(1 - x) + afac);
    u = err / t;
    x -= (t = u / (1 - 0.5 * Math.min(1, u * (a1 / x - b1 / (1 - x)))));
    if (x <= 0)
      x = 0.5 * (x + t);
    if (x >= 1)
      x = 0.5 * (x + t + 1);
    if (Math.abs(t) < EPS * x && j > 0)
      break;
  }
  return x;
};


// Returns the incomplete beta function I_x(a,b)
jStat.ibeta = function ibeta(x, a, b) {
  // Factors in front of the continued fraction.
  var bt = (x === 0 || x === 1) ?  0 :
    Math.exp(jStat.gammaln(a + b) - jStat.gammaln(a) -
             jStat.gammaln(b) + a * Math.log(x) + b *
             Math.log(1 - x));
  if (x < 0 || x > 1)
    return false;
  if (x < (a + 1) / (a + b + 2))
    // Use continued fraction directly.
    return bt * jStat.betacf(x, a, b) / a;
  // else use continued fraction after making the symmetry transformation.
  return 1 - bt * jStat.betacf(1 - x, b, a) / b;
};


// Returns a normal deviate (mu=0, sigma=1).
// If n and m are specified it returns a object of normal deviates.
jStat.randn = function randn(n, m) {
  var u, v, x, y, q, mat;
  if (!m)
    m = n;
  if (n)
    return jStat.create(n, m, function() { return jStat.randn(); });
  do {
    u = Math.random();
    v = 1.7156 * (Math.random() - 0.5);
    x = u - 0.449871;
    y = Math.abs(v) + 0.386595;
    q = x * x + y * (0.19600 * y - 0.25472 * x);
  } while (q > 0.27597 && (q > 0.27846 || v * v > -4 * Math.log(u) * u * u));
  return v / u;
};


// Returns a gamma deviate by the method of Marsaglia and Tsang.
jStat.randg = function randg(shape, n, m) {
  var oalph = shape;
  var a1, a2, u, v, x, mat;
  if (!m)
    m = n;
  if (!shape)
    shape = 1;
  if (n) {
    mat = jStat.zeros(n,m);
    mat.alter(function() { return jStat.randg(shape); });
    return mat;
  }
  if (shape < 1)
    shape += 1;
  a1 = shape - 1 / 3;
  a2 = 1 / Math.sqrt(9 * a1);
  do {
    do {
      x = jStat.randn();
      v = 1 + a2 * x;
    } while(v <= 0);
    v = v * v * v;
    u = Math.random();
  } while(u > 1 - 0.331 * Math.pow(x, 4) &&
          Math.log(u) > 0.5 * x*x + a1 * (1 - v + Math.log(v)));
  // alpha > 1
  if (shape == oalph)
    return a1 * v;
  // alpha < 1
  do {
    u = Math.random();
  } while(u === 0);
  return Math.pow(u, 1 / oalph) * a1 * v;
};


// making use of static methods on the instance
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    jStat.fn[passfunc] = function() {
      return jStat(
          jStat.map(this, function(value) { return jStat[passfunc](value); }));
    }
  })(funcs[i]);
})('gammaln gammafn factorial factorialln'.split(' '));


(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    jStat.fn[passfunc] = function() {
      return jStat(jStat[passfunc].apply(null, arguments));
    };
  })(funcs[i]);
})('randn'.split(' '));

}(this.jStat, Math));
(function(jStat, Math) {

// generate all distribution instance methods
(function(list) {
  for (var i = 0; i < list.length; i++) (function(func) {
    // distribution instance method
    jStat[func] = function(a, b, c) {
      if (!(this instanceof arguments.callee))
        return new arguments.callee(a, b, c);
      this._a = a;
      this._b = b;
      this._c = c;
      return this;
    };
    // distribution method to be used on a jStat instance
    jStat.fn[func] = function(a, b, c) {
      var newthis = jStat[func](a, b, c);
      newthis.data = this;
      return newthis;
    };
    // sample instance method
    jStat[func].prototype.sample = function(arr) {
      var a = this._a;
      var b = this._b;
      var c = this._c;
      if (arr)
        return jStat.alter(arr, function() {
          return jStat[func].sample(a, b, c);
        });
      else
        return jStat[func].sample(a, b, c);
    };
    // generate the pdf, cdf and inv instance methods
    (function(vals) {
      for (var i = 0; i < vals.length; i++) (function(fnfunc) {
        jStat[func].prototype[fnfunc] = function(x) {
          var a = this._a;
          var b = this._b;
          var c = this._c;
          if (!x && x !== 0)
            x = this.data;
          if (typeof x !== 'number') {
            return jStat.fn.map.call(x, function(x) {
              return jStat[func][fnfunc](x, a, b, c);
            });
          }
          return jStat[func][fnfunc](x, a, b, c);
        };
      })(vals[i]);
    })('pdf cdf inv'.split(' '));
    // generate the mean, median, mode and variance instance methods
    (function(vals) {
      for (var i = 0; i < vals.length; i++) (function(fnfunc) {
        jStat[func].prototype[fnfunc] = function() {
          return jStat[func][fnfunc](this._a, this._b, this._c);
        };
      })(vals[i]);
    })('mean median mode variance'.split(' '));
  })(list[i]);
})((
  'beta centralF cauchy chisquare exponential gamma invgamma kumaraswamy ' +
  'laplace lognormal noncentralt normal pareto studentt weibull uniform ' +
  'binomial negbin hypgeom poisson triangular'
).split(' '));



// extend beta function with static methods
jStat.extend(jStat.beta, {
  pdf: function pdf(x, alpha, beta) {
    // PDF is zero outside the support
    if (x > 1 || x < 0)
      return 0;
    // PDF is one for the uniform case
    if (alpha == 1 && beta == 1)
      return 1;

    if (alpha < 512 && beta < 512) {
      return (Math.pow(x, alpha - 1) * Math.pow(1 - x, beta - 1)) /
          jStat.betafn(alpha, beta);
    } else {
      return Math.exp((alpha - 1) * Math.log(x) +
                      (beta - 1) * Math.log(1 - x) -
                      jStat.betaln(alpha, beta));
    }
  },

  cdf: function cdf(x, alpha, beta) {
    return (x > 1 || x < 0) ? (x > 1) * 1 : jStat.ibeta(x, alpha, beta);
  },

  inv: function inv(x, alpha, beta) {
    return jStat.ibetainv(x, alpha, beta);
  },

  mean: function mean(alpha, beta) {
    return alpha / (alpha + beta);
  },

  median: function median(alpha, beta) {
    return jStat.ibetainv(0.5, alpha, beta);
  },

  mode: function mode(alpha, beta) {
    return (alpha - 1 ) / ( alpha + beta - 2);
  },

  // return a random sample
  sample: function sample(alpha, beta) {
    var u = jStat.randg(alpha);
    return u / (u + jStat.randg(beta));
  },

  variance: function variance(alpha, beta) {
    return (alpha * beta) / (Math.pow(alpha + beta, 2) * (alpha + beta + 1));
  }
});

// extend F function with static methods
jStat.extend(jStat.centralF, {
  // This implementation of the pdf function avoids float overflow
  // See the way that R calculates this value:
  // https://svn.r-project.org/R/trunk/src/nmath/df.c
  pdf: function pdf(x, df1, df2) {
    var p, q, f;

    if (x < 0)
      return 0;

    if (df1 <= 2) {
      if (x === 0 && df1 < 2) {
        return Infinity;
      }
      if (x === 0 && df1 === 2) {
        return 1;
      }
      return Math.sqrt((Math.pow(df1 * x, df1) * Math.pow(df2, df2)) /
                       (Math.pow(df1 * x + df2, df1 + df2))) /
                       (x * jStat.betafn(df1/2, df2/2));
    }

    p = (df1 * x) / (df2 + x * df1);
    q = df2 / (df2 + x * df1);
    f = df1 * q / 2.0;
    return f * jStat.binomial.pdf((df1 - 2) / 2, (df1 + df2 - 2) / 2, p);
  },

  cdf: function cdf(x, df1, df2) {
    if (x < 0)
      return 0;
    return jStat.ibeta((df1 * x) / (df1 * x + df2), df1 / 2, df2 / 2);
  },

  inv: function inv(x, df1, df2) {
    return df2 / (df1 * (1 / jStat.ibetainv(x, df1 / 2, df2 / 2) - 1));
  },

  mean: function mean(df1, df2) {
    return (df2 > 2) ? df2 / (df2 - 2) : undefined;
  },

  mode: function mode(df1, df2) {
    return (df1 > 2) ? (df2 * (df1 - 2)) / (df1 * (df2 + 2)) : undefined;
  },

  // return a random sample
  sample: function sample(df1, df2) {
    var x1 = jStat.randg(df1 / 2) * 2;
    var x2 = jStat.randg(df2 / 2) * 2;
    return (x1 / df1) / (x2 / df2);
  },

  variance: function variance(df1, df2) {
    if (df2 <= 4)
      return undefined;
    return 2 * df2 * df2 * (df1 + df2 - 2) /
        (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));
  }
});


// extend cauchy function with static methods
jStat.extend(jStat.cauchy, {
  pdf: function pdf(x, local, scale) {
    if (scale < 0) { return 0; }

    return (scale / (Math.pow(x - local, 2) + Math.pow(scale, 2))) / Math.PI;
  },

  cdf: function cdf(x, local, scale) {
    return Math.atan((x - local) / scale) / Math.PI + 0.5;
  },

  inv: function(p, local, scale) {
    return local + scale * Math.tan(Math.PI * (p - 0.5));
  },

  median: function median(local, scale) {
    return local;
  },

  mode: function mode(local, scale) {
    return local;
  },

  sample: function sample(local, scale) {
    return jStat.randn() *
        Math.sqrt(1 / (2 * jStat.randg(0.5))) * scale + local;
  }
});



// extend chisquare function with static methods
jStat.extend(jStat.chisquare, {
  pdf: function pdf(x, dof) {
    if (x < 0)
      return 0;
    return (x === 0 && dof === 2) ? 0.5 :
        Math.exp((dof / 2 - 1) * Math.log(x) - x / 2 - (dof / 2) *
                 Math.log(2) - jStat.gammaln(dof / 2));
  },

  cdf: function cdf(x, dof) {
    if (x < 0)
      return 0;
    return jStat.lowRegGamma(dof / 2, x / 2);
  },

  inv: function(p, dof) {
    return 2 * jStat.gammapinv(p, 0.5 * dof);
  },

  mean : function(dof) {
    return dof;
  },

  // TODO: this is an approximation (is there a better way?)
  median: function median(dof) {
    return dof * Math.pow(1 - (2 / (9 * dof)), 3);
  },

  mode: function mode(dof) {
    return (dof - 2 > 0) ? dof - 2 : 0;
  },

  sample: function sample(dof) {
    return jStat.randg(dof / 2) * 2;
  },

  variance: function variance(dof) {
    return 2 * dof;
  }
});



// extend exponential function with static methods
jStat.extend(jStat.exponential, {
  pdf: function pdf(x, rate) {
    return x < 0 ? 0 : rate * Math.exp(-rate * x);
  },

  cdf: function cdf(x, rate) {
    return x < 0 ? 0 : 1 - Math.exp(-rate * x);
  },

  inv: function(p, rate) {
    return -Math.log(1 - p) / rate;
  },

  mean : function(rate) {
    return 1 / rate;
  },

  median: function (rate) {
    return (1 / rate) * Math.log(2);
  },

  mode: function mode(rate) {
    return 0;
  },

  sample: function sample(rate) {
    return -1 / rate * Math.log(Math.random());
  },

  variance : function(rate) {
    return Math.pow(rate, -2);
  }
});



// extend gamma function with static methods
jStat.extend(jStat.gamma, {
  pdf: function pdf(x, shape, scale) {
    if (x < 0)
      return 0;
    return (x === 0 && shape === 1) ? 1 / scale :
            Math.exp((shape - 1) * Math.log(x) - x / scale -
                    jStat.gammaln(shape) - shape * Math.log(scale));
  },

  cdf: function cdf(x, shape, scale) {
    if (x < 0)
      return 0;
    return jStat.lowRegGamma(shape, x / scale);
  },

  inv: function(p, shape, scale) {
    return jStat.gammapinv(p, shape) * scale;
  },

  mean : function(shape, scale) {
    return shape * scale;
  },

  mode: function mode(shape, scale) {
    if(shape > 1) return (shape - 1) * scale;
    return undefined;
  },

  sample: function sample(shape, scale) {
    return jStat.randg(shape) * scale;
  },

  variance: function variance(shape, scale) {
    return shape * scale * scale;
  }
});

// extend inverse gamma function with static methods
jStat.extend(jStat.invgamma, {
  pdf: function pdf(x, shape, scale) {
    if (x <= 0)
      return 0;
    return Math.exp(-(shape + 1) * Math.log(x) - scale / x -
                    jStat.gammaln(shape) + shape * Math.log(scale));
  },

  cdf: function cdf(x, shape, scale) {
    if (x <= 0)
      return 0;
    return 1 - jStat.lowRegGamma(shape, scale / x);
  },

  inv: function(p, shape, scale) {
    return scale / jStat.gammapinv(1 - p, shape);
  },

  mean : function(shape, scale) {
    return (shape > 1) ? scale / (shape - 1) : undefined;
  },

  mode: function mode(shape, scale) {
    return scale / (shape + 1);
  },

  sample: function sample(shape, scale) {
    return scale / jStat.randg(shape);
  },

  variance: function variance(shape, scale) {
    if (shape <= 2)
      return undefined;
    return scale * scale / ((shape - 1) * (shape - 1) * (shape - 2));
  }
});


// extend kumaraswamy function with static methods
jStat.extend(jStat.kumaraswamy, {
  pdf: function pdf(x, alpha, beta) {
    if (x === 0 && alpha === 1)
      return beta;
    else if (x === 1 && beta === 1)
      return alpha;
    return Math.exp(Math.log(alpha) + Math.log(beta) + (alpha - 1) *
                    Math.log(x) + (beta - 1) *
                    Math.log(1 - Math.pow(x, alpha)));
  },

  cdf: function cdf(x, alpha, beta) {
    if (x < 0)
      return 0;
    else if (x > 1)
      return 1;
    return (1 - Math.pow(1 - Math.pow(x, alpha), beta));
  },

  inv: function inv(p, alpha, beta) {
    return Math.pow(1 - Math.pow(1 - p, 1 / beta), 1 / alpha);
  },

  mean : function(alpha, beta) {
    return (beta * jStat.gammafn(1 + 1 / alpha) *
            jStat.gammafn(beta)) / (jStat.gammafn(1 + 1 / alpha + beta));
  },

  median: function median(alpha, beta) {
    return Math.pow(1 - Math.pow(2, -1 / beta), 1 / alpha);
  },

  mode: function mode(alpha, beta) {
    if (!(alpha >= 1 && beta >= 1 && (alpha !== 1 && beta !== 1)))
      return undefined;
    return Math.pow((alpha - 1) / (alpha * beta - 1), 1 / alpha);
  },

  variance: function variance(alpha, beta) {
    throw new Error('variance not yet implemented');
    // TODO: complete this
  }
});



// extend lognormal function with static methods
jStat.extend(jStat.lognormal, {
  pdf: function pdf(x, mu, sigma) {
    if (x <= 0)
      return 0;
    return Math.exp(-Math.log(x) - 0.5 * Math.log(2 * Math.PI) -
                    Math.log(sigma) - Math.pow(Math.log(x) - mu, 2) /
                    (2 * sigma * sigma));
  },

  cdf: function cdf(x, mu, sigma) {
    if (x < 0)
      return 0;
    return 0.5 +
        (0.5 * jStat.erf((Math.log(x) - mu) / Math.sqrt(2 * sigma * sigma)));
  },

  inv: function(p, mu, sigma) {
    return Math.exp(-1.41421356237309505 * sigma * jStat.erfcinv(2 * p) + mu);
  },

  mean: function mean(mu, sigma) {
    return Math.exp(mu + sigma * sigma / 2);
  },

  median: function median(mu, sigma) {
    return Math.exp(mu);
  },

  mode: function mode(mu, sigma) {
    return Math.exp(mu - sigma * sigma);
  },

  sample: function sample(mu, sigma) {
    return Math.exp(jStat.randn() * sigma + mu);
  },

  variance: function variance(mu, sigma) {
    return (Math.exp(sigma * sigma) - 1) * Math.exp(2 * mu + sigma * sigma);
  }
});



// extend noncentralt function with static methods
jStat.extend(jStat.noncentralt, {
  pdf: function pdf(x, dof, ncp) {
    var tol = 1e-14;
    if (Math.abs(ncp) < tol)  // ncp approx 0; use student-t
      return jStat.studentt.pdf(x, dof)

    if (Math.abs(x) < tol) {  // different formula for x == 0
      return Math.exp(jStat.gammaln((dof + 1) / 2) - ncp * ncp / 2 -
                      0.5 * Math.log(Math.PI * dof) - jStat.gammaln(dof / 2));
    }

    // formula for x != 0
    return dof / x *
        (jStat.noncentralt.cdf(x * Math.sqrt(1 + 2 / dof), dof+2, ncp) -
         jStat.noncentralt.cdf(x, dof, ncp));
  },

  cdf: function cdf(x, dof, ncp) {
    var tol = 1e-14;
    var min_iterations = 200;

    if (Math.abs(ncp) < tol)  // ncp approx 0; use student-t
      return jStat.studentt.cdf(x, dof);

    // turn negative x into positive and flip result afterwards
    var flip = false;
    if (x < 0) {
      flip = true;
      ncp = -ncp;
    }

    var prob = jStat.normal.cdf(-ncp, 0, 1);
    var value = tol + 1;
    // use value at last two steps to determine convergence
    var lastvalue = value;
    var y = x * x / (x * x + dof);
    var j = 0;
    var p = Math.exp(-ncp * ncp / 2);
    var q = Math.exp(-ncp * ncp / 2 - 0.5 * Math.log(2) -
                     jStat.gammaln(3 / 2)) * ncp;
    while (j < min_iterations || lastvalue > tol || value > tol) {
      lastvalue = value;
      if (j > 0) {
        p *= (ncp * ncp) / (2 * j);
        q *= (ncp * ncp) / (2 * (j + 1 / 2));
      }
      value = p * jStat.beta.cdf(y, j + 0.5, dof / 2) +
          q * jStat.beta.cdf(y, j+1, dof/2);
      prob += 0.5 * value;
      j++;
    }

    return flip ? (1 - prob) : prob;
  }
});


// extend normal function with static methods
jStat.extend(jStat.normal, {
  pdf: function pdf(x, mean, std) {
    return Math.exp(-0.5 * Math.log(2 * Math.PI) -
                    Math.log(std) - Math.pow(x - mean, 2) / (2 * std * std));
  },

  cdf: function cdf(x, mean, std) {
    return 0.5 * (1 + jStat.erf((x - mean) / Math.sqrt(2 * std * std)));
  },

  inv: function(p, mean, std) {
    return -1.41421356237309505 * std * jStat.erfcinv(2 * p) + mean;
  },

  mean : function(mean, std) {
    return mean;
  },

  median: function median(mean, std) {
    return mean;
  },

  mode: function (mean, std) {
    return mean;
  },

  sample: function sample(mean, std) {
    return jStat.randn() * std + mean;
  },

  variance : function(mean, std) {
    return std * std;
  }
});



// extend pareto function with static methods
jStat.extend(jStat.pareto, {
  pdf: function pdf(x, scale, shape) {
    if (x < scale)
      return 0;
    return (shape * Math.pow(scale, shape)) / Math.pow(x, shape + 1);
  },

  cdf: function cdf(x, scale, shape) {
    if (x < scale)
      return 0;
    return 1 - Math.pow(scale / x, shape);
  },

  inv: function inv(p, scale, shape) {
    return scale / Math.pow(1 - p, 1 / shape);
  },

  mean: function mean(scale, shape) {
    if (shape <= 1)
      return undefined;
    return (shape * Math.pow(scale, shape)) / (shape - 1);
  },

  median: function median(scale, shape) {
    return scale * (shape * Math.SQRT2);
  },

  mode: function mode(scale, shape) {
    return scale;
  },

  variance : function(scale, shape) {
    if (shape <= 2)
      return undefined;
    return (scale*scale * shape) / (Math.pow(shape - 1, 2) * (shape - 2));
  }
});



// extend studentt function with static methods
jStat.extend(jStat.studentt, {
  pdf: function pdf(x, dof) {
    dof = dof > 1e100 ? 1e100 : dof;
    return (1/(Math.sqrt(dof) * jStat.betafn(0.5, dof/2))) *
        Math.pow(1 + ((x * x) / dof), -((dof + 1) / 2));
  },

  cdf: function cdf(x, dof) {
    var dof2 = dof / 2;
    return jStat.ibeta((x + Math.sqrt(x * x + dof)) /
                       (2 * Math.sqrt(x * x + dof)), dof2, dof2);
  },

  inv: function(p, dof) {
    var x = jStat.ibetainv(2 * Math.min(p, 1 - p), 0.5 * dof, 0.5);
    x = Math.sqrt(dof * (1 - x) / x);
    return (p > 0.5) ? x : -x;
  },

  mean: function mean(dof) {
    return (dof > 1) ? 0 : undefined;
  },

  median: function median(dof) {
    return 0;
  },

  mode: function mode(dof) {
    return 0;
  },

  sample: function sample(dof) {
    return jStat.randn() * Math.sqrt(dof / (2 * jStat.randg(dof / 2)));
  },

  variance: function variance(dof) {
    return (dof  > 2) ? dof / (dof - 2) : (dof > 1) ? Infinity : undefined;
  }
});



// extend weibull function with static methods
jStat.extend(jStat.weibull, {
  pdf: function pdf(x, scale, shape) {
    if (x < 0 || scale < 0 || shape < 0)
      return 0;
    return (shape / scale) * Math.pow((x / scale), (shape - 1)) *
        Math.exp(-(Math.pow((x / scale), shape)));
  },

  cdf: function cdf(x, scale, shape) {
    return x < 0 ? 0 : 1 - Math.exp(-Math.pow((x / scale), shape));
  },

  inv: function(p, scale, shape) {
    return scale * Math.pow(-Math.log(1 - p), 1 / shape);
  },

  mean : function(scale, shape) {
    return scale * jStat.gammafn(1 + 1 / shape);
  },

  median: function median(scale, shape) {
    return scale * Math.pow(Math.log(2), 1 / shape);
  },

  mode: function mode(scale, shape) {
    if (shape <= 1)
      return 0;
    return scale * Math.pow((shape - 1) / shape, 1 / shape);
  },

  sample: function sample(scale, shape) {
    return scale * Math.pow(-Math.log(Math.random()), 1 / shape);
  },

  variance: function variance(scale, shape) {
    return scale * scale * jStat.gammafn(1 + 2 / shape) -
        Math.pow(jStat.weibull.mean(scale, shape), 2);
  }
});



// extend uniform function with static methods
jStat.extend(jStat.uniform, {
  pdf: function pdf(x, a, b) {
    return (x < a || x > b) ? 0 : 1 / (b - a);
  },

  cdf: function cdf(x, a, b) {
    if (x < a)
      return 0;
    else if (x < b)
      return (x - a) / (b - a);
    return 1;
  },

  inv: function(p, a, b) {
    return a + (p * (b - a));
  },

  mean: function mean(a, b) {
    return 0.5 * (a + b);
  },

  median: function median(a, b) {
    return jStat.mean(a, b);
  },

  mode: function mode(a, b) {
    throw new Error('mode is not yet implemented');
  },

  sample: function sample(a, b) {
    return (a / 2 + b / 2) + (b / 2 - a / 2) * (2 * Math.random() - 1);
  },

  variance: function variance(a, b) {
    return Math.pow(b - a, 2) / 12;
  }
});



// extend uniform function with static methods
jStat.extend(jStat.binomial, {
  pdf: function pdf(k, n, p) {
    return (p === 0 || p === 1) ?
      ((n * p) === k ? 1 : 0) :
      jStat.combination(n, k) * Math.pow(p, k) * Math.pow(1 - p, n - k);
  },

  cdf: function cdf(x, n, p) {
    var binomarr = [],
    k = 0;
    if (x < 0) {
      return 0;
    }
    if (x < n) {
      for (; k <= x; k++) {
        binomarr[ k ] = jStat.binomial.pdf(k, n, p);
      }
      return jStat.sum(binomarr);
    }
    return 1;
  }
});



// extend uniform function with static methods
jStat.extend(jStat.negbin, {
  pdf: function pdf(k, r, p) {
    if (k !== k >>> 0)
      return false;
    if (k < 0)
      return 0;
    return jStat.combination(k + r - 1, r - 1) *
        Math.pow(1 - p, k) * Math.pow(p, r);
  },

  cdf: function cdf(x, r, p) {
    var sum = 0,
    k = 0;
    if (x < 0) return 0;
    for (; k <= x; k++) {
      sum += jStat.negbin.pdf(k, r, p);
    }
    return sum;
  }
});



// extend uniform function with static methods
jStat.extend(jStat.hypgeom, {
  pdf: function pdf(k, N, m, n) {
    // Hypergeometric PDF.

    // A simplification of the CDF algorithm below.

    // k = number of successes drawn
    // N = population size
    // m = number of successes in population
    // n = number of items drawn from population

    if(k !== k | 0) {
      return false;
    } else if(k < 0 || k < m - (N - n)) {
      // It's impossible to have this few successes drawn.
      return 0;
    } else if(k > n || k > m) {
      // It's impossible to have this many successes drawn.
      return 0;
    } else if (m * 2 > N) {
      // More than half the population is successes.

      if(n * 2 > N) {
        // More than half the population is sampled.

        return jStat.hypgeom.pdf(N - m - n + k, N, N - m, N - n)
      } else {
        // Half or less of the population is sampled.

        return jStat.hypgeom.pdf(n - k, N, N - m, n);
      }

    } else if(n * 2 > N) {
      // Half or less is successes.

      return jStat.hypgeom.pdf(m - k, N, m, N - n);

    } else if(m < n) {
      // We want to have the number of things sampled to be less than the
      // successes available. So swap the definitions of successful and sampled.
      return jStat.hypgeom.pdf(k, N, n, m);
    } else {
      // If we get here, half or less of the population was sampled, half or
      // less of it was successes, and we had fewer sampled things than
      // successes. Now we can do this complicated iterative algorithm in an
      // efficient way.

      // The basic premise of the algorithm is that we partially normalize our
      // intermediate product to keep it in a numerically good region, and then
      // finish the normalization at the end.

      // This variable holds the scaled probability of the current number of
      // successes.
      var scaledPDF = 1;

      // This keeps track of how much we have normalized.
      var samplesDone = 0;

      for(var i = 0; i < k; i++) {
        // For every possible number of successes up to that observed...

        while(scaledPDF > 1 && samplesDone < n) {
          // Intermediate result is growing too big. Apply some of the
          // normalization to shrink everything.

          scaledPDF *= 1 - (m / (N - samplesDone));

          // Say we've normalized by this sample already.
          samplesDone++;
        }

        // Work out the partially-normalized hypergeometric PDF for the next
        // number of successes
        scaledPDF *= (n - i) * (m - i) / ((i + 1) * (N - m - n + i + 1));
      }

      for(; samplesDone < n; samplesDone++) {
        // Apply all the rest of the normalization
        scaledPDF *= 1 - (m / (N - samplesDone));
      }

      // Bound answer sanely before returning.
      return Math.min(1, Math.max(0, scaledPDF));
    }
  },

  cdf: function cdf(x, N, m, n) {
    // Hypergeometric CDF.

    // This algorithm is due to Prof. Thomas S. Ferguson, <tom@math.ucla.edu>,
    // and comes from his hypergeometric test calculator at
    // <http://www.math.ucla.edu/~tom/distributions/Hypergeometric.html>.

    // x = number of successes drawn
    // N = population size
    // m = number of successes in population
    // n = number of items drawn from population

    if(x < 0 || x < m - (N - n)) {
      // It's impossible to have this few successes drawn or fewer.
      return 0;
    } else if(x >= n || x >= m) {
      // We will always have this many successes or fewer.
      return 1;
    } else if (m * 2 > N) {
      // More than half the population is successes.

      if(n * 2 > N) {
        // More than half the population is sampled.

        return jStat.hypgeom.cdf(N - m - n + x, N, N - m, N - n)
      } else {
        // Half or less of the population is sampled.

        return 1 - jStat.hypgeom.cdf(n - x - 1, N, N - m, n);
      }

    } else if(n * 2 > N) {
      // Half or less is successes.

      return 1 - jStat.hypgeom.cdf(m - x - 1, N, m, N - n);

    } else if(m < n) {
      // We want to have the number of things sampled to be less than the
      // successes available. So swap the definitions of successful and sampled.
      return jStat.hypgeom.cdf(x, N, n, m);
    } else {
      // If we get here, half or less of the population was sampled, half or
      // less of it was successes, and we had fewer sampled things than
      // successes. Now we can do this complicated iterative algorithm in an
      // efficient way.

      // The basic premise of the algorithm is that we partially normalize our
      // intermediate sum to keep it in a numerically good region, and then
      // finish the normalization at the end.

      // Holds the intermediate, scaled total CDF.
      var scaledCDF = 1;

      // This variable holds the scaled probability of the current number of
      // successes.
      var scaledPDF = 1;

      // This keeps track of how much we have normalized.
      var samplesDone = 0;

      for(var i = 0; i < x; i++) {
        // For every possible number of successes up to that observed...

        while(scaledCDF > 1 && samplesDone < n) {
          // Intermediate result is growing too big. Apply some of the
          // normalization to shrink everything.

          var factor = 1 - (m / (N - samplesDone));

          scaledPDF *= factor;
          scaledCDF *= factor;

          // Say we've normalized by this sample already.
          samplesDone++;
        }

        // Work out the partially-normalized hypergeometric PDF for the next
        // number of successes
        scaledPDF *= (n - i) * (m - i) / ((i + 1) * (N - m - n + i + 1));

        // Add to the CDF answer.
        scaledCDF += scaledPDF;
      }

      for(; samplesDone < n; samplesDone++) {
        // Apply all the rest of the normalization
        scaledCDF *= 1 - (m / (N - samplesDone));
      }

      // Bound answer sanely before returning.
      return Math.min(1, Math.max(0, scaledCDF));
    }
  }
});



// extend uniform function with static methods
jStat.extend(jStat.poisson, {
  pdf: function pdf(k, l) {
    if (l < 0 || (k % 1) !== 0 || k < 0) {
      return 0;
    }

    return Math.pow(l, k) * Math.exp(-l) / jStat.factorial(k);
  },

  cdf: function cdf(x, l) {
    var sumarr = [],
    k = 0;
    if (x < 0) return 0;
    for (; k <= x; k++) {
      sumarr.push(jStat.poisson.pdf(k, l));
    }
    return jStat.sum(sumarr);
  },

  mean : function(l) {
    return l;
  },

  variance : function(l) {
    return l;
  },

  sample: function sample(l) {
    var p = 1, k = 0, L = Math.exp(-l);
    do {
      k++;
      p *= Math.random();
    } while (p > L);
    return k - 1;
  }
});

// extend triangular function with static methods
jStat.extend(jStat.triangular, {
  pdf: function pdf(x, a, b, c) {
    if (b <= a || c < a || c > b) {
      return NaN;
    } else {
      if (x < a || x > b) {
        return 0;
      } else if (x < c) {
          return (2 * (x - a)) / ((b - a) * (c - a));
      } else if (x === c) {
          return (2 / (b - a));
      } else { // x > c
          return (2 * (b - x)) / ((b - a) * (b - c));
      }
    }
  },

  cdf: function cdf(x, a, b, c) {
    if (b <= a || c < a || c > b)
      return NaN;
    if (x <= a)
      return 0;
    else if (x >= b)
      return 1;
    if (x <= c)
      return Math.pow(x - a, 2) / ((b - a) * (c - a));
    else // x > c
      return 1 - Math.pow(b - x, 2) / ((b - a) * (b - c));
  },

  inv: function inv(p, a, b, c) {
    if (b <= a || c < a || c > b) {
      return NaN;
    } else {
      if (p <= ((c - a) / (b - a))) {
        return a + (b - a) * Math.sqrt(p * ((c - a) / (b - a)));
      } else { // p > ((c - a) / (b - a))
        return a + (b - a) * (1 - Math.sqrt((1 - p) * (1 - ((c - a) / (b - a)))));
      }
    }
  },

  mean: function mean(a, b, c) {
    return (a + b + c) / 3;
  },

  median: function median(a, b, c) {
    if (c <= (a + b) / 2) {
      return b - Math.sqrt((b - a) * (b - c)) / Math.sqrt(2);
    } else if (c > (a + b) / 2) {
      return a + Math.sqrt((b - a) * (c - a)) / Math.sqrt(2);
    }
  },

  mode: function mode(a, b, c) {
    return c;
  },

  sample: function sample(a, b, c) {
    var u = Math.random();
    if (u < ((c - a) / (b - a)))
      return a + Math.sqrt(u * (b - a) * (c - a))
    return b - Math.sqrt((1 - u) * (b - a) * (b - c));
  },

  variance: function variance(a, b, c) {
    return (a * a + b * b + c * c - a * b - a * c - b * c) / 18;
  }
});

function laplaceSign(x) { return x / Math.abs(x); }

jStat.extend(jStat.laplace, {
  pdf: function pdf(x, mu, b) {
    return (b <= 0) ? 0 : (Math.exp(-Math.abs(x - mu) / b)) / (2 * b);
  },

  cdf: function cdf(x, mu, b) {
    if (b <= 0) { return 0; }

    if(x < mu) {
      return 0.5 * Math.exp((x - mu) / b);
    } else {
      return 1 - 0.5 * Math.exp(- (x - mu) / b);
    }
  },

  mean: function(mu, b) {
    return mu;
  },

  median: function(mu, b) {
    return mu;
  },

  mode: function(mu, b) {
    return mu;
  },

  variance: function(mu, b) {
    return 2 * b * b;
  },

  sample: function sample(mu, b) {
    var u = Math.random() - 0.5;

    return mu - (b * laplaceSign(u) * Math.log(1 - (2 * Math.abs(u))));
  }
});

}(this.jStat, Math));
/* Provides functions for the solution of linear system of equations, integration, extrapolation,
 * interpolation, eigenvalue problems, differential equations and PCA analysis. */

(function(jStat, Math) {

var push = Array.prototype.push;
var isArray = jStat.utils.isArray;

function isUsable(arg) {
  return isArray(arg) || arg instanceof jStat;
}

jStat.extend({

  // add a vector/matrix to a vector/matrix or scalar
  add: function add(arr, arg) {
    // check if arg is a vector or scalar
    if (isUsable(arg)) {
      if (!isUsable(arg[0])) arg = [ arg ];
      return jStat.map(arr, function(value, row, col) {
        return value + arg[row][col];
      });
    }
    return jStat.map(arr, function(value) { return value + arg; });
  },

  // subtract a vector or scalar from the vector
  subtract: function subtract(arr, arg) {
    // check if arg is a vector or scalar
    if (isUsable(arg)) {
      if (!isUsable(arg[0])) arg = [ arg ];
      return jStat.map(arr, function(value, row, col) {
        return value - arg[row][col] || 0;
      });
    }
    return jStat.map(arr, function(value) { return value - arg; });
  },

  // matrix division
  divide: function divide(arr, arg) {
    if (isUsable(arg)) {
      if (!isUsable(arg[0])) arg = [ arg ];
      return jStat.multiply(arr, jStat.inv(arg));
    }
    return jStat.map(arr, function(value) { return value / arg; });
  },

  // matrix multiplication
  multiply: function multiply(arr, arg) {
    var row, col, nrescols, sum,
    nrow = arr.length,
    ncol = arr[0].length,
    res = jStat.zeros(nrow, nrescols = (isUsable(arg)) ? arg[0].length : ncol),
    rescols = 0;
    if (isUsable(arg)) {
      for (; rescols < nrescols; rescols++) {
        for (row = 0; row < nrow; row++) {
          sum = 0;
          for (col = 0; col < ncol; col++)
          sum += arr[row][col] * arg[col][rescols];
          res[row][rescols] = sum;
        }
      }
      return (nrow === 1 && rescols === 1) ? res[0][0] : res;
    }
    return jStat.map(arr, function(value) { return value * arg; });
  },

  // Returns the dot product of two matricies
  dot: function dot(arr, arg) {
    if (!isUsable(arr[0])) arr = [ arr ];
    if (!isUsable(arg[0])) arg = [ arg ];
    // convert column to row vector
    var left = (arr[0].length === 1 && arr.length !== 1) ? jStat.transpose(arr) : arr,
    right = (arg[0].length === 1 && arg.length !== 1) ? jStat.transpose(arg) : arg,
    res = [],
    row = 0,
    nrow = left.length,
    ncol = left[0].length,
    sum, col;
    for (; row < nrow; row++) {
      res[row] = [];
      sum = 0;
      for (col = 0; col < ncol; col++)
      sum += left[row][col] * right[row][col];
      res[row] = sum;
    }
    return (res.length === 1) ? res[0] : res;
  },

  // raise every element by a scalar
  pow: function pow(arr, arg) {
    return jStat.map(arr, function(value) { return Math.pow(value, arg); });
  },

  // exponentiate every element
  exp: function exp(arr) {
    return jStat.map(arr, function(value) { return Math.exp(value); });
  },

  // generate the natural log of every element
  log: function exp(arr) {
    return jStat.map(arr, function(value) { return Math.log(value); });
  },

  // generate the absolute values of the vector
  abs: function abs(arr) {
    return jStat.map(arr, function(value) { return Math.abs(value); });
  },

  // computes the p-norm of the vector
  // In the case that a matrix is passed, uses the first row as the vector
  norm: function norm(arr, p) {
    var nnorm = 0,
    i = 0;
    // check the p-value of the norm, and set for most common case
    if (isNaN(p)) p = 2;
    // check if multi-dimensional array, and make vector correction
    if (isUsable(arr[0])) arr = arr[0];
    // vector norm
    for (; i < arr.length; i++) {
      nnorm += Math.pow(Math.abs(arr[i]), p);
    }
    return Math.pow(nnorm, 1 / p);
  },

  // computes the angle between two vectors in rads
  // In case a matrix is passed, this uses the first row as the vector
  angle: function angle(arr, arg) {
    return Math.acos(jStat.dot(arr, arg) / (jStat.norm(arr) * jStat.norm(arg)));
  },

  // augment one matrix by another
  // Note: this function returns a matrix, not a jStat object
  aug: function aug(a, b) {
    var newarr = [];
    for (var i = 0; i < a.length; i++) {
      newarr.push(a[i].slice());
    }
    for (var i = 0; i < newarr.length; i++) {
      push.apply(newarr[i], b[i]);
    }
    return newarr;
  },

  // The inv() function calculates the inverse of a matrix
  // Create the inverse by augmenting the matrix by the identity matrix of the
  // appropriate size, and then use G-J elimination on the augmented matrix.
  inv: function inv(a) {
    var rows = a.length;
    var cols = a[0].length;
    var b = jStat.identity(rows, cols);
    var c = jStat.gauss_jordan(a, b);
    var result = [];
    var i = 0;
    var j;

    //We need to copy the inverse portion to a new matrix to rid G-J artifacts
    for (; i < rows; i++) {
      result[i] = [];
      for (j = cols; j < c[0].length; j++)
        result[i][j - cols] = c[i][j];
    }
    return result;
  },

  // calculate the determinant of a matrix
  det: function det(a) {
    var alen = a.length,
    alend = alen * 2,
    vals = new Array(alend),
    rowshift = alen - 1,
    colshift = alend - 1,
    mrow = rowshift - alen + 1,
    mcol = colshift,
    i = 0,
    result = 0,
    j;
    // check for special 2x2 case
    if (alen === 2) {
      return a[0][0] * a[1][1] - a[0][1] * a[1][0];
    }
    for (; i < alend; i++) {
      vals[i] = 1;
    }
    for (i = 0; i < alen; i++) {
      for (j = 0; j < alen; j++) {
        vals[(mrow < 0) ? mrow + alen : mrow ] *= a[i][j];
        vals[(mcol < alen) ? mcol + alen : mcol ] *= a[i][j];
        mrow++;
        mcol--;
      }
      mrow = --rowshift - alen + 1;
      mcol = --colshift;
    }
    for (i = 0; i < alen; i++) {
      result += vals[i];
    }
    for (; i < alend; i++) {
      result -= vals[i];
    }
    return result;
  },

  gauss_elimination: function gauss_elimination(a, b) {
    var i = 0,
    j = 0,
    n = a.length,
    m = a[0].length,
    factor = 1,
    sum = 0,
    x = [],
    maug, pivot, temp, k;
    a = jStat.aug(a, b);
    maug = a[0].length;
    for(i = 0; i < n; i++) {
      pivot = a[i][i];
      j = i;
      for (k = i + 1; k < m; k++) {
        if (pivot < Math.abs(a[k][i])) {
          pivot = a[k][i];
          j = k;
        }
      }
      if (j != i) {
        for(k = 0; k < maug; k++) {
          temp = a[i][k];
          a[i][k] = a[j][k];
          a[j][k] = temp;
        }
      }
      for (j = i + 1; j < n; j++) {
        factor = a[j][i] / a[i][i];
        for(k = i; k < maug; k++) {
          a[j][k] = a[j][k] - factor * a[i][k];
        }
      }
    }
    for (i = n - 1; i >= 0; i--) {
      sum = 0;
      for (j = i + 1; j<= n - 1; j++) {
        sum = sum + x[j] * a[i][j];
      }
      x[i] =(a[i][maug - 1] - sum) / a[i][i];
    }
    return x;
  },

  gauss_jordan: function gauss_jordan(a, b) {
    var m = jStat.aug(a, b),
    h = m.length,
    w = m[0].length;
    // find max pivot
    for (var y = 0; y < h; y++) {
      var maxrow = y;
      for (var y2 = y+1; y2 < h; y2++) {
        if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))
          maxrow = y2;
      }
      var tmp = m[y];
      m[y] = m[maxrow];
      m[maxrow] = tmp
      for (var y2 = y+1; y2 < h; y2++) {
        c = m[y2][y] / m[y][y];
        for (var x = y; x < w; x++) {
          m[y2][x] -= m[y][x] * c;
        }
      }
    }
    // backsubstitute
    for (var y = h-1; y >= 0; y--) {
      c = m[y][y];
      for (var y2 = 0; y2 < y; y2++) {
        for (var x = w-1; x > y-1; x--) {
          m[y2][x] -= m[y][x] * m[y2][y] / c;
        }
      }
      m[y][y] /= c;
      for (var x = h; x < w; x++) {
        m[y][x] /= c;
      }
    }
    return m;
  },

  lu: function lu(a, b) {
    throw new Error('lu not yet implemented');
  },

  cholesky: function cholesky(a, b) {
    throw new Error('cholesky not yet implemented');
  },

  gauss_jacobi: function gauss_jacobi(a, b, x, r) {
    var i = 0;
    var j = 0;
    var n = a.length;
    var l = [];
    var u = [];
    var d = [];
    var xv, c, h, xk;
    for (; i < n; i++) {
      l[i] = [];
      u[i] = [];
      d[i] = [];
      for (j = 0; j < n; j++) {
        if (i > j) {
          l[i][j] = a[i][j];
          u[i][j] = d[i][j] = 0;
        } else if (i < j) {
          u[i][j] = a[i][j];
          l[i][j] = d[i][j] = 0;
        } else {
          d[i][j] = a[i][j];
          l[i][j] = u[i][j] = 0;
        }
      }
    }
    h = jStat.multiply(jStat.multiply(jStat.inv(d), jStat.add(l, u)), -1);
    c = jStat.multiply(jStat.inv(d), b);
    xv = x;
    xk = jStat.add(jStat.multiply(h, x), c);
    i = 2;
    while (Math.abs(jStat.norm(jStat.subtract(xk,xv))) > r) {
      xv = xk;
      xk = jStat.add(jStat.multiply(h, xv), c);
      i++;
    }
    return xk;
  },

  gauss_seidel: function gauss_seidel(a, b, x, r) {
    var i = 0;
    var n = a.length;
    var l = [];
    var u = [];
    var d = [];
    var j, xv, c, h, xk;
    for (; i < n; i++) {
      l[i] = [];
      u[i] = [];
      d[i] = [];
      for (j = 0; j < n; j++) {
        if (i > j) {
          l[i][j] = a[i][j];
          u[i][j] = d[i][j] = 0;
        } else if (i < j) {
          u[i][j] = a[i][j];
          l[i][j] = d[i][j] = 0;
        } else {
          d[i][j] = a[i][j];
          l[i][j] = u[i][j] = 0;
        }
      }
    }
    h = jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d, l)), u), -1);
    c = jStat.multiply(jStat.inv(jStat.add(d, l)), b);
    xv = x;
    xk = jStat.add(jStat.multiply(h, x), c);
    i = 2;
    while (Math.abs(jStat.norm(jStat.subtract(xk, xv))) > r) {
      xv = xk;
      xk = jStat.add(jStat.multiply(h, xv), c);
      i = i + 1;
    }
    return xk;
  },

  SOR: function SOR(a, b, x, r, w) {
    var i = 0;
    var n = a.length;
    var l = [];
    var u = [];
    var d = [];
    var j, xv, c, h, xk;
    for (; i < n; i++) {
      l[i] = [];
      u[i] = [];
      d[i] = [];
      for (j = 0; j < n; j++) {
        if (i > j) {
          l[i][j] = a[i][j];
          u[i][j] = d[i][j] = 0;
        } else if (i < j) {
          u[i][j] = a[i][j];
          l[i][j] = d[i][j] = 0;
        } else {
          d[i][j] = a[i][j];
          l[i][j] = u[i][j] = 0;
        }
      }
    }
    h = jStat.multiply(jStat.inv(jStat.add(d, jStat.multiply(l, w))),
                       jStat.subtract(jStat.multiply(d, 1 - w),
                                      jStat.multiply(u, w)));
    c = jStat.multiply(jStat.multiply(jStat.inv(jStat.add(d,
        jStat.multiply(l, w))), b), w);
    xv = x;
    xk = jStat.add(jStat.multiply(h, x), c);
    i = 2;
    while (Math.abs(jStat.norm(jStat.subtract(xk, xv))) > r) {
      xv = xk;
      xk = jStat.add(jStat.multiply(h, xv), c);
      i++;
    }
    return xk;
  },

  householder: function householder(a) {
    var m = a.length;
    var n = a[0].length;
    var i = 0;
    var w = [];
    var p = [];
    var alpha, r, k, j, factor;
    for (; i < m - 1; i++) {
      alpha = 0;
      for (j = i + 1; j < n; j++)
      alpha += (a[j][i] * a[j][i]);
      factor = (a[i + 1][i] > 0) ? -1 : 1;
      alpha = factor * Math.sqrt(alpha);
      r = Math.sqrt((((alpha * alpha) - a[i + 1][i] * alpha) / 2));
      w = jStat.zeros(m, 1);
      w[i + 1][0] = (a[i + 1][i] - alpha) / (2 * r);
      for (k = i + 2; k < m; k++) w[k][0] = a[k][i] / (2 * r);
      p = jStat.subtract(jStat.identity(m, n),
          jStat.multiply(jStat.multiply(w, jStat.transpose(w)), 2));
      a = jStat.multiply(p, jStat.multiply(a, p));
    }
    return a;
  },

  // TODO: not working properly.
  QR: function QR(a, b) {
    var m = a.length;
    var n = a[0].length;
    var i = 0;
    var w = [];
    var p = [];
    var x = [];
    var j, alpha, r, k, factor, sum;
    for (; i < m - 1; i++) {
      alpha = 0;
      for (j = i + 1; j < n; j++)
        alpha += (a[j][i] * a[j][i]);
      factor = (a[i + 1][i] > 0) ? -1 : 1;
      alpha = factor * Math.sqrt(alpha);
      r = Math.sqrt((((alpha * alpha) - a[i + 1][i] * alpha) / 2));
      w = jStat.zeros(m, 1);
      w[i + 1][0] = (a[i + 1][i] - alpha) / (2 * r);
      for (k = i + 2; k < m; k++)
        w[k][0] = a[k][i] / (2 * r);
      p = jStat.subtract(jStat.identity(m, n),
          jStat.multiply(jStat.multiply(w, jStat.transpose(w)), 2));
      a = jStat.multiply(p, a);
      b = jStat.multiply(p, b);
    }
    for (i = m - 1; i >= 0; i--) {
      sum = 0;
      for (j = i + 1; j <= n - 1; j++)
      sum = x[j] * a[i][j];
      x[i] = b[i][0] / a[i][i];
    }
    return x;
  },

  jacobi: function jacobi(a) {
    var condition = 1;
    var count = 0;
    var n = a.length;
    var e = jStat.identity(n, n);
    var ev = [];
    var b, i, j, p, q, maxim, theta, s;
    // condition === 1 only if tolerance is not reached
    while (condition === 1) {
      count++;
      maxim = a[0][1];
      p = 0;
      q = 1;
      for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
          if (i != j) {
            if (maxim < Math.abs(a[i][j])) {
              maxim = Math.abs(a[i][j]);
              p = i;
              q = j;
            }
          }
        }
      }
      if (a[p][p] === a[q][q])
        theta = (a[p][q] > 0) ? Math.PI / 4 : -Math.PI / 4;
      else
        theta = Math.atan(2 * a[p][q] / (a[p][p] - a[q][q])) / 2;
      s = jStat.identity(n, n);
      s[p][p] = Math.cos(theta);
      s[p][q] = -Math.sin(theta);
      s[q][p] = Math.sin(theta);
      s[q][q] = Math.cos(theta);
      // eigen vector matrix
      e = jStat.multiply(e, s);
      b = jStat.multiply(jStat.multiply(jStat.inv(s), a), s);
      a = b;
      condition = 0;
      for (i = 1; i < n; i++) {
        for (j = 1; j < n; j++) {
          if (i != j && Math.abs(a[i][j]) > 0.001) {
            condition = 1;
          }
        }
      }
    }
    for (i = 0; i < n; i++) ev.push(a[i][i]);
    //returns both the eigenvalue and eigenmatrix
    return [e, ev];
  },

  rungekutta: function rungekutta(f, h, p, t_j, u_j, order) {
    var k1, k2, u_j1, k3, k4;
    if (order === 2) {
      while (t_j <= p) {
        k1 = h * f(t_j, u_j);
        k2 = h * f(t_j + h, u_j + k1);
        u_j1 = u_j + (k1 + k2) / 2;
        u_j = u_j1;
        t_j = t_j + h;
      }
    }
    if (order === 4) {
      while (t_j <= p) {
        k1 = h * f(t_j, u_j);
        k2 = h * f(t_j + h / 2, u_j + k1 / 2);
        k3 = h * f(t_j + h / 2, u_j + k2 / 2);
        k4 = h * f(t_j +h, u_j + k3);
        u_j1 = u_j + (k1 + 2 * k2 + 2 * k3 + k4) / 6;
        u_j = u_j1;
        t_j = t_j + h;
      }
    }
    return u_j;
  },

  romberg: function romberg(f, a, b, order) {
    var i = 0;
    var h = (b - a) / 2;
    var x = [];
    var h1 = [];
    var g = [];
    var m, a1, j, k, I, d;
    while (i < order / 2) {
      I = f(a);
      for (j = a, k = 0; j <= b; j = j + h, k++) x[k] = j;
      m = x.length;
      for (j = 1; j < m - 1; j++) {
        I += (((j % 2) !== 0) ? 4 : 2) * f(x[j]);
      }
      I = (h / 3) * (I + f(b));
      g[i] = I;
      h /= 2;
      i++;
    }
    a1 = g.length;
    m = 1;
    while (a1 !== 1) {
      for (j = 0; j < a1 - 1; j++)
      h1[j] = ((Math.pow(4, m)) * g[j + 1] - g[j]) / (Math.pow(4, m) - 1);
      a1 = h1.length;
      g = h1;
      h1 = [];
      m++;
    }
    return g;
  },

  richardson: function richardson(X, f, x, h) {
    function pos(X, x) {
      var i = 0;
      var n = X.length;
      var p;
      for (; i < n; i++)
        if (X[i] === x) p = i;
      return p;
    }
    var n = X.length,
    h_min = Math.abs(x - X[pos(X, x) + 1]),
    i = 0,
    g = [],
    h1 = [],
    y1, y2, m, a, j;
    while (h >= h_min) {
      y1 = pos(X, x + h);
      y2 = pos(X, x);
      g[i] = (f[y1] - 2 * f[y2] + f[2 * y2 - y1]) / (h * h);
      h /= 2;
      i++;
    }
    a = g.length;
    m = 1;
    while (a != 1) {
      for (j = 0; j < a - 1; j++)
      h1[j] = ((Math.pow(4, m)) * g[j + 1] - g[j]) / (Math.pow(4, m) - 1);
      a = h1.length;
      g = h1;
      h1 = [];
      m++;
    }
    return g;
  },

  simpson: function simpson(f, a, b, n) {
    var h = (b - a) / n;
    var I = f(a);
    var x = [];
    var j = a;
    var k = 0;
    var i = 1;
    var m;
    for (; j <= b; j = j + h, k++)
      x[k] = j;
    m = x.length;
    for (; i < m - 1; i++) {
      I += ((i % 2 !== 0) ? 4 : 2) * f(x[i]);
    }
    return (h / 3) * (I + f(b));
  },

  hermite: function hermite(X, F, dF, value) {
    var n = X.length;
    var p = 0;
    var i = 0;
    var l = [];
    var dl = [];
    var A = [];
    var B = [];
    var j;
    for (; i < n; i++) {
      l[i] = 1;
      for (j = 0; j < n; j++) {
        if (i != j) l[i] *= (value - X[j]) / (X[i] - X[j]);
      }
      dl[i] = 0;
      for (j = 0; j < n; j++) {
        if (i != j) dl[i] += 1 / (X [i] - X[j]);
      }
      A[i] = (1 - 2 * (value - X[i]) * dl[i]) * (l[i] * l[i]);
      B[i] = (value - X[i]) * (l[i] * l[i]);
      p += (A[i] * F[i] + B[i] * dF[i]);
    }
    return p;
  },

  lagrange: function lagrange(X, F, value) {
    var p = 0;
    var i = 0;
    var j, l;
    var n = X.length;
    for (; i < n; i++) {
      l = F[i];
      for (j = 0; j < n; j++) {
        // calculating the lagrange polynomial L_i
        if (i != j) l *= (value - X[j]) / (X[i] - X[j]);
      }
      // adding the lagrange polynomials found above
      p += l;
    }
    return p;
  },

  cubic_spline: function cubic_spline(X, F, value) {
    var n = X.length;
    var i = 0, j;
    var A = [];
    var B = [];
    var alpha = [];
    var c = [];
    var h = [];
    var b = [];
    var d = [];
    for (; i < n - 1; i++)
      h[i] = X[i + 1] - X[i];
    alpha[0] = 0;
    for (i = 1; i < n - 1; i++) {
      alpha[i] = (3 / h[i]) * (F[i + 1] - F[i]) -
          (3 / h[i-1]) * (F[i] - F[i-1]);
    }
    for (i = 1; i < n - 1; i++) {
      A[i] = [];
      B[i] = [];
      A[i][i-1] = h[i-1];
      A[i][i] = 2 * (h[i - 1] + h[i]);
      A[i][i+1] = h[i];
      B[i][0] = alpha[i];
    }
    c = jStat.multiply(jStat.inv(A), B);
    for (j = 0; j < n - 1; j++) {
      b[j] = (F[j + 1] - F[j]) / h[j] - h[j] * (c[j + 1][0] + 2 * c[j][0]) / 3;
      d[j] = (c[j + 1][0] - c[j][0]) / (3 * h[j]);
    }
    for (j = 0; j < n; j++) {
      if (X[j] > value) break;
    }
    j -= 1;
    return F[j] + (value - X[j]) * b[j] + jStat.sq(value-X[j]) *
        c[j] + (value - X[j]) * jStat.sq(value - X[j]) * d[j];
  },

  gauss_quadrature: function gauss_quadrature() {
    throw new Error('gauss_quadrature not yet implemented');
  },

  PCA: function PCA(X) {
    var m = X.length;
    var n = X[0].length;
    var flag = false;
    var i = 0;
    var j, temp1;
    var u = [];
    var D = [];
    var result = [];
    var temp2 = [];
    var Y = [];
    var Bt = [];
    var B = [];
    var C = [];
    var V = [];
    var Vt = [];
    for (i = 0; i < m; i++) {
      u[i] = jStat.sum(X[i]) / n;
    }
    for (i = 0; i < n; i++) {
      B[i] = [];
      for(j = 0; j < m; j++) {
        B[i][j] = X[j][i] - u[j];
      }
    }
    B = jStat.transpose(B);
    for (i = 0; i < m; i++) {
      C[i] = [];
      for (j = 0; j < m; j++) {
        C[i][j] = (jStat.dot([B[i]], [B[j]])) / (n - 1);
      }
    }
    result = jStat.jacobi(C);
    V = result[0];
    D = result[1];
    Vt = jStat.transpose(V);
    for (i = 0; i < D.length; i++) {
      for (j = i; j < D.length; j++) {
        if(D[i] < D[j])  {
          temp1 = D[i];
          D[i] = D[j];
          D[j] = temp1;
          temp2 = Vt[i];
          Vt[i] = Vt[j];
          Vt[j] = temp2;
        }
      }
    }
    Bt = jStat.transpose(B);
    for (i = 0; i < m; i++) {
      Y[i] = [];
      for (j = 0; j < Bt.length; j++) {
        Y[i][j] = jStat.dot([Vt[i]], [Bt[j]]);
      }
    }
    return [X, D, Vt, Y];
  }
});

// extend jStat.fn with methods that require one argument
(function(funcs) {
  for (var i = 0; i < funcs.length; i++) (function(passfunc) {
    jStat.fn[passfunc] = function(arg, func) {
      var tmpthis = this;
      // check for callback
      if (func) {
        setTimeout(function() {
          func.call(tmpthis, jStat.fn[passfunc].call(tmpthis, arg));
        }, 15);
        return this;
      }
      if (typeof jStat[passfunc](this, arg) === 'number')
        return jStat[passfunc](this, arg);
      else
        return jStat(jStat[passfunc](this, arg));
    };
  }(funcs[i]));
}('add divide multiply subtract dot pow exp log abs norm angle'.split(' ')));

}(this.jStat, Math));
(function(jStat, Math) {

var slice = [].slice;
var isNumber = jStat.utils.isNumber;
var isArray = jStat.utils.isArray;

// flag==true denotes use of sample standard deviation
// Z Statistics
jStat.extend({
  // 2 different parameter lists:
  // (value, mean, sd)
  // (value, array, flag)
  zscore: function zscore() {
    var args = slice.call(arguments);
    if (isNumber(args[1])) {
      return (args[0] - args[1]) / args[2];
    }
    return (args[0] - jStat.mean(args[1])) / jStat.stdev(args[1], args[2]);
  },

  // 3 different paramter lists:
  // (value, mean, sd, sides)
  // (zscore, sides)
  // (value, array, sides, flag)
  ztest: function ztest() {
    var args = slice.call(arguments);
    var z;
    if (isArray(args[1])) {
      // (value, array, sides, flag)
      z = jStat.zscore(args[0],args[1],args[3]);
      return (args[2] === 1) ?
        (jStat.normal.cdf(-Math.abs(z), 0, 1)) :
        (jStat.normal.cdf(-Math.abs(z), 0, 1)*2);
    } else {
      if (args.length > 2) {
        // (value, mean, sd, sides)
        z = jStat.zscore(args[0],args[1],args[2]);
        return (args[3] === 1) ?
          (jStat.normal.cdf(-Math.abs(z),0,1)) :
          (jStat.normal.cdf(-Math.abs(z),0,1)* 2);
      } else {
        // (zscore, sides)
        z = args[0];
        return (args[1] === 1) ?
          (jStat.normal.cdf(-Math.abs(z),0,1)) :
          (jStat.normal.cdf(-Math.abs(z),0,1)*2);
      }
    }
  }
});

jStat.extend(jStat.fn, {
  zscore: function zscore(value, flag) {
    return (value - this.mean()) / this.stdev(flag);
  },

  ztest: function ztest(value, sides, flag) {
    var zscore = Math.abs(this.zscore(value, flag));
    return (sides === 1) ?
      (jStat.normal.cdf(-zscore, 0, 1)) :
      (jStat.normal.cdf(-zscore, 0, 1) * 2);
  }
});

// T Statistics
jStat.extend({
  // 2 parameter lists
  // (value, mean, sd, n)
  // (value, array)
  tscore: function tscore() {
    var args = slice.call(arguments);
    return (args.length === 4) ?
      ((args[0] - args[1]) / (args[2] / Math.sqrt(args[3]))) :
      ((args[0] - jStat.mean(args[1])) /
       (jStat.stdev(args[1], true) / Math.sqrt(args[1].length)));
  },

  // 3 different paramter lists:
  // (value, mean, sd, n, sides)
  // (tscore, n, sides)
  // (value, array, sides)
  ttest: function ttest() {
    var args = slice.call(arguments);
    var tscore;
    if (args.length === 5) {
      tscore = Math.abs(jStat.tscore(args[0], args[1], args[2], args[3]));
      return (args[4] === 1) ?
        (jStat.studentt.cdf(-tscore, args[3]-1)) :
        (jStat.studentt.cdf(-tscore, args[3]-1)*2);
    }
    if (isNumber(args[1])) {
      tscore = Math.abs(args[0])
      return (args[2] == 1) ?
        (jStat.studentt.cdf(-tscore, args[1]-1)) :
        (jStat.studentt.cdf(-tscore, args[1]-1) * 2);
    }
    tscore = Math.abs(jStat.tscore(args[0], args[1]))
    return (args[2] == 1) ?
      (jStat.studentt.cdf(-tscore, args[1].length-1)) :
      (jStat.studentt.cdf(-tscore, args[1].length-1) * 2);
  }
});

jStat.extend(jStat.fn, {
  tscore: function tscore(value) {
    return (value - this.mean()) / (this.stdev(true) / Math.sqrt(this.cols()));
  },

  ttest: function ttest(value, sides) {
    return (sides === 1) ?
      (1 - jStat.studentt.cdf(Math.abs(this.tscore(value)), this.cols()-1)) :
      (jStat.studentt.cdf(-Math.abs(this.tscore(value)), this.cols()-1)*2);
  }
});

// F Statistics
jStat.extend({
  // Paramter list is as follows:
  // (array1, array2, array3, ...)
  // or it is an array of arrays
  // array of arrays conversion
  anovafscore: function anovafscore() {
    var args = slice.call(arguments),
    expVar, sample, sampMean, sampSampMean, tmpargs, unexpVar, i, j;
    if (args.length === 1) {
      tmpargs = new Array(args[0].length);
      for (i = 0; i < args[0].length; i++) {
        tmpargs[i] = args[0][i];
      }
      args = tmpargs;
    }
    // 2 sample case
    if (args.length === 2) {
      return jStat.variance(args[0]) / jStat.variance(args[1]);
    }
    // Builds sample array
    sample = new Array();
    for (i = 0; i < args.length; i++) {
      sample = sample.concat(args[i]);
    }
    sampMean = jStat.mean(sample);
    // Computes the explained variance
    expVar = 0;
    for (i = 0; i < args.length; i++) {
      expVar = expVar + args[i].length * Math.pow(jStat.mean(args[i]) - sampMean, 2);
    }
    expVar /= (args.length - 1);
    // Computes unexplained variance
    unexpVar = 0;
    for (i = 0; i < args.length; i++) {
      sampSampMean = jStat.mean(args[i]);
      for (j = 0; j < args[i].length; j++) {
        unexpVar += Math.pow(args[i][j] - sampSampMean, 2);
      }
    }
    unexpVar /= (sample.length - args.length);
    return expVar / unexpVar;
  },

  // 2 different paramter setups
  // (array1, array2, array3, ...)
  // (anovafscore, df1, df2)
  anovaftest: function anovaftest() {
    var args = slice.call(arguments),
    df1, df2, n, i;
    if (isNumber(args[0])) {
      return 1 - jStat.centralF.cdf(args[0], args[1], args[2]);
    }
    anovafscore = jStat.anovafscore(args);
    df1 = args.length - 1;
    n = 0;
    for (i = 0; i < args.length; i++) {
      n = n + args[i].length;
    }
    df2 = n - df1 - 1;
    return 1 - jStat.centralF.cdf(anovafscore, df1, df2);
  },

  ftest: function ftest(fscore, df1, df2) {
    return 1 - jStat.centralF.cdf(fscore, df1, df2);
  }
});

jStat.extend(jStat.fn, {
  anovafscore: function anovafscore() {
    return jStat.anovafscore(this.toArray());
  },

  anovaftes: function anovaftes() {
    var n = 0;
    var i;
    for (i = 0; i < this.length; i++) {
      n = n + this[i].length;
    }
    return jStat.ftest(this.anovafscore(), this.length - 1, n - this.length);
  }
});

// Error Bounds
jStat.extend({
  // 2 different parameter setups
  // (value, alpha, sd, n)
  // (value, alpha, array)
  normalci: function normalci() {
    var args = slice.call(arguments),
    ans = new Array(2),
    change;
    if (args.length === 4) {
      change = Math.abs(jStat.normal.inv(args[1] / 2, 0, 1) *
                        args[2] / Math.sqrt(args[3]));
    } else {
      change = Math.abs(jStat.normal.inv(args[1] / 2, 0, 1) *
                        jStat.stdev(args[2]) / Math.sqrt(args[2].length));
    }
    ans[0] = args[0] - change;
    ans[1] = args[0] + change;
    return ans;
  },

  // 2 different parameter setups
  // (value, alpha, sd, n)
  // (value, alpha, array)
  tci: function tci() {
    var args = slice.call(arguments),
    ans = new Array(2),
    change;
    if (args.length === 4) {
      change = Math.abs(jStat.studentt.inv(args[1] / 2, args[3] - 1) *
                        args[2] / Math.sqrt(args[3]));
    } else {
      change = Math.abs(jStat.studentt.inv(args[1] / 2, args[2].length - 1) *
                        jStat.stdev(args[2], true) / Math.sqrt(args[2].length));
    }
    ans[0] = args[0] - change;
    ans[1] = args[0] + change;
    return ans;
  },

  significant: function significant(pvalue, alpha) {
    return pvalue < alpha;
  }
});

jStat.extend(jStat.fn, {
  normalci: function normalci(value, alpha) {
    return jStat.normalci(value, alpha, this.toArray());
  },

  tci: function tci(value, alpha) {
    return jStat.tci(value, alpha, this.toArray());
  }
});

// internal method for calculating the z-score for a difference of proportions test
function differenceOfProportions(p1, n1, p2, n2) {
  if (p1 > 1 || p2 > 1 || p1 <= 0 || p2 <= 0) {
    throw new Error("Proportions should be greater than 0 and less than 1")
  }
  var pooled = (p1 * n1 + p2 * n2) / (n1 + n2);
  var se = Math.sqrt(pooled * (1 - pooled) * ((1/n1) + (1/n2)));
  return (p1 - p2) / se;
}

// Difference of Proportions
jStat.extend(jStat.fn, {
  oneSidedDifferenceOfProportions: function oneSidedDifferenceOfProportions(p1, n1, p2, n2) {
    var z = differenceOfProportions(p1, n1, p2, n2);
    return jStat.ztest(z, 1);
  },

  twoSidedDifferenceOfProportions: function twoSidedDifferenceOfProportions(p1, n1, p2, n2) {
    var z = differenceOfProportions(p1, n1, p2, n2);
    return jStat.ztest(z, 2);
  }
});

}(this.jStat, Math));

},{}],15:[function(require,module,exports){
(function (global){
/**
 * @license
 * lodash <https://lodash.com/>
 * Copyright jQuery Foundation and other contributors <https://jquery.org/>
 * Released under MIT license <https://lodash.com/license>
 * Based on Underscore.js 1.8.3 <http://underscorejs.org/LICENSE>
 * Copyright Jeremy Ashkenas, DocumentCloud and Investigative Reporters & Editors
 */
;(function() {

  /** Used as a safe reference for `undefined` in pre-ES5 environments. */
  var undefined;

  /** Used as the semantic version number. */
  var VERSION = '4.16.4';

  /** Used as the size to enable large array optimizations. */
  var LARGE_ARRAY_SIZE = 200;

  /** Error message constants. */
  var CORE_ERROR_TEXT = 'Unsupported core-js use. Try https://github.com/es-shims.',
      FUNC_ERROR_TEXT = 'Expected a function';

  /** Used to stand-in for `undefined` hash values. */
  var HASH_UNDEFINED = '__lodash_hash_undefined__';

  /** Used as the maximum memoize cache size. */
  var MAX_MEMOIZE_SIZE = 500;

  /** Used as the internal argument placeholder. */
  var PLACEHOLDER = '__lodash_placeholder__';

  /** Used to compose bitmasks for function metadata. */
  var BIND_FLAG = 1,
      BIND_KEY_FLAG = 2,
      CURRY_BOUND_FLAG = 4,
      CURRY_FLAG = 8,
      CURRY_RIGHT_FLAG = 16,
      PARTIAL_FLAG = 32,
      PARTIAL_RIGHT_FLAG = 64,
      ARY_FLAG = 128,
      REARG_FLAG = 256,
      FLIP_FLAG = 512;

  /** Used to compose bitmasks for comparison styles. */
  var UNORDERED_COMPARE_FLAG = 1,
      PARTIAL_COMPARE_FLAG = 2;

  /** Used as default options for `_.truncate`. */
  var DEFAULT_TRUNC_LENGTH = 30,
      DEFAULT_TRUNC_OMISSION = '...';

  /** Used to detect hot functions by number of calls within a span of milliseconds. */
  var HOT_COUNT = 500,
      HOT_SPAN = 16;

  /** Used to indicate the type of lazy iteratees. */
  var LAZY_FILTER_FLAG = 1,
      LAZY_MAP_FLAG = 2,
      LAZY_WHILE_FLAG = 3;

  /** Used as references for various `Number` constants. */
  var INFINITY = 1 / 0,
      MAX_SAFE_INTEGER = 9007199254740991,
      MAX_INTEGER = 1.7976931348623157e+308,
      NAN = 0 / 0;

  /** Used as references for the maximum length and index of an array. */
  var MAX_ARRAY_LENGTH = 4294967295,
      MAX_ARRAY_INDEX = MAX_ARRAY_LENGTH - 1,
      HALF_MAX_ARRAY_LENGTH = MAX_ARRAY_LENGTH >>> 1;

  /** Used to associate wrap methods with their bit flags. */
  var wrapFlags = [
    ['ary', ARY_FLAG],
    ['bind', BIND_FLAG],
    ['bindKey', BIND_KEY_FLAG],
    ['curry', CURRY_FLAG],
    ['curryRight', CURRY_RIGHT_FLAG],
    ['flip', FLIP_FLAG],
    ['partial', PARTIAL_FLAG],
    ['partialRight', PARTIAL_RIGHT_FLAG],
    ['rearg', REARG_FLAG]
  ];

  /** `Object#toString` result references. */
  var argsTag = '[object Arguments]',
      arrayTag = '[object Array]',
      boolTag = '[object Boolean]',
      dateTag = '[object Date]',
      errorTag = '[object Error]',
      funcTag = '[object Function]',
      genTag = '[object GeneratorFunction]',
      mapTag = '[object Map]',
      numberTag = '[object Number]',
      objectTag = '[object Object]',
      promiseTag = '[object Promise]',
      proxyTag = '[object Proxy]',
      regexpTag = '[object RegExp]',
      setTag = '[object Set]',
      stringTag = '[object String]',
      symbolTag = '[object Symbol]',
      weakMapTag = '[object WeakMap]',
      weakSetTag = '[object WeakSet]';

  var arrayBufferTag = '[object ArrayBuffer]',
      dataViewTag = '[object DataView]',
      float32Tag = '[object Float32Array]',
      float64Tag = '[object Float64Array]',
      int8Tag = '[object Int8Array]',
      int16Tag = '[object Int16Array]',
      int32Tag = '[object Int32Array]',
      uint8Tag = '[object Uint8Array]',
      uint8ClampedTag = '[object Uint8ClampedArray]',
      uint16Tag = '[object Uint16Array]',
      uint32Tag = '[object Uint32Array]';

  /** Used to match empty string literals in compiled template source. */
  var reEmptyStringLeading = /\b__p \+= '';/g,
      reEmptyStringMiddle = /\b(__p \+=) '' \+/g,
      reEmptyStringTrailing = /(__e\(.*?\)|\b__t\)) \+\n'';/g;

  /** Used to match HTML entities and HTML characters. */
  var reEscapedHtml = /&(?:amp|lt|gt|quot|#39);/g,
      reUnescapedHtml = /[&<>"']/g,
      reHasEscapedHtml = RegExp(reEscapedHtml.source),
      reHasUnescapedHtml = RegExp(reUnescapedHtml.source);

  /** Used to match template delimiters. */
  var reEscape = /<%-([\s\S]+?)%>/g,
      reEvaluate = /<%([\s\S]+?)%>/g,
      reInterpolate = /<%=([\s\S]+?)%>/g;

  /** Used to match property names within property paths. */
  var reIsDeepProp = /\.|\[(?:[^[\]]*|(["'])(?:(?!\1)[^\\]|\\.)*?\1)\]/,
      reIsPlainProp = /^\w*$/,
      reLeadingDot = /^\./,
      rePropName = /[^.[\]]+|\[(?:(-?\d+(?:\.\d+)?)|(["'])((?:(?!\2)[^\\]|\\.)*?)\2)\]|(?=(?:\.|\[\])(?:\.|\[\]|$))/g;

  /**
   * Used to match `RegExp`
   * [syntax characters](http://ecma-international.org/ecma-262/7.0/#sec-patterns).
   */
  var reRegExpChar = /[\\^$.*+?()[\]{}|]/g,
      reHasRegExpChar = RegExp(reRegExpChar.source);

  /** Used to match leading and trailing whitespace. */
  var reTrim = /^\s+|\s+$/g,
      reTrimStart = /^\s+/,
      reTrimEnd = /\s+$/;

  /** Used to match wrap detail comments. */
  var reWrapComment = /\{(?:\n\/\* \[wrapped with .+\] \*\/)?\n?/,
      reWrapDetails = /\{\n\/\* \[wrapped with (.+)\] \*/,
      reSplitDetails = /,? & /;

  /** Used to match words composed of alphanumeric characters. */
  var reAsciiWord = /[^\x00-\x2f\x3a-\x40\x5b-\x60\x7b-\x7f]+/g;

  /** Used to match backslashes in property paths. */
  var reEscapeChar = /\\(\\)?/g;

  /**
   * Used to match
   * [ES template delimiters](http://ecma-international.org/ecma-262/7.0/#sec-template-literal-lexical-components).
   */
  var reEsTemplate = /\$\{([^\\}]*(?:\\.[^\\}]*)*)\}/g;

  /** Used to match `RegExp` flags from their coerced string values. */
  var reFlags = /\w*$/;

  /** Used to detect bad signed hexadecimal string values. */
  var reIsBadHex = /^[-+]0x[0-9a-f]+$/i;

  /** Used to detect binary string values. */
  var reIsBinary = /^0b[01]+$/i;

  /** Used to detect host constructors (Safari). */
  var reIsHostCtor = /^\[object .+?Constructor\]$/;

  /** Used to detect octal string values. */
  var reIsOctal = /^0o[0-7]+$/i;

  /** Used to detect unsigned integer values. */
  var reIsUint = /^(?:0|[1-9]\d*)$/;

  /** Used to match Latin Unicode letters (excluding mathematical operators). */
  var reLatin = /[\xc0-\xd6\xd8-\xf6\xf8-\xff\u0100-\u017f]/g;

  /** Used to ensure capturing order of template delimiters. */
  var reNoMatch = /($^)/;

  /** Used to match unescaped characters in compiled string literals. */
  var reUnescapedString = /['\n\r\u2028\u2029\\]/g;

  /** Used to compose unicode character classes. */
  var rsAstralRange = '\\ud800-\\udfff',
      rsComboMarksRange = '\\u0300-\\u036f\\ufe20-\\ufe23',
      rsComboSymbolsRange = '\\u20d0-\\u20f0',
      rsDingbatRange = '\\u2700-\\u27bf',
      rsLowerRange = 'a-z\\xdf-\\xf6\\xf8-\\xff',
      rsMathOpRange = '\\xac\\xb1\\xd7\\xf7',
      rsNonCharRange = '\\x00-\\x2f\\x3a-\\x40\\x5b-\\x60\\x7b-\\xbf',
      rsPunctuationRange = '\\u2000-\\u206f',
      rsSpaceRange = ' \\t\\x0b\\f\\xa0\\ufeff\\n\\r\\u2028\\u2029\\u1680\\u180e\\u2000\\u2001\\u2002\\u2003\\u2004\\u2005\\u2006\\u2007\\u2008\\u2009\\u200a\\u202f\\u205f\\u3000',
      rsUpperRange = 'A-Z\\xc0-\\xd6\\xd8-\\xde',
      rsVarRange = '\\ufe0e\\ufe0f',
      rsBreakRange = rsMathOpRange + rsNonCharRange + rsPunctuationRange + rsSpaceRange;

  /** Used to compose unicode capture groups. */
  var rsApos = "['\u2019]",
      rsAstral = '[' + rsAstralRange + ']',
      rsBreak = '[' + rsBreakRange + ']',
      rsCombo = '[' + rsComboMarksRange + rsComboSymbolsRange + ']',
      rsDigits = '\\d+',
      rsDingbat = '[' + rsDingbatRange + ']',
      rsLower = '[' + rsLowerRange + ']',
      rsMisc = '[^' + rsAstralRange + rsBreakRange + rsDigits + rsDingbatRange + rsLowerRange + rsUpperRange + ']',
      rsFitz = '\\ud83c[\\udffb-\\udfff]',
      rsModifier = '(?:' + rsCombo + '|' + rsFitz + ')',
      rsNonAstral = '[^' + rsAstralRange + ']',
      rsRegional = '(?:\\ud83c[\\udde6-\\uddff]){2}',
      rsSurrPair = '[\\ud800-\\udbff][\\udc00-\\udfff]',
      rsUpper = '[' + rsUpperRange + ']',
      rsZWJ = '\\u200d';

  /** Used to compose unicode regexes. */
  var rsLowerMisc = '(?:' + rsLower + '|' + rsMisc + ')',
      rsUpperMisc = '(?:' + rsUpper + '|' + rsMisc + ')',
      rsOptLowerContr = '(?:' + rsApos + '(?:d|ll|m|re|s|t|ve))?',
      rsOptUpperContr = '(?:' + rsApos + '(?:D|LL|M|RE|S|T|VE))?',
      reOptMod = rsModifier + '?',
      rsOptVar = '[' + rsVarRange + ']?',
      rsOptJoin = '(?:' + rsZWJ + '(?:' + [rsNonAstral, rsRegional, rsSurrPair].join('|') + ')' + rsOptVar + reOptMod + ')*',
      rsSeq = rsOptVar + reOptMod + rsOptJoin,
      rsEmoji = '(?:' + [rsDingbat, rsRegional, rsSurrPair].join('|') + ')' + rsSeq,
      rsSymbol = '(?:' + [rsNonAstral + rsCombo + '?', rsCombo, rsRegional, rsSurrPair, rsAstral].join('|') + ')';

  /** Used to match apostrophes. */
  var reApos = RegExp(rsApos, 'g');

  /**
   * Used to match [combining diacritical marks](https://en.wikipedia.org/wiki/Combining_Diacritical_Marks) and
   * [combining diacritical marks for symbols](https://en.wikipedia.org/wiki/Combining_Diacritical_Marks_for_Symbols).
   */
  var reComboMark = RegExp(rsCombo, 'g');

  /** Used to match [string symbols](https://mathiasbynens.be/notes/javascript-unicode). */
  var reUnicode = RegExp(rsFitz + '(?=' + rsFitz + ')|' + rsSymbol + rsSeq, 'g');

  /** Used to match complex or compound words. */
  var reUnicodeWord = RegExp([
    rsUpper + '?' + rsLower + '+' + rsOptLowerContr + '(?=' + [rsBreak, rsUpper, '$'].join('|') + ')',
    rsUpperMisc + '+' + rsOptUpperContr + '(?=' + [rsBreak, rsUpper + rsLowerMisc, '$'].join('|') + ')',
    rsUpper + '?' + rsLowerMisc + '+' + rsOptLowerContr,
    rsUpper + '+' + rsOptUpperContr,
    rsDigits,
    rsEmoji
  ].join('|'), 'g');

  /** Used to detect strings with [zero-width joiners or code points from the astral planes](http://eev.ee/blog/2015/09/12/dark-corners-of-unicode/). */
  var reHasUnicode = RegExp('[' + rsZWJ + rsAstralRange  + rsComboMarksRange + rsComboSymbolsRange + rsVarRange + ']');

  /** Used to detect strings that need a more robust regexp to match words. */
  var reHasUnicodeWord = /[a-z][A-Z]|[A-Z]{2,}[a-z]|[0-9][a-zA-Z]|[a-zA-Z][0-9]|[^a-zA-Z0-9 ]/;

  /** Used to assign default `context` object properties. */
  var contextProps = [
    'Array', 'Buffer', 'DataView', 'Date', 'Error', 'Float32Array', 'Float64Array',
    'Function', 'Int8Array', 'Int16Array', 'Int32Array', 'Map', 'Math', 'Object',
    'Promise', 'RegExp', 'Set', 'String', 'Symbol', 'TypeError', 'Uint8Array',
    'Uint8ClampedArray', 'Uint16Array', 'Uint32Array', 'WeakMap',
    '_', 'clearTimeout', 'isFinite', 'parseInt', 'setTimeout'
  ];

  /** Used to make template sourceURLs easier to identify. */
  var templateCounter = -1;

  /** Used to identify `toStringTag` values of typed arrays. */
  var typedArrayTags = {};
  typedArrayTags[float32Tag] = typedArrayTags[float64Tag] =
  typedArrayTags[int8Tag] = typedArrayTags[int16Tag] =
  typedArrayTags[int32Tag] = typedArrayTags[uint8Tag] =
  typedArrayTags[uint8ClampedTag] = typedArrayTags[uint16Tag] =
  typedArrayTags[uint32Tag] = true;
  typedArrayTags[argsTag] = typedArrayTags[arrayTag] =
  typedArrayTags[arrayBufferTag] = typedArrayTags[boolTag] =
  typedArrayTags[dataViewTag] = typedArrayTags[dateTag] =
  typedArrayTags[errorTag] = typedArrayTags[funcTag] =
  typedArrayTags[mapTag] = typedArrayTags[numberTag] =
  typedArrayTags[objectTag] = typedArrayTags[regexpTag] =
  typedArrayTags[setTag] = typedArrayTags[stringTag] =
  typedArrayTags[weakMapTag] = false;

  /** Used to identify `toStringTag` values supported by `_.clone`. */
  var cloneableTags = {};
  cloneableTags[argsTag] = cloneableTags[arrayTag] =
  cloneableTags[arrayBufferTag] = cloneableTags[dataViewTag] =
  cloneableTags[boolTag] = cloneableTags[dateTag] =
  cloneableTags[float32Tag] = cloneableTags[float64Tag] =
  cloneableTags[int8Tag] = cloneableTags[int16Tag] =
  cloneableTags[int32Tag] = cloneableTags[mapTag] =
  cloneableTags[numberTag] = cloneableTags[objectTag] =
  cloneableTags[regexpTag] = cloneableTags[setTag] =
  cloneableTags[stringTag] = cloneableTags[symbolTag] =
  cloneableTags[uint8Tag] = cloneableTags[uint8ClampedTag] =
  cloneableTags[uint16Tag] = cloneableTags[uint32Tag] = true;
  cloneableTags[errorTag] = cloneableTags[funcTag] =
  cloneableTags[weakMapTag] = false;

  /** Used to map Latin Unicode letters to basic Latin letters. */
  var deburredLetters = {
    // Latin-1 Supplement block.
    '\xc0': 'A',  '\xc1': 'A', '\xc2': 'A', '\xc3': 'A', '\xc4': 'A', '\xc5': 'A',
    '\xe0': 'a',  '\xe1': 'a', '\xe2': 'a', '\xe3': 'a', '\xe4': 'a', '\xe5': 'a',
    '\xc7': 'C',  '\xe7': 'c',
    '\xd0': 'D',  '\xf0': 'd',
    '\xc8': 'E',  '\xc9': 'E', '\xca': 'E', '\xcb': 'E',
    '\xe8': 'e',  '\xe9': 'e', '\xea': 'e', '\xeb': 'e',
    '\xcc': 'I',  '\xcd': 'I', '\xce': 'I', '\xcf': 'I',
    '\xec': 'i',  '\xed': 'i', '\xee': 'i', '\xef': 'i',
    '\xd1': 'N',  '\xf1': 'n',
    '\xd2': 'O',  '\xd3': 'O', '\xd4': 'O', '\xd5': 'O', '\xd6': 'O', '\xd8': 'O',
    '\xf2': 'o',  '\xf3': 'o', '\xf4': 'o', '\xf5': 'o', '\xf6': 'o', '\xf8': 'o',
    '\xd9': 'U',  '\xda': 'U', '\xdb': 'U', '\xdc': 'U',
    '\xf9': 'u',  '\xfa': 'u', '\xfb': 'u', '\xfc': 'u',
    '\xdd': 'Y',  '\xfd': 'y', '\xff': 'y',
    '\xc6': 'Ae', '\xe6': 'ae',
    '\xde': 'Th', '\xfe': 'th',
    '\xdf': 'ss',
    // Latin Extended-A block.
    '\u0100': 'A',  '\u0102': 'A', '\u0104': 'A',
    '\u0101': 'a',  '\u0103': 'a', '\u0105': 'a',
    '\u0106': 'C',  '\u0108': 'C', '\u010a': 'C', '\u010c': 'C',
    '\u0107': 'c',  '\u0109': 'c', '\u010b': 'c', '\u010d': 'c',
    '\u010e': 'D',  '\u0110': 'D', '\u010f': 'd', '\u0111': 'd',
    '\u0112': 'E',  '\u0114': 'E', '\u0116': 'E', '\u0118': 'E', '\u011a': 'E',
    '\u0113': 'e',  '\u0115': 'e', '\u0117': 'e', '\u0119': 'e', '\u011b': 'e',
    '\u011c': 'G',  '\u011e': 'G', '\u0120': 'G', '\u0122': 'G',
    '\u011d': 'g',  '\u011f': 'g', '\u0121': 'g', '\u0123': 'g',
    '\u0124': 'H',  '\u0126': 'H', '\u0125': 'h', '\u0127': 'h',
    '\u0128': 'I',  '\u012a': 'I', '\u012c': 'I', '\u012e': 'I', '\u0130': 'I',
    '\u0129': 'i',  '\u012b': 'i', '\u012d': 'i', '\u012f': 'i', '\u0131': 'i',
    '\u0134': 'J',  '\u0135': 'j',
    '\u0136': 'K',  '\u0137': 'k', '\u0138': 'k',
    '\u0139': 'L',  '\u013b': 'L', '\u013d': 'L', '\u013f': 'L', '\u0141': 'L',
    '\u013a': 'l',  '\u013c': 'l', '\u013e': 'l', '\u0140': 'l', '\u0142': 'l',
    '\u0143': 'N',  '\u0145': 'N', '\u0147': 'N', '\u014a': 'N',
    '\u0144': 'n',  '\u0146': 'n', '\u0148': 'n', '\u014b': 'n',
    '\u014c': 'O',  '\u014e': 'O', '\u0150': 'O',
    '\u014d': 'o',  '\u014f': 'o', '\u0151': 'o',
    '\u0154': 'R',  '\u0156': 'R', '\u0158': 'R',
    '\u0155': 'r',  '\u0157': 'r', '\u0159': 'r',
    '\u015a': 'S',  '\u015c': 'S', '\u015e': 'S', '\u0160': 'S',
    '\u015b': 's',  '\u015d': 's', '\u015f': 's', '\u0161': 's',
    '\u0162': 'T',  '\u0164': 'T', '\u0166': 'T',
    '\u0163': 't',  '\u0165': 't', '\u0167': 't',
    '\u0168': 'U',  '\u016a': 'U', '\u016c': 'U', '\u016e': 'U', '\u0170': 'U', '\u0172': 'U',
    '\u0169': 'u',  '\u016b': 'u', '\u016d': 'u', '\u016f': 'u', '\u0171': 'u', '\u0173': 'u',
    '\u0174': 'W',  '\u0175': 'w',
    '\u0176': 'Y',  '\u0177': 'y', '\u0178': 'Y',
    '\u0179': 'Z',  '\u017b': 'Z', '\u017d': 'Z',
    '\u017a': 'z',  '\u017c': 'z', '\u017e': 'z',
    '\u0132': 'IJ', '\u0133': 'ij',
    '\u0152': 'Oe', '\u0153': 'oe',
    '\u0149': "'n", '\u017f': 's'
  };

  /** Used to map characters to HTML entities. */
  var htmlEscapes = {
    '&': '&amp;',
    '<': '&lt;',
    '>': '&gt;',
    '"': '&quot;',
    "'": '&#39;'
  };

  /** Used to map HTML entities to characters. */
  var htmlUnescapes = {
    '&amp;': '&',
    '&lt;': '<',
    '&gt;': '>',
    '&quot;': '"',
    '&#39;': "'"
  };

  /** Used to escape characters for inclusion in compiled string literals. */
  var stringEscapes = {
    '\\': '\\',
    "'": "'",
    '\n': 'n',
    '\r': 'r',
    '\u2028': 'u2028',
    '\u2029': 'u2029'
  };

  /** Built-in method references without a dependency on `root`. */
  var freeParseFloat = parseFloat,
      freeParseInt = parseInt;

  /** Detect free variable `global` from Node.js. */
  var freeGlobal = typeof global == 'object' && global && global.Object === Object && global;

  /** Detect free variable `self`. */
  var freeSelf = typeof self == 'object' && self && self.Object === Object && self;

  /** Used as a reference to the global object. */
  var root = freeGlobal || freeSelf || Function('return this')();

  /** Detect free variable `exports`. */
  var freeExports = typeof exports == 'object' && exports && !exports.nodeType && exports;

  /** Detect free variable `module`. */
  var freeModule = freeExports && typeof module == 'object' && module && !module.nodeType && module;

  /** Detect the popular CommonJS extension `module.exports`. */
  var moduleExports = freeModule && freeModule.exports === freeExports;

  /** Detect free variable `process` from Node.js. */
  var freeProcess = moduleExports && freeGlobal.process;

  /** Used to access faster Node.js helpers. */
  var nodeUtil = (function() {
    try {
      return freeProcess && freeProcess.binding('util');
    } catch (e) {}
  }());

  /* Node.js helper references. */
  var nodeIsArrayBuffer = nodeUtil && nodeUtil.isArrayBuffer,
      nodeIsDate = nodeUtil && nodeUtil.isDate,
      nodeIsMap = nodeUtil && nodeUtil.isMap,
      nodeIsRegExp = nodeUtil && nodeUtil.isRegExp,
      nodeIsSet = nodeUtil && nodeUtil.isSet,
      nodeIsTypedArray = nodeUtil && nodeUtil.isTypedArray;

  /*--------------------------------------------------------------------------*/

  /**
   * Adds the key-value `pair` to `map`.
   *
   * @private
   * @param {Object} map The map to modify.
   * @param {Array} pair The key-value pair to add.
   * @returns {Object} Returns `map`.
   */
  function addMapEntry(map, pair) {
    // Don't return `map.set` because it's not chainable in IE 11.
    map.set(pair[0], pair[1]);
    return map;
  }

  /**
   * Adds `value` to `set`.
   *
   * @private
   * @param {Object} set The set to modify.
   * @param {*} value The value to add.
   * @returns {Object} Returns `set`.
   */
  function addSetEntry(set, value) {
    // Don't return `set.add` because it's not chainable in IE 11.
    set.add(value);
    return set;
  }

  /**
   * A faster alternative to `Function#apply`, this function invokes `func`
   * with the `this` binding of `thisArg` and the arguments of `args`.
   *
   * @private
   * @param {Function} func The function to invoke.
   * @param {*} thisArg The `this` binding of `func`.
   * @param {Array} args The arguments to invoke `func` with.
   * @returns {*} Returns the result of `func`.
   */
  function apply(func, thisArg, args) {
    switch (args.length) {
      case 0: return func.call(thisArg);
      case 1: return func.call(thisArg, args[0]);
      case 2: return func.call(thisArg, args[0], args[1]);
      case 3: return func.call(thisArg, args[0], args[1], args[2]);
    }
    return func.apply(thisArg, args);
  }

  /**
   * A specialized version of `baseAggregator` for arrays.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} setter The function to set `accumulator` values.
   * @param {Function} iteratee The iteratee to transform keys.
   * @param {Object} accumulator The initial aggregated object.
   * @returns {Function} Returns `accumulator`.
   */
  function arrayAggregator(array, setter, iteratee, accumulator) {
    var index = -1,
        length = array ? array.length : 0;

    while (++index < length) {
      var value = array[index];
      setter(accumulator, value, iteratee(value), array);
    }
    return accumulator;
  }

  /**
   * A specialized version of `_.forEach` for arrays without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @returns {Array} Returns `array`.
   */
  function arrayEach(array, iteratee) {
    var index = -1,
        length = array ? array.length : 0;

    while (++index < length) {
      if (iteratee(array[index], index, array) === false) {
        break;
      }
    }
    return array;
  }

  /**
   * A specialized version of `_.forEachRight` for arrays without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @returns {Array} Returns `array`.
   */
  function arrayEachRight(array, iteratee) {
    var length = array ? array.length : 0;

    while (length--) {
      if (iteratee(array[length], length, array) === false) {
        break;
      }
    }
    return array;
  }

  /**
   * A specialized version of `_.every` for arrays without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} predicate The function invoked per iteration.
   * @returns {boolean} Returns `true` if all elements pass the predicate check,
   *  else `false`.
   */
  function arrayEvery(array, predicate) {
    var index = -1,
        length = array ? array.length : 0;

    while (++index < length) {
      if (!predicate(array[index], index, array)) {
        return false;
      }
    }
    return true;
  }

  /**
   * A specialized version of `_.filter` for arrays without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} predicate The function invoked per iteration.
   * @returns {Array} Returns the new filtered array.
   */
  function arrayFilter(array, predicate) {
    var index = -1,
        length = array ? array.length : 0,
        resIndex = 0,
        result = [];

    while (++index < length) {
      var value = array[index];
      if (predicate(value, index, array)) {
        result[resIndex++] = value;
      }
    }
    return result;
  }

  /**
   * A specialized version of `_.includes` for arrays without support for
   * specifying an index to search from.
   *
   * @private
   * @param {Array} [array] The array to inspect.
   * @param {*} target The value to search for.
   * @returns {boolean} Returns `true` if `target` is found, else `false`.
   */
  function arrayIncludes(array, value) {
    var length = array ? array.length : 0;
    return !!length && baseIndexOf(array, value, 0) > -1;
  }

  /**
   * This function is like `arrayIncludes` except that it accepts a comparator.
   *
   * @private
   * @param {Array} [array] The array to inspect.
   * @param {*} target The value to search for.
   * @param {Function} comparator The comparator invoked per element.
   * @returns {boolean} Returns `true` if `target` is found, else `false`.
   */
  function arrayIncludesWith(array, value, comparator) {
    var index = -1,
        length = array ? array.length : 0;

    while (++index < length) {
      if (comparator(value, array[index])) {
        return true;
      }
    }
    return false;
  }

  /**
   * A specialized version of `_.map` for arrays without support for iteratee
   * shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @returns {Array} Returns the new mapped array.
   */
  function arrayMap(array, iteratee) {
    var index = -1,
        length = array ? array.length : 0,
        result = Array(length);

    while (++index < length) {
      result[index] = iteratee(array[index], index, array);
    }
    return result;
  }

  /**
   * Appends the elements of `values` to `array`.
   *
   * @private
   * @param {Array} array The array to modify.
   * @param {Array} values The values to append.
   * @returns {Array} Returns `array`.
   */
  function arrayPush(array, values) {
    var index = -1,
        length = values.length,
        offset = array.length;

    while (++index < length) {
      array[offset + index] = values[index];
    }
    return array;
  }

  /**
   * A specialized version of `_.reduce` for arrays without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @param {*} [accumulator] The initial value.
   * @param {boolean} [initAccum] Specify using the first element of `array` as
   *  the initial value.
   * @returns {*} Returns the accumulated value.
   */
  function arrayReduce(array, iteratee, accumulator, initAccum) {
    var index = -1,
        length = array ? array.length : 0;

    if (initAccum && length) {
      accumulator = array[++index];
    }
    while (++index < length) {
      accumulator = iteratee(accumulator, array[index], index, array);
    }
    return accumulator;
  }

  /**
   * A specialized version of `_.reduceRight` for arrays without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @param {*} [accumulator] The initial value.
   * @param {boolean} [initAccum] Specify using the last element of `array` as
   *  the initial value.
   * @returns {*} Returns the accumulated value.
   */
  function arrayReduceRight(array, iteratee, accumulator, initAccum) {
    var length = array ? array.length : 0;
    if (initAccum && length) {
      accumulator = array[--length];
    }
    while (length--) {
      accumulator = iteratee(accumulator, array[length], length, array);
    }
    return accumulator;
  }

  /**
   * A specialized version of `_.some` for arrays without support for iteratee
   * shorthands.
   *
   * @private
   * @param {Array} [array] The array to iterate over.
   * @param {Function} predicate The function invoked per iteration.
   * @returns {boolean} Returns `true` if any element passes the predicate check,
   *  else `false`.
   */
  function arraySome(array, predicate) {
    var index = -1,
        length = array ? array.length : 0;

    while (++index < length) {
      if (predicate(array[index], index, array)) {
        return true;
      }
    }
    return false;
  }

  /**
   * Gets the size of an ASCII `string`.
   *
   * @private
   * @param {string} string The string inspect.
   * @returns {number} Returns the string size.
   */
  var asciiSize = baseProperty('length');

  /**
   * Converts an ASCII `string` to an array.
   *
   * @private
   * @param {string} string The string to convert.
   * @returns {Array} Returns the converted array.
   */
  function asciiToArray(string) {
    return string.split('');
  }

  /**
   * Splits an ASCII `string` into an array of its words.
   *
   * @private
   * @param {string} The string to inspect.
   * @returns {Array} Returns the words of `string`.
   */
  function asciiWords(string) {
    return string.match(reAsciiWord) || [];
  }

  /**
   * The base implementation of methods like `_.findKey` and `_.findLastKey`,
   * without support for iteratee shorthands, which iterates over `collection`
   * using `eachFunc`.
   *
   * @private
   * @param {Array|Object} collection The collection to inspect.
   * @param {Function} predicate The function invoked per iteration.
   * @param {Function} eachFunc The function to iterate over `collection`.
   * @returns {*} Returns the found element or its key, else `undefined`.
   */
  function baseFindKey(collection, predicate, eachFunc) {
    var result;
    eachFunc(collection, function(value, key, collection) {
      if (predicate(value, key, collection)) {
        result = key;
        return false;
      }
    });
    return result;
  }

  /**
   * The base implementation of `_.findIndex` and `_.findLastIndex` without
   * support for iteratee shorthands.
   *
   * @private
   * @param {Array} array The array to inspect.
   * @param {Function} predicate The function invoked per iteration.
   * @param {number} fromIndex The index to search from.
   * @param {boolean} [fromRight] Specify iterating from right to left.
   * @returns {number} Returns the index of the matched value, else `-1`.
   */
  function baseFindIndex(array, predicate, fromIndex, fromRight) {
    var length = array.length,
        index = fromIndex + (fromRight ? 1 : -1);

    while ((fromRight ? index-- : ++index < length)) {
      if (predicate(array[index], index, array)) {
        return index;
      }
    }
    return -1;
  }

  /**
   * The base implementation of `_.indexOf` without `fromIndex` bounds checks.
   *
   * @private
   * @param {Array} array The array to inspect.
   * @param {*} value The value to search for.
   * @param {number} fromIndex The index to search from.
   * @returns {number} Returns the index of the matched value, else `-1`.
   */
  function baseIndexOf(array, value, fromIndex) {
    return value === value
      ? strictIndexOf(array, value, fromIndex)
      : baseFindIndex(array, baseIsNaN, fromIndex);
  }

  /**
   * This function is like `baseIndexOf` except that it accepts a comparator.
   *
   * @private
   * @param {Array} array The array to inspect.
   * @param {*} value The value to search for.
   * @param {number} fromIndex The index to search from.
   * @param {Function} comparator The comparator invoked per element.
   * @returns {number} Returns the index of the matched value, else `-1`.
   */
  function baseIndexOfWith(array, value, fromIndex, comparator) {
    var index = fromIndex - 1,
        length = array.length;

    while (++index < length) {
      if (comparator(array[index], value)) {
        return index;
      }
    }
    return -1;
  }

  /**
   * The base implementation of `_.isNaN` without support for number objects.
   *
   * @private
   * @param {*} value The value to check.
   * @returns {boolean} Returns `true` if `value` is `NaN`, else `false`.
   */
  function baseIsNaN(value) {
    return value !== value;
  }

  /**
   * The base implementation of `_.mean` and `_.meanBy` without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} array The array to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @returns {number} Returns the mean.
   */
  function baseMean(array, iteratee) {
    var length = array ? array.length : 0;
    return length ? (baseSum(array, iteratee) / length) : NAN;
  }

  /**
   * The base implementation of `_.property` without support for deep paths.
   *
   * @private
   * @param {string} key The key of the property to get.
   * @returns {Function} Returns the new accessor function.
   */
  function baseProperty(key) {
    return function(object) {
      return object == null ? undefined : object[key];
    };
  }

  /**
   * The base implementation of `_.propertyOf` without support for deep paths.
   *
   * @private
   * @param {Object} object The object to query.
   * @returns {Function} Returns the new accessor function.
   */
  function basePropertyOf(object) {
    return function(key) {
      return object == null ? undefined : object[key];
    };
  }

  /**
   * The base implementation of `_.reduce` and `_.reduceRight`, without support
   * for iteratee shorthands, which iterates over `collection` using `eachFunc`.
   *
   * @private
   * @param {Array|Object} collection The collection to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @param {*} accumulator The initial value.
   * @param {boolean} initAccum Specify using the first or last element of
   *  `collection` as the initial value.
   * @param {Function} eachFunc The function to iterate over `collection`.
   * @returns {*} Returns the accumulated value.
   */
  function baseReduce(collection, iteratee, accumulator, initAccum, eachFunc) {
    eachFunc(collection, function(value, index, collection) {
      accumulator = initAccum
        ? (initAccum = false, value)
        : iteratee(accumulator, value, index, collection);
    });
    return accumulator;
  }

  /**
   * The base implementation of `_.sortBy` which uses `comparer` to define the
   * sort order of `array` and replaces criteria objects with their corresponding
   * values.
   *
   * @private
   * @param {Array} array The array to sort.
   * @param {Function} comparer The function to define sort order.
   * @returns {Array} Returns `array`.
   */
  function baseSortBy(array, comparer) {
    var length = array.length;

    array.sort(comparer);
    while (length--) {
      array[length] = array[length].value;
    }
    return array;
  }

  /**
   * The base implementation of `_.sum` and `_.sumBy` without support for
   * iteratee shorthands.
   *
   * @private
   * @param {Array} array The array to iterate over.
   * @param {Function} iteratee The function invoked per iteration.
   * @returns {number} Returns the sum.
   */
  function baseSum(array, iteratee) {
    var result,
        index = -1,
        length = array.length;

    while (++index < length) {
      var current = iteratee(array[index]);
      if (current !== undefined) {
        result = result === undefined ? current : (result + current);
      }
    }
    return result;
  }

  /**
   * The base implementation of `_.times` without support for iteratee shorthands
   * or max array length checks.
   *
   * @private
   * @param {number} n The number of times to invoke `iteratee`.
   * @param {Function} iteratee The function invoked per iteration.
   * @returns {Array} Returns the array of results.
   */
  function baseTimes(n, iteratee) {
    var index = -1,
        result = Array(n);

    while (++index < n) {
      result[index] = iteratee(index);
    }
    return result;
  }

  /**
   * The base implementation of `_.toPairs` and `_.toPairsIn` which creates an array
   * of key-value pairs for `object` corresponding to the property names of `props`.
   *
   * @private
   * @param {Object} object The object to query.
   * @param {Array} props The property names to get values for.
   * @returns {Object} Returns the key-value pairs.
   */
  function baseToPairs(object, props) {
    return arrayMap(props, function(key) {
      return [key, object[key]];
    });
  }

  /**
   * The base implementation of `_.unary` without support for storing metadata.
   *
   * @private
   * @param {Function} func The function to cap arguments for.
   * @returns {Function} Returns the new capped function.
   */
  function baseUnary(func) {
    return function(value) {
      return func(value);
    };
  }

  /**
   * The base implementation of `_.values` and `_.valuesIn` which creates an
   * array of `object` property values corresponding to the property names
   * of `props`.
   *
   * @private
   * @param {Object} object The object to query.
   * @param {Array} props The property names to get values for.
   * @returns {Object} Returns the array of property values.
   */
  function baseValues(object, props) {
    return arrayMap(props, function(key) {
      return object[key];
    });
  }

  /**
   * Checks if a `cache` value for `key` exists.
   *
   * @private
   * @param {Object} cache The cache to query.
   * @param {string} key The key of the entry to check.
   * @returns {boolean} Returns `true` if an entry for `key` exists, else `false`.
   */
  function cacheHas(cache, key) {
    return cache.has(key);
  }

  /**
   * Used by `_.trim` and `_.trimStart` to get the index of the first string symbol
   * that is not found in the character symbols.
   *
   * @private
   * @param {Array} strSymbols The string symbols to inspect.
   * @param {Array} chrSymbols The character symbols to find.
   * @returns {number} Returns the index of the first unmatched string symbol.
   */
  function charsStartIndex(strSymbols, chrSymbols) {
    var index = -1,
        length = strSymbols.length;

    while (++index < length && baseIndexOf(chrSymbols, strSymbols[index], 0) > -1) {}
    return index;
  }

  /**
   * Used by `_.trim` and `_.trimEnd` to get the index of the last string symbol
   * that is not found in the character symbols.
   *
   * @private
   * @param {Array} strSymbols The string symbols to inspect.
   * @param {Array} chrSymbols The character symbols to find.
   * @returns {number} Returns the index of the last unmatched string symbol.
   */
  function charsEndIndex(strSymbols, chrSymbols) {
    var index = strSymbols.length;

    while (index-- && baseIndexOf(chrSymbols, strSymbols[index], 0) > -1) {}
    return index;
  }

  /**
   * Gets the number of `placeholder` occurrences in `array`.
   *
   * @private
   * @param {Array} array The array to inspect.
   * @param {*} placeholder The placeholder to search for.
   * @returns {number} Returns the placeholder count.
   */
  function countHolders(array, placeholder) {
    var length = array.length,
        result = 0;

    while (length--) {
      if (array[length] === placeholder) {
        ++result;
      }
    }
    return result;
  }

  /**
   * Used by `_.deburr` to convert Latin-1 Supplement and Latin Extended-A
   * letters to basic Latin letters.
   *
   * @private
   * @param {string} letter The matched letter to deburr.
   * @returns {string} Returns the deburred letter.
   */
  var deburrLetter = basePropertyOf(deburredLetters);

  /**
   * Used by `_.escape` to convert characters to HTML entities.
   *
   * @private
   * @param {string} chr The matched character to escape.
   * @returns {string} Returns the escaped character.
   */
  var escapeHtmlChar = basePropertyOf(htmlEscapes);

  /**
   * Used by `_.template` to escape characters for inclusion in compiled string literals.
   *
   * @private
   * @param {string} chr The matched character to escape.
   * @returns {string} Returns the escaped character.
   */
  function escapeStringChar(chr) {
    return '\\' + stringEscapes[chr];
  }

  /**
   * Gets the value at `key` of `object`.
   *
   * @private
   * @param {Object} [object] The object to query.
   * @param {string} key The key of the property to get.
   * @returns {*} Returns the property value.
   */
  function getValue(object, key) {
    return object == null ? undefined : object[key];
  }

  /**
   * Checks if `string` contains Unicode symbols.
   *
   * @private
   * @param {string} string The string to inspect.
   * @returns {boolean} Returns `true` if a symbol is found, else `false`.
   */
  function hasUnicode(string) {
    return reHasUnicode.test(string);
  }

  /**
   * Checks if `string` contains a word composed of Unicode symbols.
   *
   * @private
   * @param {string} string The string to inspect.
   * @returns {boolean} Returns `true` if a word is found, else `false`.
   */
  function hasUnicodeWord(string) {
    return reHasUnicodeWord.test(string);
  }

  /**
   * Converts `iterator` to an array.
   *
   * @private
   * @param {Object} iterator The iterator to convert.
   * @returns {Array} Returns the converted array.
   */
  function iteratorToArray(iterator) {
    var data,
        result = [];

    while (!(data = iterator.next()).done) {
      result.push(data.value);
    }
    return result;
  }

  /**
   * Converts `map` to its key-value pairs.
   *
   * @private
   * @param {Object} map The map to convert.
   * @returns {Array} Returns the key-value pairs.
   */
  function mapToArray(map) {
    var index = -1,
        result = Array(map.size);

    map.forEach(function(value, key) {
      result[++index] = [key, value];
    });
    return result;
  }

  /**
   * Creates a unary function that invokes `func` with its argument transformed.
   *
   * @private
   * @param {Function} func The function to wrap.
   * @param {Function} transform The argument transform.
   * @returns {Function} Returns the new function.
   */
  function overArg(func, transform) {
    return function(arg) {
      return func(transform(arg));
    };
  }

  /**
   * Replaces all `placeholder` elements in `array` with an internal placeholder
   * and returns an array of their indexes.
   *
   * @private
   * @param {Array} array The array to modify.
   * @param {*} placeholder The placeholder to replace.
   * @returns {Array} Returns the new array of placeholder indexes.
   */
  function replaceHolders(array, placeholder) {
    var index = -1,
        length = array.length,
        resIndex = 0,
        result = [];

    while (++index < length) {
      var value = array[index];
      if (value === placeholder || value === PLACEHOLDER) {
        array[index] = PLACEHOLDER;
        result[resIndex++] = index;
      }
    }
    return result;
  }

  /**
   * Converts `set` to an array of its values.
   *
   * @private
   * @param {Object} set The set to convert.
   * @returns {Array} Returns the values.
   */
  function setToArray(set) {
    var index = -1,
        result = Array(set.size);

    set.forEach(function(value) {
      result[++index] = value;
    });
    return result;
  }

  /**
   * Converts `set` to its value-value pairs.
   *
   * @private
   * @param {Object} set The set to convert.
   * @returns {Array} Returns the value-value pairs.
   */
  function setToPairs(set) {
    var index = -1,
        result = Array(set.size);

    set.forEach(function(value) {
      result[++index] = [value, value];
    });
    return result;
  }

  /**
   * A specialized version of `_.indexOf` which performs strict equality
   * comparisons of values, i.e. `===`.
   *
   * @private
   * @param {Array} array The array to inspect.
   * @param {*} value The value to search for.
   * @param {number} fromIndex The index to search from.
   * @returns {number} Returns the index of the matched value, else `-1`.
   */
  function strictIndexOf(array, value, fromIndex) {
    var index = fromIndex - 1,
        length = array.length;

    while (++index < length) {
      if (array[index] === value) {
        return index;
      }
    }
    return -1;
  }

  /**
   * A specialized version of `_.lastIndexOf` which performs strict equality
   * comparisons of values, i.e. `===`.
   *
   * @private
   * @param {Array} array The array to inspect.
   * @param {*} value The value to search for.
   * @param {number} fromIndex The index to search from.
   * @returns {number} Returns the index of the matched value, else `-1`.
   */
  function strictLastIndexOf(array, value, fromIndex) {
    var index = fromIndex + 1;
    while (index--) {
      if (array[index] === value) {
        return index;
      }
    }
    return index;
  }

  /**
   * Gets the number of symbols in `string`.
   *
   * @private
   * @param {string} string The string to inspect.
   * @returns {number} Returns the string size.
   */
  function stringSize(string) {
    return hasUnicode(string)
      ? unicodeSize(string)
      : asciiSize(string);
  }

  /**
   * Converts `string` to an array.
   *
   * @private
   * @param {string} string The string to convert.
   * @returns {Array} Returns the converted array.
   */
  function stringToArray(string) {
    return hasUnicode(string)
      ? unicodeToArray(string)
      : asciiToArray(string);
  }

  /**
   * Used by `_.unescape` to convert HTML entities to characters.
   *
   * @private
   * @param {string} chr The matched character to unescape.
   * @returns {string} Returns the unescaped character.
   */
  var unescapeHtmlChar = basePropertyOf(htmlUnescapes);

  /**
   * Gets the size of a Unicode `string`.
   *
   * @private
   * @param {string} string The string inspect.
   * @returns {number} Returns the string size.
   */
  function unicodeSize(string) {
    var result = reUnicode.lastIndex = 0;
    while (reUnicode.test(string)) {
      ++result;
    }
    return result;
  }

  /**
   * Converts a Unicode `string` to an array.
   *
   * @private
   * @param {string} string The string to convert.
   * @returns {Array} Returns the converted array.
   */
  function unicodeToArray(string) {
    return string.match(reUnicode) || [];
  }

  /**
   * Splits a Unicode `string` into an array of its words.
   *
   * @private
   * @param {string} The string to inspect.
   * @returns {Array} Returns the words of `string`.
   */
  function unicodeWords(string) {
    return string.match(reUnicodeWord) || [];
  }

  /*--------------------------------------------------------------------------*/

  /**
   * Create a new pristine `lodash` function using the `context` object.
   *
   * @static
   * @memberOf _
   * @since 1.1.0
   * @category Util
   * @param {Object} [context=root] The context object.
   * @returns {Function} Returns a new `lodash` function.
   * @example
   *
   * _.mixin({ 'foo': _.constant('foo') });
   *
   * var lodash = _.runInContext();
   * lodash.mixin({ 'bar': lodash.constant('bar') });
   *
   * _.isFunction(_.foo);
   * // => true
   * _.isFunction(_.bar);
   * // => false
   *
   * lodash.isFunction(lodash.foo);
   * // => false
   * lodash.isFunction(lodash.bar);
   * // => true
   *
   * // Create a suped-up `defer` in Node.js.
   * var defer = _.runInContext({ 'setTimeout': setImmediate }).defer;
   */
  var runInContext = (function runInContext(context) {
    context = context ? _.defaults(root.Object(), context, _.pick(root, contextProps)) : root;

    /** Built-in constructor references. */
    var Array = context.Array,
        Date = context.Date,
        Error = context.Error,
        Function = context.Function,
        Math = context.Math,
        Object = context.Object,
        RegExp = context.RegExp,
        String = context.String,
        TypeError = context.TypeError;

    /** Used for built-in method references. */
    var arrayProto = Array.prototype,
        funcProto = Function.prototype,
        objectProto = Object.prototype;

    /** Used to detect overreaching core-js shims. */
    var coreJsData = context['__core-js_shared__'];

    /** Used to detect methods masquerading as native. */
    var maskSrcKey = (function() {
      var uid = /[^.]+$/.exec(coreJsData && coreJsData.keys && coreJsData.keys.IE_PROTO || '');
      return uid ? ('Symbol(src)_1.' + uid) : '';
    }());

    /** Used to resolve the decompiled source of functions. */
    var funcToString = funcProto.toString;

    /** Used to check objects for own properties. */
    var hasOwnProperty = objectProto.hasOwnProperty;

    /** Used to generate unique IDs. */
    var idCounter = 0;

    /** Used to infer the `Object` constructor. */
    var objectCtorString = funcToString.call(Object);

    /**
     * Used to resolve the
     * [`toStringTag`](http://ecma-international.org/ecma-262/7.0/#sec-object.prototype.tostring)
     * of values.
     */
    var objectToString = objectProto.toString;

    /** Used to restore the original `_` reference in `_.noConflict`. */
    var oldDash = root._;

    /** Used to detect if a method is native. */
    var reIsNative = RegExp('^' +
      funcToString.call(hasOwnProperty).replace(reRegExpChar, '\\$&')
      .replace(/hasOwnProperty|(function).*?(?=\\\()| for .+?(?=\\\])/g, '$1.*?') + '$'
    );

    /** Built-in value references. */
    var Buffer = moduleExports ? context.Buffer : undefined,
        Symbol = context.Symbol,
        Uint8Array = context.Uint8Array,
        allocUnsafe = Buffer ? Buffer.allocUnsafe : undefined,
        getPrototype = overArg(Object.getPrototypeOf, Object),
        iteratorSymbol = Symbol ? Symbol.iterator : undefined,
        objectCreate = Object.create,
        propertyIsEnumerable = objectProto.propertyIsEnumerable,
        splice = arrayProto.splice,
        spreadableSymbol = Symbol ? Symbol.isConcatSpreadable : undefined;

    var defineProperty = (function() {
      try {
        var func = getNative(Object, 'defineProperty');
        func({}, '', {});
        return func;
      } catch (e) {}
    }());

    /** Mocked built-ins. */
    var ctxClearTimeout = context.clearTimeout !== root.clearTimeout && context.clearTimeout,
        ctxNow = Date && Date.now !== root.Date.now && Date.now,
        ctxSetTimeout = context.setTimeout !== root.setTimeout && context.setTimeout;

    /* Built-in method references for those with the same name as other `lodash` methods. */
    var nativeCeil = Math.ceil,
        nativeFloor = Math.floor,
        nativeGetSymbols = Object.getOwnPropertySymbols,
        nativeIsBuffer = Buffer ? Buffer.isBuffer : undefined,
        nativeIsFinite = context.isFinite,
        nativeJoin = arrayProto.join,
        nativeKeys = overArg(Object.keys, Object),
        nativeMax = Math.max,
        nativeMin = Math.min,
        nativeNow = Date.now,
        nativeParseInt = context.parseInt,
        nativeRandom = Math.random,
        nativeReverse = arrayProto.reverse;

    /* Built-in method references that are verified to be native. */
    var DataView = getNative(context, 'DataView'),
        Map = getNative(context, 'Map'),
        Promise = getNative(context, 'Promise'),
        Set = getNative(context, 'Set'),
        WeakMap = getNative(context, 'WeakMap'),
        nativeCreate = getNative(Object, 'create');

    /** Used to store function metadata. */
    var metaMap = WeakMap && new WeakMap;

    /** Used to lookup unminified function names. */
    var realNames = {};

    /** Used to detect maps, sets, and weakmaps. */
    var dataViewCtorString = toSource(DataView),
        mapCtorString = toSource(Map),
        promiseCtorString = toSource(Promise),
        setCtorString = toSource(Set),
        weakMapCtorString = toSource(WeakMap);

    /** Used to convert symbols to primitives and strings. */
    var symbolProto = Symbol ? Symbol.prototype : undefined,
        symbolValueOf = symbolProto ? symbolProto.valueOf : undefined,
        symbolToString = symbolProto ? symbolProto.toString : undefined;

    /*------------------------------------------------------------------------*/

    /**
     * Creates a `lodash` object which wraps `value` to enable implicit method
     * chain sequences. Methods that operate on and return arrays, collections,
     * and functions can be chained together. Methods that retrieve a single value
     * or may return a primitive value will automatically end the chain sequence
     * and return the unwrapped value. Otherwise, the value must be unwrapped
     * with `_#value`.
     *
     * Explicit chain sequences, which must be unwrapped with `_#value`, may be
     * enabled using `_.chain`.
     *
     * The execution of chained methods is lazy, that is, it's deferred until
     * `_#value` is implicitly or explicitly called.
     *
     * Lazy evaluation allows several methods to support shortcut fusion.
     * Shortcut fusion is an optimization to merge iteratee calls; this avoids
     * the creation of intermediate arrays and can greatly reduce the number of
     * iteratee executions. Sections of a chain sequence qualify for shortcut
     * fusion if the section is applied to an array of at least `200` elements
     * and any iteratees accept only one argument. The heuristic for whether a
     * section qualifies for shortcut fusion is subject to change.
     *
     * Chaining is supported in custom builds as long as the `_#value` method is
     * directly or indirectly included in the build.
     *
     * In addition to lodash methods, wrappers have `Array` and `String` methods.
     *
     * The wrapper `Array` methods are:
     * `concat`, `join`, `pop`, `push`, `shift`, `sort`, `splice`, and `unshift`
     *
     * The wrapper `String` methods are:
     * `replace` and `split`
     *
     * The wrapper methods that support shortcut fusion are:
     * `at`, `compact`, `drop`, `dropRight`, `dropWhile`, `filter`, `find`,
     * `findLast`, `head`, `initial`, `last`, `map`, `reject`, `reverse`, `slice`,
     * `tail`, `take`, `takeRight`, `takeRightWhile`, `takeWhile`, and `toArray`
     *
     * The chainable wrapper methods are:
     * `after`, `ary`, `assign`, `assignIn`, `assignInWith`, `assignWith`, `at`,
     * `before`, `bind`, `bindAll`, `bindKey`, `castArray`, `chain`, `chunk`,
     * `commit`, `compact`, `concat`, `conforms`, `constant`, `countBy`, `create`,
     * `curry`, `debounce`, `defaults`, `defaultsDeep`, `defer`, `delay`,
     * `difference`, `differenceBy`, `differenceWith`, `drop`, `dropRight`,
     * `dropRightWhile`, `dropWhile`, `extend`, `extendWith`, `fill`, `filter`,
     * `flatMap`, `flatMapDeep`, `flatMapDepth`, `flatten`, `flattenDeep`,
     * `flattenDepth`, `flip`, `flow`, `flowRight`, `fromPairs`, `functions`,
     * `functionsIn`, `groupBy`, `initial`, `intersection`, `intersectionBy`,
     * `intersectionWith`, `invert`, `invertBy`, `invokeMap`, `iteratee`, `keyBy`,
     * `keys`, `keysIn`, `map`, `mapKeys`, `mapValues`, `matches`, `matchesProperty`,
     * `memoize`, `merge`, `mergeWith`, `method`, `methodOf`, `mixin`, `negate`,
     * `nthArg`, `omit`, `omitBy`, `once`, `orderBy`, `over`, `overArgs`,
     * `overEvery`, `overSome`, `partial`, `partialRight`, `partition`, `pick`,
     * `pickBy`, `plant`, `property`, `propertyOf`, `pull`, `pullAll`, `pullAllBy`,
     * `pullAllWith`, `pullAt`, `push`, `range`, `rangeRight`, `rearg`, `reject`,
     * `remove`, `rest`, `reverse`, `sampleSize`, `set`, `setWith`, `shuffle`,
     * `slice`, `sort`, `sortBy`, `splice`, `spread`, `tail`, `take`, `takeRight`,
     * `takeRightWhile`, `takeWhile`, `tap`, `throttle`, `thru`, `toArray`,
     * `toPairs`, `toPairsIn`, `toPath`, `toPlainObject`, `transform`, `unary`,
     * `union`, `unionBy`, `unionWith`, `uniq`, `uniqBy`, `uniqWith`, `unset`,
     * `unshift`, `unzip`, `unzipWith`, `update`, `updateWith`, `values`,
     * `valuesIn`, `without`, `wrap`, `xor`, `xorBy`, `xorWith`, `zip`,
     * `zipObject`, `zipObjectDeep`, and `zipWith`
     *
     * The wrapper methods that are **not** chainable by default are:
     * `add`, `attempt`, `camelCase`, `capitalize`, `ceil`, `clamp`, `clone`,
     * `cloneDeep`, `cloneDeepWith`, `cloneWith`, `conformsTo`, `deburr`,
     * `defaultTo`, `divide`, `each`, `eachRight`, `endsWith`, `eq`, `escape`,
     * `escapeRegExp`, `every`, `find`, `findIndex`, `findKey`, `findLast`,
     * `findLastIndex`, `findLastKey`, `first`, `floor`, `forEach`, `forEachRight`,
     * `forIn`, `forInRight`, `forOwn`, `forOwnRight`, `get`, `gt`, `gte`, `has`,
     * `hasIn`, `head`, `identity`, `includes`, `indexOf`, `inRange`, `invoke`,
     * `isArguments`, `isArray`, `isArrayBuffer`, `isArrayLike`, `isArrayLikeObject`,
     * `isBoolean`, `isBuffer`, `isDate`, `isElement`, `isEmpty`, `isEqual`,
     * `isEqualWith`, `isError`, `isFinite`, `isFunction`, `isInteger`, `isLength`,
     * `isMap`, `isMatch`, `isMatchWith`, `isNaN`, `isNative`, `isNil`, `isNull`,
     * `isNumber`, `isObject`, `isObjectLike`, `isPlainObject`, `isRegExp`,
     * `isSafeInteger`, `isSet`, `isString`, `isUndefined`, `isTypedArray`,
     * `isWeakMap`, `isWeakSet`, `join`, `kebabCase`, `last`, `lastIndexOf`,
     * `lowerCase`, `lowerFirst`, `lt`, `lte`, `max`, `maxBy`, `mean`, `meanBy`,
     * `min`, `minBy`, `multiply`, `noConflict`, `noop`, `now`, `nth`, `pad`,
     * `padEnd`, `padStart`, `parseInt`, `pop`, `random`, `reduce`, `reduceRight`,
     * `repeat`, `result`, `round`, `runInContext`, `sample`, `shift`, `size`,
     * `snakeCase`, `some`, `sortedIndex`, `sortedIndexBy`, `sortedLastIndex`,
     * `sortedLastIndexBy`, `startCase`, `startsWith`, `stubArray`, `stubFalse`,
     * `stubObject`, `stubString`, `stubTrue`, `subtract`, `sum`, `sumBy`,
     * `template`, `times`, `toFinite`, `toInteger`, `toJSON`, `toLength`,
     * `toLower`, `toNumber`, `toSafeInteger`, `toString`, `toUpper`, `trim`,
     * `trimEnd`, `trimStart`, `truncate`, `unescape`, `uniqueId`, `upperCase`,
     * `upperFirst`, `value`, and `words`
     *
     * @name _
     * @constructor
     * @category Seq
     * @param {*} value The value to wrap in a `lodash` instance.
     * @returns {Object} Returns the new `lodash` wrapper instance.
     * @example
     *
     * function square(n) {
     *   return n * n;
     * }
     *
     * var wrapped = _([1, 2, 3]);
     *
     * // Returns an unwrapped value.
     * wrapped.reduce(_.add);
     * // => 6
     *
     * // Returns a wrapped value.
     * var squares = wrapped.map(square);
     *
     * _.isArray(squares);
     * // => false
     *
     * _.isArray(squares.value());
     * // => true
     */
    function lodash(value) {
      if (isObjectLike(value) && !isArray(value) && !(value instanceof LazyWrapper)) {
        if (value instanceof LodashWrapper) {
          return value;
        }
        if (hasOwnProperty.call(value, '__wrapped__')) {
          return wrapperClone(value);
        }
      }
      return new LodashWrapper(value);
    }

    /**
     * The base implementation of `_.create` without support for assigning
     * properties to the created object.
     *
     * @private
     * @param {Object} proto The object to inherit from.
     * @returns {Object} Returns the new object.
     */
    var baseCreate = (function() {
      function object() {}
      return function(proto) {
        if (!isObject(proto)) {
          return {};
        }
        if (objectCreate) {
          return objectCreate(proto);
        }
        object.prototype = proto;
        var result = new object;
        object.prototype = undefined;
        return result;
      };
    }());

    /**
     * The function whose prototype chain sequence wrappers inherit from.
     *
     * @private
     */
    function baseLodash() {
      // No operation performed.
    }

    /**
     * The base constructor for creating `lodash` wrapper objects.
     *
     * @private
     * @param {*} value The value to wrap.
     * @param {boolean} [chainAll] Enable explicit method chain sequences.
     */
    function LodashWrapper(value, chainAll) {
      this.__wrapped__ = value;
      this.__actions__ = [];
      this.__chain__ = !!chainAll;
      this.__index__ = 0;
      this.__values__ = undefined;
    }

    /**
     * By default, the template delimiters used by lodash are like those in
     * embedded Ruby (ERB). Change the following template settings to use
     * alternative delimiters.
     *
     * @static
     * @memberOf _
     * @type {Object}
     */
    lodash.templateSettings = {

      /**
       * Used to detect `data` property values to be HTML-escaped.
       *
       * @memberOf _.templateSettings
       * @type {RegExp}
       */
      'escape': reEscape,

      /**
       * Used to detect code to be evaluated.
       *
       * @memberOf _.templateSettings
       * @type {RegExp}
       */
      'evaluate': reEvaluate,

      /**
       * Used to detect `data` property values to inject.
       *
       * @memberOf _.templateSettings
       * @type {RegExp}
       */
      'interpolate': reInterpolate,

      /**
       * Used to reference the data object in the template text.
       *
       * @memberOf _.templateSettings
       * @type {string}
       */
      'variable': '',

      /**
       * Used to import variables into the compiled template.
       *
       * @memberOf _.templateSettings
       * @type {Object}
       */
      'imports': {

        /**
         * A reference to the `lodash` function.
         *
         * @memberOf _.templateSettings.imports
         * @type {Function}
         */
        '_': lodash
      }
    };

    // Ensure wrappers are instances of `baseLodash`.
    lodash.prototype = baseLodash.prototype;
    lodash.prototype.constructor = lodash;

    LodashWrapper.prototype = baseCreate(baseLodash.prototype);
    LodashWrapper.prototype.constructor = LodashWrapper;

    /*------------------------------------------------------------------------*/

    /**
     * Creates a lazy wrapper object which wraps `value` to enable lazy evaluation.
     *
     * @private
     * @constructor
     * @param {*} value The value to wrap.
     */
    function LazyWrapper(value) {
      this.__wrapped__ = value;
      this.__actions__ = [];
      this.__dir__ = 1;
      this.__filtered__ = false;
      this.__iteratees__ = [];
      this.__takeCount__ = MAX_ARRAY_LENGTH;
      this.__views__ = [];
    }

    /**
     * Creates a clone of the lazy wrapper object.
     *
     * @private
     * @name clone
     * @memberOf LazyWrapper
     * @returns {Object} Returns the cloned `LazyWrapper` object.
     */
    function lazyClone() {
      var result = new LazyWrapper(this.__wrapped__);
      result.__actions__ = copyArray(this.__actions__);
      result.__dir__ = this.__dir__;
      result.__filtered__ = this.__filtered__;
      result.__iteratees__ = copyArray(this.__iteratees__);
      result.__takeCount__ = this.__takeCount__;
      result.__views__ = copyArray(this.__views__);
      return result;
    }

    /**
     * Reverses the direction of lazy iteration.
     *
     * @private
     * @name reverse
     * @memberOf LazyWrapper
     * @returns {Object} Returns the new reversed `LazyWrapper` object.
     */
    function lazyReverse() {
      if (this.__filtered__) {
        var result = new LazyWrapper(this);
        result.__dir__ = -1;
        result.__filtered__ = true;
      } else {
        result = this.clone();
        result.__dir__ *= -1;
      }
      return result;
    }

    /**
     * Extracts the unwrapped value from its lazy wrapper.
     *
     * @private
     * @name value
     * @memberOf LazyWrapper
     * @returns {*} Returns the unwrapped value.
     */
    function lazyValue() {
      var array = this.__wrapped__.value(),
          dir = this.__dir__,
          isArr = isArray(array),
          isRight = dir < 0,
          arrLength = isArr ? array.length : 0,
          view = getView(0, arrLength, this.__views__),
          start = view.start,
          end = view.end,
          length = end - start,
          index = isRight ? end : (start - 1),
          iteratees = this.__iteratees__,
          iterLength = iteratees.length,
          resIndex = 0,
          takeCount = nativeMin(length, this.__takeCount__);

      if (!isArr || arrLength < LARGE_ARRAY_SIZE ||
          (arrLength == length && takeCount == length)) {
        return baseWrapperValue(array, this.__actions__);
      }
      var result = [];

      outer:
      while (length-- && resIndex < takeCount) {
        index += dir;

        var iterIndex = -1,
            value = array[index];

        while (++iterIndex < iterLength) {
          var data = iteratees[iterIndex],
              iteratee = data.iteratee,
              type = data.type,
              computed = iteratee(value);

          if (type == LAZY_MAP_FLAG) {
            value = computed;
          } else if (!computed) {
            if (type == LAZY_FILTER_FLAG) {
              continue outer;
            } else {
              break outer;
            }
          }
        }
        result[resIndex++] = value;
      }
      return result;
    }

    // Ensure `LazyWrapper` is an instance of `baseLodash`.
    LazyWrapper.prototype = baseCreate(baseLodash.prototype);
    LazyWrapper.prototype.constructor = LazyWrapper;

    /*------------------------------------------------------------------------*/

    /**
     * Creates a hash object.
     *
     * @private
     * @constructor
     * @param {Array} [entries] The key-value pairs to cache.
     */
    function Hash(entries) {
      var index = -1,
          length = entries ? entries.length : 0;

      this.clear();
      while (++index < length) {
        var entry = entries[index];
        this.set(entry[0], entry[1]);
      }
    }

    /**
     * Removes all key-value entries from the hash.
     *
     * @private
     * @name clear
     * @memberOf Hash
     */
    function hashClear() {
      this.__data__ = nativeCreate ? nativeCreate(null) : {};
      this.size = 0;
    }

    /**
     * Removes `key` and its value from the hash.
     *
     * @private
     * @name delete
     * @memberOf Hash
     * @param {Object} hash The hash to modify.
     * @param {string} key The key of the value to remove.
     * @returns {boolean} Returns `true` if the entry was removed, else `false`.
     */
    function hashDelete(key) {
      var result = this.has(key) && delete this.__data__[key];
      this.size -= result ? 1 : 0;
      return result;
    }

    /**
     * Gets the hash value for `key`.
     *
     * @private
     * @name get
     * @memberOf Hash
     * @param {string} key The key of the value to get.
     * @returns {*} Returns the entry value.
     */
    function hashGet(key) {
      var data = this.__data__;
      if (nativeCreate) {
        var result = data[key];
        return result === HASH_UNDEFINED ? undefined : result;
      }
      return hasOwnProperty.call(data, key) ? data[key] : undefined;
    }

    /**
     * Checks if a hash value for `key` exists.
     *
     * @private
     * @name has
     * @memberOf Hash
     * @param {string} key The key of the entry to check.
     * @returns {boolean} Returns `true` if an entry for `key` exists, else `false`.
     */
    function hashHas(key) {
      var data = this.__data__;
      return nativeCreate ? data[key] !== undefined : hasOwnProperty.call(data, key);
    }

    /**
     * Sets the hash `key` to `value`.
     *
     * @private
     * @name set
     * @memberOf Hash
     * @param {string} key The key of the value to set.
     * @param {*} value The value to set.
     * @returns {Object} Returns the hash instance.
     */
    function hashSet(key, value) {
      var data = this.__data__;
      this.size += this.has(key) ? 0 : 1;
      data[key] = (nativeCreate && value === undefined) ? HASH_UNDEFINED : value;
      return this;
    }

    // Add methods to `Hash`.
    Hash.prototype.clear = hashClear;
    Hash.prototype['delete'] = hashDelete;
    Hash.prototype.get = hashGet;
    Hash.prototype.has = hashHas;
    Hash.prototype.set = hashSet;

    /*------------------------------------------------------------------------*/

    /**
     * Creates an list cache object.
     *
     * @private
     * @constructor
     * @param {Array} [entries] The key-value pairs to cache.
     */
    function ListCache(entries) {
      var index = -1,
          length = entries ? entries.length : 0;

      this.clear();
      while (++index < length) {
        var entry = entries[index];
        this.set(entry[0], entry[1]);
      }
    }

    /**
     * Removes all key-value entries from the list cache.
     *
     * @private
     * @name clear
     * @memberOf ListCache
     */
    function listCacheClear() {
      this.__data__ = [];
      this.size = 0;
    }

    /**
     * Removes `key` and its value from the list cache.
     *
     * @private
     * @name delete
     * @memberOf ListCache
     * @param {string} key The key of the value to remove.
     * @returns {boolean} Returns `true` if the entry was removed, else `false`.
     */
    function listCacheDelete(key) {
      var data = this.__data__,
          index = assocIndexOf(data, key);

      if (index < 0) {
        return false;
      }
      var lastIndex = data.length - 1;
      if (index == lastIndex) {
        data.pop();
      } else {
        splice.call(data, index, 1);
      }
      --this.size;
      return true;
    }

    /**
     * Gets the list cache value for `key`.
     *
     * @private
     * @name get
     * @memberOf ListCache
     * @param {string} key The key of the value to get.
     * @returns {*} Returns the entry value.
     */
    function listCacheGet(key) {
      var data = this.__data__,
          index = assocIndexOf(data, key);

      return index < 0 ? undefined : data[index][1];
    }

    /**
     * Checks if a list cache value for `key` exists.
     *
     * @private
     * @name has
     * @memberOf ListCache
     * @param {string} key The key of the entry to check.
     * @returns {boolean} Returns `true` if an entry for `key` exists, else `false`.
     */
    function listCacheHas(key) {
      return assocIndexOf(this.__data__, key) > -1;
    }

    /**
     * Sets the list cache `key` to `value`.
     *
     * @private
     * @name set
     * @memberOf ListCache
     * @param {string} key The key of the value to set.
     * @param {*} value The value to set.
     * @returns {Object} Returns the list cache instance.
     */
    function listCacheSet(key, value) {
      var data = this.__data__,
          index = assocIndexOf(data, key);

      if (index < 0) {
        ++this.size;
        data.push([key, value]);
      } else {
        data[index][1] = value;
      }
      return this;
    }

    // Add methods to `ListCache`.
    ListCache.prototype.clear = listCacheClear;
    ListCache.prototype['delete'] = listCacheDelete;
    ListCache.prototype.get = listCacheGet;
    ListCache.prototype.has = listCacheHas;
    ListCache.prototype.set = listCacheSet;

    /*------------------------------------------------------------------------*/

    /**
     * Creates a map cache object to store key-value pairs.
     *
     * @private
     * @constructor
     * @param {Array} [entries] The key-value pairs to cache.
     */
    function MapCache(entries) {
      var index = -1,
          length = entries ? entries.length : 0;

      this.clear();
      while (++index < length) {
        var entry = entries[index];
        this.set(entry[0], entry[1]);
      }
    }

    /**
     * Removes all key-value entries from the map.
     *
     * @private
     * @name clear
     * @memberOf MapCache
     */
    function mapCacheClear() {
      this.size = 0;
      this.__data__ = {
        'hash': new Hash,
        'map': new (Map || ListCache),
        'string': new Hash
      };
    }

    /**
     * Removes `key` and its value from the map.
     *
     * @private
     * @name delete
     * @memberOf MapCache
     * @param {string} key The key of the value to remove.
     * @returns {boolean} Returns `true` if the entry was removed, else `false`.
     */
    function mapCacheDelete(key) {
      var result = getMapData(this, key)['delete'](key);
      this.size -= result ? 1 : 0;
      return result;
    }

    /**
     * Gets the map value for `key`.
     *
     * @private
     * @name get
     * @memberOf MapCache
     * @param {string} key The key of the value to get.
     * @returns {*} Returns the entry value.
     */
    function mapCacheGet(key) {
      return getMapData(this, key).get(key);
    }

    /**
     * Checks if a map value for `key` exists.
     *
     * @private
     * @name has
     * @memberOf MapCache
     * @param {string} key The key of the entry to check.
     * @returns {boolean} Returns `true` if an entry for `key` exists, else `false`.
     */
    function mapCacheHas(key) {
      return getMapData(this, key).has(key);
    }

    /**
     * Sets the map `key` to `value`.
     *
     * @private
     * @name set
     * @memberOf MapCache
     * @param {string} key The key of the value to set.
     * @param {*} value The value to set.
     * @returns {Object} Returns the map cache instance.
     */
    function mapCacheSet(key, value) {
      var data = getMapData(this, key),
          size = data.size;

      data.set(key, value);
      this.size += data.size == size ? 0 : 1;
      return this;
    }

    // Add methods to `MapCache`.
    MapCache.prototype.clear = mapCacheClear;
    MapCache.prototype['delete'] = mapCacheDelete;
    MapCache.prototype.get = mapCacheGet;
    MapCache.prototype.has = mapCacheHas;
    MapCache.prototype.set = mapCacheSet;

    /*------------------------------------------------------------------------*/

    /**
     *
     * Creates an array cache object to store unique values.
     *
     * @private
     * @constructor
     * @param {Array} [values] The values to cache.
     */
    function SetCache(values) {
      var index = -1,
          length = values ? values.length : 0;

      this.__data__ = new MapCache;
      while (++index < length) {
        this.add(values[index]);
      }
    }

    /**
     * Adds `value` to the array cache.
     *
     * @private
     * @name add
     * @memberOf SetCache
     * @alias push
     * @param {*} value The value to cache.
     * @returns {Object} Returns the cache instance.
     */
    function setCacheAdd(value) {
      this.__data__.set(value, HASH_UNDEFINED);
      return this;
    }

    /**
     * Checks if `value` is in the array cache.
     *
     * @private
     * @name has
     * @memberOf SetCache
     * @param {*} value The value to search for.
     * @returns {number} Returns `true` if `value` is found, else `false`.
     */
    function setCacheHas(value) {
      return this.__data__.has(value);
    }

    // Add methods to `SetCache`.
    SetCache.prototype.add = SetCache.prototype.push = setCacheAdd;
    SetCache.prototype.has = setCacheHas;

    /*------------------------------------------------------------------------*/

    /**
     * Creates a stack cache object to store key-value pairs.
     *
     * @private
     * @constructor
     * @param {Array} [entries] The key-value pairs to cache.
     */
    function Stack(entries) {
      var data = this.__data__ = new ListCache(entries);
      this.size = data.size;
    }

    /**
     * Removes all key-value entries from the stack.
     *
     * @private
     * @name clear
     * @memberOf Stack
     */
    function stackClear() {
      this.__data__ = new ListCache;
      this.size = 0;
    }

    /**
     * Removes `key` and its value from the stack.
     *
     * @private
     * @name delete
     * @memberOf Stack
     * @param {string} key The key of the value to remove.
     * @returns {boolean} Returns `true` if the entry was removed, else `false`.
     */
    function stackDelete(key) {
      var data = this.__data__,
          result = data['delete'](key);

      this.size = data.size;
      return result;
    }

    /**
     * Gets the stack value for `key`.
     *
     * @private
     * @name get
     * @memberOf Stack
     * @param {string} key The key of the value to get.
     * @returns {*} Returns the entry value.
     */
    function stackGet(key) {
      return this.__data__.get(key);
    }

    /**
     * Checks if a stack value for `key` exists.
     *
     * @private
     * @name has
     * @memberOf Stack
     * @param {string} key The key of the entry to check.
     * @returns {boolean} Returns `true` if an entry for `key` exists, else `false`.
     */
    function stackHas(key) {
      return this.__data__.has(key);
    }

    /**
     * Sets the stack `key` to `value`.
     *
     * @private
     * @name set
     * @memberOf Stack
     * @param {string} key The key of the value to set.
     * @param {*} value The value to set.
     * @returns {Object} Returns the stack cache instance.
     */
    function stackSet(key, value) {
      var data = this.__data__;
      if (data instanceof ListCache) {
        var pairs = data.__data__;
        if (!Map || (pairs.length < LARGE_ARRAY_SIZE - 1)) {
          pairs.push([key, value]);
          this.size = ++data.size;
          return this;
        }
        data = this.__data__ = new MapCache(pairs);
      }
      data.set(key, value);
      this.size = data.size;
      return this;
    }

    // Add methods to `Stack`.
    Stack.prototype.clear = stackClear;
    Stack.prototype['delete'] = stackDelete;
    Stack.prototype.get = stackGet;
    Stack.prototype.has = stackHas;
    Stack.prototype.set = stackSet;

    /*------------------------------------------------------------------------*/

    /**
     * Creates an array of the enumerable property names of the array-like `value`.
     *
     * @private
     * @param {*} value The value to query.
     * @param {boolean} inherited Specify returning inherited property names.
     * @returns {Array} Returns the array of property names.
     */
    function arrayLikeKeys(value, inherited) {
      var isArr = isArray(value),
          isArg = !isArr && isArguments(value),
          isBuff = !isArr && !isArg && isBuffer(value),
          isType = !isArr && !isArg && !isBuff && isTypedArray(value),
          skipIndexes = isArr || isArg || isBuff || isType,
          result = skipIndexes ? baseTimes(value.length, String) : [],
          length = result.length;

      for (var key in value) {
        if ((inherited || hasOwnProperty.call(value, key)) &&
            !(skipIndexes && (
               // Safari 9 has enumerable `arguments.length` in strict mode.
               key == 'length' ||
               // Node.js 0.10 has enumerable non-index properties on buffers.
               (isBuff && (key == 'offset' || key == 'parent')) ||
               // PhantomJS 2 has enumerable non-index properties on typed arrays.
               (isType && (key == 'buffer' || key == 'byteLength' || key == 'byteOffset')) ||
               // Skip index properties.
               isIndex(key, length)
            ))) {
          result.push(key);
        }
      }
      return result;
    }

    /**
     * A specialized version of `_.sample` for arrays.
     *
     * @private
     * @param {Array} array The array to sample.
     * @returns {*} Returns the random element.
     */
    function arraySample(array) {
      var length = array.length;
      return length ? array[baseRandom(0, length - 1)] : undefined;
    }

    /**
     * A specialized version of `_.sampleSize` for arrays.
     *
     * @private
     * @param {Array} array The array to sample.
     * @param {number} n The number of elements to sample.
     * @returns {Array} Returns the random elements.
     */
    function arraySampleSize(array, n) {
      return shuffleSelf(copyArray(array), baseClamp(n, 0, array.length));
    }

    /**
     * A specialized version of `_.shuffle` for arrays.
     *
     * @private
     * @param {Array} array The array to shuffle.
     * @returns {Array} Returns the new shuffled array.
     */
    function arrayShuffle(array) {
      return shuffleSelf(copyArray(array));
    }

    /**
     * Used by `_.defaults` to customize its `_.assignIn` use.
     *
     * @private
     * @param {*} objValue The destination value.
     * @param {*} srcValue The source value.
     * @param {string} key The key of the property to assign.
     * @param {Object} object The parent object of `objValue`.
     * @returns {*} Returns the value to assign.
     */
    function assignInDefaults(objValue, srcValue, key, object) {
      if (objValue === undefined ||
          (eq(objValue, objectProto[key]) && !hasOwnProperty.call(object, key))) {
        return srcValue;
      }
      return objValue;
    }

    /**
     * This function is like `assignValue` except that it doesn't assign
     * `undefined` values.
     *
     * @private
     * @param {Object} object The object to modify.
     * @param {string} key The key of the property to assign.
     * @param {*} value The value to assign.
     */
    function assignMergeValue(object, key, value) {
      if ((value !== undefined && !eq(object[key], value)) ||
          (value === undefined && !(key in object))) {
        baseAssignValue(object, key, value);
      }
    }

    /**
     * Assigns `value` to `key` of `object` if the existing value is not equivalent
     * using [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons.
     *
     * @private
     * @param {Object} object The object to modify.
     * @param {string} key The key of the property to assign.
     * @param {*} value The value to assign.
     */
    function assignValue(object, key, value) {
      var objValue = object[key];
      if (!(hasOwnProperty.call(object, key) && eq(objValue, value)) ||
          (value === undefined && !(key in object))) {
        baseAssignValue(object, key, value);
      }
    }

    /**
     * Gets the index at which the `key` is found in `array` of key-value pairs.
     *
     * @private
     * @param {Array} array The array to inspect.
     * @param {*} key The key to search for.
     * @returns {number} Returns the index of the matched value, else `-1`.
     */
    function assocIndexOf(array, key) {
      var length = array.length;
      while (length--) {
        if (eq(array[length][0], key)) {
          return length;
        }
      }
      return -1;
    }

    /**
     * Aggregates elements of `collection` on `accumulator` with keys transformed
     * by `iteratee` and values set by `setter`.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} setter The function to set `accumulator` values.
     * @param {Function} iteratee The iteratee to transform keys.
     * @param {Object} accumulator The initial aggregated object.
     * @returns {Function} Returns `accumulator`.
     */
    function baseAggregator(collection, setter, iteratee, accumulator) {
      baseEach(collection, function(value, key, collection) {
        setter(accumulator, value, iteratee(value), collection);
      });
      return accumulator;
    }

    /**
     * The base implementation of `_.assign` without support for multiple sources
     * or `customizer` functions.
     *
     * @private
     * @param {Object} object The destination object.
     * @param {Object} source The source object.
     * @returns {Object} Returns `object`.
     */
    function baseAssign(object, source) {
      return object && copyObject(source, keys(source), object);
    }

    /**
     * The base implementation of `assignValue` and `assignMergeValue` without
     * value checks.
     *
     * @private
     * @param {Object} object The object to modify.
     * @param {string} key The key of the property to assign.
     * @param {*} value The value to assign.
     */
    function baseAssignValue(object, key, value) {
      if (key == '__proto__' && defineProperty) {
        defineProperty(object, key, {
          'configurable': true,
          'enumerable': true,
          'value': value,
          'writable': true
        });
      } else {
        object[key] = value;
      }
    }

    /**
     * The base implementation of `_.at` without support for individual paths.
     *
     * @private
     * @param {Object} object The object to iterate over.
     * @param {string[]} paths The property paths of elements to pick.
     * @returns {Array} Returns the picked elements.
     */
    function baseAt(object, paths) {
      var index = -1,
          isNil = object == null,
          length = paths.length,
          result = Array(length);

      while (++index < length) {
        result[index] = isNil ? undefined : get(object, paths[index]);
      }
      return result;
    }

    /**
     * The base implementation of `_.clamp` which doesn't coerce arguments.
     *
     * @private
     * @param {number} number The number to clamp.
     * @param {number} [lower] The lower bound.
     * @param {number} upper The upper bound.
     * @returns {number} Returns the clamped number.
     */
    function baseClamp(number, lower, upper) {
      if (number === number) {
        if (upper !== undefined) {
          number = number <= upper ? number : upper;
        }
        if (lower !== undefined) {
          number = number >= lower ? number : lower;
        }
      }
      return number;
    }

    /**
     * The base implementation of `_.clone` and `_.cloneDeep` which tracks
     * traversed objects.
     *
     * @private
     * @param {*} value The value to clone.
     * @param {boolean} [isDeep] Specify a deep clone.
     * @param {boolean} [isFull] Specify a clone including symbols.
     * @param {Function} [customizer] The function to customize cloning.
     * @param {string} [key] The key of `value`.
     * @param {Object} [object] The parent object of `value`.
     * @param {Object} [stack] Tracks traversed objects and their clone counterparts.
     * @returns {*} Returns the cloned value.
     */
    function baseClone(value, isDeep, isFull, customizer, key, object, stack) {
      var result;
      if (customizer) {
        result = object ? customizer(value, key, object, stack) : customizer(value);
      }
      if (result !== undefined) {
        return result;
      }
      if (!isObject(value)) {
        return value;
      }
      var isArr = isArray(value);
      if (isArr) {
        result = initCloneArray(value);
        if (!isDeep) {
          return copyArray(value, result);
        }
      } else {
        var tag = getTag(value),
            isFunc = tag == funcTag || tag == genTag;

        if (isBuffer(value)) {
          return cloneBuffer(value, isDeep);
        }
        if (tag == objectTag || tag == argsTag || (isFunc && !object)) {
          result = initCloneObject(isFunc ? {} : value);
          if (!isDeep) {
            return copySymbols(value, baseAssign(result, value));
          }
        } else {
          if (!cloneableTags[tag]) {
            return object ? value : {};
          }
          result = initCloneByTag(value, tag, baseClone, isDeep);
        }
      }
      // Check for circular references and return its corresponding clone.
      stack || (stack = new Stack);
      var stacked = stack.get(value);
      if (stacked) {
        return stacked;
      }
      stack.set(value, result);

      var props = isArr ? undefined : (isFull ? getAllKeys : keys)(value);
      arrayEach(props || value, function(subValue, key) {
        if (props) {
          key = subValue;
          subValue = value[key];
        }
        // Recursively populate clone (susceptible to call stack limits).
        assignValue(result, key, baseClone(subValue, isDeep, isFull, customizer, key, value, stack));
      });
      return result;
    }

    /**
     * The base implementation of `_.conforms` which doesn't clone `source`.
     *
     * @private
     * @param {Object} source The object of property predicates to conform to.
     * @returns {Function} Returns the new spec function.
     */
    function baseConforms(source) {
      var props = keys(source);
      return function(object) {
        return baseConformsTo(object, source, props);
      };
    }

    /**
     * The base implementation of `_.conformsTo` which accepts `props` to check.
     *
     * @private
     * @param {Object} object The object to inspect.
     * @param {Object} source The object of property predicates to conform to.
     * @returns {boolean} Returns `true` if `object` conforms, else `false`.
     */
    function baseConformsTo(object, source, props) {
      var length = props.length;
      if (object == null) {
        return !length;
      }
      object = Object(object);
      while (length--) {
        var key = props[length],
            predicate = source[key],
            value = object[key];

        if ((value === undefined && !(key in object)) || !predicate(value)) {
          return false;
        }
      }
      return true;
    }

    /**
     * The base implementation of `_.delay` and `_.defer` which accepts `args`
     * to provide to `func`.
     *
     * @private
     * @param {Function} func The function to delay.
     * @param {number} wait The number of milliseconds to delay invocation.
     * @param {Array} args The arguments to provide to `func`.
     * @returns {number|Object} Returns the timer id or timeout object.
     */
    function baseDelay(func, wait, args) {
      if (typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      return setTimeout(function() { func.apply(undefined, args); }, wait);
    }

    /**
     * The base implementation of methods like `_.difference` without support
     * for excluding multiple arrays or iteratee shorthands.
     *
     * @private
     * @param {Array} array The array to inspect.
     * @param {Array} values The values to exclude.
     * @param {Function} [iteratee] The iteratee invoked per element.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new array of filtered values.
     */
    function baseDifference(array, values, iteratee, comparator) {
      var index = -1,
          includes = arrayIncludes,
          isCommon = true,
          length = array.length,
          result = [],
          valuesLength = values.length;

      if (!length) {
        return result;
      }
      if (iteratee) {
        values = arrayMap(values, baseUnary(iteratee));
      }
      if (comparator) {
        includes = arrayIncludesWith;
        isCommon = false;
      }
      else if (values.length >= LARGE_ARRAY_SIZE) {
        includes = cacheHas;
        isCommon = false;
        values = new SetCache(values);
      }
      outer:
      while (++index < length) {
        var value = array[index],
            computed = iteratee ? iteratee(value) : value;

        value = (comparator || value !== 0) ? value : 0;
        if (isCommon && computed === computed) {
          var valuesIndex = valuesLength;
          while (valuesIndex--) {
            if (values[valuesIndex] === computed) {
              continue outer;
            }
          }
          result.push(value);
        }
        else if (!includes(values, computed, comparator)) {
          result.push(value);
        }
      }
      return result;
    }

    /**
     * The base implementation of `_.forEach` without support for iteratee shorthands.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} iteratee The function invoked per iteration.
     * @returns {Array|Object} Returns `collection`.
     */
    var baseEach = createBaseEach(baseForOwn);

    /**
     * The base implementation of `_.forEachRight` without support for iteratee shorthands.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} iteratee The function invoked per iteration.
     * @returns {Array|Object} Returns `collection`.
     */
    var baseEachRight = createBaseEach(baseForOwnRight, true);

    /**
     * The base implementation of `_.every` without support for iteratee shorthands.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} predicate The function invoked per iteration.
     * @returns {boolean} Returns `true` if all elements pass the predicate check,
     *  else `false`
     */
    function baseEvery(collection, predicate) {
      var result = true;
      baseEach(collection, function(value, index, collection) {
        result = !!predicate(value, index, collection);
        return result;
      });
      return result;
    }

    /**
     * The base implementation of methods like `_.max` and `_.min` which accepts a
     * `comparator` to determine the extremum value.
     *
     * @private
     * @param {Array} array The array to iterate over.
     * @param {Function} iteratee The iteratee invoked per iteration.
     * @param {Function} comparator The comparator used to compare values.
     * @returns {*} Returns the extremum value.
     */
    function baseExtremum(array, iteratee, comparator) {
      var index = -1,
          length = array.length;

      while (++index < length) {
        var value = array[index],
            current = iteratee(value);

        if (current != null && (computed === undefined
              ? (current === current && !isSymbol(current))
              : comparator(current, computed)
            )) {
          var computed = current,
              result = value;
        }
      }
      return result;
    }

    /**
     * The base implementation of `_.fill` without an iteratee call guard.
     *
     * @private
     * @param {Array} array The array to fill.
     * @param {*} value The value to fill `array` with.
     * @param {number} [start=0] The start position.
     * @param {number} [end=array.length] The end position.
     * @returns {Array} Returns `array`.
     */
    function baseFill(array, value, start, end) {
      var length = array.length;

      start = toInteger(start);
      if (start < 0) {
        start = -start > length ? 0 : (length + start);
      }
      end = (end === undefined || end > length) ? length : toInteger(end);
      if (end < 0) {
        end += length;
      }
      end = start > end ? 0 : toLength(end);
      while (start < end) {
        array[start++] = value;
      }
      return array;
    }

    /**
     * The base implementation of `_.filter` without support for iteratee shorthands.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} predicate The function invoked per iteration.
     * @returns {Array} Returns the new filtered array.
     */
    function baseFilter(collection, predicate) {
      var result = [];
      baseEach(collection, function(value, index, collection) {
        if (predicate(value, index, collection)) {
          result.push(value);
        }
      });
      return result;
    }

    /**
     * The base implementation of `_.flatten` with support for restricting flattening.
     *
     * @private
     * @param {Array} array The array to flatten.
     * @param {number} depth The maximum recursion depth.
     * @param {boolean} [predicate=isFlattenable] The function invoked per iteration.
     * @param {boolean} [isStrict] Restrict to values that pass `predicate` checks.
     * @param {Array} [result=[]] The initial result value.
     * @returns {Array} Returns the new flattened array.
     */
    function baseFlatten(array, depth, predicate, isStrict, result) {
      var index = -1,
          length = array.length;

      predicate || (predicate = isFlattenable);
      result || (result = []);

      while (++index < length) {
        var value = array[index];
        if (depth > 0 && predicate(value)) {
          if (depth > 1) {
            // Recursively flatten arrays (susceptible to call stack limits).
            baseFlatten(value, depth - 1, predicate, isStrict, result);
          } else {
            arrayPush(result, value);
          }
        } else if (!isStrict) {
          result[result.length] = value;
        }
      }
      return result;
    }

    /**
     * The base implementation of `baseForOwn` which iterates over `object`
     * properties returned by `keysFunc` and invokes `iteratee` for each property.
     * Iteratee functions may exit iteration early by explicitly returning `false`.
     *
     * @private
     * @param {Object} object The object to iterate over.
     * @param {Function} iteratee The function invoked per iteration.
     * @param {Function} keysFunc The function to get the keys of `object`.
     * @returns {Object} Returns `object`.
     */
    var baseFor = createBaseFor();

    /**
     * This function is like `baseFor` except that it iterates over properties
     * in the opposite order.
     *
     * @private
     * @param {Object} object The object to iterate over.
     * @param {Function} iteratee The function invoked per iteration.
     * @param {Function} keysFunc The function to get the keys of `object`.
     * @returns {Object} Returns `object`.
     */
    var baseForRight = createBaseFor(true);

    /**
     * The base implementation of `_.forOwn` without support for iteratee shorthands.
     *
     * @private
     * @param {Object} object The object to iterate over.
     * @param {Function} iteratee The function invoked per iteration.
     * @returns {Object} Returns `object`.
     */
    function baseForOwn(object, iteratee) {
      return object && baseFor(object, iteratee, keys);
    }

    /**
     * The base implementation of `_.forOwnRight` without support for iteratee shorthands.
     *
     * @private
     * @param {Object} object The object to iterate over.
     * @param {Function} iteratee The function invoked per iteration.
     * @returns {Object} Returns `object`.
     */
    function baseForOwnRight(object, iteratee) {
      return object && baseForRight(object, iteratee, keys);
    }

    /**
     * The base implementation of `_.functions` which creates an array of
     * `object` function property names filtered from `props`.
     *
     * @private
     * @param {Object} object The object to inspect.
     * @param {Array} props The property names to filter.
     * @returns {Array} Returns the function names.
     */
    function baseFunctions(object, props) {
      return arrayFilter(props, function(key) {
        return isFunction(object[key]);
      });
    }

    /**
     * The base implementation of `_.get` without support for default values.
     *
     * @private
     * @param {Object} object The object to query.
     * @param {Array|string} path The path of the property to get.
     * @returns {*} Returns the resolved value.
     */
    function baseGet(object, path) {
      path = isKey(path, object) ? [path] : castPath(path);

      var index = 0,
          length = path.length;

      while (object != null && index < length) {
        object = object[toKey(path[index++])];
      }
      return (index && index == length) ? object : undefined;
    }

    /**
     * The base implementation of `getAllKeys` and `getAllKeysIn` which uses
     * `keysFunc` and `symbolsFunc` to get the enumerable property names and
     * symbols of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @param {Function} keysFunc The function to get the keys of `object`.
     * @param {Function} symbolsFunc The function to get the symbols of `object`.
     * @returns {Array} Returns the array of property names and symbols.
     */
    function baseGetAllKeys(object, keysFunc, symbolsFunc) {
      var result = keysFunc(object);
      return isArray(object) ? result : arrayPush(result, symbolsFunc(object));
    }

    /**
     * The base implementation of `getTag`.
     *
     * @private
     * @param {*} value The value to query.
     * @returns {string} Returns the `toStringTag`.
     */
    function baseGetTag(value) {
      return objectToString.call(value);
    }

    /**
     * The base implementation of `_.gt` which doesn't coerce arguments.
     *
     * @private
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if `value` is greater than `other`,
     *  else `false`.
     */
    function baseGt(value, other) {
      return value > other;
    }

    /**
     * The base implementation of `_.has` without support for deep paths.
     *
     * @private
     * @param {Object} [object] The object to query.
     * @param {Array|string} key The key to check.
     * @returns {boolean} Returns `true` if `key` exists, else `false`.
     */
    function baseHas(object, key) {
      return object != null && hasOwnProperty.call(object, key);
    }

    /**
     * The base implementation of `_.hasIn` without support for deep paths.
     *
     * @private
     * @param {Object} [object] The object to query.
     * @param {Array|string} key The key to check.
     * @returns {boolean} Returns `true` if `key` exists, else `false`.
     */
    function baseHasIn(object, key) {
      return object != null && key in Object(object);
    }

    /**
     * The base implementation of `_.inRange` which doesn't coerce arguments.
     *
     * @private
     * @param {number} number The number to check.
     * @param {number} start The start of the range.
     * @param {number} end The end of the range.
     * @returns {boolean} Returns `true` if `number` is in the range, else `false`.
     */
    function baseInRange(number, start, end) {
      return number >= nativeMin(start, end) && number < nativeMax(start, end);
    }

    /**
     * The base implementation of methods like `_.intersection`, without support
     * for iteratee shorthands, that accepts an array of arrays to inspect.
     *
     * @private
     * @param {Array} arrays The arrays to inspect.
     * @param {Function} [iteratee] The iteratee invoked per element.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new array of shared values.
     */
    function baseIntersection(arrays, iteratee, comparator) {
      var includes = comparator ? arrayIncludesWith : arrayIncludes,
          length = arrays[0].length,
          othLength = arrays.length,
          othIndex = othLength,
          caches = Array(othLength),
          maxLength = Infinity,
          result = [];

      while (othIndex--) {
        var array = arrays[othIndex];
        if (othIndex && iteratee) {
          array = arrayMap(array, baseUnary(iteratee));
        }
        maxLength = nativeMin(array.length, maxLength);
        caches[othIndex] = !comparator && (iteratee || (length >= 120 && array.length >= 120))
          ? new SetCache(othIndex && array)
          : undefined;
      }
      array = arrays[0];

      var index = -1,
          seen = caches[0];

      outer:
      while (++index < length && result.length < maxLength) {
        var value = array[index],
            computed = iteratee ? iteratee(value) : value;

        value = (comparator || value !== 0) ? value : 0;
        if (!(seen
              ? cacheHas(seen, computed)
              : includes(result, computed, comparator)
            )) {
          othIndex = othLength;
          while (--othIndex) {
            var cache = caches[othIndex];
            if (!(cache
                  ? cacheHas(cache, computed)
                  : includes(arrays[othIndex], computed, comparator))
                ) {
              continue outer;
            }
          }
          if (seen) {
            seen.push(computed);
          }
          result.push(value);
        }
      }
      return result;
    }

    /**
     * The base implementation of `_.invert` and `_.invertBy` which inverts
     * `object` with values transformed by `iteratee` and set by `setter`.
     *
     * @private
     * @param {Object} object The object to iterate over.
     * @param {Function} setter The function to set `accumulator` values.
     * @param {Function} iteratee The iteratee to transform values.
     * @param {Object} accumulator The initial inverted object.
     * @returns {Function} Returns `accumulator`.
     */
    function baseInverter(object, setter, iteratee, accumulator) {
      baseForOwn(object, function(value, key, object) {
        setter(accumulator, iteratee(value), key, object);
      });
      return accumulator;
    }

    /**
     * The base implementation of `_.invoke` without support for individual
     * method arguments.
     *
     * @private
     * @param {Object} object The object to query.
     * @param {Array|string} path The path of the method to invoke.
     * @param {Array} args The arguments to invoke the method with.
     * @returns {*} Returns the result of the invoked method.
     */
    function baseInvoke(object, path, args) {
      if (!isKey(path, object)) {
        path = castPath(path);
        object = parent(object, path);
        path = last(path);
      }
      var func = object == null ? object : object[toKey(path)];
      return func == null ? undefined : apply(func, object, args);
    }

    /**
     * The base implementation of `_.isArguments`.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an `arguments` object,
     */
    function baseIsArguments(value) {
      return isObjectLike(value) && objectToString.call(value) == argsTag;
    }

    /**
     * The base implementation of `_.isArrayBuffer` without Node.js optimizations.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an array buffer, else `false`.
     */
    function baseIsArrayBuffer(value) {
      return isObjectLike(value) && objectToString.call(value) == arrayBufferTag;
    }

    /**
     * The base implementation of `_.isDate` without Node.js optimizations.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a date object, else `false`.
     */
    function baseIsDate(value) {
      return isObjectLike(value) && objectToString.call(value) == dateTag;
    }

    /**
     * The base implementation of `_.isEqual` which supports partial comparisons
     * and tracks traversed objects.
     *
     * @private
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @param {Function} [customizer] The function to customize comparisons.
     * @param {boolean} [bitmask] The bitmask of comparison flags.
     *  The bitmask may be composed of the following flags:
     *     1 - Unordered comparison
     *     2 - Partial comparison
     * @param {Object} [stack] Tracks traversed `value` and `other` objects.
     * @returns {boolean} Returns `true` if the values are equivalent, else `false`.
     */
    function baseIsEqual(value, other, customizer, bitmask, stack) {
      if (value === other) {
        return true;
      }
      if (value == null || other == null || (!isObject(value) && !isObjectLike(other))) {
        return value !== value && other !== other;
      }
      return baseIsEqualDeep(value, other, baseIsEqual, customizer, bitmask, stack);
    }

    /**
     * A specialized version of `baseIsEqual` for arrays and objects which performs
     * deep comparisons and tracks traversed objects enabling objects with circular
     * references to be compared.
     *
     * @private
     * @param {Object} object The object to compare.
     * @param {Object} other The other object to compare.
     * @param {Function} equalFunc The function to determine equivalents of values.
     * @param {Function} [customizer] The function to customize comparisons.
     * @param {number} [bitmask] The bitmask of comparison flags. See `baseIsEqual`
     *  for more details.
     * @param {Object} [stack] Tracks traversed `object` and `other` objects.
     * @returns {boolean} Returns `true` if the objects are equivalent, else `false`.
     */
    function baseIsEqualDeep(object, other, equalFunc, customizer, bitmask, stack) {
      var objIsArr = isArray(object),
          othIsArr = isArray(other),
          objTag = arrayTag,
          othTag = arrayTag;

      if (!objIsArr) {
        objTag = getTag(object);
        objTag = objTag == argsTag ? objectTag : objTag;
      }
      if (!othIsArr) {
        othTag = getTag(other);
        othTag = othTag == argsTag ? objectTag : othTag;
      }
      var objIsObj = objTag == objectTag,
          othIsObj = othTag == objectTag,
          isSameTag = objTag == othTag;

      if (isSameTag && isBuffer(object)) {
        if (!isBuffer(other)) {
          return false;
        }
        objIsArr = true;
        objIsObj = false;
      }
      if (isSameTag && !objIsObj) {
        stack || (stack = new Stack);
        return (objIsArr || isTypedArray(object))
          ? equalArrays(object, other, equalFunc, customizer, bitmask, stack)
          : equalByTag(object, other, objTag, equalFunc, customizer, bitmask, stack);
      }
      if (!(bitmask & PARTIAL_COMPARE_FLAG)) {
        var objIsWrapped = objIsObj && hasOwnProperty.call(object, '__wrapped__'),
            othIsWrapped = othIsObj && hasOwnProperty.call(other, '__wrapped__');

        if (objIsWrapped || othIsWrapped) {
          var objUnwrapped = objIsWrapped ? object.value() : object,
              othUnwrapped = othIsWrapped ? other.value() : other;

          stack || (stack = new Stack);
          return equalFunc(objUnwrapped, othUnwrapped, customizer, bitmask, stack);
        }
      }
      if (!isSameTag) {
        return false;
      }
      stack || (stack = new Stack);
      return equalObjects(object, other, equalFunc, customizer, bitmask, stack);
    }

    /**
     * The base implementation of `_.isMap` without Node.js optimizations.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a map, else `false`.
     */
    function baseIsMap(value) {
      return isObjectLike(value) && getTag(value) == mapTag;
    }

    /**
     * The base implementation of `_.isMatch` without support for iteratee shorthands.
     *
     * @private
     * @param {Object} object The object to inspect.
     * @param {Object} source The object of property values to match.
     * @param {Array} matchData The property names, values, and compare flags to match.
     * @param {Function} [customizer] The function to customize comparisons.
     * @returns {boolean} Returns `true` if `object` is a match, else `false`.
     */
    function baseIsMatch(object, source, matchData, customizer) {
      var index = matchData.length,
          length = index,
          noCustomizer = !customizer;

      if (object == null) {
        return !length;
      }
      object = Object(object);
      while (index--) {
        var data = matchData[index];
        if ((noCustomizer && data[2])
              ? data[1] !== object[data[0]]
              : !(data[0] in object)
            ) {
          return false;
        }
      }
      while (++index < length) {
        data = matchData[index];
        var key = data[0],
            objValue = object[key],
            srcValue = data[1];

        if (noCustomizer && data[2]) {
          if (objValue === undefined && !(key in object)) {
            return false;
          }
        } else {
          var stack = new Stack;
          if (customizer) {
            var result = customizer(objValue, srcValue, key, object, source, stack);
          }
          if (!(result === undefined
                ? baseIsEqual(srcValue, objValue, customizer, UNORDERED_COMPARE_FLAG | PARTIAL_COMPARE_FLAG, stack)
                : result
              )) {
            return false;
          }
        }
      }
      return true;
    }

    /**
     * The base implementation of `_.isNative` without bad shim checks.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a native function,
     *  else `false`.
     */
    function baseIsNative(value) {
      if (!isObject(value) || isMasked(value)) {
        return false;
      }
      var pattern = isFunction(value) ? reIsNative : reIsHostCtor;
      return pattern.test(toSource(value));
    }

    /**
     * The base implementation of `_.isRegExp` without Node.js optimizations.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a regexp, else `false`.
     */
    function baseIsRegExp(value) {
      return isObject(value) && objectToString.call(value) == regexpTag;
    }

    /**
     * The base implementation of `_.isSet` without Node.js optimizations.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a set, else `false`.
     */
    function baseIsSet(value) {
      return isObjectLike(value) && getTag(value) == setTag;
    }

    /**
     * The base implementation of `_.isTypedArray` without Node.js optimizations.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a typed array, else `false`.
     */
    function baseIsTypedArray(value) {
      return isObjectLike(value) &&
        isLength(value.length) && !!typedArrayTags[objectToString.call(value)];
    }

    /**
     * The base implementation of `_.iteratee`.
     *
     * @private
     * @param {*} [value=_.identity] The value to convert to an iteratee.
     * @returns {Function} Returns the iteratee.
     */
    function baseIteratee(value) {
      // Don't store the `typeof` result in a variable to avoid a JIT bug in Safari 9.
      // See https://bugs.webkit.org/show_bug.cgi?id=156034 for more details.
      if (typeof value == 'function') {
        return value;
      }
      if (value == null) {
        return identity;
      }
      if (typeof value == 'object') {
        return isArray(value)
          ? baseMatchesProperty(value[0], value[1])
          : baseMatches(value);
      }
      return property(value);
    }

    /**
     * The base implementation of `_.keys` which doesn't treat sparse arrays as dense.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property names.
     */
    function baseKeys(object) {
      if (!isPrototype(object)) {
        return nativeKeys(object);
      }
      var result = [];
      for (var key in Object(object)) {
        if (hasOwnProperty.call(object, key) && key != 'constructor') {
          result.push(key);
        }
      }
      return result;
    }

    /**
     * The base implementation of `_.keysIn` which doesn't treat sparse arrays as dense.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property names.
     */
    function baseKeysIn(object) {
      if (!isObject(object)) {
        return nativeKeysIn(object);
      }
      var isProto = isPrototype(object),
          result = [];

      for (var key in object) {
        if (!(key == 'constructor' && (isProto || !hasOwnProperty.call(object, key)))) {
          result.push(key);
        }
      }
      return result;
    }

    /**
     * The base implementation of `_.lt` which doesn't coerce arguments.
     *
     * @private
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if `value` is less than `other`,
     *  else `false`.
     */
    function baseLt(value, other) {
      return value < other;
    }

    /**
     * The base implementation of `_.map` without support for iteratee shorthands.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} iteratee The function invoked per iteration.
     * @returns {Array} Returns the new mapped array.
     */
    function baseMap(collection, iteratee) {
      var index = -1,
          result = isArrayLike(collection) ? Array(collection.length) : [];

      baseEach(collection, function(value, key, collection) {
        result[++index] = iteratee(value, key, collection);
      });
      return result;
    }

    /**
     * The base implementation of `_.matches` which doesn't clone `source`.
     *
     * @private
     * @param {Object} source The object of property values to match.
     * @returns {Function} Returns the new spec function.
     */
    function baseMatches(source) {
      var matchData = getMatchData(source);
      if (matchData.length == 1 && matchData[0][2]) {
        return matchesStrictComparable(matchData[0][0], matchData[0][1]);
      }
      return function(object) {
        return object === source || baseIsMatch(object, source, matchData);
      };
    }

    /**
     * The base implementation of `_.matchesProperty` which doesn't clone `srcValue`.
     *
     * @private
     * @param {string} path The path of the property to get.
     * @param {*} srcValue The value to match.
     * @returns {Function} Returns the new spec function.
     */
    function baseMatchesProperty(path, srcValue) {
      if (isKey(path) && isStrictComparable(srcValue)) {
        return matchesStrictComparable(toKey(path), srcValue);
      }
      return function(object) {
        var objValue = get(object, path);
        return (objValue === undefined && objValue === srcValue)
          ? hasIn(object, path)
          : baseIsEqual(srcValue, objValue, undefined, UNORDERED_COMPARE_FLAG | PARTIAL_COMPARE_FLAG);
      };
    }

    /**
     * The base implementation of `_.merge` without support for multiple sources.
     *
     * @private
     * @param {Object} object The destination object.
     * @param {Object} source The source object.
     * @param {number} srcIndex The index of `source`.
     * @param {Function} [customizer] The function to customize merged values.
     * @param {Object} [stack] Tracks traversed source values and their merged
     *  counterparts.
     */
    function baseMerge(object, source, srcIndex, customizer, stack) {
      if (object === source) {
        return;
      }
      baseFor(source, function(srcValue, key) {
        if (isObject(srcValue)) {
          stack || (stack = new Stack);
          baseMergeDeep(object, source, key, srcIndex, baseMerge, customizer, stack);
        }
        else {
          var newValue = customizer
            ? customizer(object[key], srcValue, (key + ''), object, source, stack)
            : undefined;

          if (newValue === undefined) {
            newValue = srcValue;
          }
          assignMergeValue(object, key, newValue);
        }
      }, keysIn);
    }

    /**
     * A specialized version of `baseMerge` for arrays and objects which performs
     * deep merges and tracks traversed objects enabling objects with circular
     * references to be merged.
     *
     * @private
     * @param {Object} object The destination object.
     * @param {Object} source The source object.
     * @param {string} key The key of the value to merge.
     * @param {number} srcIndex The index of `source`.
     * @param {Function} mergeFunc The function to merge values.
     * @param {Function} [customizer] The function to customize assigned values.
     * @param {Object} [stack] Tracks traversed source values and their merged
     *  counterparts.
     */
    function baseMergeDeep(object, source, key, srcIndex, mergeFunc, customizer, stack) {
      var objValue = object[key],
          srcValue = source[key],
          stacked = stack.get(srcValue);

      if (stacked) {
        assignMergeValue(object, key, stacked);
        return;
      }
      var newValue = customizer
        ? customizer(objValue, srcValue, (key + ''), object, source, stack)
        : undefined;

      var isCommon = newValue === undefined;

      if (isCommon) {
        var isArr = isArray(srcValue),
            isBuff = !isArr && isBuffer(srcValue),
            isTyped = !isArr && !isBuff && isTypedArray(srcValue);

        newValue = srcValue;
        if (isArr || isBuff || isTyped) {
          if (isArray(objValue)) {
            newValue = objValue;
          }
          else if (isArrayLikeObject(objValue)) {
            newValue = copyArray(objValue);
          }
          else if (isBuff) {
            isCommon = false;
            newValue = cloneBuffer(srcValue, true);
          }
          else if (isTyped) {
            isCommon = false;
            newValue = cloneTypedArray(srcValue, true);
          }
          else {
            newValue = [];
          }
        }
        else if (isPlainObject(srcValue) || isArguments(srcValue)) {
          newValue = objValue;
          if (isArguments(objValue)) {
            newValue = toPlainObject(objValue);
          }
          else if (!isObject(objValue) || (srcIndex && isFunction(objValue))) {
            newValue = initCloneObject(srcValue);
          }
        }
        else {
          isCommon = false;
        }
      }
      if (isCommon) {
        // Recursively merge objects and arrays (susceptible to call stack limits).
        stack.set(srcValue, newValue);
        mergeFunc(newValue, srcValue, srcIndex, customizer, stack);
        stack['delete'](srcValue);
      }
      assignMergeValue(object, key, newValue);
    }

    /**
     * The base implementation of `_.nth` which doesn't coerce arguments.
     *
     * @private
     * @param {Array} array The array to query.
     * @param {number} n The index of the element to return.
     * @returns {*} Returns the nth element of `array`.
     */
    function baseNth(array, n) {
      var length = array.length;
      if (!length) {
        return;
      }
      n += n < 0 ? length : 0;
      return isIndex(n, length) ? array[n] : undefined;
    }

    /**
     * The base implementation of `_.orderBy` without param guards.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function[]|Object[]|string[]} iteratees The iteratees to sort by.
     * @param {string[]} orders The sort orders of `iteratees`.
     * @returns {Array} Returns the new sorted array.
     */
    function baseOrderBy(collection, iteratees, orders) {
      var index = -1;
      iteratees = arrayMap(iteratees.length ? iteratees : [identity], baseUnary(getIteratee()));

      var result = baseMap(collection, function(value, key, collection) {
        var criteria = arrayMap(iteratees, function(iteratee) {
          return iteratee(value);
        });
        return { 'criteria': criteria, 'index': ++index, 'value': value };
      });

      return baseSortBy(result, function(object, other) {
        return compareMultiple(object, other, orders);
      });
    }

    /**
     * The base implementation of `_.pick` without support for individual
     * property identifiers.
     *
     * @private
     * @param {Object} object The source object.
     * @param {string[]} props The property identifiers to pick.
     * @returns {Object} Returns the new object.
     */
    function basePick(object, props) {
      object = Object(object);
      return basePickBy(object, props, function(value, key) {
        return key in object;
      });
    }

    /**
     * The base implementation of  `_.pickBy` without support for iteratee shorthands.
     *
     * @private
     * @param {Object} object The source object.
     * @param {string[]} props The property identifiers to pick from.
     * @param {Function} predicate The function invoked per property.
     * @returns {Object} Returns the new object.
     */
    function basePickBy(object, props, predicate) {
      var index = -1,
          length = props.length,
          result = {};

      while (++index < length) {
        var key = props[index],
            value = object[key];

        if (predicate(value, key)) {
          baseAssignValue(result, key, value);
        }
      }
      return result;
    }

    /**
     * A specialized version of `baseProperty` which supports deep paths.
     *
     * @private
     * @param {Array|string} path The path of the property to get.
     * @returns {Function} Returns the new accessor function.
     */
    function basePropertyDeep(path) {
      return function(object) {
        return baseGet(object, path);
      };
    }

    /**
     * The base implementation of `_.pullAllBy` without support for iteratee
     * shorthands.
     *
     * @private
     * @param {Array} array The array to modify.
     * @param {Array} values The values to remove.
     * @param {Function} [iteratee] The iteratee invoked per element.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns `array`.
     */
    function basePullAll(array, values, iteratee, comparator) {
      var indexOf = comparator ? baseIndexOfWith : baseIndexOf,
          index = -1,
          length = values.length,
          seen = array;

      if (array === values) {
        values = copyArray(values);
      }
      if (iteratee) {
        seen = arrayMap(array, baseUnary(iteratee));
      }
      while (++index < length) {
        var fromIndex = 0,
            value = values[index],
            computed = iteratee ? iteratee(value) : value;

        while ((fromIndex = indexOf(seen, computed, fromIndex, comparator)) > -1) {
          if (seen !== array) {
            splice.call(seen, fromIndex, 1);
          }
          splice.call(array, fromIndex, 1);
        }
      }
      return array;
    }

    /**
     * The base implementation of `_.pullAt` without support for individual
     * indexes or capturing the removed elements.
     *
     * @private
     * @param {Array} array The array to modify.
     * @param {number[]} indexes The indexes of elements to remove.
     * @returns {Array} Returns `array`.
     */
    function basePullAt(array, indexes) {
      var length = array ? indexes.length : 0,
          lastIndex = length - 1;

      while (length--) {
        var index = indexes[length];
        if (length == lastIndex || index !== previous) {
          var previous = index;
          if (isIndex(index)) {
            splice.call(array, index, 1);
          }
          else if (!isKey(index, array)) {
            var path = castPath(index),
                object = parent(array, path);

            if (object != null) {
              delete object[toKey(last(path))];
            }
          }
          else {
            delete array[toKey(index)];
          }
        }
      }
      return array;
    }

    /**
     * The base implementation of `_.random` without support for returning
     * floating-point numbers.
     *
     * @private
     * @param {number} lower The lower bound.
     * @param {number} upper The upper bound.
     * @returns {number} Returns the random number.
     */
    function baseRandom(lower, upper) {
      return lower + nativeFloor(nativeRandom() * (upper - lower + 1));
    }

    /**
     * The base implementation of `_.range` and `_.rangeRight` which doesn't
     * coerce arguments.
     *
     * @private
     * @param {number} start The start of the range.
     * @param {number} end The end of the range.
     * @param {number} step The value to increment or decrement by.
     * @param {boolean} [fromRight] Specify iterating from right to left.
     * @returns {Array} Returns the range of numbers.
     */
    function baseRange(start, end, step, fromRight) {
      var index = -1,
          length = nativeMax(nativeCeil((end - start) / (step || 1)), 0),
          result = Array(length);

      while (length--) {
        result[fromRight ? length : ++index] = start;
        start += step;
      }
      return result;
    }

    /**
     * The base implementation of `_.repeat` which doesn't coerce arguments.
     *
     * @private
     * @param {string} string The string to repeat.
     * @param {number} n The number of times to repeat the string.
     * @returns {string} Returns the repeated string.
     */
    function baseRepeat(string, n) {
      var result = '';
      if (!string || n < 1 || n > MAX_SAFE_INTEGER) {
        return result;
      }
      // Leverage the exponentiation by squaring algorithm for a faster repeat.
      // See https://en.wikipedia.org/wiki/Exponentiation_by_squaring for more details.
      do {
        if (n % 2) {
          result += string;
        }
        n = nativeFloor(n / 2);
        if (n) {
          string += string;
        }
      } while (n);

      return result;
    }

    /**
     * The base implementation of `_.rest` which doesn't validate or coerce arguments.
     *
     * @private
     * @param {Function} func The function to apply a rest parameter to.
     * @param {number} [start=func.length-1] The start position of the rest parameter.
     * @returns {Function} Returns the new function.
     */
    function baseRest(func, start) {
      return setToString(overRest(func, start, identity), func + '');
    }

    /**
     * The base implementation of `_.sample`.
     *
     * @private
     * @param {Array|Object} collection The collection to sample.
     * @returns {*} Returns the random element.
     */
    function baseSample(collection) {
      return arraySample(values(collection));
    }

    /**
     * The base implementation of `_.sampleSize` without param guards.
     *
     * @private
     * @param {Array|Object} collection The collection to sample.
     * @param {number} n The number of elements to sample.
     * @returns {Array} Returns the random elements.
     */
    function baseSampleSize(collection, n) {
      var array = values(collection);
      return shuffleSelf(array, baseClamp(n, 0, array.length));
    }

    /**
     * The base implementation of `_.set`.
     *
     * @private
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to set.
     * @param {*} value The value to set.
     * @param {Function} [customizer] The function to customize path creation.
     * @returns {Object} Returns `object`.
     */
    function baseSet(object, path, value, customizer) {
      if (!isObject(object)) {
        return object;
      }
      path = isKey(path, object) ? [path] : castPath(path);

      var index = -1,
          length = path.length,
          lastIndex = length - 1,
          nested = object;

      while (nested != null && ++index < length) {
        var key = toKey(path[index]),
            newValue = value;

        if (index != lastIndex) {
          var objValue = nested[key];
          newValue = customizer ? customizer(objValue, key, nested) : undefined;
          if (newValue === undefined) {
            newValue = isObject(objValue)
              ? objValue
              : (isIndex(path[index + 1]) ? [] : {});
          }
        }
        assignValue(nested, key, newValue);
        nested = nested[key];
      }
      return object;
    }

    /**
     * The base implementation of `setData` without support for hot loop shorting.
     *
     * @private
     * @param {Function} func The function to associate metadata with.
     * @param {*} data The metadata.
     * @returns {Function} Returns `func`.
     */
    var baseSetData = !metaMap ? identity : function(func, data) {
      metaMap.set(func, data);
      return func;
    };

    /**
     * The base implementation of `setToString` without support for hot loop shorting.
     *
     * @private
     * @param {Function} func The function to modify.
     * @param {Function} string The `toString` result.
     * @returns {Function} Returns `func`.
     */
    var baseSetToString = !defineProperty ? identity : function(func, string) {
      return defineProperty(func, 'toString', {
        'configurable': true,
        'enumerable': false,
        'value': constant(string),
        'writable': true
      });
    };

    /**
     * The base implementation of `_.shuffle`.
     *
     * @private
     * @param {Array|Object} collection The collection to shuffle.
     * @returns {Array} Returns the new shuffled array.
     */
    function baseShuffle(collection) {
      return shuffleSelf(values(collection));
    }

    /**
     * The base implementation of `_.slice` without an iteratee call guard.
     *
     * @private
     * @param {Array} array The array to slice.
     * @param {number} [start=0] The start position.
     * @param {number} [end=array.length] The end position.
     * @returns {Array} Returns the slice of `array`.
     */
    function baseSlice(array, start, end) {
      var index = -1,
          length = array.length;

      if (start < 0) {
        start = -start > length ? 0 : (length + start);
      }
      end = end > length ? length : end;
      if (end < 0) {
        end += length;
      }
      length = start > end ? 0 : ((end - start) >>> 0);
      start >>>= 0;

      var result = Array(length);
      while (++index < length) {
        result[index] = array[index + start];
      }
      return result;
    }

    /**
     * The base implementation of `_.some` without support for iteratee shorthands.
     *
     * @private
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} predicate The function invoked per iteration.
     * @returns {boolean} Returns `true` if any element passes the predicate check,
     *  else `false`.
     */
    function baseSome(collection, predicate) {
      var result;

      baseEach(collection, function(value, index, collection) {
        result = predicate(value, index, collection);
        return !result;
      });
      return !!result;
    }

    /**
     * The base implementation of `_.sortedIndex` and `_.sortedLastIndex` which
     * performs a binary search of `array` to determine the index at which `value`
     * should be inserted into `array` in order to maintain its sort order.
     *
     * @private
     * @param {Array} array The sorted array to inspect.
     * @param {*} value The value to evaluate.
     * @param {boolean} [retHighest] Specify returning the highest qualified index.
     * @returns {number} Returns the index at which `value` should be inserted
     *  into `array`.
     */
    function baseSortedIndex(array, value, retHighest) {
      var low = 0,
          high = array ? array.length : low;

      if (typeof value == 'number' && value === value && high <= HALF_MAX_ARRAY_LENGTH) {
        while (low < high) {
          var mid = (low + high) >>> 1,
              computed = array[mid];

          if (computed !== null && !isSymbol(computed) &&
              (retHighest ? (computed <= value) : (computed < value))) {
            low = mid + 1;
          } else {
            high = mid;
          }
        }
        return high;
      }
      return baseSortedIndexBy(array, value, identity, retHighest);
    }

    /**
     * The base implementation of `_.sortedIndexBy` and `_.sortedLastIndexBy`
     * which invokes `iteratee` for `value` and each element of `array` to compute
     * their sort ranking. The iteratee is invoked with one argument; (value).
     *
     * @private
     * @param {Array} array The sorted array to inspect.
     * @param {*} value The value to evaluate.
     * @param {Function} iteratee The iteratee invoked per element.
     * @param {boolean} [retHighest] Specify returning the highest qualified index.
     * @returns {number} Returns the index at which `value` should be inserted
     *  into `array`.
     */
    function baseSortedIndexBy(array, value, iteratee, retHighest) {
      value = iteratee(value);

      var low = 0,
          high = array ? array.length : 0,
          valIsNaN = value !== value,
          valIsNull = value === null,
          valIsSymbol = isSymbol(value),
          valIsUndefined = value === undefined;

      while (low < high) {
        var mid = nativeFloor((low + high) / 2),
            computed = iteratee(array[mid]),
            othIsDefined = computed !== undefined,
            othIsNull = computed === null,
            othIsReflexive = computed === computed,
            othIsSymbol = isSymbol(computed);

        if (valIsNaN) {
          var setLow = retHighest || othIsReflexive;
        } else if (valIsUndefined) {
          setLow = othIsReflexive && (retHighest || othIsDefined);
        } else if (valIsNull) {
          setLow = othIsReflexive && othIsDefined && (retHighest || !othIsNull);
        } else if (valIsSymbol) {
          setLow = othIsReflexive && othIsDefined && !othIsNull && (retHighest || !othIsSymbol);
        } else if (othIsNull || othIsSymbol) {
          setLow = false;
        } else {
          setLow = retHighest ? (computed <= value) : (computed < value);
        }
        if (setLow) {
          low = mid + 1;
        } else {
          high = mid;
        }
      }
      return nativeMin(high, MAX_ARRAY_INDEX);
    }

    /**
     * The base implementation of `_.sortedUniq` and `_.sortedUniqBy` without
     * support for iteratee shorthands.
     *
     * @private
     * @param {Array} array The array to inspect.
     * @param {Function} [iteratee] The iteratee invoked per element.
     * @returns {Array} Returns the new duplicate free array.
     */
    function baseSortedUniq(array, iteratee) {
      var index = -1,
          length = array.length,
          resIndex = 0,
          result = [];

      while (++index < length) {
        var value = array[index],
            computed = iteratee ? iteratee(value) : value;

        if (!index || !eq(computed, seen)) {
          var seen = computed;
          result[resIndex++] = value === 0 ? 0 : value;
        }
      }
      return result;
    }

    /**
     * The base implementation of `_.toNumber` which doesn't ensure correct
     * conversions of binary, hexadecimal, or octal string values.
     *
     * @private
     * @param {*} value The value to process.
     * @returns {number} Returns the number.
     */
    function baseToNumber(value) {
      if (typeof value == 'number') {
        return value;
      }
      if (isSymbol(value)) {
        return NAN;
      }
      return +value;
    }

    /**
     * The base implementation of `_.toString` which doesn't convert nullish
     * values to empty strings.
     *
     * @private
     * @param {*} value The value to process.
     * @returns {string} Returns the string.
     */
    function baseToString(value) {
      // Exit early for strings to avoid a performance hit in some environments.
      if (typeof value == 'string') {
        return value;
      }
      if (isArray(value)) {
        // Recursively convert values (susceptible to call stack limits).
        return arrayMap(value, baseToString) + '';
      }
      if (isSymbol(value)) {
        return symbolToString ? symbolToString.call(value) : '';
      }
      var result = (value + '');
      return (result == '0' && (1 / value) == -INFINITY) ? '-0' : result;
    }

    /**
     * The base implementation of `_.uniqBy` without support for iteratee shorthands.
     *
     * @private
     * @param {Array} array The array to inspect.
     * @param {Function} [iteratee] The iteratee invoked per element.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new duplicate free array.
     */
    function baseUniq(array, iteratee, comparator) {
      var index = -1,
          includes = arrayIncludes,
          length = array.length,
          isCommon = true,
          result = [],
          seen = result;

      if (comparator) {
        isCommon = false;
        includes = arrayIncludesWith;
      }
      else if (length >= LARGE_ARRAY_SIZE) {
        var set = iteratee ? null : createSet(array);
        if (set) {
          return setToArray(set);
        }
        isCommon = false;
        includes = cacheHas;
        seen = new SetCache;
      }
      else {
        seen = iteratee ? [] : result;
      }
      outer:
      while (++index < length) {
        var value = array[index],
            computed = iteratee ? iteratee(value) : value;

        value = (comparator || value !== 0) ? value : 0;
        if (isCommon && computed === computed) {
          var seenIndex = seen.length;
          while (seenIndex--) {
            if (seen[seenIndex] === computed) {
              continue outer;
            }
          }
          if (iteratee) {
            seen.push(computed);
          }
          result.push(value);
        }
        else if (!includes(seen, computed, comparator)) {
          if (seen !== result) {
            seen.push(computed);
          }
          result.push(value);
        }
      }
      return result;
    }

    /**
     * The base implementation of `_.unset`.
     *
     * @private
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to unset.
     * @returns {boolean} Returns `true` if the property is deleted, else `false`.
     */
    function baseUnset(object, path) {
      path = isKey(path, object) ? [path] : castPath(path);
      object = parent(object, path);

      var key = toKey(last(path));
      return !(object != null && hasOwnProperty.call(object, key)) || delete object[key];
    }

    /**
     * The base implementation of `_.update`.
     *
     * @private
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to update.
     * @param {Function} updater The function to produce the updated value.
     * @param {Function} [customizer] The function to customize path creation.
     * @returns {Object} Returns `object`.
     */
    function baseUpdate(object, path, updater, customizer) {
      return baseSet(object, path, updater(baseGet(object, path)), customizer);
    }

    /**
     * The base implementation of methods like `_.dropWhile` and `_.takeWhile`
     * without support for iteratee shorthands.
     *
     * @private
     * @param {Array} array The array to query.
     * @param {Function} predicate The function invoked per iteration.
     * @param {boolean} [isDrop] Specify dropping elements instead of taking them.
     * @param {boolean} [fromRight] Specify iterating from right to left.
     * @returns {Array} Returns the slice of `array`.
     */
    function baseWhile(array, predicate, isDrop, fromRight) {
      var length = array.length,
          index = fromRight ? length : -1;

      while ((fromRight ? index-- : ++index < length) &&
        predicate(array[index], index, array)) {}

      return isDrop
        ? baseSlice(array, (fromRight ? 0 : index), (fromRight ? index + 1 : length))
        : baseSlice(array, (fromRight ? index + 1 : 0), (fromRight ? length : index));
    }

    /**
     * The base implementation of `wrapperValue` which returns the result of
     * performing a sequence of actions on the unwrapped `value`, where each
     * successive action is supplied the return value of the previous.
     *
     * @private
     * @param {*} value The unwrapped value.
     * @param {Array} actions Actions to perform to resolve the unwrapped value.
     * @returns {*} Returns the resolved value.
     */
    function baseWrapperValue(value, actions) {
      var result = value;
      if (result instanceof LazyWrapper) {
        result = result.value();
      }
      return arrayReduce(actions, function(result, action) {
        return action.func.apply(action.thisArg, arrayPush([result], action.args));
      }, result);
    }

    /**
     * The base implementation of methods like `_.xor`, without support for
     * iteratee shorthands, that accepts an array of arrays to inspect.
     *
     * @private
     * @param {Array} arrays The arrays to inspect.
     * @param {Function} [iteratee] The iteratee invoked per element.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new array of values.
     */
    function baseXor(arrays, iteratee, comparator) {
      var index = -1,
          length = arrays.length;

      while (++index < length) {
        var result = result
          ? arrayPush(
              baseDifference(result, arrays[index], iteratee, comparator),
              baseDifference(arrays[index], result, iteratee, comparator)
            )
          : arrays[index];
      }
      return (result && result.length) ? baseUniq(result, iteratee, comparator) : [];
    }

    /**
     * This base implementation of `_.zipObject` which assigns values using `assignFunc`.
     *
     * @private
     * @param {Array} props The property identifiers.
     * @param {Array} values The property values.
     * @param {Function} assignFunc The function to assign values.
     * @returns {Object} Returns the new object.
     */
    function baseZipObject(props, values, assignFunc) {
      var index = -1,
          length = props.length,
          valsLength = values.length,
          result = {};

      while (++index < length) {
        var value = index < valsLength ? values[index] : undefined;
        assignFunc(result, props[index], value);
      }
      return result;
    }

    /**
     * Casts `value` to an empty array if it's not an array like object.
     *
     * @private
     * @param {*} value The value to inspect.
     * @returns {Array|Object} Returns the cast array-like object.
     */
    function castArrayLikeObject(value) {
      return isArrayLikeObject(value) ? value : [];
    }

    /**
     * Casts `value` to `identity` if it's not a function.
     *
     * @private
     * @param {*} value The value to inspect.
     * @returns {Function} Returns cast function.
     */
    function castFunction(value) {
      return typeof value == 'function' ? value : identity;
    }

    /**
     * Casts `value` to a path array if it's not one.
     *
     * @private
     * @param {*} value The value to inspect.
     * @returns {Array} Returns the cast property path array.
     */
    function castPath(value) {
      return isArray(value) ? value : stringToPath(value);
    }

    /**
     * A `baseRest` alias which can be replaced with `identity` by module
     * replacement plugins.
     *
     * @private
     * @type {Function}
     * @param {Function} func The function to apply a rest parameter to.
     * @returns {Function} Returns the new function.
     */
    var castRest = baseRest;

    /**
     * Casts `array` to a slice if it's needed.
     *
     * @private
     * @param {Array} array The array to inspect.
     * @param {number} start The start position.
     * @param {number} [end=array.length] The end position.
     * @returns {Array} Returns the cast slice.
     */
    function castSlice(array, start, end) {
      var length = array.length;
      end = end === undefined ? length : end;
      return (!start && end >= length) ? array : baseSlice(array, start, end);
    }

    /**
     * A simple wrapper around the global [`clearTimeout`](https://mdn.io/clearTimeout).
     *
     * @private
     * @param {number|Object} id The timer id or timeout object of the timer to clear.
     */
    var clearTimeout = ctxClearTimeout || function(id) {
      return root.clearTimeout(id);
    };

    /**
     * Creates a clone of  `buffer`.
     *
     * @private
     * @param {Buffer} buffer The buffer to clone.
     * @param {boolean} [isDeep] Specify a deep clone.
     * @returns {Buffer} Returns the cloned buffer.
     */
    function cloneBuffer(buffer, isDeep) {
      if (isDeep) {
        return buffer.slice();
      }
      var length = buffer.length,
          result = allocUnsafe ? allocUnsafe(length) : new buffer.constructor(length);

      buffer.copy(result);
      return result;
    }

    /**
     * Creates a clone of `arrayBuffer`.
     *
     * @private
     * @param {ArrayBuffer} arrayBuffer The array buffer to clone.
     * @returns {ArrayBuffer} Returns the cloned array buffer.
     */
    function cloneArrayBuffer(arrayBuffer) {
      var result = new arrayBuffer.constructor(arrayBuffer.byteLength);
      new Uint8Array(result).set(new Uint8Array(arrayBuffer));
      return result;
    }

    /**
     * Creates a clone of `dataView`.
     *
     * @private
     * @param {Object} dataView The data view to clone.
     * @param {boolean} [isDeep] Specify a deep clone.
     * @returns {Object} Returns the cloned data view.
     */
    function cloneDataView(dataView, isDeep) {
      var buffer = isDeep ? cloneArrayBuffer(dataView.buffer) : dataView.buffer;
      return new dataView.constructor(buffer, dataView.byteOffset, dataView.byteLength);
    }

    /**
     * Creates a clone of `map`.
     *
     * @private
     * @param {Object} map The map to clone.
     * @param {Function} cloneFunc The function to clone values.
     * @param {boolean} [isDeep] Specify a deep clone.
     * @returns {Object} Returns the cloned map.
     */
    function cloneMap(map, isDeep, cloneFunc) {
      var array = isDeep ? cloneFunc(mapToArray(map), true) : mapToArray(map);
      return arrayReduce(array, addMapEntry, new map.constructor);
    }

    /**
     * Creates a clone of `regexp`.
     *
     * @private
     * @param {Object} regexp The regexp to clone.
     * @returns {Object} Returns the cloned regexp.
     */
    function cloneRegExp(regexp) {
      var result = new regexp.constructor(regexp.source, reFlags.exec(regexp));
      result.lastIndex = regexp.lastIndex;
      return result;
    }

    /**
     * Creates a clone of `set`.
     *
     * @private
     * @param {Object} set The set to clone.
     * @param {Function} cloneFunc The function to clone values.
     * @param {boolean} [isDeep] Specify a deep clone.
     * @returns {Object} Returns the cloned set.
     */
    function cloneSet(set, isDeep, cloneFunc) {
      var array = isDeep ? cloneFunc(setToArray(set), true) : setToArray(set);
      return arrayReduce(array, addSetEntry, new set.constructor);
    }

    /**
     * Creates a clone of the `symbol` object.
     *
     * @private
     * @param {Object} symbol The symbol object to clone.
     * @returns {Object} Returns the cloned symbol object.
     */
    function cloneSymbol(symbol) {
      return symbolValueOf ? Object(symbolValueOf.call(symbol)) : {};
    }

    /**
     * Creates a clone of `typedArray`.
     *
     * @private
     * @param {Object} typedArray The typed array to clone.
     * @param {boolean} [isDeep] Specify a deep clone.
     * @returns {Object} Returns the cloned typed array.
     */
    function cloneTypedArray(typedArray, isDeep) {
      var buffer = isDeep ? cloneArrayBuffer(typedArray.buffer) : typedArray.buffer;
      return new typedArray.constructor(buffer, typedArray.byteOffset, typedArray.length);
    }

    /**
     * Compares values to sort them in ascending order.
     *
     * @private
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {number} Returns the sort order indicator for `value`.
     */
    function compareAscending(value, other) {
      if (value !== other) {
        var valIsDefined = value !== undefined,
            valIsNull = value === null,
            valIsReflexive = value === value,
            valIsSymbol = isSymbol(value);

        var othIsDefined = other !== undefined,
            othIsNull = other === null,
            othIsReflexive = other === other,
            othIsSymbol = isSymbol(other);

        if ((!othIsNull && !othIsSymbol && !valIsSymbol && value > other) ||
            (valIsSymbol && othIsDefined && othIsReflexive && !othIsNull && !othIsSymbol) ||
            (valIsNull && othIsDefined && othIsReflexive) ||
            (!valIsDefined && othIsReflexive) ||
            !valIsReflexive) {
          return 1;
        }
        if ((!valIsNull && !valIsSymbol && !othIsSymbol && value < other) ||
            (othIsSymbol && valIsDefined && valIsReflexive && !valIsNull && !valIsSymbol) ||
            (othIsNull && valIsDefined && valIsReflexive) ||
            (!othIsDefined && valIsReflexive) ||
            !othIsReflexive) {
          return -1;
        }
      }
      return 0;
    }

    /**
     * Used by `_.orderBy` to compare multiple properties of a value to another
     * and stable sort them.
     *
     * If `orders` is unspecified, all values are sorted in ascending order. Otherwise,
     * specify an order of "desc" for descending or "asc" for ascending sort order
     * of corresponding values.
     *
     * @private
     * @param {Object} object The object to compare.
     * @param {Object} other The other object to compare.
     * @param {boolean[]|string[]} orders The order to sort by for each property.
     * @returns {number} Returns the sort order indicator for `object`.
     */
    function compareMultiple(object, other, orders) {
      var index = -1,
          objCriteria = object.criteria,
          othCriteria = other.criteria,
          length = objCriteria.length,
          ordersLength = orders.length;

      while (++index < length) {
        var result = compareAscending(objCriteria[index], othCriteria[index]);
        if (result) {
          if (index >= ordersLength) {
            return result;
          }
          var order = orders[index];
          return result * (order == 'desc' ? -1 : 1);
        }
      }
      // Fixes an `Array#sort` bug in the JS engine embedded in Adobe applications
      // that causes it, under certain circumstances, to provide the same value for
      // `object` and `other`. See https://github.com/jashkenas/underscore/pull/1247
      // for more details.
      //
      // This also ensures a stable sort in V8 and other engines.
      // See https://bugs.chromium.org/p/v8/issues/detail?id=90 for more details.
      return object.index - other.index;
    }

    /**
     * Creates an array that is the composition of partially applied arguments,
     * placeholders, and provided arguments into a single array of arguments.
     *
     * @private
     * @param {Array} args The provided arguments.
     * @param {Array} partials The arguments to prepend to those provided.
     * @param {Array} holders The `partials` placeholder indexes.
     * @params {boolean} [isCurried] Specify composing for a curried function.
     * @returns {Array} Returns the new array of composed arguments.
     */
    function composeArgs(args, partials, holders, isCurried) {
      var argsIndex = -1,
          argsLength = args.length,
          holdersLength = holders.length,
          leftIndex = -1,
          leftLength = partials.length,
          rangeLength = nativeMax(argsLength - holdersLength, 0),
          result = Array(leftLength + rangeLength),
          isUncurried = !isCurried;

      while (++leftIndex < leftLength) {
        result[leftIndex] = partials[leftIndex];
      }
      while (++argsIndex < holdersLength) {
        if (isUncurried || argsIndex < argsLength) {
          result[holders[argsIndex]] = args[argsIndex];
        }
      }
      while (rangeLength--) {
        result[leftIndex++] = args[argsIndex++];
      }
      return result;
    }

    /**
     * This function is like `composeArgs` except that the arguments composition
     * is tailored for `_.partialRight`.
     *
     * @private
     * @param {Array} args The provided arguments.
     * @param {Array} partials The arguments to append to those provided.
     * @param {Array} holders The `partials` placeholder indexes.
     * @params {boolean} [isCurried] Specify composing for a curried function.
     * @returns {Array} Returns the new array of composed arguments.
     */
    function composeArgsRight(args, partials, holders, isCurried) {
      var argsIndex = -1,
          argsLength = args.length,
          holdersIndex = -1,
          holdersLength = holders.length,
          rightIndex = -1,
          rightLength = partials.length,
          rangeLength = nativeMax(argsLength - holdersLength, 0),
          result = Array(rangeLength + rightLength),
          isUncurried = !isCurried;

      while (++argsIndex < rangeLength) {
        result[argsIndex] = args[argsIndex];
      }
      var offset = argsIndex;
      while (++rightIndex < rightLength) {
        result[offset + rightIndex] = partials[rightIndex];
      }
      while (++holdersIndex < holdersLength) {
        if (isUncurried || argsIndex < argsLength) {
          result[offset + holders[holdersIndex]] = args[argsIndex++];
        }
      }
      return result;
    }

    /**
     * Copies the values of `source` to `array`.
     *
     * @private
     * @param {Array} source The array to copy values from.
     * @param {Array} [array=[]] The array to copy values to.
     * @returns {Array} Returns `array`.
     */
    function copyArray(source, array) {
      var index = -1,
          length = source.length;

      array || (array = Array(length));
      while (++index < length) {
        array[index] = source[index];
      }
      return array;
    }

    /**
     * Copies properties of `source` to `object`.
     *
     * @private
     * @param {Object} source The object to copy properties from.
     * @param {Array} props The property identifiers to copy.
     * @param {Object} [object={}] The object to copy properties to.
     * @param {Function} [customizer] The function to customize copied values.
     * @returns {Object} Returns `object`.
     */
    function copyObject(source, props, object, customizer) {
      var isNew = !object;
      object || (object = {});

      var index = -1,
          length = props.length;

      while (++index < length) {
        var key = props[index];

        var newValue = customizer
          ? customizer(object[key], source[key], key, object, source)
          : undefined;

        if (newValue === undefined) {
          newValue = source[key];
        }
        if (isNew) {
          baseAssignValue(object, key, newValue);
        } else {
          assignValue(object, key, newValue);
        }
      }
      return object;
    }

    /**
     * Copies own symbol properties of `source` to `object`.
     *
     * @private
     * @param {Object} source The object to copy symbols from.
     * @param {Object} [object={}] The object to copy symbols to.
     * @returns {Object} Returns `object`.
     */
    function copySymbols(source, object) {
      return copyObject(source, getSymbols(source), object);
    }

    /**
     * Creates a function like `_.groupBy`.
     *
     * @private
     * @param {Function} setter The function to set accumulator values.
     * @param {Function} [initializer] The accumulator object initializer.
     * @returns {Function} Returns the new aggregator function.
     */
    function createAggregator(setter, initializer) {
      return function(collection, iteratee) {
        var func = isArray(collection) ? arrayAggregator : baseAggregator,
            accumulator = initializer ? initializer() : {};

        return func(collection, setter, getIteratee(iteratee, 2), accumulator);
      };
    }

    /**
     * Creates a function like `_.assign`.
     *
     * @private
     * @param {Function} assigner The function to assign values.
     * @returns {Function} Returns the new assigner function.
     */
    function createAssigner(assigner) {
      return baseRest(function(object, sources) {
        var index = -1,
            length = sources.length,
            customizer = length > 1 ? sources[length - 1] : undefined,
            guard = length > 2 ? sources[2] : undefined;

        customizer = (assigner.length > 3 && typeof customizer == 'function')
          ? (length--, customizer)
          : undefined;

        if (guard && isIterateeCall(sources[0], sources[1], guard)) {
          customizer = length < 3 ? undefined : customizer;
          length = 1;
        }
        object = Object(object);
        while (++index < length) {
          var source = sources[index];
          if (source) {
            assigner(object, source, index, customizer);
          }
        }
        return object;
      });
    }

    /**
     * Creates a `baseEach` or `baseEachRight` function.
     *
     * @private
     * @param {Function} eachFunc The function to iterate over a collection.
     * @param {boolean} [fromRight] Specify iterating from right to left.
     * @returns {Function} Returns the new base function.
     */
    function createBaseEach(eachFunc, fromRight) {
      return function(collection, iteratee) {
        if (collection == null) {
          return collection;
        }
        if (!isArrayLike(collection)) {
          return eachFunc(collection, iteratee);
        }
        var length = collection.length,
            index = fromRight ? length : -1,
            iterable = Object(collection);

        while ((fromRight ? index-- : ++index < length)) {
          if (iteratee(iterable[index], index, iterable) === false) {
            break;
          }
        }
        return collection;
      };
    }

    /**
     * Creates a base function for methods like `_.forIn` and `_.forOwn`.
     *
     * @private
     * @param {boolean} [fromRight] Specify iterating from right to left.
     * @returns {Function} Returns the new base function.
     */
    function createBaseFor(fromRight) {
      return function(object, iteratee, keysFunc) {
        var index = -1,
            iterable = Object(object),
            props = keysFunc(object),
            length = props.length;

        while (length--) {
          var key = props[fromRight ? length : ++index];
          if (iteratee(iterable[key], key, iterable) === false) {
            break;
          }
        }
        return object;
      };
    }

    /**
     * Creates a function that wraps `func` to invoke it with the optional `this`
     * binding of `thisArg`.
     *
     * @private
     * @param {Function} func The function to wrap.
     * @param {number} bitmask The bitmask flags. See `createWrap` for more details.
     * @param {*} [thisArg] The `this` binding of `func`.
     * @returns {Function} Returns the new wrapped function.
     */
    function createBind(func, bitmask, thisArg) {
      var isBind = bitmask & BIND_FLAG,
          Ctor = createCtor(func);

      function wrapper() {
        var fn = (this && this !== root && this instanceof wrapper) ? Ctor : func;
        return fn.apply(isBind ? thisArg : this, arguments);
      }
      return wrapper;
    }

    /**
     * Creates a function like `_.lowerFirst`.
     *
     * @private
     * @param {string} methodName The name of the `String` case method to use.
     * @returns {Function} Returns the new case function.
     */
    function createCaseFirst(methodName) {
      return function(string) {
        string = toString(string);

        var strSymbols = hasUnicode(string)
          ? stringToArray(string)
          : undefined;

        var chr = strSymbols
          ? strSymbols[0]
          : string.charAt(0);

        var trailing = strSymbols
          ? castSlice(strSymbols, 1).join('')
          : string.slice(1);

        return chr[methodName]() + trailing;
      };
    }

    /**
     * Creates a function like `_.camelCase`.
     *
     * @private
     * @param {Function} callback The function to combine each word.
     * @returns {Function} Returns the new compounder function.
     */
    function createCompounder(callback) {
      return function(string) {
        return arrayReduce(words(deburr(string).replace(reApos, '')), callback, '');
      };
    }

    /**
     * Creates a function that produces an instance of `Ctor` regardless of
     * whether it was invoked as part of a `new` expression or by `call` or `apply`.
     *
     * @private
     * @param {Function} Ctor The constructor to wrap.
     * @returns {Function} Returns the new wrapped function.
     */
    function createCtor(Ctor) {
      return function() {
        // Use a `switch` statement to work with class constructors. See
        // http://ecma-international.org/ecma-262/7.0/#sec-ecmascript-function-objects-call-thisargument-argumentslist
        // for more details.
        var args = arguments;
        switch (args.length) {
          case 0: return new Ctor;
          case 1: return new Ctor(args[0]);
          case 2: return new Ctor(args[0], args[1]);
          case 3: return new Ctor(args[0], args[1], args[2]);
          case 4: return new Ctor(args[0], args[1], args[2], args[3]);
          case 5: return new Ctor(args[0], args[1], args[2], args[3], args[4]);
          case 6: return new Ctor(args[0], args[1], args[2], args[3], args[4], args[5]);
          case 7: return new Ctor(args[0], args[1], args[2], args[3], args[4], args[5], args[6]);
        }
        var thisBinding = baseCreate(Ctor.prototype),
            result = Ctor.apply(thisBinding, args);

        // Mimic the constructor's `return` behavior.
        // See https://es5.github.io/#x13.2.2 for more details.
        return isObject(result) ? result : thisBinding;
      };
    }

    /**
     * Creates a function that wraps `func` to enable currying.
     *
     * @private
     * @param {Function} func The function to wrap.
     * @param {number} bitmask The bitmask flags. See `createWrap` for more details.
     * @param {number} arity The arity of `func`.
     * @returns {Function} Returns the new wrapped function.
     */
    function createCurry(func, bitmask, arity) {
      var Ctor = createCtor(func);

      function wrapper() {
        var length = arguments.length,
            args = Array(length),
            index = length,
            placeholder = getHolder(wrapper);

        while (index--) {
          args[index] = arguments[index];
        }
        var holders = (length < 3 && args[0] !== placeholder && args[length - 1] !== placeholder)
          ? []
          : replaceHolders(args, placeholder);

        length -= holders.length;
        if (length < arity) {
          return createRecurry(
            func, bitmask, createHybrid, wrapper.placeholder, undefined,
            args, holders, undefined, undefined, arity - length);
        }
        var fn = (this && this !== root && this instanceof wrapper) ? Ctor : func;
        return apply(fn, this, args);
      }
      return wrapper;
    }

    /**
     * Creates a `_.find` or `_.findLast` function.
     *
     * @private
     * @param {Function} findIndexFunc The function to find the collection index.
     * @returns {Function} Returns the new find function.
     */
    function createFind(findIndexFunc) {
      return function(collection, predicate, fromIndex) {
        var iterable = Object(collection);
        if (!isArrayLike(collection)) {
          var iteratee = getIteratee(predicate, 3);
          collection = keys(collection);
          predicate = function(key) { return iteratee(iterable[key], key, iterable); };
        }
        var index = findIndexFunc(collection, predicate, fromIndex);
        return index > -1 ? iterable[iteratee ? collection[index] : index] : undefined;
      };
    }

    /**
     * Creates a `_.flow` or `_.flowRight` function.
     *
     * @private
     * @param {boolean} [fromRight] Specify iterating from right to left.
     * @returns {Function} Returns the new flow function.
     */
    function createFlow(fromRight) {
      return flatRest(function(funcs) {
        var length = funcs.length,
            index = length,
            prereq = LodashWrapper.prototype.thru;

        if (fromRight) {
          funcs.reverse();
        }
        while (index--) {
          var func = funcs[index];
          if (typeof func != 'function') {
            throw new TypeError(FUNC_ERROR_TEXT);
          }
          if (prereq && !wrapper && getFuncName(func) == 'wrapper') {
            var wrapper = new LodashWrapper([], true);
          }
        }
        index = wrapper ? index : length;
        while (++index < length) {
          func = funcs[index];

          var funcName = getFuncName(func),
              data = funcName == 'wrapper' ? getData(func) : undefined;

          if (data && isLaziable(data[0]) &&
                data[1] == (ARY_FLAG | CURRY_FLAG | PARTIAL_FLAG | REARG_FLAG) &&
                !data[4].length && data[9] == 1
              ) {
            wrapper = wrapper[getFuncName(data[0])].apply(wrapper, data[3]);
          } else {
            wrapper = (func.length == 1 && isLaziable(func))
              ? wrapper[funcName]()
              : wrapper.thru(func);
          }
        }
        return function() {
          var args = arguments,
              value = args[0];

          if (wrapper && args.length == 1 &&
              isArray(value) && value.length >= LARGE_ARRAY_SIZE) {
            return wrapper.plant(value).value();
          }
          var index = 0,
              result = length ? funcs[index].apply(this, args) : value;

          while (++index < length) {
            result = funcs[index].call(this, result);
          }
          return result;
        };
      });
    }

    /**
     * Creates a function that wraps `func` to invoke it with optional `this`
     * binding of `thisArg`, partial application, and currying.
     *
     * @private
     * @param {Function|string} func The function or method name to wrap.
     * @param {number} bitmask The bitmask flags. See `createWrap` for more details.
     * @param {*} [thisArg] The `this` binding of `func`.
     * @param {Array} [partials] The arguments to prepend to those provided to
     *  the new function.
     * @param {Array} [holders] The `partials` placeholder indexes.
     * @param {Array} [partialsRight] The arguments to append to those provided
     *  to the new function.
     * @param {Array} [holdersRight] The `partialsRight` placeholder indexes.
     * @param {Array} [argPos] The argument positions of the new function.
     * @param {number} [ary] The arity cap of `func`.
     * @param {number} [arity] The arity of `func`.
     * @returns {Function} Returns the new wrapped function.
     */
    function createHybrid(func, bitmask, thisArg, partials, holders, partialsRight, holdersRight, argPos, ary, arity) {
      var isAry = bitmask & ARY_FLAG,
          isBind = bitmask & BIND_FLAG,
          isBindKey = bitmask & BIND_KEY_FLAG,
          isCurried = bitmask & (CURRY_FLAG | CURRY_RIGHT_FLAG),
          isFlip = bitmask & FLIP_FLAG,
          Ctor = isBindKey ? undefined : createCtor(func);

      function wrapper() {
        var length = arguments.length,
            args = Array(length),
            index = length;

        while (index--) {
          args[index] = arguments[index];
        }
        if (isCurried) {
          var placeholder = getHolder(wrapper),
              holdersCount = countHolders(args, placeholder);
        }
        if (partials) {
          args = composeArgs(args, partials, holders, isCurried);
        }
        if (partialsRight) {
          args = composeArgsRight(args, partialsRight, holdersRight, isCurried);
        }
        length -= holdersCount;
        if (isCurried && length < arity) {
          var newHolders = replaceHolders(args, placeholder);
          return createRecurry(
            func, bitmask, createHybrid, wrapper.placeholder, thisArg,
            args, newHolders, argPos, ary, arity - length
          );
        }
        var thisBinding = isBind ? thisArg : this,
            fn = isBindKey ? thisBinding[func] : func;

        length = args.length;
        if (argPos) {
          args = reorder(args, argPos);
        } else if (isFlip && length > 1) {
          args.reverse();
        }
        if (isAry && ary < length) {
          args.length = ary;
        }
        if (this && this !== root && this instanceof wrapper) {
          fn = Ctor || createCtor(fn);
        }
        return fn.apply(thisBinding, args);
      }
      return wrapper;
    }

    /**
     * Creates a function like `_.invertBy`.
     *
     * @private
     * @param {Function} setter The function to set accumulator values.
     * @param {Function} toIteratee The function to resolve iteratees.
     * @returns {Function} Returns the new inverter function.
     */
    function createInverter(setter, toIteratee) {
      return function(object, iteratee) {
        return baseInverter(object, setter, toIteratee(iteratee), {});
      };
    }

    /**
     * Creates a function that performs a mathematical operation on two values.
     *
     * @private
     * @param {Function} operator The function to perform the operation.
     * @param {number} [defaultValue] The value used for `undefined` arguments.
     * @returns {Function} Returns the new mathematical operation function.
     */
    function createMathOperation(operator, defaultValue) {
      return function(value, other) {
        var result;
        if (value === undefined && other === undefined) {
          return defaultValue;
        }
        if (value !== undefined) {
          result = value;
        }
        if (other !== undefined) {
          if (result === undefined) {
            return other;
          }
          if (typeof value == 'string' || typeof other == 'string') {
            value = baseToString(value);
            other = baseToString(other);
          } else {
            value = baseToNumber(value);
            other = baseToNumber(other);
          }
          result = operator(value, other);
        }
        return result;
      };
    }

    /**
     * Creates a function like `_.over`.
     *
     * @private
     * @param {Function} arrayFunc The function to iterate over iteratees.
     * @returns {Function} Returns the new over function.
     */
    function createOver(arrayFunc) {
      return flatRest(function(iteratees) {
        iteratees = arrayMap(iteratees, baseUnary(getIteratee()));
        return baseRest(function(args) {
          var thisArg = this;
          return arrayFunc(iteratees, function(iteratee) {
            return apply(iteratee, thisArg, args);
          });
        });
      });
    }

    /**
     * Creates the padding for `string` based on `length`. The `chars` string
     * is truncated if the number of characters exceeds `length`.
     *
     * @private
     * @param {number} length The padding length.
     * @param {string} [chars=' '] The string used as padding.
     * @returns {string} Returns the padding for `string`.
     */
    function createPadding(length, chars) {
      chars = chars === undefined ? ' ' : baseToString(chars);

      var charsLength = chars.length;
      if (charsLength < 2) {
        return charsLength ? baseRepeat(chars, length) : chars;
      }
      var result = baseRepeat(chars, nativeCeil(length / stringSize(chars)));
      return hasUnicode(chars)
        ? castSlice(stringToArray(result), 0, length).join('')
        : result.slice(0, length);
    }

    /**
     * Creates a function that wraps `func` to invoke it with the `this` binding
     * of `thisArg` and `partials` prepended to the arguments it receives.
     *
     * @private
     * @param {Function} func The function to wrap.
     * @param {number} bitmask The bitmask flags. See `createWrap` for more details.
     * @param {*} thisArg The `this` binding of `func`.
     * @param {Array} partials The arguments to prepend to those provided to
     *  the new function.
     * @returns {Function} Returns the new wrapped function.
     */
    function createPartial(func, bitmask, thisArg, partials) {
      var isBind = bitmask & BIND_FLAG,
          Ctor = createCtor(func);

      function wrapper() {
        var argsIndex = -1,
            argsLength = arguments.length,
            leftIndex = -1,
            leftLength = partials.length,
            args = Array(leftLength + argsLength),
            fn = (this && this !== root && this instanceof wrapper) ? Ctor : func;

        while (++leftIndex < leftLength) {
          args[leftIndex] = partials[leftIndex];
        }
        while (argsLength--) {
          args[leftIndex++] = arguments[++argsIndex];
        }
        return apply(fn, isBind ? thisArg : this, args);
      }
      return wrapper;
    }

    /**
     * Creates a `_.range` or `_.rangeRight` function.
     *
     * @private
     * @param {boolean} [fromRight] Specify iterating from right to left.
     * @returns {Function} Returns the new range function.
     */
    function createRange(fromRight) {
      return function(start, end, step) {
        if (step && typeof step != 'number' && isIterateeCall(start, end, step)) {
          end = step = undefined;
        }
        // Ensure the sign of `-0` is preserved.
        start = toFinite(start);
        if (end === undefined) {
          end = start;
          start = 0;
        } else {
          end = toFinite(end);
        }
        step = step === undefined ? (start < end ? 1 : -1) : toFinite(step);
        return baseRange(start, end, step, fromRight);
      };
    }

    /**
     * Creates a function that performs a relational operation on two values.
     *
     * @private
     * @param {Function} operator The function to perform the operation.
     * @returns {Function} Returns the new relational operation function.
     */
    function createRelationalOperation(operator) {
      return function(value, other) {
        if (!(typeof value == 'string' && typeof other == 'string')) {
          value = toNumber(value);
          other = toNumber(other);
        }
        return operator(value, other);
      };
    }

    /**
     * Creates a function that wraps `func` to continue currying.
     *
     * @private
     * @param {Function} func The function to wrap.
     * @param {number} bitmask The bitmask flags. See `createWrap` for more details.
     * @param {Function} wrapFunc The function to create the `func` wrapper.
     * @param {*} placeholder The placeholder value.
     * @param {*} [thisArg] The `this` binding of `func`.
     * @param {Array} [partials] The arguments to prepend to those provided to
     *  the new function.
     * @param {Array} [holders] The `partials` placeholder indexes.
     * @param {Array} [argPos] The argument positions of the new function.
     * @param {number} [ary] The arity cap of `func`.
     * @param {number} [arity] The arity of `func`.
     * @returns {Function} Returns the new wrapped function.
     */
    function createRecurry(func, bitmask, wrapFunc, placeholder, thisArg, partials, holders, argPos, ary, arity) {
      var isCurry = bitmask & CURRY_FLAG,
          newHolders = isCurry ? holders : undefined,
          newHoldersRight = isCurry ? undefined : holders,
          newPartials = isCurry ? partials : undefined,
          newPartialsRight = isCurry ? undefined : partials;

      bitmask |= (isCurry ? PARTIAL_FLAG : PARTIAL_RIGHT_FLAG);
      bitmask &= ~(isCurry ? PARTIAL_RIGHT_FLAG : PARTIAL_FLAG);

      if (!(bitmask & CURRY_BOUND_FLAG)) {
        bitmask &= ~(BIND_FLAG | BIND_KEY_FLAG);
      }
      var newData = [
        func, bitmask, thisArg, newPartials, newHolders, newPartialsRight,
        newHoldersRight, argPos, ary, arity
      ];

      var result = wrapFunc.apply(undefined, newData);
      if (isLaziable(func)) {
        setData(result, newData);
      }
      result.placeholder = placeholder;
      return setWrapToString(result, func, bitmask);
    }

    /**
     * Creates a function like `_.round`.
     *
     * @private
     * @param {string} methodName The name of the `Math` method to use when rounding.
     * @returns {Function} Returns the new round function.
     */
    function createRound(methodName) {
      var func = Math[methodName];
      return function(number, precision) {
        number = toNumber(number);
        precision = nativeMin(toInteger(precision), 292);
        if (precision) {
          // Shift with exponential notation to avoid floating-point issues.
          // See [MDN](https://mdn.io/round#Examples) for more details.
          var pair = (toString(number) + 'e').split('e'),
              value = func(pair[0] + 'e' + (+pair[1] + precision));

          pair = (toString(value) + 'e').split('e');
          return +(pair[0] + 'e' + (+pair[1] - precision));
        }
        return func(number);
      };
    }

    /**
     * Creates a set object of `values`.
     *
     * @private
     * @param {Array} values The values to add to the set.
     * @returns {Object} Returns the new set.
     */
    var createSet = !(Set && (1 / setToArray(new Set([,-0]))[1]) == INFINITY) ? noop : function(values) {
      return new Set(values);
    };

    /**
     * Creates a `_.toPairs` or `_.toPairsIn` function.
     *
     * @private
     * @param {Function} keysFunc The function to get the keys of a given object.
     * @returns {Function} Returns the new pairs function.
     */
    function createToPairs(keysFunc) {
      return function(object) {
        var tag = getTag(object);
        if (tag == mapTag) {
          return mapToArray(object);
        }
        if (tag == setTag) {
          return setToPairs(object);
        }
        return baseToPairs(object, keysFunc(object));
      };
    }

    /**
     * Creates a function that either curries or invokes `func` with optional
     * `this` binding and partially applied arguments.
     *
     * @private
     * @param {Function|string} func The function or method name to wrap.
     * @param {number} bitmask The bitmask flags.
     *  The bitmask may be composed of the following flags:
     *     1 - `_.bind`
     *     2 - `_.bindKey`
     *     4 - `_.curry` or `_.curryRight` of a bound function
     *     8 - `_.curry`
     *    16 - `_.curryRight`
     *    32 - `_.partial`
     *    64 - `_.partialRight`
     *   128 - `_.rearg`
     *   256 - `_.ary`
     *   512 - `_.flip`
     * @param {*} [thisArg] The `this` binding of `func`.
     * @param {Array} [partials] The arguments to be partially applied.
     * @param {Array} [holders] The `partials` placeholder indexes.
     * @param {Array} [argPos] The argument positions of the new function.
     * @param {number} [ary] The arity cap of `func`.
     * @param {number} [arity] The arity of `func`.
     * @returns {Function} Returns the new wrapped function.
     */
    function createWrap(func, bitmask, thisArg, partials, holders, argPos, ary, arity) {
      var isBindKey = bitmask & BIND_KEY_FLAG;
      if (!isBindKey && typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      var length = partials ? partials.length : 0;
      if (!length) {
        bitmask &= ~(PARTIAL_FLAG | PARTIAL_RIGHT_FLAG);
        partials = holders = undefined;
      }
      ary = ary === undefined ? ary : nativeMax(toInteger(ary), 0);
      arity = arity === undefined ? arity : toInteger(arity);
      length -= holders ? holders.length : 0;

      if (bitmask & PARTIAL_RIGHT_FLAG) {
        var partialsRight = partials,
            holdersRight = holders;

        partials = holders = undefined;
      }
      var data = isBindKey ? undefined : getData(func);

      var newData = [
        func, bitmask, thisArg, partials, holders, partialsRight, holdersRight,
        argPos, ary, arity
      ];

      if (data) {
        mergeData(newData, data);
      }
      func = newData[0];
      bitmask = newData[1];
      thisArg = newData[2];
      partials = newData[3];
      holders = newData[4];
      arity = newData[9] = newData[9] == null
        ? (isBindKey ? 0 : func.length)
        : nativeMax(newData[9] - length, 0);

      if (!arity && bitmask & (CURRY_FLAG | CURRY_RIGHT_FLAG)) {
        bitmask &= ~(CURRY_FLAG | CURRY_RIGHT_FLAG);
      }
      if (!bitmask || bitmask == BIND_FLAG) {
        var result = createBind(func, bitmask, thisArg);
      } else if (bitmask == CURRY_FLAG || bitmask == CURRY_RIGHT_FLAG) {
        result = createCurry(func, bitmask, arity);
      } else if ((bitmask == PARTIAL_FLAG || bitmask == (BIND_FLAG | PARTIAL_FLAG)) && !holders.length) {
        result = createPartial(func, bitmask, thisArg, partials);
      } else {
        result = createHybrid.apply(undefined, newData);
      }
      var setter = data ? baseSetData : setData;
      return setWrapToString(setter(result, newData), func, bitmask);
    }

    /**
     * A specialized version of `baseIsEqualDeep` for arrays with support for
     * partial deep comparisons.
     *
     * @private
     * @param {Array} array The array to compare.
     * @param {Array} other The other array to compare.
     * @param {Function} equalFunc The function to determine equivalents of values.
     * @param {Function} customizer The function to customize comparisons.
     * @param {number} bitmask The bitmask of comparison flags. See `baseIsEqual`
     *  for more details.
     * @param {Object} stack Tracks traversed `array` and `other` objects.
     * @returns {boolean} Returns `true` if the arrays are equivalent, else `false`.
     */
    function equalArrays(array, other, equalFunc, customizer, bitmask, stack) {
      var isPartial = bitmask & PARTIAL_COMPARE_FLAG,
          arrLength = array.length,
          othLength = other.length;

      if (arrLength != othLength && !(isPartial && othLength > arrLength)) {
        return false;
      }
      // Assume cyclic values are equal.
      var stacked = stack.get(array);
      if (stacked && stack.get(other)) {
        return stacked == other;
      }
      var index = -1,
          result = true,
          seen = (bitmask & UNORDERED_COMPARE_FLAG) ? new SetCache : undefined;

      stack.set(array, other);
      stack.set(other, array);

      // Ignore non-index properties.
      while (++index < arrLength) {
        var arrValue = array[index],
            othValue = other[index];

        if (customizer) {
          var compared = isPartial
            ? customizer(othValue, arrValue, index, other, array, stack)
            : customizer(arrValue, othValue, index, array, other, stack);
        }
        if (compared !== undefined) {
          if (compared) {
            continue;
          }
          result = false;
          break;
        }
        // Recursively compare arrays (susceptible to call stack limits).
        if (seen) {
          if (!arraySome(other, function(othValue, othIndex) {
                if (!cacheHas(seen, othIndex) &&
                    (arrValue === othValue || equalFunc(arrValue, othValue, customizer, bitmask, stack))) {
                  return seen.push(othIndex);
                }
              })) {
            result = false;
            break;
          }
        } else if (!(
              arrValue === othValue ||
                equalFunc(arrValue, othValue, customizer, bitmask, stack)
            )) {
          result = false;
          break;
        }
      }
      stack['delete'](array);
      stack['delete'](other);
      return result;
    }

    /**
     * A specialized version of `baseIsEqualDeep` for comparing objects of
     * the same `toStringTag`.
     *
     * **Note:** This function only supports comparing values with tags of
     * `Boolean`, `Date`, `Error`, `Number`, `RegExp`, or `String`.
     *
     * @private
     * @param {Object} object The object to compare.
     * @param {Object} other The other object to compare.
     * @param {string} tag The `toStringTag` of the objects to compare.
     * @param {Function} equalFunc The function to determine equivalents of values.
     * @param {Function} customizer The function to customize comparisons.
     * @param {number} bitmask The bitmask of comparison flags. See `baseIsEqual`
     *  for more details.
     * @param {Object} stack Tracks traversed `object` and `other` objects.
     * @returns {boolean} Returns `true` if the objects are equivalent, else `false`.
     */
    function equalByTag(object, other, tag, equalFunc, customizer, bitmask, stack) {
      switch (tag) {
        case dataViewTag:
          if ((object.byteLength != other.byteLength) ||
              (object.byteOffset != other.byteOffset)) {
            return false;
          }
          object = object.buffer;
          other = other.buffer;

        case arrayBufferTag:
          if ((object.byteLength != other.byteLength) ||
              !equalFunc(new Uint8Array(object), new Uint8Array(other))) {
            return false;
          }
          return true;

        case boolTag:
        case dateTag:
        case numberTag:
          // Coerce booleans to `1` or `0` and dates to milliseconds.
          // Invalid dates are coerced to `NaN`.
          return eq(+object, +other);

        case errorTag:
          return object.name == other.name && object.message == other.message;

        case regexpTag:
        case stringTag:
          // Coerce regexes to strings and treat strings, primitives and objects,
          // as equal. See http://www.ecma-international.org/ecma-262/7.0/#sec-regexp.prototype.tostring
          // for more details.
          return object == (other + '');

        case mapTag:
          var convert = mapToArray;

        case setTag:
          var isPartial = bitmask & PARTIAL_COMPARE_FLAG;
          convert || (convert = setToArray);

          if (object.size != other.size && !isPartial) {
            return false;
          }
          // Assume cyclic values are equal.
          var stacked = stack.get(object);
          if (stacked) {
            return stacked == other;
          }
          bitmask |= UNORDERED_COMPARE_FLAG;

          // Recursively compare objects (susceptible to call stack limits).
          stack.set(object, other);
          var result = equalArrays(convert(object), convert(other), equalFunc, customizer, bitmask, stack);
          stack['delete'](object);
          return result;

        case symbolTag:
          if (symbolValueOf) {
            return symbolValueOf.call(object) == symbolValueOf.call(other);
          }
      }
      return false;
    }

    /**
     * A specialized version of `baseIsEqualDeep` for objects with support for
     * partial deep comparisons.
     *
     * @private
     * @param {Object} object The object to compare.
     * @param {Object} other The other object to compare.
     * @param {Function} equalFunc The function to determine equivalents of values.
     * @param {Function} customizer The function to customize comparisons.
     * @param {number} bitmask The bitmask of comparison flags. See `baseIsEqual`
     *  for more details.
     * @param {Object} stack Tracks traversed `object` and `other` objects.
     * @returns {boolean} Returns `true` if the objects are equivalent, else `false`.
     */
    function equalObjects(object, other, equalFunc, customizer, bitmask, stack) {
      var isPartial = bitmask & PARTIAL_COMPARE_FLAG,
          objProps = keys(object),
          objLength = objProps.length,
          othProps = keys(other),
          othLength = othProps.length;

      if (objLength != othLength && !isPartial) {
        return false;
      }
      var index = objLength;
      while (index--) {
        var key = objProps[index];
        if (!(isPartial ? key in other : hasOwnProperty.call(other, key))) {
          return false;
        }
      }
      // Assume cyclic values are equal.
      var stacked = stack.get(object);
      if (stacked && stack.get(other)) {
        return stacked == other;
      }
      var result = true;
      stack.set(object, other);
      stack.set(other, object);

      var skipCtor = isPartial;
      while (++index < objLength) {
        key = objProps[index];
        var objValue = object[key],
            othValue = other[key];

        if (customizer) {
          var compared = isPartial
            ? customizer(othValue, objValue, key, other, object, stack)
            : customizer(objValue, othValue, key, object, other, stack);
        }
        // Recursively compare objects (susceptible to call stack limits).
        if (!(compared === undefined
              ? (objValue === othValue || equalFunc(objValue, othValue, customizer, bitmask, stack))
              : compared
            )) {
          result = false;
          break;
        }
        skipCtor || (skipCtor = key == 'constructor');
      }
      if (result && !skipCtor) {
        var objCtor = object.constructor,
            othCtor = other.constructor;

        // Non `Object` object instances with different constructors are not equal.
        if (objCtor != othCtor &&
            ('constructor' in object && 'constructor' in other) &&
            !(typeof objCtor == 'function' && objCtor instanceof objCtor &&
              typeof othCtor == 'function' && othCtor instanceof othCtor)) {
          result = false;
        }
      }
      stack['delete'](object);
      stack['delete'](other);
      return result;
    }

    /**
     * A specialized version of `baseRest` which flattens the rest array.
     *
     * @private
     * @param {Function} func The function to apply a rest parameter to.
     * @returns {Function} Returns the new function.
     */
    function flatRest(func) {
      return setToString(overRest(func, undefined, flatten), func + '');
    }

    /**
     * Creates an array of own enumerable property names and symbols of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property names and symbols.
     */
    function getAllKeys(object) {
      return baseGetAllKeys(object, keys, getSymbols);
    }

    /**
     * Creates an array of own and inherited enumerable property names and
     * symbols of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property names and symbols.
     */
    function getAllKeysIn(object) {
      return baseGetAllKeys(object, keysIn, getSymbolsIn);
    }

    /**
     * Gets metadata for `func`.
     *
     * @private
     * @param {Function} func The function to query.
     * @returns {*} Returns the metadata for `func`.
     */
    var getData = !metaMap ? noop : function(func) {
      return metaMap.get(func);
    };

    /**
     * Gets the name of `func`.
     *
     * @private
     * @param {Function} func The function to query.
     * @returns {string} Returns the function name.
     */
    function getFuncName(func) {
      var result = (func.name + ''),
          array = realNames[result],
          length = hasOwnProperty.call(realNames, result) ? array.length : 0;

      while (length--) {
        var data = array[length],
            otherFunc = data.func;
        if (otherFunc == null || otherFunc == func) {
          return data.name;
        }
      }
      return result;
    }

    /**
     * Gets the argument placeholder value for `func`.
     *
     * @private
     * @param {Function} func The function to inspect.
     * @returns {*} Returns the placeholder value.
     */
    function getHolder(func) {
      var object = hasOwnProperty.call(lodash, 'placeholder') ? lodash : func;
      return object.placeholder;
    }

    /**
     * Gets the appropriate "iteratee" function. If `_.iteratee` is customized,
     * this function returns the custom method, otherwise it returns `baseIteratee`.
     * If arguments are provided, the chosen function is invoked with them and
     * its result is returned.
     *
     * @private
     * @param {*} [value] The value to convert to an iteratee.
     * @param {number} [arity] The arity of the created iteratee.
     * @returns {Function} Returns the chosen function or its result.
     */
    function getIteratee() {
      var result = lodash.iteratee || iteratee;
      result = result === iteratee ? baseIteratee : result;
      return arguments.length ? result(arguments[0], arguments[1]) : result;
    }

    /**
     * Gets the data for `map`.
     *
     * @private
     * @param {Object} map The map to query.
     * @param {string} key The reference key.
     * @returns {*} Returns the map data.
     */
    function getMapData(map, key) {
      var data = map.__data__;
      return isKeyable(key)
        ? data[typeof key == 'string' ? 'string' : 'hash']
        : data.map;
    }

    /**
     * Gets the property names, values, and compare flags of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the match data of `object`.
     */
    function getMatchData(object) {
      var result = keys(object),
          length = result.length;

      while (length--) {
        var key = result[length],
            value = object[key];

        result[length] = [key, value, isStrictComparable(value)];
      }
      return result;
    }

    /**
     * Gets the native function at `key` of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @param {string} key The key of the method to get.
     * @returns {*} Returns the function if it's native, else `undefined`.
     */
    function getNative(object, key) {
      var value = getValue(object, key);
      return baseIsNative(value) ? value : undefined;
    }

    /**
     * Creates an array of the own enumerable symbol properties of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of symbols.
     */
    var getSymbols = nativeGetSymbols ? overArg(nativeGetSymbols, Object) : stubArray;

    /**
     * Creates an array of the own and inherited enumerable symbol properties
     * of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of symbols.
     */
    var getSymbolsIn = !nativeGetSymbols ? stubArray : function(object) {
      var result = [];
      while (object) {
        arrayPush(result, getSymbols(object));
        object = getPrototype(object);
      }
      return result;
    };

    /**
     * Gets the `toStringTag` of `value`.
     *
     * @private
     * @param {*} value The value to query.
     * @returns {string} Returns the `toStringTag`.
     */
    var getTag = baseGetTag;

    // Fallback for data views, maps, sets, and weak maps in IE 11 and promises in Node.js < 6.
    if ((DataView && getTag(new DataView(new ArrayBuffer(1))) != dataViewTag) ||
        (Map && getTag(new Map) != mapTag) ||
        (Promise && getTag(Promise.resolve()) != promiseTag) ||
        (Set && getTag(new Set) != setTag) ||
        (WeakMap && getTag(new WeakMap) != weakMapTag)) {
      getTag = function(value) {
        var result = objectToString.call(value),
            Ctor = result == objectTag ? value.constructor : undefined,
            ctorString = Ctor ? toSource(Ctor) : undefined;

        if (ctorString) {
          switch (ctorString) {
            case dataViewCtorString: return dataViewTag;
            case mapCtorString: return mapTag;
            case promiseCtorString: return promiseTag;
            case setCtorString: return setTag;
            case weakMapCtorString: return weakMapTag;
          }
        }
        return result;
      };
    }

    /**
     * Gets the view, applying any `transforms` to the `start` and `end` positions.
     *
     * @private
     * @param {number} start The start of the view.
     * @param {number} end The end of the view.
     * @param {Array} transforms The transformations to apply to the view.
     * @returns {Object} Returns an object containing the `start` and `end`
     *  positions of the view.
     */
    function getView(start, end, transforms) {
      var index = -1,
          length = transforms.length;

      while (++index < length) {
        var data = transforms[index],
            size = data.size;

        switch (data.type) {
          case 'drop':      start += size; break;
          case 'dropRight': end -= size; break;
          case 'take':      end = nativeMin(end, start + size); break;
          case 'takeRight': start = nativeMax(start, end - size); break;
        }
      }
      return { 'start': start, 'end': end };
    }

    /**
     * Extracts wrapper details from the `source` body comment.
     *
     * @private
     * @param {string} source The source to inspect.
     * @returns {Array} Returns the wrapper details.
     */
    function getWrapDetails(source) {
      var match = source.match(reWrapDetails);
      return match ? match[1].split(reSplitDetails) : [];
    }

    /**
     * Checks if `path` exists on `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @param {Array|string} path The path to check.
     * @param {Function} hasFunc The function to check properties.
     * @returns {boolean} Returns `true` if `path` exists, else `false`.
     */
    function hasPath(object, path, hasFunc) {
      path = isKey(path, object) ? [path] : castPath(path);

      var index = -1,
          length = path.length,
          result = false;

      while (++index < length) {
        var key = toKey(path[index]);
        if (!(result = object != null && hasFunc(object, key))) {
          break;
        }
        object = object[key];
      }
      if (result || ++index != length) {
        return result;
      }
      length = object ? object.length : 0;
      return !!length && isLength(length) && isIndex(key, length) &&
        (isArray(object) || isArguments(object));
    }

    /**
     * Initializes an array clone.
     *
     * @private
     * @param {Array} array The array to clone.
     * @returns {Array} Returns the initialized clone.
     */
    function initCloneArray(array) {
      var length = array.length,
          result = array.constructor(length);

      // Add properties assigned by `RegExp#exec`.
      if (length && typeof array[0] == 'string' && hasOwnProperty.call(array, 'index')) {
        result.index = array.index;
        result.input = array.input;
      }
      return result;
    }

    /**
     * Initializes an object clone.
     *
     * @private
     * @param {Object} object The object to clone.
     * @returns {Object} Returns the initialized clone.
     */
    function initCloneObject(object) {
      return (typeof object.constructor == 'function' && !isPrototype(object))
        ? baseCreate(getPrototype(object))
        : {};
    }

    /**
     * Initializes an object clone based on its `toStringTag`.
     *
     * **Note:** This function only supports cloning values with tags of
     * `Boolean`, `Date`, `Error`, `Number`, `RegExp`, or `String`.
     *
     * @private
     * @param {Object} object The object to clone.
     * @param {string} tag The `toStringTag` of the object to clone.
     * @param {Function} cloneFunc The function to clone values.
     * @param {boolean} [isDeep] Specify a deep clone.
     * @returns {Object} Returns the initialized clone.
     */
    function initCloneByTag(object, tag, cloneFunc, isDeep) {
      var Ctor = object.constructor;
      switch (tag) {
        case arrayBufferTag:
          return cloneArrayBuffer(object);

        case boolTag:
        case dateTag:
          return new Ctor(+object);

        case dataViewTag:
          return cloneDataView(object, isDeep);

        case float32Tag: case float64Tag:
        case int8Tag: case int16Tag: case int32Tag:
        case uint8Tag: case uint8ClampedTag: case uint16Tag: case uint32Tag:
          return cloneTypedArray(object, isDeep);

        case mapTag:
          return cloneMap(object, isDeep, cloneFunc);

        case numberTag:
        case stringTag:
          return new Ctor(object);

        case regexpTag:
          return cloneRegExp(object);

        case setTag:
          return cloneSet(object, isDeep, cloneFunc);

        case symbolTag:
          return cloneSymbol(object);
      }
    }

    /**
     * Inserts wrapper `details` in a comment at the top of the `source` body.
     *
     * @private
     * @param {string} source The source to modify.
     * @returns {Array} details The details to insert.
     * @returns {string} Returns the modified source.
     */
    function insertWrapDetails(source, details) {
      var length = details.length;
      if (!length) {
        return source;
      }
      var lastIndex = length - 1;
      details[lastIndex] = (length > 1 ? '& ' : '') + details[lastIndex];
      details = details.join(length > 2 ? ', ' : ' ');
      return source.replace(reWrapComment, '{\n/* [wrapped with ' + details + '] */\n');
    }

    /**
     * Checks if `value` is a flattenable `arguments` object or array.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is flattenable, else `false`.
     */
    function isFlattenable(value) {
      return isArray(value) || isArguments(value) ||
        !!(spreadableSymbol && value && value[spreadableSymbol]);
    }

    /**
     * Checks if `value` is a valid array-like index.
     *
     * @private
     * @param {*} value The value to check.
     * @param {number} [length=MAX_SAFE_INTEGER] The upper bounds of a valid index.
     * @returns {boolean} Returns `true` if `value` is a valid index, else `false`.
     */
    function isIndex(value, length) {
      length = length == null ? MAX_SAFE_INTEGER : length;
      return !!length &&
        (typeof value == 'number' || reIsUint.test(value)) &&
        (value > -1 && value % 1 == 0 && value < length);
    }

    /**
     * Checks if the given arguments are from an iteratee call.
     *
     * @private
     * @param {*} value The potential iteratee value argument.
     * @param {*} index The potential iteratee index or key argument.
     * @param {*} object The potential iteratee object argument.
     * @returns {boolean} Returns `true` if the arguments are from an iteratee call,
     *  else `false`.
     */
    function isIterateeCall(value, index, object) {
      if (!isObject(object)) {
        return false;
      }
      var type = typeof index;
      if (type == 'number'
            ? (isArrayLike(object) && isIndex(index, object.length))
            : (type == 'string' && index in object)
          ) {
        return eq(object[index], value);
      }
      return false;
    }

    /**
     * Checks if `value` is a property name and not a property path.
     *
     * @private
     * @param {*} value The value to check.
     * @param {Object} [object] The object to query keys on.
     * @returns {boolean} Returns `true` if `value` is a property name, else `false`.
     */
    function isKey(value, object) {
      if (isArray(value)) {
        return false;
      }
      var type = typeof value;
      if (type == 'number' || type == 'symbol' || type == 'boolean' ||
          value == null || isSymbol(value)) {
        return true;
      }
      return reIsPlainProp.test(value) || !reIsDeepProp.test(value) ||
        (object != null && value in Object(object));
    }

    /**
     * Checks if `value` is suitable for use as unique object key.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is suitable, else `false`.
     */
    function isKeyable(value) {
      var type = typeof value;
      return (type == 'string' || type == 'number' || type == 'symbol' || type == 'boolean')
        ? (value !== '__proto__')
        : (value === null);
    }

    /**
     * Checks if `func` has a lazy counterpart.
     *
     * @private
     * @param {Function} func The function to check.
     * @returns {boolean} Returns `true` if `func` has a lazy counterpart,
     *  else `false`.
     */
    function isLaziable(func) {
      var funcName = getFuncName(func),
          other = lodash[funcName];

      if (typeof other != 'function' || !(funcName in LazyWrapper.prototype)) {
        return false;
      }
      if (func === other) {
        return true;
      }
      var data = getData(other);
      return !!data && func === data[0];
    }

    /**
     * Checks if `func` has its source masked.
     *
     * @private
     * @param {Function} func The function to check.
     * @returns {boolean} Returns `true` if `func` is masked, else `false`.
     */
    function isMasked(func) {
      return !!maskSrcKey && (maskSrcKey in func);
    }

    /**
     * Checks if `func` is capable of being masked.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `func` is maskable, else `false`.
     */
    var isMaskable = coreJsData ? isFunction : stubFalse;

    /**
     * Checks if `value` is likely a prototype object.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a prototype, else `false`.
     */
    function isPrototype(value) {
      var Ctor = value && value.constructor,
          proto = (typeof Ctor == 'function' && Ctor.prototype) || objectProto;

      return value === proto;
    }

    /**
     * Checks if `value` is suitable for strict equality comparisons, i.e. `===`.
     *
     * @private
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` if suitable for strict
     *  equality comparisons, else `false`.
     */
    function isStrictComparable(value) {
      return value === value && !isObject(value);
    }

    /**
     * A specialized version of `matchesProperty` for source values suitable
     * for strict equality comparisons, i.e. `===`.
     *
     * @private
     * @param {string} key The key of the property to get.
     * @param {*} srcValue The value to match.
     * @returns {Function} Returns the new spec function.
     */
    function matchesStrictComparable(key, srcValue) {
      return function(object) {
        if (object == null) {
          return false;
        }
        return object[key] === srcValue &&
          (srcValue !== undefined || (key in Object(object)));
      };
    }

    /**
     * A specialized version of `_.memoize` which clears the memoized function's
     * cache when it exceeds `MAX_MEMOIZE_SIZE`.
     *
     * @private
     * @param {Function} func The function to have its output memoized.
     * @returns {Function} Returns the new memoized function.
     */
    function memoizeCapped(func) {
      var result = memoize(func, function(key) {
        if (cache.size === MAX_MEMOIZE_SIZE) {
          cache.clear();
        }
        return key;
      });

      var cache = result.cache;
      return result;
    }

    /**
     * Merges the function metadata of `source` into `data`.
     *
     * Merging metadata reduces the number of wrappers used to invoke a function.
     * This is possible because methods like `_.bind`, `_.curry`, and `_.partial`
     * may be applied regardless of execution order. Methods like `_.ary` and
     * `_.rearg` modify function arguments, making the order in which they are
     * executed important, preventing the merging of metadata. However, we make
     * an exception for a safe combined case where curried functions have `_.ary`
     * and or `_.rearg` applied.
     *
     * @private
     * @param {Array} data The destination metadata.
     * @param {Array} source The source metadata.
     * @returns {Array} Returns `data`.
     */
    function mergeData(data, source) {
      var bitmask = data[1],
          srcBitmask = source[1],
          newBitmask = bitmask | srcBitmask,
          isCommon = newBitmask < (BIND_FLAG | BIND_KEY_FLAG | ARY_FLAG);

      var isCombo =
        ((srcBitmask == ARY_FLAG) && (bitmask == CURRY_FLAG)) ||
        ((srcBitmask == ARY_FLAG) && (bitmask == REARG_FLAG) && (data[7].length <= source[8])) ||
        ((srcBitmask == (ARY_FLAG | REARG_FLAG)) && (source[7].length <= source[8]) && (bitmask == CURRY_FLAG));

      // Exit early if metadata can't be merged.
      if (!(isCommon || isCombo)) {
        return data;
      }
      // Use source `thisArg` if available.
      if (srcBitmask & BIND_FLAG) {
        data[2] = source[2];
        // Set when currying a bound function.
        newBitmask |= bitmask & BIND_FLAG ? 0 : CURRY_BOUND_FLAG;
      }
      // Compose partial arguments.
      var value = source[3];
      if (value) {
        var partials = data[3];
        data[3] = partials ? composeArgs(partials, value, source[4]) : value;
        data[4] = partials ? replaceHolders(data[3], PLACEHOLDER) : source[4];
      }
      // Compose partial right arguments.
      value = source[5];
      if (value) {
        partials = data[5];
        data[5] = partials ? composeArgsRight(partials, value, source[6]) : value;
        data[6] = partials ? replaceHolders(data[5], PLACEHOLDER) : source[6];
      }
      // Use source `argPos` if available.
      value = source[7];
      if (value) {
        data[7] = value;
      }
      // Use source `ary` if it's smaller.
      if (srcBitmask & ARY_FLAG) {
        data[8] = data[8] == null ? source[8] : nativeMin(data[8], source[8]);
      }
      // Use source `arity` if one is not provided.
      if (data[9] == null) {
        data[9] = source[9];
      }
      // Use source `func` and merge bitmasks.
      data[0] = source[0];
      data[1] = newBitmask;

      return data;
    }

    /**
     * Used by `_.defaultsDeep` to customize its `_.merge` use.
     *
     * @private
     * @param {*} objValue The destination value.
     * @param {*} srcValue The source value.
     * @param {string} key The key of the property to merge.
     * @param {Object} object The parent object of `objValue`.
     * @param {Object} source The parent object of `srcValue`.
     * @param {Object} [stack] Tracks traversed source values and their merged
     *  counterparts.
     * @returns {*} Returns the value to assign.
     */
    function mergeDefaults(objValue, srcValue, key, object, source, stack) {
      if (isObject(objValue) && isObject(srcValue)) {
        // Recursively merge objects and arrays (susceptible to call stack limits).
        stack.set(srcValue, objValue);
        baseMerge(objValue, srcValue, undefined, mergeDefaults, stack);
        stack['delete'](srcValue);
      }
      return objValue;
    }

    /**
     * This function is like
     * [`Object.keys`](http://ecma-international.org/ecma-262/7.0/#sec-object.keys)
     * except that it includes inherited enumerable properties.
     *
     * @private
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property names.
     */
    function nativeKeysIn(object) {
      var result = [];
      if (object != null) {
        for (var key in Object(object)) {
          result.push(key);
        }
      }
      return result;
    }

    /**
     * A specialized version of `baseRest` which transforms the rest array.
     *
     * @private
     * @param {Function} func The function to apply a rest parameter to.
     * @param {number} [start=func.length-1] The start position of the rest parameter.
     * @param {Function} transform The rest array transform.
     * @returns {Function} Returns the new function.
     */
    function overRest(func, start, transform) {
      start = nativeMax(start === undefined ? (func.length - 1) : start, 0);
      return function() {
        var args = arguments,
            index = -1,
            length = nativeMax(args.length - start, 0),
            array = Array(length);

        while (++index < length) {
          array[index] = args[start + index];
        }
        index = -1;
        var otherArgs = Array(start + 1);
        while (++index < start) {
          otherArgs[index] = args[index];
        }
        otherArgs[start] = transform(array);
        return apply(func, this, otherArgs);
      };
    }

    /**
     * Gets the parent value at `path` of `object`.
     *
     * @private
     * @param {Object} object The object to query.
     * @param {Array} path The path to get the parent value of.
     * @returns {*} Returns the parent value.
     */
    function parent(object, path) {
      return path.length == 1 ? object : baseGet(object, baseSlice(path, 0, -1));
    }

    /**
     * Reorder `array` according to the specified indexes where the element at
     * the first index is assigned as the first element, the element at
     * the second index is assigned as the second element, and so on.
     *
     * @private
     * @param {Array} array The array to reorder.
     * @param {Array} indexes The arranged array indexes.
     * @returns {Array} Returns `array`.
     */
    function reorder(array, indexes) {
      var arrLength = array.length,
          length = nativeMin(indexes.length, arrLength),
          oldArray = copyArray(array);

      while (length--) {
        var index = indexes[length];
        array[length] = isIndex(index, arrLength) ? oldArray[index] : undefined;
      }
      return array;
    }

    /**
     * Sets metadata for `func`.
     *
     * **Note:** If this function becomes hot, i.e. is invoked a lot in a short
     * period of time, it will trip its breaker and transition to an identity
     * function to avoid garbage collection pauses in V8. See
     * [V8 issue 2070](https://bugs.chromium.org/p/v8/issues/detail?id=2070)
     * for more details.
     *
     * @private
     * @param {Function} func The function to associate metadata with.
     * @param {*} data The metadata.
     * @returns {Function} Returns `func`.
     */
    var setData = shortOut(baseSetData);

    /**
     * A simple wrapper around the global [`setTimeout`](https://mdn.io/setTimeout).
     *
     * @private
     * @param {Function} func The function to delay.
     * @param {number} wait The number of milliseconds to delay invocation.
     * @returns {number|Object} Returns the timer id or timeout object.
     */
    var setTimeout = ctxSetTimeout || function(func, wait) {
      return root.setTimeout(func, wait);
    };

    /**
     * Sets the `toString` method of `func` to return `string`.
     *
     * @private
     * @param {Function} func The function to modify.
     * @param {Function} string The `toString` result.
     * @returns {Function} Returns `func`.
     */
    var setToString = shortOut(baseSetToString);

    /**
     * Sets the `toString` method of `wrapper` to mimic the source of `reference`
     * with wrapper details in a comment at the top of the source body.
     *
     * @private
     * @param {Function} wrapper The function to modify.
     * @param {Function} reference The reference function.
     * @param {number} bitmask The bitmask flags. See `createWrap` for more details.
     * @returns {Function} Returns `wrapper`.
     */
    function setWrapToString(wrapper, reference, bitmask) {
      var source = (reference + '');
      return setToString(wrapper, insertWrapDetails(source, updateWrapDetails(getWrapDetails(source), bitmask)));
    }

    /**
     * Creates a function that'll short out and invoke `identity` instead
     * of `func` when it's called `HOT_COUNT` or more times in `HOT_SPAN`
     * milliseconds.
     *
     * @private
     * @param {Function} func The function to restrict.
     * @returns {Function} Returns the new shortable function.
     */
    function shortOut(func) {
      var count = 0,
          lastCalled = 0;

      return function() {
        var stamp = nativeNow(),
            remaining = HOT_SPAN - (stamp - lastCalled);

        lastCalled = stamp;
        if (remaining > 0) {
          if (++count >= HOT_COUNT) {
            return arguments[0];
          }
        } else {
          count = 0;
        }
        return func.apply(undefined, arguments);
      };
    }

    /**
     * A specialized version of `_.shuffle` which mutates and sets the size of `array`.
     *
     * @private
     * @param {Array} array The array to shuffle.
     * @param {number} [size=array.length] The size of `array`.
     * @returns {Array} Returns `array`.
     */
    function shuffleSelf(array, size) {
      var index = -1,
          length = array.length,
          lastIndex = length - 1;

      size = size === undefined ? length : size;
      while (++index < size) {
        var rand = baseRandom(index, lastIndex),
            value = array[rand];

        array[rand] = array[index];
        array[index] = value;
      }
      array.length = size;
      return array;
    }

    /**
     * Converts `string` to a property path array.
     *
     * @private
     * @param {string} string The string to convert.
     * @returns {Array} Returns the property path array.
     */
    var stringToPath = memoizeCapped(function(string) {
      string = toString(string);

      var result = [];
      if (reLeadingDot.test(string)) {
        result.push('');
      }
      string.replace(rePropName, function(match, number, quote, string) {
        result.push(quote ? string.replace(reEscapeChar, '$1') : (number || match));
      });
      return result;
    });

    /**
     * Converts `value` to a string key if it's not a string or symbol.
     *
     * @private
     * @param {*} value The value to inspect.
     * @returns {string|symbol} Returns the key.
     */
    function toKey(value) {
      if (typeof value == 'string' || isSymbol(value)) {
        return value;
      }
      var result = (value + '');
      return (result == '0' && (1 / value) == -INFINITY) ? '-0' : result;
    }

    /**
     * Converts `func` to its source code.
     *
     * @private
     * @param {Function} func The function to process.
     * @returns {string} Returns the source code.
     */
    function toSource(func) {
      if (func != null) {
        try {
          return funcToString.call(func);
        } catch (e) {}
        try {
          return (func + '');
        } catch (e) {}
      }
      return '';
    }

    /**
     * Updates wrapper `details` based on `bitmask` flags.
     *
     * @private
     * @returns {Array} details The details to modify.
     * @param {number} bitmask The bitmask flags. See `createWrap` for more details.
     * @returns {Array} Returns `details`.
     */
    function updateWrapDetails(details, bitmask) {
      arrayEach(wrapFlags, function(pair) {
        var value = '_.' + pair[0];
        if ((bitmask & pair[1]) && !arrayIncludes(details, value)) {
          details.push(value);
        }
      });
      return details.sort();
    }

    /**
     * Creates a clone of `wrapper`.
     *
     * @private
     * @param {Object} wrapper The wrapper to clone.
     * @returns {Object} Returns the cloned wrapper.
     */
    function wrapperClone(wrapper) {
      if (wrapper instanceof LazyWrapper) {
        return wrapper.clone();
      }
      var result = new LodashWrapper(wrapper.__wrapped__, wrapper.__chain__);
      result.__actions__ = copyArray(wrapper.__actions__);
      result.__index__  = wrapper.__index__;
      result.__values__ = wrapper.__values__;
      return result;
    }

    /*------------------------------------------------------------------------*/

    /**
     * Creates an array of elements split into groups the length of `size`.
     * If `array` can't be split evenly, the final chunk will be the remaining
     * elements.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to process.
     * @param {number} [size=1] The length of each chunk
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Array} Returns the new array of chunks.
     * @example
     *
     * _.chunk(['a', 'b', 'c', 'd'], 2);
     * // => [['a', 'b'], ['c', 'd']]
     *
     * _.chunk(['a', 'b', 'c', 'd'], 3);
     * // => [['a', 'b', 'c'], ['d']]
     */
    function chunk(array, size, guard) {
      if ((guard ? isIterateeCall(array, size, guard) : size === undefined)) {
        size = 1;
      } else {
        size = nativeMax(toInteger(size), 0);
      }
      var length = array ? array.length : 0;
      if (!length || size < 1) {
        return [];
      }
      var index = 0,
          resIndex = 0,
          result = Array(nativeCeil(length / size));

      while (index < length) {
        result[resIndex++] = baseSlice(array, index, (index += size));
      }
      return result;
    }

    /**
     * Creates an array with all falsey values removed. The values `false`, `null`,
     * `0`, `""`, `undefined`, and `NaN` are falsey.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to compact.
     * @returns {Array} Returns the new array of filtered values.
     * @example
     *
     * _.compact([0, 1, false, 2, '', 3]);
     * // => [1, 2, 3]
     */
    function compact(array) {
      var index = -1,
          length = array ? array.length : 0,
          resIndex = 0,
          result = [];

      while (++index < length) {
        var value = array[index];
        if (value) {
          result[resIndex++] = value;
        }
      }
      return result;
    }

    /**
     * Creates a new array concatenating `array` with any additional arrays
     * and/or values.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to concatenate.
     * @param {...*} [values] The values to concatenate.
     * @returns {Array} Returns the new concatenated array.
     * @example
     *
     * var array = [1];
     * var other = _.concat(array, 2, [3], [[4]]);
     *
     * console.log(other);
     * // => [1, 2, 3, [4]]
     *
     * console.log(array);
     * // => [1]
     */
    function concat() {
      var length = arguments.length;
      if (!length) {
        return [];
      }
      var args = Array(length - 1),
          array = arguments[0],
          index = length;

      while (index--) {
        args[index - 1] = arguments[index];
      }
      return arrayPush(isArray(array) ? copyArray(array) : [array], baseFlatten(args, 1));
    }

    /**
     * Creates an array of `array` values not included in the other given arrays
     * using [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons. The order and references of result values are
     * determined by the first array.
     *
     * **Note:** Unlike `_.pullAll`, this method returns a new array.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {...Array} [values] The values to exclude.
     * @returns {Array} Returns the new array of filtered values.
     * @see _.without, _.xor
     * @example
     *
     * _.difference([2, 1], [2, 3]);
     * // => [1]
     */
    var difference = baseRest(function(array, values) {
      return isArrayLikeObject(array)
        ? baseDifference(array, baseFlatten(values, 1, isArrayLikeObject, true))
        : [];
    });

    /**
     * This method is like `_.difference` except that it accepts `iteratee` which
     * is invoked for each element of `array` and `values` to generate the criterion
     * by which they're compared. The order and references of result values are
     * determined by the first array. The iteratee is invoked with one argument:
     * (value).
     *
     * **Note:** Unlike `_.pullAllBy`, this method returns a new array.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {...Array} [values] The values to exclude.
     * @param {Function} [iteratee=_.identity] The iteratee invoked per element.
     * @returns {Array} Returns the new array of filtered values.
     * @example
     *
     * _.differenceBy([2.1, 1.2], [2.3, 3.4], Math.floor);
     * // => [1.2]
     *
     * // The `_.property` iteratee shorthand.
     * _.differenceBy([{ 'x': 2 }, { 'x': 1 }], [{ 'x': 1 }], 'x');
     * // => [{ 'x': 2 }]
     */
    var differenceBy = baseRest(function(array, values) {
      var iteratee = last(values);
      if (isArrayLikeObject(iteratee)) {
        iteratee = undefined;
      }
      return isArrayLikeObject(array)
        ? baseDifference(array, baseFlatten(values, 1, isArrayLikeObject, true), getIteratee(iteratee, 2))
        : [];
    });

    /**
     * This method is like `_.difference` except that it accepts `comparator`
     * which is invoked to compare elements of `array` to `values`. The order and
     * references of result values are determined by the first array. The comparator
     * is invoked with two arguments: (arrVal, othVal).
     *
     * **Note:** Unlike `_.pullAllWith`, this method returns a new array.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {...Array} [values] The values to exclude.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new array of filtered values.
     * @example
     *
     * var objects = [{ 'x': 1, 'y': 2 }, { 'x': 2, 'y': 1 }];
     *
     * _.differenceWith(objects, [{ 'x': 1, 'y': 2 }], _.isEqual);
     * // => [{ 'x': 2, 'y': 1 }]
     */
    var differenceWith = baseRest(function(array, values) {
      var comparator = last(values);
      if (isArrayLikeObject(comparator)) {
        comparator = undefined;
      }
      return isArrayLikeObject(array)
        ? baseDifference(array, baseFlatten(values, 1, isArrayLikeObject, true), undefined, comparator)
        : [];
    });

    /**
     * Creates a slice of `array` with `n` elements dropped from the beginning.
     *
     * @static
     * @memberOf _
     * @since 0.5.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {number} [n=1] The number of elements to drop.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * _.drop([1, 2, 3]);
     * // => [2, 3]
     *
     * _.drop([1, 2, 3], 2);
     * // => [3]
     *
     * _.drop([1, 2, 3], 5);
     * // => []
     *
     * _.drop([1, 2, 3], 0);
     * // => [1, 2, 3]
     */
    function drop(array, n, guard) {
      var length = array ? array.length : 0;
      if (!length) {
        return [];
      }
      n = (guard || n === undefined) ? 1 : toInteger(n);
      return baseSlice(array, n < 0 ? 0 : n, length);
    }

    /**
     * Creates a slice of `array` with `n` elements dropped from the end.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {number} [n=1] The number of elements to drop.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * _.dropRight([1, 2, 3]);
     * // => [1, 2]
     *
     * _.dropRight([1, 2, 3], 2);
     * // => [1]
     *
     * _.dropRight([1, 2, 3], 5);
     * // => []
     *
     * _.dropRight([1, 2, 3], 0);
     * // => [1, 2, 3]
     */
    function dropRight(array, n, guard) {
      var length = array ? array.length : 0;
      if (!length) {
        return [];
      }
      n = (guard || n === undefined) ? 1 : toInteger(n);
      n = length - n;
      return baseSlice(array, 0, n < 0 ? 0 : n);
    }

    /**
     * Creates a slice of `array` excluding elements dropped from the end.
     * Elements are dropped until `predicate` returns falsey. The predicate is
     * invoked with three arguments: (value, index, array).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {Function} [predicate=_.identity] The function invoked per iteration.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'active': true },
     *   { 'user': 'fred',    'active': false },
     *   { 'user': 'pebbles', 'active': false }
     * ];
     *
     * _.dropRightWhile(users, function(o) { return !o.active; });
     * // => objects for ['barney']
     *
     * // The `_.matches` iteratee shorthand.
     * _.dropRightWhile(users, { 'user': 'pebbles', 'active': false });
     * // => objects for ['barney', 'fred']
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.dropRightWhile(users, ['active', false]);
     * // => objects for ['barney']
     *
     * // The `_.property` iteratee shorthand.
     * _.dropRightWhile(users, 'active');
     * // => objects for ['barney', 'fred', 'pebbles']
     */
    function dropRightWhile(array, predicate) {
      return (array && array.length)
        ? baseWhile(array, getIteratee(predicate, 3), true, true)
        : [];
    }

    /**
     * Creates a slice of `array` excluding elements dropped from the beginning.
     * Elements are dropped until `predicate` returns falsey. The predicate is
     * invoked with three arguments: (value, index, array).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'active': false },
     *   { 'user': 'fred',    'active': false },
     *   { 'user': 'pebbles', 'active': true }
     * ];
     *
     * _.dropWhile(users, function(o) { return !o.active; });
     * // => objects for ['pebbles']
     *
     * // The `_.matches` iteratee shorthand.
     * _.dropWhile(users, { 'user': 'barney', 'active': false });
     * // => objects for ['fred', 'pebbles']
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.dropWhile(users, ['active', false]);
     * // => objects for ['pebbles']
     *
     * // The `_.property` iteratee shorthand.
     * _.dropWhile(users, 'active');
     * // => objects for ['barney', 'fred', 'pebbles']
     */
    function dropWhile(array, predicate) {
      return (array && array.length)
        ? baseWhile(array, getIteratee(predicate, 3), true)
        : [];
    }

    /**
     * Fills elements of `array` with `value` from `start` up to, but not
     * including, `end`.
     *
     * **Note:** This method mutates `array`.
     *
     * @static
     * @memberOf _
     * @since 3.2.0
     * @category Array
     * @param {Array} array The array to fill.
     * @param {*} value The value to fill `array` with.
     * @param {number} [start=0] The start position.
     * @param {number} [end=array.length] The end position.
     * @returns {Array} Returns `array`.
     * @example
     *
     * var array = [1, 2, 3];
     *
     * _.fill(array, 'a');
     * console.log(array);
     * // => ['a', 'a', 'a']
     *
     * _.fill(Array(3), 2);
     * // => [2, 2, 2]
     *
     * _.fill([4, 6, 8, 10], '*', 1, 3);
     * // => [4, '*', '*', 10]
     */
    function fill(array, value, start, end) {
      var length = array ? array.length : 0;
      if (!length) {
        return [];
      }
      if (start && typeof start != 'number' && isIterateeCall(array, value, start)) {
        start = 0;
        end = length;
      }
      return baseFill(array, value, start, end);
    }

    /**
     * This method is like `_.find` except that it returns the index of the first
     * element `predicate` returns truthy for instead of the element itself.
     *
     * @static
     * @memberOf _
     * @since 1.1.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @param {number} [fromIndex=0] The index to search from.
     * @returns {number} Returns the index of the found element, else `-1`.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'active': false },
     *   { 'user': 'fred',    'active': false },
     *   { 'user': 'pebbles', 'active': true }
     * ];
     *
     * _.findIndex(users, function(o) { return o.user == 'barney'; });
     * // => 0
     *
     * // The `_.matches` iteratee shorthand.
     * _.findIndex(users, { 'user': 'fred', 'active': false });
     * // => 1
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.findIndex(users, ['active', false]);
     * // => 0
     *
     * // The `_.property` iteratee shorthand.
     * _.findIndex(users, 'active');
     * // => 2
     */
    function findIndex(array, predicate, fromIndex) {
      var length = array ? array.length : 0;
      if (!length) {
        return -1;
      }
      var index = fromIndex == null ? 0 : toInteger(fromIndex);
      if (index < 0) {
        index = nativeMax(length + index, 0);
      }
      return baseFindIndex(array, getIteratee(predicate, 3), index);
    }

    /**
     * This method is like `_.findIndex` except that it iterates over elements
     * of `collection` from right to left.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @param {number} [fromIndex=array.length-1] The index to search from.
     * @returns {number} Returns the index of the found element, else `-1`.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'active': true },
     *   { 'user': 'fred',    'active': false },
     *   { 'user': 'pebbles', 'active': false }
     * ];
     *
     * _.findLastIndex(users, function(o) { return o.user == 'pebbles'; });
     * // => 2
     *
     * // The `_.matches` iteratee shorthand.
     * _.findLastIndex(users, { 'user': 'barney', 'active': true });
     * // => 0
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.findLastIndex(users, ['active', false]);
     * // => 2
     *
     * // The `_.property` iteratee shorthand.
     * _.findLastIndex(users, 'active');
     * // => 0
     */
    function findLastIndex(array, predicate, fromIndex) {
      var length = array ? array.length : 0;
      if (!length) {
        return -1;
      }
      var index = length - 1;
      if (fromIndex !== undefined) {
        index = toInteger(fromIndex);
        index = fromIndex < 0
          ? nativeMax(length + index, 0)
          : nativeMin(index, length - 1);
      }
      return baseFindIndex(array, getIteratee(predicate, 3), index, true);
    }

    /**
     * Flattens `array` a single level deep.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to flatten.
     * @returns {Array} Returns the new flattened array.
     * @example
     *
     * _.flatten([1, [2, [3, [4]], 5]]);
     * // => [1, 2, [3, [4]], 5]
     */
    function flatten(array) {
      var length = array ? array.length : 0;
      return length ? baseFlatten(array, 1) : [];
    }

    /**
     * Recursively flattens `array`.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to flatten.
     * @returns {Array} Returns the new flattened array.
     * @example
     *
     * _.flattenDeep([1, [2, [3, [4]], 5]]);
     * // => [1, 2, 3, 4, 5]
     */
    function flattenDeep(array) {
      var length = array ? array.length : 0;
      return length ? baseFlatten(array, INFINITY) : [];
    }

    /**
     * Recursively flatten `array` up to `depth` times.
     *
     * @static
     * @memberOf _
     * @since 4.4.0
     * @category Array
     * @param {Array} array The array to flatten.
     * @param {number} [depth=1] The maximum recursion depth.
     * @returns {Array} Returns the new flattened array.
     * @example
     *
     * var array = [1, [2, [3, [4]], 5]];
     *
     * _.flattenDepth(array, 1);
     * // => [1, 2, [3, [4]], 5]
     *
     * _.flattenDepth(array, 2);
     * // => [1, 2, 3, [4], 5]
     */
    function flattenDepth(array, depth) {
      var length = array ? array.length : 0;
      if (!length) {
        return [];
      }
      depth = depth === undefined ? 1 : toInteger(depth);
      return baseFlatten(array, depth);
    }

    /**
     * The inverse of `_.toPairs`; this method returns an object composed
     * from key-value `pairs`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} pairs The key-value pairs.
     * @returns {Object} Returns the new object.
     * @example
     *
     * _.fromPairs([['a', 1], ['b', 2]]);
     * // => { 'a': 1, 'b': 2 }
     */
    function fromPairs(pairs) {
      var index = -1,
          length = pairs ? pairs.length : 0,
          result = {};

      while (++index < length) {
        var pair = pairs[index];
        result[pair[0]] = pair[1];
      }
      return result;
    }

    /**
     * Gets the first element of `array`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @alias first
     * @category Array
     * @param {Array} array The array to query.
     * @returns {*} Returns the first element of `array`.
     * @example
     *
     * _.head([1, 2, 3]);
     * // => 1
     *
     * _.head([]);
     * // => undefined
     */
    function head(array) {
      return (array && array.length) ? array[0] : undefined;
    }

    /**
     * Gets the index at which the first occurrence of `value` is found in `array`
     * using [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons. If `fromIndex` is negative, it's used as the
     * offset from the end of `array`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {*} value The value to search for.
     * @param {number} [fromIndex=0] The index to search from.
     * @returns {number} Returns the index of the matched value, else `-1`.
     * @example
     *
     * _.indexOf([1, 2, 1, 2], 2);
     * // => 1
     *
     * // Search from the `fromIndex`.
     * _.indexOf([1, 2, 1, 2], 2, 2);
     * // => 3
     */
    function indexOf(array, value, fromIndex) {
      var length = array ? array.length : 0;
      if (!length) {
        return -1;
      }
      var index = fromIndex == null ? 0 : toInteger(fromIndex);
      if (index < 0) {
        index = nativeMax(length + index, 0);
      }
      return baseIndexOf(array, value, index);
    }

    /**
     * Gets all but the last element of `array`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to query.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * _.initial([1, 2, 3]);
     * // => [1, 2]
     */
    function initial(array) {
      var length = array ? array.length : 0;
      return length ? baseSlice(array, 0, -1) : [];
    }

    /**
     * Creates an array of unique values that are included in all given arrays
     * using [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons. The order and references of result values are
     * determined by the first array.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @returns {Array} Returns the new array of intersecting values.
     * @example
     *
     * _.intersection([2, 1], [2, 3]);
     * // => [2]
     */
    var intersection = baseRest(function(arrays) {
      var mapped = arrayMap(arrays, castArrayLikeObject);
      return (mapped.length && mapped[0] === arrays[0])
        ? baseIntersection(mapped)
        : [];
    });

    /**
     * This method is like `_.intersection` except that it accepts `iteratee`
     * which is invoked for each element of each `arrays` to generate the criterion
     * by which they're compared. The order and references of result values are
     * determined by the first array. The iteratee is invoked with one argument:
     * (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @param {Function} [iteratee=_.identity] The iteratee invoked per element.
     * @returns {Array} Returns the new array of intersecting values.
     * @example
     *
     * _.intersectionBy([2.1, 1.2], [2.3, 3.4], Math.floor);
     * // => [2.1]
     *
     * // The `_.property` iteratee shorthand.
     * _.intersectionBy([{ 'x': 1 }], [{ 'x': 2 }, { 'x': 1 }], 'x');
     * // => [{ 'x': 1 }]
     */
    var intersectionBy = baseRest(function(arrays) {
      var iteratee = last(arrays),
          mapped = arrayMap(arrays, castArrayLikeObject);

      if (iteratee === last(mapped)) {
        iteratee = undefined;
      } else {
        mapped.pop();
      }
      return (mapped.length && mapped[0] === arrays[0])
        ? baseIntersection(mapped, getIteratee(iteratee, 2))
        : [];
    });

    /**
     * This method is like `_.intersection` except that it accepts `comparator`
     * which is invoked to compare elements of `arrays`. The order and references
     * of result values are determined by the first array. The comparator is
     * invoked with two arguments: (arrVal, othVal).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new array of intersecting values.
     * @example
     *
     * var objects = [{ 'x': 1, 'y': 2 }, { 'x': 2, 'y': 1 }];
     * var others = [{ 'x': 1, 'y': 1 }, { 'x': 1, 'y': 2 }];
     *
     * _.intersectionWith(objects, others, _.isEqual);
     * // => [{ 'x': 1, 'y': 2 }]
     */
    var intersectionWith = baseRest(function(arrays) {
      var comparator = last(arrays),
          mapped = arrayMap(arrays, castArrayLikeObject);

      if (comparator === last(mapped)) {
        comparator = undefined;
      } else {
        mapped.pop();
      }
      return (mapped.length && mapped[0] === arrays[0])
        ? baseIntersection(mapped, undefined, comparator)
        : [];
    });

    /**
     * Converts all elements in `array` into a string separated by `separator`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to convert.
     * @param {string} [separator=','] The element separator.
     * @returns {string} Returns the joined string.
     * @example
     *
     * _.join(['a', 'b', 'c'], '~');
     * // => 'a~b~c'
     */
    function join(array, separator) {
      return array ? nativeJoin.call(array, separator) : '';
    }

    /**
     * Gets the last element of `array`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to query.
     * @returns {*} Returns the last element of `array`.
     * @example
     *
     * _.last([1, 2, 3]);
     * // => 3
     */
    function last(array) {
      var length = array ? array.length : 0;
      return length ? array[length - 1] : undefined;
    }

    /**
     * This method is like `_.indexOf` except that it iterates over elements of
     * `array` from right to left.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {*} value The value to search for.
     * @param {number} [fromIndex=array.length-1] The index to search from.
     * @returns {number} Returns the index of the matched value, else `-1`.
     * @example
     *
     * _.lastIndexOf([1, 2, 1, 2], 2);
     * // => 3
     *
     * // Search from the `fromIndex`.
     * _.lastIndexOf([1, 2, 1, 2], 2, 2);
     * // => 1
     */
    function lastIndexOf(array, value, fromIndex) {
      var length = array ? array.length : 0;
      if (!length) {
        return -1;
      }
      var index = length;
      if (fromIndex !== undefined) {
        index = toInteger(fromIndex);
        index = index < 0 ? nativeMax(length + index, 0) : nativeMin(index, length - 1);
      }
      return value === value
        ? strictLastIndexOf(array, value, index)
        : baseFindIndex(array, baseIsNaN, index, true);
    }

    /**
     * Gets the element at index `n` of `array`. If `n` is negative, the nth
     * element from the end is returned.
     *
     * @static
     * @memberOf _
     * @since 4.11.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {number} [n=0] The index of the element to return.
     * @returns {*} Returns the nth element of `array`.
     * @example
     *
     * var array = ['a', 'b', 'c', 'd'];
     *
     * _.nth(array, 1);
     * // => 'b'
     *
     * _.nth(array, -2);
     * // => 'c';
     */
    function nth(array, n) {
      return (array && array.length) ? baseNth(array, toInteger(n)) : undefined;
    }

    /**
     * Removes all given values from `array` using
     * [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons.
     *
     * **Note:** Unlike `_.without`, this method mutates `array`. Use `_.remove`
     * to remove elements from an array by predicate.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Array
     * @param {Array} array The array to modify.
     * @param {...*} [values] The values to remove.
     * @returns {Array} Returns `array`.
     * @example
     *
     * var array = ['a', 'b', 'c', 'a', 'b', 'c'];
     *
     * _.pull(array, 'a', 'c');
     * console.log(array);
     * // => ['b', 'b']
     */
    var pull = baseRest(pullAll);

    /**
     * This method is like `_.pull` except that it accepts an array of values to remove.
     *
     * **Note:** Unlike `_.difference`, this method mutates `array`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to modify.
     * @param {Array} values The values to remove.
     * @returns {Array} Returns `array`.
     * @example
     *
     * var array = ['a', 'b', 'c', 'a', 'b', 'c'];
     *
     * _.pullAll(array, ['a', 'c']);
     * console.log(array);
     * // => ['b', 'b']
     */
    function pullAll(array, values) {
      return (array && array.length && values && values.length)
        ? basePullAll(array, values)
        : array;
    }

    /**
     * This method is like `_.pullAll` except that it accepts `iteratee` which is
     * invoked for each element of `array` and `values` to generate the criterion
     * by which they're compared. The iteratee is invoked with one argument: (value).
     *
     * **Note:** Unlike `_.differenceBy`, this method mutates `array`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to modify.
     * @param {Array} values The values to remove.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee invoked per element.
     * @returns {Array} Returns `array`.
     * @example
     *
     * var array = [{ 'x': 1 }, { 'x': 2 }, { 'x': 3 }, { 'x': 1 }];
     *
     * _.pullAllBy(array, [{ 'x': 1 }, { 'x': 3 }], 'x');
     * console.log(array);
     * // => [{ 'x': 2 }]
     */
    function pullAllBy(array, values, iteratee) {
      return (array && array.length && values && values.length)
        ? basePullAll(array, values, getIteratee(iteratee, 2))
        : array;
    }

    /**
     * This method is like `_.pullAll` except that it accepts `comparator` which
     * is invoked to compare elements of `array` to `values`. The comparator is
     * invoked with two arguments: (arrVal, othVal).
     *
     * **Note:** Unlike `_.differenceWith`, this method mutates `array`.
     *
     * @static
     * @memberOf _
     * @since 4.6.0
     * @category Array
     * @param {Array} array The array to modify.
     * @param {Array} values The values to remove.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns `array`.
     * @example
     *
     * var array = [{ 'x': 1, 'y': 2 }, { 'x': 3, 'y': 4 }, { 'x': 5, 'y': 6 }];
     *
     * _.pullAllWith(array, [{ 'x': 3, 'y': 4 }], _.isEqual);
     * console.log(array);
     * // => [{ 'x': 1, 'y': 2 }, { 'x': 5, 'y': 6 }]
     */
    function pullAllWith(array, values, comparator) {
      return (array && array.length && values && values.length)
        ? basePullAll(array, values, undefined, comparator)
        : array;
    }

    /**
     * Removes elements from `array` corresponding to `indexes` and returns an
     * array of removed elements.
     *
     * **Note:** Unlike `_.at`, this method mutates `array`.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to modify.
     * @param {...(number|number[])} [indexes] The indexes of elements to remove.
     * @returns {Array} Returns the new array of removed elements.
     * @example
     *
     * var array = ['a', 'b', 'c', 'd'];
     * var pulled = _.pullAt(array, [1, 3]);
     *
     * console.log(array);
     * // => ['a', 'c']
     *
     * console.log(pulled);
     * // => ['b', 'd']
     */
    var pullAt = flatRest(function(array, indexes) {
      var length = array ? array.length : 0,
          result = baseAt(array, indexes);

      basePullAt(array, arrayMap(indexes, function(index) {
        return isIndex(index, length) ? +index : index;
      }).sort(compareAscending));

      return result;
    });

    /**
     * Removes all elements from `array` that `predicate` returns truthy for
     * and returns an array of the removed elements. The predicate is invoked
     * with three arguments: (value, index, array).
     *
     * **Note:** Unlike `_.filter`, this method mutates `array`. Use `_.pull`
     * to pull elements from an array by value.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Array
     * @param {Array} array The array to modify.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @returns {Array} Returns the new array of removed elements.
     * @example
     *
     * var array = [1, 2, 3, 4];
     * var evens = _.remove(array, function(n) {
     *   return n % 2 == 0;
     * });
     *
     * console.log(array);
     * // => [1, 3]
     *
     * console.log(evens);
     * // => [2, 4]
     */
    function remove(array, predicate) {
      var result = [];
      if (!(array && array.length)) {
        return result;
      }
      var index = -1,
          indexes = [],
          length = array.length;

      predicate = getIteratee(predicate, 3);
      while (++index < length) {
        var value = array[index];
        if (predicate(value, index, array)) {
          result.push(value);
          indexes.push(index);
        }
      }
      basePullAt(array, indexes);
      return result;
    }

    /**
     * Reverses `array` so that the first element becomes the last, the second
     * element becomes the second to last, and so on.
     *
     * **Note:** This method mutates `array` and is based on
     * [`Array#reverse`](https://mdn.io/Array/reverse).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to modify.
     * @returns {Array} Returns `array`.
     * @example
     *
     * var array = [1, 2, 3];
     *
     * _.reverse(array);
     * // => [3, 2, 1]
     *
     * console.log(array);
     * // => [3, 2, 1]
     */
    function reverse(array) {
      return array ? nativeReverse.call(array) : array;
    }

    /**
     * Creates a slice of `array` from `start` up to, but not including, `end`.
     *
     * **Note:** This method is used instead of
     * [`Array#slice`](https://mdn.io/Array/slice) to ensure dense arrays are
     * returned.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to slice.
     * @param {number} [start=0] The start position.
     * @param {number} [end=array.length] The end position.
     * @returns {Array} Returns the slice of `array`.
     */
    function slice(array, start, end) {
      var length = array ? array.length : 0;
      if (!length) {
        return [];
      }
      if (end && typeof end != 'number' && isIterateeCall(array, start, end)) {
        start = 0;
        end = length;
      }
      else {
        start = start == null ? 0 : toInteger(start);
        end = end === undefined ? length : toInteger(end);
      }
      return baseSlice(array, start, end);
    }

    /**
     * Uses a binary search to determine the lowest index at which `value`
     * should be inserted into `array` in order to maintain its sort order.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The sorted array to inspect.
     * @param {*} value The value to evaluate.
     * @returns {number} Returns the index at which `value` should be inserted
     *  into `array`.
     * @example
     *
     * _.sortedIndex([30, 50], 40);
     * // => 1
     */
    function sortedIndex(array, value) {
      return baseSortedIndex(array, value);
    }

    /**
     * This method is like `_.sortedIndex` except that it accepts `iteratee`
     * which is invoked for `value` and each element of `array` to compute their
     * sort ranking. The iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The sorted array to inspect.
     * @param {*} value The value to evaluate.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee invoked per element.
     * @returns {number} Returns the index at which `value` should be inserted
     *  into `array`.
     * @example
     *
     * var objects = [{ 'x': 4 }, { 'x': 5 }];
     *
     * _.sortedIndexBy(objects, { 'x': 4 }, function(o) { return o.x; });
     * // => 0
     *
     * // The `_.property` iteratee shorthand.
     * _.sortedIndexBy(objects, { 'x': 4 }, 'x');
     * // => 0
     */
    function sortedIndexBy(array, value, iteratee) {
      return baseSortedIndexBy(array, value, getIteratee(iteratee, 2));
    }

    /**
     * This method is like `_.indexOf` except that it performs a binary
     * search on a sorted `array`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {*} value The value to search for.
     * @returns {number} Returns the index of the matched value, else `-1`.
     * @example
     *
     * _.sortedIndexOf([4, 5, 5, 5, 6], 5);
     * // => 1
     */
    function sortedIndexOf(array, value) {
      var length = array ? array.length : 0;
      if (length) {
        var index = baseSortedIndex(array, value);
        if (index < length && eq(array[index], value)) {
          return index;
        }
      }
      return -1;
    }

    /**
     * This method is like `_.sortedIndex` except that it returns the highest
     * index at which `value` should be inserted into `array` in order to
     * maintain its sort order.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The sorted array to inspect.
     * @param {*} value The value to evaluate.
     * @returns {number} Returns the index at which `value` should be inserted
     *  into `array`.
     * @example
     *
     * _.sortedLastIndex([4, 5, 5, 5, 6], 5);
     * // => 4
     */
    function sortedLastIndex(array, value) {
      return baseSortedIndex(array, value, true);
    }

    /**
     * This method is like `_.sortedLastIndex` except that it accepts `iteratee`
     * which is invoked for `value` and each element of `array` to compute their
     * sort ranking. The iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The sorted array to inspect.
     * @param {*} value The value to evaluate.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee invoked per element.
     * @returns {number} Returns the index at which `value` should be inserted
     *  into `array`.
     * @example
     *
     * var objects = [{ 'x': 4 }, { 'x': 5 }];
     *
     * _.sortedLastIndexBy(objects, { 'x': 4 }, function(o) { return o.x; });
     * // => 1
     *
     * // The `_.property` iteratee shorthand.
     * _.sortedLastIndexBy(objects, { 'x': 4 }, 'x');
     * // => 1
     */
    function sortedLastIndexBy(array, value, iteratee) {
      return baseSortedIndexBy(array, value, getIteratee(iteratee, 2), true);
    }

    /**
     * This method is like `_.lastIndexOf` except that it performs a binary
     * search on a sorted `array`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {*} value The value to search for.
     * @returns {number} Returns the index of the matched value, else `-1`.
     * @example
     *
     * _.sortedLastIndexOf([4, 5, 5, 5, 6], 5);
     * // => 3
     */
    function sortedLastIndexOf(array, value) {
      var length = array ? array.length : 0;
      if (length) {
        var index = baseSortedIndex(array, value, true) - 1;
        if (eq(array[index], value)) {
          return index;
        }
      }
      return -1;
    }

    /**
     * This method is like `_.uniq` except that it's designed and optimized
     * for sorted arrays.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @returns {Array} Returns the new duplicate free array.
     * @example
     *
     * _.sortedUniq([1, 1, 2]);
     * // => [1, 2]
     */
    function sortedUniq(array) {
      return (array && array.length)
        ? baseSortedUniq(array)
        : [];
    }

    /**
     * This method is like `_.uniqBy` except that it's designed and optimized
     * for sorted arrays.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {Function} [iteratee] The iteratee invoked per element.
     * @returns {Array} Returns the new duplicate free array.
     * @example
     *
     * _.sortedUniqBy([1.1, 1.2, 2.3, 2.4], Math.floor);
     * // => [1.1, 2.3]
     */
    function sortedUniqBy(array, iteratee) {
      return (array && array.length)
        ? baseSortedUniq(array, getIteratee(iteratee, 2))
        : [];
    }

    /**
     * Gets all but the first element of `array`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to query.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * _.tail([1, 2, 3]);
     * // => [2, 3]
     */
    function tail(array) {
      var length = array ? array.length : 0;
      return length ? baseSlice(array, 1, length) : [];
    }

    /**
     * Creates a slice of `array` with `n` elements taken from the beginning.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {number} [n=1] The number of elements to take.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * _.take([1, 2, 3]);
     * // => [1]
     *
     * _.take([1, 2, 3], 2);
     * // => [1, 2]
     *
     * _.take([1, 2, 3], 5);
     * // => [1, 2, 3]
     *
     * _.take([1, 2, 3], 0);
     * // => []
     */
    function take(array, n, guard) {
      if (!(array && array.length)) {
        return [];
      }
      n = (guard || n === undefined) ? 1 : toInteger(n);
      return baseSlice(array, 0, n < 0 ? 0 : n);
    }

    /**
     * Creates a slice of `array` with `n` elements taken from the end.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {number} [n=1] The number of elements to take.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * _.takeRight([1, 2, 3]);
     * // => [3]
     *
     * _.takeRight([1, 2, 3], 2);
     * // => [2, 3]
     *
     * _.takeRight([1, 2, 3], 5);
     * // => [1, 2, 3]
     *
     * _.takeRight([1, 2, 3], 0);
     * // => []
     */
    function takeRight(array, n, guard) {
      var length = array ? array.length : 0;
      if (!length) {
        return [];
      }
      n = (guard || n === undefined) ? 1 : toInteger(n);
      n = length - n;
      return baseSlice(array, n < 0 ? 0 : n, length);
    }

    /**
     * Creates a slice of `array` with elements taken from the end. Elements are
     * taken until `predicate` returns falsey. The predicate is invoked with
     * three arguments: (value, index, array).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'active': true },
     *   { 'user': 'fred',    'active': false },
     *   { 'user': 'pebbles', 'active': false }
     * ];
     *
     * _.takeRightWhile(users, function(o) { return !o.active; });
     * // => objects for ['fred', 'pebbles']
     *
     * // The `_.matches` iteratee shorthand.
     * _.takeRightWhile(users, { 'user': 'pebbles', 'active': false });
     * // => objects for ['pebbles']
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.takeRightWhile(users, ['active', false]);
     * // => objects for ['fred', 'pebbles']
     *
     * // The `_.property` iteratee shorthand.
     * _.takeRightWhile(users, 'active');
     * // => []
     */
    function takeRightWhile(array, predicate) {
      return (array && array.length)
        ? baseWhile(array, getIteratee(predicate, 3), false, true)
        : [];
    }

    /**
     * Creates a slice of `array` with elements taken from the beginning. Elements
     * are taken until `predicate` returns falsey. The predicate is invoked with
     * three arguments: (value, index, array).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Array
     * @param {Array} array The array to query.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @returns {Array} Returns the slice of `array`.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'active': false },
     *   { 'user': 'fred',    'active': false},
     *   { 'user': 'pebbles', 'active': true }
     * ];
     *
     * _.takeWhile(users, function(o) { return !o.active; });
     * // => objects for ['barney', 'fred']
     *
     * // The `_.matches` iteratee shorthand.
     * _.takeWhile(users, { 'user': 'barney', 'active': false });
     * // => objects for ['barney']
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.takeWhile(users, ['active', false]);
     * // => objects for ['barney', 'fred']
     *
     * // The `_.property` iteratee shorthand.
     * _.takeWhile(users, 'active');
     * // => []
     */
    function takeWhile(array, predicate) {
      return (array && array.length)
        ? baseWhile(array, getIteratee(predicate, 3))
        : [];
    }

    /**
     * Creates an array of unique values, in order, from all given arrays using
     * [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @returns {Array} Returns the new array of combined values.
     * @example
     *
     * _.union([2], [1, 2]);
     * // => [2, 1]
     */
    var union = baseRest(function(arrays) {
      return baseUniq(baseFlatten(arrays, 1, isArrayLikeObject, true));
    });

    /**
     * This method is like `_.union` except that it accepts `iteratee` which is
     * invoked for each element of each `arrays` to generate the criterion by
     * which uniqueness is computed. Result values are chosen from the first
     * array in which the value occurs. The iteratee is invoked with one argument:
     * (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee invoked per element.
     * @returns {Array} Returns the new array of combined values.
     * @example
     *
     * _.unionBy([2.1], [1.2, 2.3], Math.floor);
     * // => [2.1, 1.2]
     *
     * // The `_.property` iteratee shorthand.
     * _.unionBy([{ 'x': 1 }], [{ 'x': 2 }, { 'x': 1 }], 'x');
     * // => [{ 'x': 1 }, { 'x': 2 }]
     */
    var unionBy = baseRest(function(arrays) {
      var iteratee = last(arrays);
      if (isArrayLikeObject(iteratee)) {
        iteratee = undefined;
      }
      return baseUniq(baseFlatten(arrays, 1, isArrayLikeObject, true), getIteratee(iteratee, 2));
    });

    /**
     * This method is like `_.union` except that it accepts `comparator` which
     * is invoked to compare elements of `arrays`. Result values are chosen from
     * the first array in which the value occurs. The comparator is invoked
     * with two arguments: (arrVal, othVal).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new array of combined values.
     * @example
     *
     * var objects = [{ 'x': 1, 'y': 2 }, { 'x': 2, 'y': 1 }];
     * var others = [{ 'x': 1, 'y': 1 }, { 'x': 1, 'y': 2 }];
     *
     * _.unionWith(objects, others, _.isEqual);
     * // => [{ 'x': 1, 'y': 2 }, { 'x': 2, 'y': 1 }, { 'x': 1, 'y': 1 }]
     */
    var unionWith = baseRest(function(arrays) {
      var comparator = last(arrays);
      if (isArrayLikeObject(comparator)) {
        comparator = undefined;
      }
      return baseUniq(baseFlatten(arrays, 1, isArrayLikeObject, true), undefined, comparator);
    });

    /**
     * Creates a duplicate-free version of an array, using
     * [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons, in which only the first occurrence of each element
     * is kept. The order of result values is determined by the order they occur
     * in the array.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @returns {Array} Returns the new duplicate free array.
     * @example
     *
     * _.uniq([2, 1, 2]);
     * // => [2, 1]
     */
    function uniq(array) {
      return (array && array.length)
        ? baseUniq(array)
        : [];
    }

    /**
     * This method is like `_.uniq` except that it accepts `iteratee` which is
     * invoked for each element in `array` to generate the criterion by which
     * uniqueness is computed. The order of result values is determined by the
     * order they occur in the array. The iteratee is invoked with one argument:
     * (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee invoked per element.
     * @returns {Array} Returns the new duplicate free array.
     * @example
     *
     * _.uniqBy([2.1, 1.2, 2.3], Math.floor);
     * // => [2.1, 1.2]
     *
     * // The `_.property` iteratee shorthand.
     * _.uniqBy([{ 'x': 1 }, { 'x': 2 }, { 'x': 1 }], 'x');
     * // => [{ 'x': 1 }, { 'x': 2 }]
     */
    function uniqBy(array, iteratee) {
      return (array && array.length)
        ? baseUniq(array, getIteratee(iteratee, 2))
        : [];
    }

    /**
     * This method is like `_.uniq` except that it accepts `comparator` which
     * is invoked to compare elements of `array`. The order of result values is
     * determined by the order they occur in the array.The comparator is invoked
     * with two arguments: (arrVal, othVal).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new duplicate free array.
     * @example
     *
     * var objects = [{ 'x': 1, 'y': 2 }, { 'x': 2, 'y': 1 }, { 'x': 1, 'y': 2 }];
     *
     * _.uniqWith(objects, _.isEqual);
     * // => [{ 'x': 1, 'y': 2 }, { 'x': 2, 'y': 1 }]
     */
    function uniqWith(array, comparator) {
      return (array && array.length)
        ? baseUniq(array, undefined, comparator)
        : [];
    }

    /**
     * This method is like `_.zip` except that it accepts an array of grouped
     * elements and creates an array regrouping the elements to their pre-zip
     * configuration.
     *
     * @static
     * @memberOf _
     * @since 1.2.0
     * @category Array
     * @param {Array} array The array of grouped elements to process.
     * @returns {Array} Returns the new array of regrouped elements.
     * @example
     *
     * var zipped = _.zip(['a', 'b'], [1, 2], [true, false]);
     * // => [['a', 1, true], ['b', 2, false]]
     *
     * _.unzip(zipped);
     * // => [['a', 'b'], [1, 2], [true, false]]
     */
    function unzip(array) {
      if (!(array && array.length)) {
        return [];
      }
      var length = 0;
      array = arrayFilter(array, function(group) {
        if (isArrayLikeObject(group)) {
          length = nativeMax(group.length, length);
          return true;
        }
      });
      return baseTimes(length, function(index) {
        return arrayMap(array, baseProperty(index));
      });
    }

    /**
     * This method is like `_.unzip` except that it accepts `iteratee` to specify
     * how regrouped values should be combined. The iteratee is invoked with the
     * elements of each group: (...group).
     *
     * @static
     * @memberOf _
     * @since 3.8.0
     * @category Array
     * @param {Array} array The array of grouped elements to process.
     * @param {Function} [iteratee=_.identity] The function to combine
     *  regrouped values.
     * @returns {Array} Returns the new array of regrouped elements.
     * @example
     *
     * var zipped = _.zip([1, 2], [10, 20], [100, 200]);
     * // => [[1, 10, 100], [2, 20, 200]]
     *
     * _.unzipWith(zipped, _.add);
     * // => [3, 30, 300]
     */
    function unzipWith(array, iteratee) {
      if (!(array && array.length)) {
        return [];
      }
      var result = unzip(array);
      if (iteratee == null) {
        return result;
      }
      return arrayMap(result, function(group) {
        return apply(iteratee, undefined, group);
      });
    }

    /**
     * Creates an array excluding all given values using
     * [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * for equality comparisons.
     *
     * **Note:** Unlike `_.pull`, this method returns a new array.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {Array} array The array to inspect.
     * @param {...*} [values] The values to exclude.
     * @returns {Array} Returns the new array of filtered values.
     * @see _.difference, _.xor
     * @example
     *
     * _.without([2, 1, 2, 3], 1, 2);
     * // => [3]
     */
    var without = baseRest(function(array, values) {
      return isArrayLikeObject(array)
        ? baseDifference(array, values)
        : [];
    });

    /**
     * Creates an array of unique values that is the
     * [symmetric difference](https://en.wikipedia.org/wiki/Symmetric_difference)
     * of the given arrays. The order of result values is determined by the order
     * they occur in the arrays.
     *
     * @static
     * @memberOf _
     * @since 2.4.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @returns {Array} Returns the new array of filtered values.
     * @see _.difference, _.without
     * @example
     *
     * _.xor([2, 1], [2, 3]);
     * // => [1, 3]
     */
    var xor = baseRest(function(arrays) {
      return baseXor(arrayFilter(arrays, isArrayLikeObject));
    });

    /**
     * This method is like `_.xor` except that it accepts `iteratee` which is
     * invoked for each element of each `arrays` to generate the criterion by
     * which by which they're compared. The order of result values is determined
     * by the order they occur in the arrays. The iteratee is invoked with one
     * argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee invoked per element.
     * @returns {Array} Returns the new array of filtered values.
     * @example
     *
     * _.xorBy([2.1, 1.2], [2.3, 3.4], Math.floor);
     * // => [1.2, 3.4]
     *
     * // The `_.property` iteratee shorthand.
     * _.xorBy([{ 'x': 1 }], [{ 'x': 2 }, { 'x': 1 }], 'x');
     * // => [{ 'x': 2 }]
     */
    var xorBy = baseRest(function(arrays) {
      var iteratee = last(arrays);
      if (isArrayLikeObject(iteratee)) {
        iteratee = undefined;
      }
      return baseXor(arrayFilter(arrays, isArrayLikeObject), getIteratee(iteratee, 2));
    });

    /**
     * This method is like `_.xor` except that it accepts `comparator` which is
     * invoked to compare elements of `arrays`. The order of result values is
     * determined by the order they occur in the arrays. The comparator is invoked
     * with two arguments: (arrVal, othVal).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Array
     * @param {...Array} [arrays] The arrays to inspect.
     * @param {Function} [comparator] The comparator invoked per element.
     * @returns {Array} Returns the new array of filtered values.
     * @example
     *
     * var objects = [{ 'x': 1, 'y': 2 }, { 'x': 2, 'y': 1 }];
     * var others = [{ 'x': 1, 'y': 1 }, { 'x': 1, 'y': 2 }];
     *
     * _.xorWith(objects, others, _.isEqual);
     * // => [{ 'x': 2, 'y': 1 }, { 'x': 1, 'y': 1 }]
     */
    var xorWith = baseRest(function(arrays) {
      var comparator = last(arrays);
      if (isArrayLikeObject(comparator)) {
        comparator = undefined;
      }
      return baseXor(arrayFilter(arrays, isArrayLikeObject), undefined, comparator);
    });

    /**
     * Creates an array of grouped elements, the first of which contains the
     * first elements of the given arrays, the second of which contains the
     * second elements of the given arrays, and so on.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Array
     * @param {...Array} [arrays] The arrays to process.
     * @returns {Array} Returns the new array of grouped elements.
     * @example
     *
     * _.zip(['a', 'b'], [1, 2], [true, false]);
     * // => [['a', 1, true], ['b', 2, false]]
     */
    var zip = baseRest(unzip);

    /**
     * This method is like `_.fromPairs` except that it accepts two arrays,
     * one of property identifiers and one of corresponding values.
     *
     * @static
     * @memberOf _
     * @since 0.4.0
     * @category Array
     * @param {Array} [props=[]] The property identifiers.
     * @param {Array} [values=[]] The property values.
     * @returns {Object} Returns the new object.
     * @example
     *
     * _.zipObject(['a', 'b'], [1, 2]);
     * // => { 'a': 1, 'b': 2 }
     */
    function zipObject(props, values) {
      return baseZipObject(props || [], values || [], assignValue);
    }

    /**
     * This method is like `_.zipObject` except that it supports property paths.
     *
     * @static
     * @memberOf _
     * @since 4.1.0
     * @category Array
     * @param {Array} [props=[]] The property identifiers.
     * @param {Array} [values=[]] The property values.
     * @returns {Object} Returns the new object.
     * @example
     *
     * _.zipObjectDeep(['a.b[0].c', 'a.b[1].d'], [1, 2]);
     * // => { 'a': { 'b': [{ 'c': 1 }, { 'd': 2 }] } }
     */
    function zipObjectDeep(props, values) {
      return baseZipObject(props || [], values || [], baseSet);
    }

    /**
     * This method is like `_.zip` except that it accepts `iteratee` to specify
     * how grouped values should be combined. The iteratee is invoked with the
     * elements of each group: (...group).
     *
     * @static
     * @memberOf _
     * @since 3.8.0
     * @category Array
     * @param {...Array} [arrays] The arrays to process.
     * @param {Function} [iteratee=_.identity] The function to combine grouped values.
     * @returns {Array} Returns the new array of grouped elements.
     * @example
     *
     * _.zipWith([1, 2], [10, 20], [100, 200], function(a, b, c) {
     *   return a + b + c;
     * });
     * // => [111, 222]
     */
    var zipWith = baseRest(function(arrays) {
      var length = arrays.length,
          iteratee = length > 1 ? arrays[length - 1] : undefined;

      iteratee = typeof iteratee == 'function' ? (arrays.pop(), iteratee) : undefined;
      return unzipWith(arrays, iteratee);
    });

    /*------------------------------------------------------------------------*/

    /**
     * Creates a `lodash` wrapper instance that wraps `value` with explicit method
     * chain sequences enabled. The result of such sequences must be unwrapped
     * with `_#value`.
     *
     * @static
     * @memberOf _
     * @since 1.3.0
     * @category Seq
     * @param {*} value The value to wrap.
     * @returns {Object} Returns the new `lodash` wrapper instance.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'age': 36 },
     *   { 'user': 'fred',    'age': 40 },
     *   { 'user': 'pebbles', 'age': 1 }
     * ];
     *
     * var youngest = _
     *   .chain(users)
     *   .sortBy('age')
     *   .map(function(o) {
     *     return o.user + ' is ' + o.age;
     *   })
     *   .head()
     *   .value();
     * // => 'pebbles is 1'
     */
    function chain(value) {
      var result = lodash(value);
      result.__chain__ = true;
      return result;
    }

    /**
     * This method invokes `interceptor` and returns `value`. The interceptor
     * is invoked with one argument; (value). The purpose of this method is to
     * "tap into" a method chain sequence in order to modify intermediate results.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Seq
     * @param {*} value The value to provide to `interceptor`.
     * @param {Function} interceptor The function to invoke.
     * @returns {*} Returns `value`.
     * @example
     *
     * _([1, 2, 3])
     *  .tap(function(array) {
     *    // Mutate input array.
     *    array.pop();
     *  })
     *  .reverse()
     *  .value();
     * // => [2, 1]
     */
    function tap(value, interceptor) {
      interceptor(value);
      return value;
    }

    /**
     * This method is like `_.tap` except that it returns the result of `interceptor`.
     * The purpose of this method is to "pass thru" values replacing intermediate
     * results in a method chain sequence.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Seq
     * @param {*} value The value to provide to `interceptor`.
     * @param {Function} interceptor The function to invoke.
     * @returns {*} Returns the result of `interceptor`.
     * @example
     *
     * _('  abc  ')
     *  .chain()
     *  .trim()
     *  .thru(function(value) {
     *    return [value];
     *  })
     *  .value();
     * // => ['abc']
     */
    function thru(value, interceptor) {
      return interceptor(value);
    }

    /**
     * This method is the wrapper version of `_.at`.
     *
     * @name at
     * @memberOf _
     * @since 1.0.0
     * @category Seq
     * @param {...(string|string[])} [paths] The property paths of elements to pick.
     * @returns {Object} Returns the new `lodash` wrapper instance.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c': 3 } }, 4] };
     *
     * _(object).at(['a[0].b.c', 'a[1]']).value();
     * // => [3, 4]
     */
    var wrapperAt = flatRest(function(paths) {
      var length = paths.length,
          start = length ? paths[0] : 0,
          value = this.__wrapped__,
          interceptor = function(object) { return baseAt(object, paths); };

      if (length > 1 || this.__actions__.length ||
          !(value instanceof LazyWrapper) || !isIndex(start)) {
        return this.thru(interceptor);
      }
      value = value.slice(start, +start + (length ? 1 : 0));
      value.__actions__.push({
        'func': thru,
        'args': [interceptor],
        'thisArg': undefined
      });
      return new LodashWrapper(value, this.__chain__).thru(function(array) {
        if (length && !array.length) {
          array.push(undefined);
        }
        return array;
      });
    });

    /**
     * Creates a `lodash` wrapper instance with explicit method chain sequences enabled.
     *
     * @name chain
     * @memberOf _
     * @since 0.1.0
     * @category Seq
     * @returns {Object} Returns the new `lodash` wrapper instance.
     * @example
     *
     * var users = [
     *   { 'user': 'barney', 'age': 36 },
     *   { 'user': 'fred',   'age': 40 }
     * ];
     *
     * // A sequence without explicit chaining.
     * _(users).head();
     * // => { 'user': 'barney', 'age': 36 }
     *
     * // A sequence with explicit chaining.
     * _(users)
     *   .chain()
     *   .head()
     *   .pick('user')
     *   .value();
     * // => { 'user': 'barney' }
     */
    function wrapperChain() {
      return chain(this);
    }

    /**
     * Executes the chain sequence and returns the wrapped result.
     *
     * @name commit
     * @memberOf _
     * @since 3.2.0
     * @category Seq
     * @returns {Object} Returns the new `lodash` wrapper instance.
     * @example
     *
     * var array = [1, 2];
     * var wrapped = _(array).push(3);
     *
     * console.log(array);
     * // => [1, 2]
     *
     * wrapped = wrapped.commit();
     * console.log(array);
     * // => [1, 2, 3]
     *
     * wrapped.last();
     * // => 3
     *
     * console.log(array);
     * // => [1, 2, 3]
     */
    function wrapperCommit() {
      return new LodashWrapper(this.value(), this.__chain__);
    }

    /**
     * Gets the next value on a wrapped object following the
     * [iterator protocol](https://mdn.io/iteration_protocols#iterator).
     *
     * @name next
     * @memberOf _
     * @since 4.0.0
     * @category Seq
     * @returns {Object} Returns the next iterator value.
     * @example
     *
     * var wrapped = _([1, 2]);
     *
     * wrapped.next();
     * // => { 'done': false, 'value': 1 }
     *
     * wrapped.next();
     * // => { 'done': false, 'value': 2 }
     *
     * wrapped.next();
     * // => { 'done': true, 'value': undefined }
     */
    function wrapperNext() {
      if (this.__values__ === undefined) {
        this.__values__ = toArray(this.value());
      }
      var done = this.__index__ >= this.__values__.length,
          value = done ? undefined : this.__values__[this.__index__++];

      return { 'done': done, 'value': value };
    }

    /**
     * Enables the wrapper to be iterable.
     *
     * @name Symbol.iterator
     * @memberOf _
     * @since 4.0.0
     * @category Seq
     * @returns {Object} Returns the wrapper object.
     * @example
     *
     * var wrapped = _([1, 2]);
     *
     * wrapped[Symbol.iterator]() === wrapped;
     * // => true
     *
     * Array.from(wrapped);
     * // => [1, 2]
     */
    function wrapperToIterator() {
      return this;
    }

    /**
     * Creates a clone of the chain sequence planting `value` as the wrapped value.
     *
     * @name plant
     * @memberOf _
     * @since 3.2.0
     * @category Seq
     * @param {*} value The value to plant.
     * @returns {Object} Returns the new `lodash` wrapper instance.
     * @example
     *
     * function square(n) {
     *   return n * n;
     * }
     *
     * var wrapped = _([1, 2]).map(square);
     * var other = wrapped.plant([3, 4]);
     *
     * other.value();
     * // => [9, 16]
     *
     * wrapped.value();
     * // => [1, 4]
     */
    function wrapperPlant(value) {
      var result,
          parent = this;

      while (parent instanceof baseLodash) {
        var clone = wrapperClone(parent);
        clone.__index__ = 0;
        clone.__values__ = undefined;
        if (result) {
          previous.__wrapped__ = clone;
        } else {
          result = clone;
        }
        var previous = clone;
        parent = parent.__wrapped__;
      }
      previous.__wrapped__ = value;
      return result;
    }

    /**
     * This method is the wrapper version of `_.reverse`.
     *
     * **Note:** This method mutates the wrapped array.
     *
     * @name reverse
     * @memberOf _
     * @since 0.1.0
     * @category Seq
     * @returns {Object} Returns the new `lodash` wrapper instance.
     * @example
     *
     * var array = [1, 2, 3];
     *
     * _(array).reverse().value()
     * // => [3, 2, 1]
     *
     * console.log(array);
     * // => [3, 2, 1]
     */
    function wrapperReverse() {
      var value = this.__wrapped__;
      if (value instanceof LazyWrapper) {
        var wrapped = value;
        if (this.__actions__.length) {
          wrapped = new LazyWrapper(this);
        }
        wrapped = wrapped.reverse();
        wrapped.__actions__.push({
          'func': thru,
          'args': [reverse],
          'thisArg': undefined
        });
        return new LodashWrapper(wrapped, this.__chain__);
      }
      return this.thru(reverse);
    }

    /**
     * Executes the chain sequence to resolve the unwrapped value.
     *
     * @name value
     * @memberOf _
     * @since 0.1.0
     * @alias toJSON, valueOf
     * @category Seq
     * @returns {*} Returns the resolved unwrapped value.
     * @example
     *
     * _([1, 2, 3]).value();
     * // => [1, 2, 3]
     */
    function wrapperValue() {
      return baseWrapperValue(this.__wrapped__, this.__actions__);
    }

    /*------------------------------------------------------------------------*/

    /**
     * Creates an object composed of keys generated from the results of running
     * each element of `collection` thru `iteratee`. The corresponding value of
     * each key is the number of times the key was returned by `iteratee`. The
     * iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 0.5.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee to transform keys.
     * @returns {Object} Returns the composed aggregate object.
     * @example
     *
     * _.countBy([6.1, 4.2, 6.3], Math.floor);
     * // => { '4': 1, '6': 2 }
     *
     * // The `_.property` iteratee shorthand.
     * _.countBy(['one', 'two', 'three'], 'length');
     * // => { '3': 2, '5': 1 }
     */
    var countBy = createAggregator(function(result, value, key) {
      if (hasOwnProperty.call(result, key)) {
        ++result[key];
      } else {
        baseAssignValue(result, key, 1);
      }
    });

    /**
     * Checks if `predicate` returns truthy for **all** elements of `collection`.
     * Iteration is stopped once `predicate` returns falsey. The predicate is
     * invoked with three arguments: (value, index|key, collection).
     *
     * **Note:** This method returns `true` for
     * [empty collections](https://en.wikipedia.org/wiki/Empty_set) because
     * [everything is true](https://en.wikipedia.org/wiki/Vacuous_truth) of
     * elements of empty collections.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {boolean} Returns `true` if all elements pass the predicate check,
     *  else `false`.
     * @example
     *
     * _.every([true, 1, null, 'yes'], Boolean);
     * // => false
     *
     * var users = [
     *   { 'user': 'barney', 'age': 36, 'active': false },
     *   { 'user': 'fred',   'age': 40, 'active': false }
     * ];
     *
     * // The `_.matches` iteratee shorthand.
     * _.every(users, { 'user': 'barney', 'active': false });
     * // => false
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.every(users, ['active', false]);
     * // => true
     *
     * // The `_.property` iteratee shorthand.
     * _.every(users, 'active');
     * // => false
     */
    function every(collection, predicate, guard) {
      var func = isArray(collection) ? arrayEvery : baseEvery;
      if (guard && isIterateeCall(collection, predicate, guard)) {
        predicate = undefined;
      }
      return func(collection, getIteratee(predicate, 3));
    }

    /**
     * Iterates over elements of `collection`, returning an array of all elements
     * `predicate` returns truthy for. The predicate is invoked with three
     * arguments: (value, index|key, collection).
     *
     * **Note:** Unlike `_.remove`, this method returns a new array.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @returns {Array} Returns the new filtered array.
     * @see _.reject
     * @example
     *
     * var users = [
     *   { 'user': 'barney', 'age': 36, 'active': true },
     *   { 'user': 'fred',   'age': 40, 'active': false }
     * ];
     *
     * _.filter(users, function(o) { return !o.active; });
     * // => objects for ['fred']
     *
     * // The `_.matches` iteratee shorthand.
     * _.filter(users, { 'age': 36, 'active': true });
     * // => objects for ['barney']
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.filter(users, ['active', false]);
     * // => objects for ['fred']
     *
     * // The `_.property` iteratee shorthand.
     * _.filter(users, 'active');
     * // => objects for ['barney']
     */
    function filter(collection, predicate) {
      var func = isArray(collection) ? arrayFilter : baseFilter;
      return func(collection, getIteratee(predicate, 3));
    }

    /**
     * Iterates over elements of `collection`, returning the first element
     * `predicate` returns truthy for. The predicate is invoked with three
     * arguments: (value, index|key, collection).
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to inspect.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @param {number} [fromIndex=0] The index to search from.
     * @returns {*} Returns the matched element, else `undefined`.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'age': 36, 'active': true },
     *   { 'user': 'fred',    'age': 40, 'active': false },
     *   { 'user': 'pebbles', 'age': 1,  'active': true }
     * ];
     *
     * _.find(users, function(o) { return o.age < 40; });
     * // => object for 'barney'
     *
     * // The `_.matches` iteratee shorthand.
     * _.find(users, { 'age': 1, 'active': true });
     * // => object for 'pebbles'
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.find(users, ['active', false]);
     * // => object for 'fred'
     *
     * // The `_.property` iteratee shorthand.
     * _.find(users, 'active');
     * // => object for 'barney'
     */
    var find = createFind(findIndex);

    /**
     * This method is like `_.find` except that it iterates over elements of
     * `collection` from right to left.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to inspect.
     * @param {Function} [predicate=_.identity]
     *  The function invoked per iteration.
     * @param {number} [fromIndex=collection.length-1] The index to search from.
     * @returns {*} Returns the matched element, else `undefined`.
     * @example
     *
     * _.findLast([1, 2, 3, 4], function(n) {
     *   return n % 2 == 1;
     * });
     * // => 3
     */
    var findLast = createFind(findLastIndex);

    /**
     * Creates a flattened array of values by running each element in `collection`
     * thru `iteratee` and flattening the mapped results. The iteratee is invoked
     * with three arguments: (value, index|key, collection).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity]
     *  The function invoked per iteration.
     * @returns {Array} Returns the new flattened array.
     * @example
     *
     * function duplicate(n) {
     *   return [n, n];
     * }
     *
     * _.flatMap([1, 2], duplicate);
     * // => [1, 1, 2, 2]
     */
    function flatMap(collection, iteratee) {
      return baseFlatten(map(collection, iteratee), 1);
    }

    /**
     * This method is like `_.flatMap` except that it recursively flattens the
     * mapped results.
     *
     * @static
     * @memberOf _
     * @since 4.7.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity]
     *  The function invoked per iteration.
     * @returns {Array} Returns the new flattened array.
     * @example
     *
     * function duplicate(n) {
     *   return [[[n, n]]];
     * }
     *
     * _.flatMapDeep([1, 2], duplicate);
     * // => [1, 1, 2, 2]
     */
    function flatMapDeep(collection, iteratee) {
      return baseFlatten(map(collection, iteratee), INFINITY);
    }

    /**
     * This method is like `_.flatMap` except that it recursively flattens the
     * mapped results up to `depth` times.
     *
     * @static
     * @memberOf _
     * @since 4.7.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity]
     *  The function invoked per iteration.
     * @param {number} [depth=1] The maximum recursion depth.
     * @returns {Array} Returns the new flattened array.
     * @example
     *
     * function duplicate(n) {
     *   return [[[n, n]]];
     * }
     *
     * _.flatMapDepth([1, 2], duplicate, 2);
     * // => [[1, 1], [2, 2]]
     */
    function flatMapDepth(collection, iteratee, depth) {
      depth = depth === undefined ? 1 : toInteger(depth);
      return baseFlatten(map(collection, iteratee), depth);
    }

    /**
     * Iterates over elements of `collection` and invokes `iteratee` for each element.
     * The iteratee is invoked with three arguments: (value, index|key, collection).
     * Iteratee functions may exit iteration early by explicitly returning `false`.
     *
     * **Note:** As with other "Collections" methods, objects with a "length"
     * property are iterated like arrays. To avoid this behavior use `_.forIn`
     * or `_.forOwn` for object iteration.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @alias each
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Array|Object} Returns `collection`.
     * @see _.forEachRight
     * @example
     *
     * _.forEach([1, 2], function(value) {
     *   console.log(value);
     * });
     * // => Logs `1` then `2`.
     *
     * _.forEach({ 'a': 1, 'b': 2 }, function(value, key) {
     *   console.log(key);
     * });
     * // => Logs 'a' then 'b' (iteration order is not guaranteed).
     */
    function forEach(collection, iteratee) {
      var func = isArray(collection) ? arrayEach : baseEach;
      return func(collection, getIteratee(iteratee, 3));
    }

    /**
     * This method is like `_.forEach` except that it iterates over elements of
     * `collection` from right to left.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @alias eachRight
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Array|Object} Returns `collection`.
     * @see _.forEach
     * @example
     *
     * _.forEachRight([1, 2], function(value) {
     *   console.log(value);
     * });
     * // => Logs `2` then `1`.
     */
    function forEachRight(collection, iteratee) {
      var func = isArray(collection) ? arrayEachRight : baseEachRight;
      return func(collection, getIteratee(iteratee, 3));
    }

    /**
     * Creates an object composed of keys generated from the results of running
     * each element of `collection` thru `iteratee`. The order of grouped values
     * is determined by the order they occur in `collection`. The corresponding
     * value of each key is an array of elements responsible for generating the
     * key. The iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee to transform keys.
     * @returns {Object} Returns the composed aggregate object.
     * @example
     *
     * _.groupBy([6.1, 4.2, 6.3], Math.floor);
     * // => { '4': [4.2], '6': [6.1, 6.3] }
     *
     * // The `_.property` iteratee shorthand.
     * _.groupBy(['one', 'two', 'three'], 'length');
     * // => { '3': ['one', 'two'], '5': ['three'] }
     */
    var groupBy = createAggregator(function(result, value, key) {
      if (hasOwnProperty.call(result, key)) {
        result[key].push(value);
      } else {
        baseAssignValue(result, key, [value]);
      }
    });

    /**
     * Checks if `value` is in `collection`. If `collection` is a string, it's
     * checked for a substring of `value`, otherwise
     * [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * is used for equality comparisons. If `fromIndex` is negative, it's used as
     * the offset from the end of `collection`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object|string} collection The collection to inspect.
     * @param {*} value The value to search for.
     * @param {number} [fromIndex=0] The index to search from.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.reduce`.
     * @returns {boolean} Returns `true` if `value` is found, else `false`.
     * @example
     *
     * _.includes([1, 2, 3], 1);
     * // => true
     *
     * _.includes([1, 2, 3], 1, 2);
     * // => false
     *
     * _.includes({ 'a': 1, 'b': 2 }, 1);
     * // => true
     *
     * _.includes('abcd', 'bc');
     * // => true
     */
    function includes(collection, value, fromIndex, guard) {
      collection = isArrayLike(collection) ? collection : values(collection);
      fromIndex = (fromIndex && !guard) ? toInteger(fromIndex) : 0;

      var length = collection.length;
      if (fromIndex < 0) {
        fromIndex = nativeMax(length + fromIndex, 0);
      }
      return isString(collection)
        ? (fromIndex <= length && collection.indexOf(value, fromIndex) > -1)
        : (!!length && baseIndexOf(collection, value, fromIndex) > -1);
    }

    /**
     * Invokes the method at `path` of each element in `collection`, returning
     * an array of the results of each invoked method. Any additional arguments
     * are provided to each invoked method. If `path` is a function, it's invoked
     * for, and `this` bound to, each element in `collection`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Array|Function|string} path The path of the method to invoke or
     *  the function invoked per iteration.
     * @param {...*} [args] The arguments to invoke each method with.
     * @returns {Array} Returns the array of results.
     * @example
     *
     * _.invokeMap([[5, 1, 7], [3, 2, 1]], 'sort');
     * // => [[1, 5, 7], [1, 2, 3]]
     *
     * _.invokeMap([123, 456], String.prototype.split, '');
     * // => [['1', '2', '3'], ['4', '5', '6']]
     */
    var invokeMap = baseRest(function(collection, path, args) {
      var index = -1,
          isFunc = typeof path == 'function',
          isProp = isKey(path),
          result = isArrayLike(collection) ? Array(collection.length) : [];

      baseEach(collection, function(value) {
        var func = isFunc ? path : ((isProp && value != null) ? value[path] : undefined);
        result[++index] = func ? apply(func, value, args) : baseInvoke(value, path, args);
      });
      return result;
    });

    /**
     * Creates an object composed of keys generated from the results of running
     * each element of `collection` thru `iteratee`. The corresponding value of
     * each key is the last element responsible for generating the key. The
     * iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity]
     *  The iteratee to transform keys.
     * @returns {Object} Returns the composed aggregate object.
     * @example
     *
     * var array = [
     *   { 'dir': 'left', 'code': 97 },
     *   { 'dir': 'right', 'code': 100 }
     * ];
     *
     * _.keyBy(array, function(o) {
     *   return String.fromCharCode(o.code);
     * });
     * // => { 'a': { 'dir': 'left', 'code': 97 }, 'd': { 'dir': 'right', 'code': 100 } }
     *
     * _.keyBy(array, 'dir');
     * // => { 'left': { 'dir': 'left', 'code': 97 }, 'right': { 'dir': 'right', 'code': 100 } }
     */
    var keyBy = createAggregator(function(result, value, key) {
      baseAssignValue(result, key, value);
    });

    /**
     * Creates an array of values by running each element in `collection` thru
     * `iteratee`. The iteratee is invoked with three arguments:
     * (value, index|key, collection).
     *
     * Many lodash methods are guarded to work as iteratees for methods like
     * `_.every`, `_.filter`, `_.map`, `_.mapValues`, `_.reject`, and `_.some`.
     *
     * The guarded methods are:
     * `ary`, `chunk`, `curry`, `curryRight`, `drop`, `dropRight`, `every`,
     * `fill`, `invert`, `parseInt`, `random`, `range`, `rangeRight`, `repeat`,
     * `sampleSize`, `slice`, `some`, `sortBy`, `split`, `take`, `takeRight`,
     * `template`, `trim`, `trimEnd`, `trimStart`, and `words`
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Array} Returns the new mapped array.
     * @example
     *
     * function square(n) {
     *   return n * n;
     * }
     *
     * _.map([4, 8], square);
     * // => [16, 64]
     *
     * _.map({ 'a': 4, 'b': 8 }, square);
     * // => [16, 64] (iteration order is not guaranteed)
     *
     * var users = [
     *   { 'user': 'barney' },
     *   { 'user': 'fred' }
     * ];
     *
     * // The `_.property` iteratee shorthand.
     * _.map(users, 'user');
     * // => ['barney', 'fred']
     */
    function map(collection, iteratee) {
      var func = isArray(collection) ? arrayMap : baseMap;
      return func(collection, getIteratee(iteratee, 3));
    }

    /**
     * This method is like `_.sortBy` except that it allows specifying the sort
     * orders of the iteratees to sort by. If `orders` is unspecified, all values
     * are sorted in ascending order. Otherwise, specify an order of "desc" for
     * descending or "asc" for ascending sort order of corresponding values.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Array[]|Function[]|Object[]|string[]} [iteratees=[_.identity]]
     *  The iteratees to sort by.
     * @param {string[]} [orders] The sort orders of `iteratees`.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.reduce`.
     * @returns {Array} Returns the new sorted array.
     * @example
     *
     * var users = [
     *   { 'user': 'fred',   'age': 48 },
     *   { 'user': 'barney', 'age': 34 },
     *   { 'user': 'fred',   'age': 40 },
     *   { 'user': 'barney', 'age': 36 }
     * ];
     *
     * // Sort by `user` in ascending order and by `age` in descending order.
     * _.orderBy(users, ['user', 'age'], ['asc', 'desc']);
     * // => objects for [['barney', 36], ['barney', 34], ['fred', 48], ['fred', 40]]
     */
    function orderBy(collection, iteratees, orders, guard) {
      if (collection == null) {
        return [];
      }
      if (!isArray(iteratees)) {
        iteratees = iteratees == null ? [] : [iteratees];
      }
      orders = guard ? undefined : orders;
      if (!isArray(orders)) {
        orders = orders == null ? [] : [orders];
      }
      return baseOrderBy(collection, iteratees, orders);
    }

    /**
     * Creates an array of elements split into two groups, the first of which
     * contains elements `predicate` returns truthy for, the second of which
     * contains elements `predicate` returns falsey for. The predicate is
     * invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [predicate=_.identity] The function invoked per iteration.
     * @returns {Array} Returns the array of grouped elements.
     * @example
     *
     * var users = [
     *   { 'user': 'barney',  'age': 36, 'active': false },
     *   { 'user': 'fred',    'age': 40, 'active': true },
     *   { 'user': 'pebbles', 'age': 1,  'active': false }
     * ];
     *
     * _.partition(users, function(o) { return o.active; });
     * // => objects for [['fred'], ['barney', 'pebbles']]
     *
     * // The `_.matches` iteratee shorthand.
     * _.partition(users, { 'age': 1, 'active': false });
     * // => objects for [['pebbles'], ['barney', 'fred']]
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.partition(users, ['active', false]);
     * // => objects for [['barney', 'pebbles'], ['fred']]
     *
     * // The `_.property` iteratee shorthand.
     * _.partition(users, 'active');
     * // => objects for [['fred'], ['barney', 'pebbles']]
     */
    var partition = createAggregator(function(result, value, key) {
      result[key ? 0 : 1].push(value);
    }, function() { return [[], []]; });

    /**
     * Reduces `collection` to a value which is the accumulated result of running
     * each element in `collection` thru `iteratee`, where each successive
     * invocation is supplied the return value of the previous. If `accumulator`
     * is not given, the first element of `collection` is used as the initial
     * value. The iteratee is invoked with four arguments:
     * (accumulator, value, index|key, collection).
     *
     * Many lodash methods are guarded to work as iteratees for methods like
     * `_.reduce`, `_.reduceRight`, and `_.transform`.
     *
     * The guarded methods are:
     * `assign`, `defaults`, `defaultsDeep`, `includes`, `merge`, `orderBy`,
     * and `sortBy`
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @param {*} [accumulator] The initial value.
     * @returns {*} Returns the accumulated value.
     * @see _.reduceRight
     * @example
     *
     * _.reduce([1, 2], function(sum, n) {
     *   return sum + n;
     * }, 0);
     * // => 3
     *
     * _.reduce({ 'a': 1, 'b': 2, 'c': 1 }, function(result, value, key) {
     *   (result[value] || (result[value] = [])).push(key);
     *   return result;
     * }, {});
     * // => { '1': ['a', 'c'], '2': ['b'] } (iteration order is not guaranteed)
     */
    function reduce(collection, iteratee, accumulator) {
      var func = isArray(collection) ? arrayReduce : baseReduce,
          initAccum = arguments.length < 3;

      return func(collection, getIteratee(iteratee, 4), accumulator, initAccum, baseEach);
    }

    /**
     * This method is like `_.reduce` except that it iterates over elements of
     * `collection` from right to left.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @param {*} [accumulator] The initial value.
     * @returns {*} Returns the accumulated value.
     * @see _.reduce
     * @example
     *
     * var array = [[0, 1], [2, 3], [4, 5]];
     *
     * _.reduceRight(array, function(flattened, other) {
     *   return flattened.concat(other);
     * }, []);
     * // => [4, 5, 2, 3, 0, 1]
     */
    function reduceRight(collection, iteratee, accumulator) {
      var func = isArray(collection) ? arrayReduceRight : baseReduce,
          initAccum = arguments.length < 3;

      return func(collection, getIteratee(iteratee, 4), accumulator, initAccum, baseEachRight);
    }

    /**
     * The opposite of `_.filter`; this method returns the elements of `collection`
     * that `predicate` does **not** return truthy for.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [predicate=_.identity] The function invoked per iteration.
     * @returns {Array} Returns the new filtered array.
     * @see _.filter
     * @example
     *
     * var users = [
     *   { 'user': 'barney', 'age': 36, 'active': false },
     *   { 'user': 'fred',   'age': 40, 'active': true }
     * ];
     *
     * _.reject(users, function(o) { return !o.active; });
     * // => objects for ['fred']
     *
     * // The `_.matches` iteratee shorthand.
     * _.reject(users, { 'age': 40, 'active': true });
     * // => objects for ['barney']
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.reject(users, ['active', false]);
     * // => objects for ['fred']
     *
     * // The `_.property` iteratee shorthand.
     * _.reject(users, 'active');
     * // => objects for ['barney']
     */
    function reject(collection, predicate) {
      var func = isArray(collection) ? arrayFilter : baseFilter;
      return func(collection, negate(getIteratee(predicate, 3)));
    }

    /**
     * Gets a random element from `collection`.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to sample.
     * @returns {*} Returns the random element.
     * @example
     *
     * _.sample([1, 2, 3, 4]);
     * // => 2
     */
    function sample(collection) {
      var func = isArray(collection) ? arraySample : baseSample;
      return func(collection);
    }

    /**
     * Gets `n` random elements at unique keys from `collection` up to the
     * size of `collection`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Collection
     * @param {Array|Object} collection The collection to sample.
     * @param {number} [n=1] The number of elements to sample.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Array} Returns the random elements.
     * @example
     *
     * _.sampleSize([1, 2, 3], 2);
     * // => [3, 1]
     *
     * _.sampleSize([1, 2, 3], 4);
     * // => [2, 3, 1]
     */
    function sampleSize(collection, n, guard) {
      if ((guard ? isIterateeCall(collection, n, guard) : n === undefined)) {
        n = 1;
      } else {
        n = toInteger(n);
      }
      var func = isArray(collection) ? arraySampleSize : baseSampleSize;
      return func(collection, n);
    }

    /**
     * Creates an array of shuffled values, using a version of the
     * [Fisher-Yates shuffle](https://en.wikipedia.org/wiki/Fisher-Yates_shuffle).
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to shuffle.
     * @returns {Array} Returns the new shuffled array.
     * @example
     *
     * _.shuffle([1, 2, 3, 4]);
     * // => [4, 1, 3, 2]
     */
    function shuffle(collection) {
      var func = isArray(collection) ? arrayShuffle : baseShuffle;
      return func(collection);
    }

    /**
     * Gets the size of `collection` by returning its length for array-like
     * values or the number of own enumerable string keyed properties for objects.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object|string} collection The collection to inspect.
     * @returns {number} Returns the collection size.
     * @example
     *
     * _.size([1, 2, 3]);
     * // => 3
     *
     * _.size({ 'a': 1, 'b': 2 });
     * // => 2
     *
     * _.size('pebbles');
     * // => 7
     */
    function size(collection) {
      if (collection == null) {
        return 0;
      }
      if (isArrayLike(collection)) {
        return isString(collection) ? stringSize(collection) : collection.length;
      }
      var tag = getTag(collection);
      if (tag == mapTag || tag == setTag) {
        return collection.size;
      }
      return baseKeys(collection).length;
    }

    /**
     * Checks if `predicate` returns truthy for **any** element of `collection`.
     * Iteration is stopped once `predicate` returns truthy. The predicate is
     * invoked with three arguments: (value, index|key, collection).
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {Function} [predicate=_.identity] The function invoked per iteration.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {boolean} Returns `true` if any element passes the predicate check,
     *  else `false`.
     * @example
     *
     * _.some([null, 0, 'yes', false], Boolean);
     * // => true
     *
     * var users = [
     *   { 'user': 'barney', 'active': true },
     *   { 'user': 'fred',   'active': false }
     * ];
     *
     * // The `_.matches` iteratee shorthand.
     * _.some(users, { 'user': 'barney', 'active': false });
     * // => false
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.some(users, ['active', false]);
     * // => true
     *
     * // The `_.property` iteratee shorthand.
     * _.some(users, 'active');
     * // => true
     */
    function some(collection, predicate, guard) {
      var func = isArray(collection) ? arraySome : baseSome;
      if (guard && isIterateeCall(collection, predicate, guard)) {
        predicate = undefined;
      }
      return func(collection, getIteratee(predicate, 3));
    }

    /**
     * Creates an array of elements, sorted in ascending order by the results of
     * running each element in a collection thru each iteratee. This method
     * performs a stable sort, that is, it preserves the original sort order of
     * equal elements. The iteratees are invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Collection
     * @param {Array|Object} collection The collection to iterate over.
     * @param {...(Function|Function[])} [iteratees=[_.identity]]
     *  The iteratees to sort by.
     * @returns {Array} Returns the new sorted array.
     * @example
     *
     * var users = [
     *   { 'user': 'fred',   'age': 48 },
     *   { 'user': 'barney', 'age': 36 },
     *   { 'user': 'fred',   'age': 40 },
     *   { 'user': 'barney', 'age': 34 }
     * ];
     *
     * _.sortBy(users, [function(o) { return o.user; }]);
     * // => objects for [['barney', 36], ['barney', 34], ['fred', 48], ['fred', 40]]
     *
     * _.sortBy(users, ['user', 'age']);
     * // => objects for [['barney', 34], ['barney', 36], ['fred', 40], ['fred', 48]]
     */
    var sortBy = baseRest(function(collection, iteratees) {
      if (collection == null) {
        return [];
      }
      var length = iteratees.length;
      if (length > 1 && isIterateeCall(collection, iteratees[0], iteratees[1])) {
        iteratees = [];
      } else if (length > 2 && isIterateeCall(iteratees[0], iteratees[1], iteratees[2])) {
        iteratees = [iteratees[0]];
      }
      return baseOrderBy(collection, baseFlatten(iteratees, 1), []);
    });

    /*------------------------------------------------------------------------*/

    /**
     * Gets the timestamp of the number of milliseconds that have elapsed since
     * the Unix epoch (1 January 1970 00:00:00 UTC).
     *
     * @static
     * @memberOf _
     * @since 2.4.0
     * @category Date
     * @returns {number} Returns the timestamp.
     * @example
     *
     * _.defer(function(stamp) {
     *   console.log(_.now() - stamp);
     * }, _.now());
     * // => Logs the number of milliseconds it took for the deferred invocation.
     */
    var now = ctxNow || function() {
      return root.Date.now();
    };

    /*------------------------------------------------------------------------*/

    /**
     * The opposite of `_.before`; this method creates a function that invokes
     * `func` once it's called `n` or more times.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {number} n The number of calls before `func` is invoked.
     * @param {Function} func The function to restrict.
     * @returns {Function} Returns the new restricted function.
     * @example
     *
     * var saves = ['profile', 'settings'];
     *
     * var done = _.after(saves.length, function() {
     *   console.log('done saving!');
     * });
     *
     * _.forEach(saves, function(type) {
     *   asyncSave({ 'type': type, 'complete': done });
     * });
     * // => Logs 'done saving!' after the two async saves have completed.
     */
    function after(n, func) {
      if (typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      n = toInteger(n);
      return function() {
        if (--n < 1) {
          return func.apply(this, arguments);
        }
      };
    }

    /**
     * Creates a function that invokes `func`, with up to `n` arguments,
     * ignoring any additional arguments.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Function
     * @param {Function} func The function to cap arguments for.
     * @param {number} [n=func.length] The arity cap.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Function} Returns the new capped function.
     * @example
     *
     * _.map(['6', '8', '10'], _.ary(parseInt, 1));
     * // => [6, 8, 10]
     */
    function ary(func, n, guard) {
      n = guard ? undefined : n;
      n = (func && n == null) ? func.length : n;
      return createWrap(func, ARY_FLAG, undefined, undefined, undefined, undefined, n);
    }

    /**
     * Creates a function that invokes `func`, with the `this` binding and arguments
     * of the created function, while it's called less than `n` times. Subsequent
     * calls to the created function return the result of the last `func` invocation.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Function
     * @param {number} n The number of calls at which `func` is no longer invoked.
     * @param {Function} func The function to restrict.
     * @returns {Function} Returns the new restricted function.
     * @example
     *
     * jQuery(element).on('click', _.before(5, addContactToList));
     * // => Allows adding up to 4 contacts to the list.
     */
    function before(n, func) {
      var result;
      if (typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      n = toInteger(n);
      return function() {
        if (--n > 0) {
          result = func.apply(this, arguments);
        }
        if (n <= 1) {
          func = undefined;
        }
        return result;
      };
    }

    /**
     * Creates a function that invokes `func` with the `this` binding of `thisArg`
     * and `partials` prepended to the arguments it receives.
     *
     * The `_.bind.placeholder` value, which defaults to `_` in monolithic builds,
     * may be used as a placeholder for partially applied arguments.
     *
     * **Note:** Unlike native `Function#bind`, this method doesn't set the "length"
     * property of bound functions.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {Function} func The function to bind.
     * @param {*} thisArg The `this` binding of `func`.
     * @param {...*} [partials] The arguments to be partially applied.
     * @returns {Function} Returns the new bound function.
     * @example
     *
     * function greet(greeting, punctuation) {
     *   return greeting + ' ' + this.user + punctuation;
     * }
     *
     * var object = { 'user': 'fred' };
     *
     * var bound = _.bind(greet, object, 'hi');
     * bound('!');
     * // => 'hi fred!'
     *
     * // Bound with placeholders.
     * var bound = _.bind(greet, object, _, '!');
     * bound('hi');
     * // => 'hi fred!'
     */
    var bind = baseRest(function(func, thisArg, partials) {
      var bitmask = BIND_FLAG;
      if (partials.length) {
        var holders = replaceHolders(partials, getHolder(bind));
        bitmask |= PARTIAL_FLAG;
      }
      return createWrap(func, bitmask, thisArg, partials, holders);
    });

    /**
     * Creates a function that invokes the method at `object[key]` with `partials`
     * prepended to the arguments it receives.
     *
     * This method differs from `_.bind` by allowing bound functions to reference
     * methods that may be redefined or don't yet exist. See
     * [Peter Michaux's article](http://peter.michaux.ca/articles/lazy-function-definition-pattern)
     * for more details.
     *
     * The `_.bindKey.placeholder` value, which defaults to `_` in monolithic
     * builds, may be used as a placeholder for partially applied arguments.
     *
     * @static
     * @memberOf _
     * @since 0.10.0
     * @category Function
     * @param {Object} object The object to invoke the method on.
     * @param {string} key The key of the method.
     * @param {...*} [partials] The arguments to be partially applied.
     * @returns {Function} Returns the new bound function.
     * @example
     *
     * var object = {
     *   'user': 'fred',
     *   'greet': function(greeting, punctuation) {
     *     return greeting + ' ' + this.user + punctuation;
     *   }
     * };
     *
     * var bound = _.bindKey(object, 'greet', 'hi');
     * bound('!');
     * // => 'hi fred!'
     *
     * object.greet = function(greeting, punctuation) {
     *   return greeting + 'ya ' + this.user + punctuation;
     * };
     *
     * bound('!');
     * // => 'hiya fred!'
     *
     * // Bound with placeholders.
     * var bound = _.bindKey(object, 'greet', _, '!');
     * bound('hi');
     * // => 'hiya fred!'
     */
    var bindKey = baseRest(function(object, key, partials) {
      var bitmask = BIND_FLAG | BIND_KEY_FLAG;
      if (partials.length) {
        var holders = replaceHolders(partials, getHolder(bindKey));
        bitmask |= PARTIAL_FLAG;
      }
      return createWrap(key, bitmask, object, partials, holders);
    });

    /**
     * Creates a function that accepts arguments of `func` and either invokes
     * `func` returning its result, if at least `arity` number of arguments have
     * been provided, or returns a function that accepts the remaining `func`
     * arguments, and so on. The arity of `func` may be specified if `func.length`
     * is not sufficient.
     *
     * The `_.curry.placeholder` value, which defaults to `_` in monolithic builds,
     * may be used as a placeholder for provided arguments.
     *
     * **Note:** This method doesn't set the "length" property of curried functions.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Function
     * @param {Function} func The function to curry.
     * @param {number} [arity=func.length] The arity of `func`.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Function} Returns the new curried function.
     * @example
     *
     * var abc = function(a, b, c) {
     *   return [a, b, c];
     * };
     *
     * var curried = _.curry(abc);
     *
     * curried(1)(2)(3);
     * // => [1, 2, 3]
     *
     * curried(1, 2)(3);
     * // => [1, 2, 3]
     *
     * curried(1, 2, 3);
     * // => [1, 2, 3]
     *
     * // Curried with placeholders.
     * curried(1)(_, 3)(2);
     * // => [1, 2, 3]
     */
    function curry(func, arity, guard) {
      arity = guard ? undefined : arity;
      var result = createWrap(func, CURRY_FLAG, undefined, undefined, undefined, undefined, undefined, arity);
      result.placeholder = curry.placeholder;
      return result;
    }

    /**
     * This method is like `_.curry` except that arguments are applied to `func`
     * in the manner of `_.partialRight` instead of `_.partial`.
     *
     * The `_.curryRight.placeholder` value, which defaults to `_` in monolithic
     * builds, may be used as a placeholder for provided arguments.
     *
     * **Note:** This method doesn't set the "length" property of curried functions.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Function
     * @param {Function} func The function to curry.
     * @param {number} [arity=func.length] The arity of `func`.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Function} Returns the new curried function.
     * @example
     *
     * var abc = function(a, b, c) {
     *   return [a, b, c];
     * };
     *
     * var curried = _.curryRight(abc);
     *
     * curried(3)(2)(1);
     * // => [1, 2, 3]
     *
     * curried(2, 3)(1);
     * // => [1, 2, 3]
     *
     * curried(1, 2, 3);
     * // => [1, 2, 3]
     *
     * // Curried with placeholders.
     * curried(3)(1, _)(2);
     * // => [1, 2, 3]
     */
    function curryRight(func, arity, guard) {
      arity = guard ? undefined : arity;
      var result = createWrap(func, CURRY_RIGHT_FLAG, undefined, undefined, undefined, undefined, undefined, arity);
      result.placeholder = curryRight.placeholder;
      return result;
    }

    /**
     * Creates a debounced function that delays invoking `func` until after `wait`
     * milliseconds have elapsed since the last time the debounced function was
     * invoked. The debounced function comes with a `cancel` method to cancel
     * delayed `func` invocations and a `flush` method to immediately invoke them.
     * Provide `options` to indicate whether `func` should be invoked on the
     * leading and/or trailing edge of the `wait` timeout. The `func` is invoked
     * with the last arguments provided to the debounced function. Subsequent
     * calls to the debounced function return the result of the last `func`
     * invocation.
     *
     * **Note:** If `leading` and `trailing` options are `true`, `func` is
     * invoked on the trailing edge of the timeout only if the debounced function
     * is invoked more than once during the `wait` timeout.
     *
     * If `wait` is `0` and `leading` is `false`, `func` invocation is deferred
     * until to the next tick, similar to `setTimeout` with a timeout of `0`.
     *
     * See [David Corbacho's article](https://css-tricks.com/debouncing-throttling-explained-examples/)
     * for details over the differences between `_.debounce` and `_.throttle`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {Function} func The function to debounce.
     * @param {number} [wait=0] The number of milliseconds to delay.
     * @param {Object} [options={}] The options object.
     * @param {boolean} [options.leading=false]
     *  Specify invoking on the leading edge of the timeout.
     * @param {number} [options.maxWait]
     *  The maximum time `func` is allowed to be delayed before it's invoked.
     * @param {boolean} [options.trailing=true]
     *  Specify invoking on the trailing edge of the timeout.
     * @returns {Function} Returns the new debounced function.
     * @example
     *
     * // Avoid costly calculations while the window size is in flux.
     * jQuery(window).on('resize', _.debounce(calculateLayout, 150));
     *
     * // Invoke `sendMail` when clicked, debouncing subsequent calls.
     * jQuery(element).on('click', _.debounce(sendMail, 300, {
     *   'leading': true,
     *   'trailing': false
     * }));
     *
     * // Ensure `batchLog` is invoked once after 1 second of debounced calls.
     * var debounced = _.debounce(batchLog, 250, { 'maxWait': 1000 });
     * var source = new EventSource('/stream');
     * jQuery(source).on('message', debounced);
     *
     * // Cancel the trailing debounced invocation.
     * jQuery(window).on('popstate', debounced.cancel);
     */
    function debounce(func, wait, options) {
      var lastArgs,
          lastThis,
          maxWait,
          result,
          timerId,
          lastCallTime,
          lastInvokeTime = 0,
          leading = false,
          maxing = false,
          trailing = true;

      if (typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      wait = toNumber(wait) || 0;
      if (isObject(options)) {
        leading = !!options.leading;
        maxing = 'maxWait' in options;
        maxWait = maxing ? nativeMax(toNumber(options.maxWait) || 0, wait) : maxWait;
        trailing = 'trailing' in options ? !!options.trailing : trailing;
      }

      function invokeFunc(time) {
        var args = lastArgs,
            thisArg = lastThis;

        lastArgs = lastThis = undefined;
        lastInvokeTime = time;
        result = func.apply(thisArg, args);
        return result;
      }

      function leadingEdge(time) {
        // Reset any `maxWait` timer.
        lastInvokeTime = time;
        // Start the timer for the trailing edge.
        timerId = setTimeout(timerExpired, wait);
        // Invoke the leading edge.
        return leading ? invokeFunc(time) : result;
      }

      function remainingWait(time) {
        var timeSinceLastCall = time - lastCallTime,
            timeSinceLastInvoke = time - lastInvokeTime,
            result = wait - timeSinceLastCall;

        return maxing ? nativeMin(result, maxWait - timeSinceLastInvoke) : result;
      }

      function shouldInvoke(time) {
        var timeSinceLastCall = time - lastCallTime,
            timeSinceLastInvoke = time - lastInvokeTime;

        // Either this is the first call, activity has stopped and we're at the
        // trailing edge, the system time has gone backwards and we're treating
        // it as the trailing edge, or we've hit the `maxWait` limit.
        return (lastCallTime === undefined || (timeSinceLastCall >= wait) ||
          (timeSinceLastCall < 0) || (maxing && timeSinceLastInvoke >= maxWait));
      }

      function timerExpired() {
        var time = now();
        if (shouldInvoke(time)) {
          return trailingEdge(time);
        }
        // Restart the timer.
        timerId = setTimeout(timerExpired, remainingWait(time));
      }

      function trailingEdge(time) {
        timerId = undefined;

        // Only invoke if we have `lastArgs` which means `func` has been
        // debounced at least once.
        if (trailing && lastArgs) {
          return invokeFunc(time);
        }
        lastArgs = lastThis = undefined;
        return result;
      }

      function cancel() {
        if (timerId !== undefined) {
          clearTimeout(timerId);
        }
        lastInvokeTime = 0;
        lastArgs = lastCallTime = lastThis = timerId = undefined;
      }

      function flush() {
        return timerId === undefined ? result : trailingEdge(now());
      }

      function debounced() {
        var time = now(),
            isInvoking = shouldInvoke(time);

        lastArgs = arguments;
        lastThis = this;
        lastCallTime = time;

        if (isInvoking) {
          if (timerId === undefined) {
            return leadingEdge(lastCallTime);
          }
          if (maxing) {
            // Handle invocations in a tight loop.
            timerId = setTimeout(timerExpired, wait);
            return invokeFunc(lastCallTime);
          }
        }
        if (timerId === undefined) {
          timerId = setTimeout(timerExpired, wait);
        }
        return result;
      }
      debounced.cancel = cancel;
      debounced.flush = flush;
      return debounced;
    }

    /**
     * Defers invoking the `func` until the current call stack has cleared. Any
     * additional arguments are provided to `func` when it's invoked.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {Function} func The function to defer.
     * @param {...*} [args] The arguments to invoke `func` with.
     * @returns {number} Returns the timer id.
     * @example
     *
     * _.defer(function(text) {
     *   console.log(text);
     * }, 'deferred');
     * // => Logs 'deferred' after one millisecond.
     */
    var defer = baseRest(function(func, args) {
      return baseDelay(func, 1, args);
    });

    /**
     * Invokes `func` after `wait` milliseconds. Any additional arguments are
     * provided to `func` when it's invoked.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {Function} func The function to delay.
     * @param {number} wait The number of milliseconds to delay invocation.
     * @param {...*} [args] The arguments to invoke `func` with.
     * @returns {number} Returns the timer id.
     * @example
     *
     * _.delay(function(text) {
     *   console.log(text);
     * }, 1000, 'later');
     * // => Logs 'later' after one second.
     */
    var delay = baseRest(function(func, wait, args) {
      return baseDelay(func, toNumber(wait) || 0, args);
    });

    /**
     * Creates a function that invokes `func` with arguments reversed.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Function
     * @param {Function} func The function to flip arguments for.
     * @returns {Function} Returns the new flipped function.
     * @example
     *
     * var flipped = _.flip(function() {
     *   return _.toArray(arguments);
     * });
     *
     * flipped('a', 'b', 'c', 'd');
     * // => ['d', 'c', 'b', 'a']
     */
    function flip(func) {
      return createWrap(func, FLIP_FLAG);
    }

    /**
     * Creates a function that memoizes the result of `func`. If `resolver` is
     * provided, it determines the cache key for storing the result based on the
     * arguments provided to the memoized function. By default, the first argument
     * provided to the memoized function is used as the map cache key. The `func`
     * is invoked with the `this` binding of the memoized function.
     *
     * **Note:** The cache is exposed as the `cache` property on the memoized
     * function. Its creation may be customized by replacing the `_.memoize.Cache`
     * constructor with one whose instances implement the
     * [`Map`](http://ecma-international.org/ecma-262/7.0/#sec-properties-of-the-map-prototype-object)
     * method interface of `delete`, `get`, `has`, and `set`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {Function} func The function to have its output memoized.
     * @param {Function} [resolver] The function to resolve the cache key.
     * @returns {Function} Returns the new memoized function.
     * @example
     *
     * var object = { 'a': 1, 'b': 2 };
     * var other = { 'c': 3, 'd': 4 };
     *
     * var values = _.memoize(_.values);
     * values(object);
     * // => [1, 2]
     *
     * values(other);
     * // => [3, 4]
     *
     * object.a = 2;
     * values(object);
     * // => [1, 2]
     *
     * // Modify the result cache.
     * values.cache.set(object, ['a', 'b']);
     * values(object);
     * // => ['a', 'b']
     *
     * // Replace `_.memoize.Cache`.
     * _.memoize.Cache = WeakMap;
     */
    function memoize(func, resolver) {
      if (typeof func != 'function' || (resolver && typeof resolver != 'function')) {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      var memoized = function() {
        var args = arguments,
            key = resolver ? resolver.apply(this, args) : args[0],
            cache = memoized.cache;

        if (cache.has(key)) {
          return cache.get(key);
        }
        var result = func.apply(this, args);
        memoized.cache = cache.set(key, result) || cache;
        return result;
      };
      memoized.cache = new (memoize.Cache || MapCache);
      return memoized;
    }

    // Expose `MapCache`.
    memoize.Cache = MapCache;

    /**
     * Creates a function that negates the result of the predicate `func`. The
     * `func` predicate is invoked with the `this` binding and arguments of the
     * created function.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Function
     * @param {Function} predicate The predicate to negate.
     * @returns {Function} Returns the new negated function.
     * @example
     *
     * function isEven(n) {
     *   return n % 2 == 0;
     * }
     *
     * _.filter([1, 2, 3, 4, 5, 6], _.negate(isEven));
     * // => [1, 3, 5]
     */
    function negate(predicate) {
      if (typeof predicate != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      return function() {
        var args = arguments;
        switch (args.length) {
          case 0: return !predicate.call(this);
          case 1: return !predicate.call(this, args[0]);
          case 2: return !predicate.call(this, args[0], args[1]);
          case 3: return !predicate.call(this, args[0], args[1], args[2]);
        }
        return !predicate.apply(this, args);
      };
    }

    /**
     * Creates a function that is restricted to invoking `func` once. Repeat calls
     * to the function return the value of the first invocation. The `func` is
     * invoked with the `this` binding and arguments of the created function.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {Function} func The function to restrict.
     * @returns {Function} Returns the new restricted function.
     * @example
     *
     * var initialize = _.once(createApplication);
     * initialize();
     * initialize();
     * // => `createApplication` is invoked once
     */
    function once(func) {
      return before(2, func);
    }

    /**
     * Creates a function that invokes `func` with its arguments transformed.
     *
     * @static
     * @since 4.0.0
     * @memberOf _
     * @category Function
     * @param {Function} func The function to wrap.
     * @param {...(Function|Function[])} [transforms=[_.identity]]
     *  The argument transforms.
     * @returns {Function} Returns the new function.
     * @example
     *
     * function doubled(n) {
     *   return n * 2;
     * }
     *
     * function square(n) {
     *   return n * n;
     * }
     *
     * var func = _.overArgs(function(x, y) {
     *   return [x, y];
     * }, [square, doubled]);
     *
     * func(9, 3);
     * // => [81, 6]
     *
     * func(10, 5);
     * // => [100, 10]
     */
    var overArgs = castRest(function(func, transforms) {
      transforms = (transforms.length == 1 && isArray(transforms[0]))
        ? arrayMap(transforms[0], baseUnary(getIteratee()))
        : arrayMap(baseFlatten(transforms, 1), baseUnary(getIteratee()));

      var funcsLength = transforms.length;
      return baseRest(function(args) {
        var index = -1,
            length = nativeMin(args.length, funcsLength);

        while (++index < length) {
          args[index] = transforms[index].call(this, args[index]);
        }
        return apply(func, this, args);
      });
    });

    /**
     * Creates a function that invokes `func` with `partials` prepended to the
     * arguments it receives. This method is like `_.bind` except it does **not**
     * alter the `this` binding.
     *
     * The `_.partial.placeholder` value, which defaults to `_` in monolithic
     * builds, may be used as a placeholder for partially applied arguments.
     *
     * **Note:** This method doesn't set the "length" property of partially
     * applied functions.
     *
     * @static
     * @memberOf _
     * @since 0.2.0
     * @category Function
     * @param {Function} func The function to partially apply arguments to.
     * @param {...*} [partials] The arguments to be partially applied.
     * @returns {Function} Returns the new partially applied function.
     * @example
     *
     * function greet(greeting, name) {
     *   return greeting + ' ' + name;
     * }
     *
     * var sayHelloTo = _.partial(greet, 'hello');
     * sayHelloTo('fred');
     * // => 'hello fred'
     *
     * // Partially applied with placeholders.
     * var greetFred = _.partial(greet, _, 'fred');
     * greetFred('hi');
     * // => 'hi fred'
     */
    var partial = baseRest(function(func, partials) {
      var holders = replaceHolders(partials, getHolder(partial));
      return createWrap(func, PARTIAL_FLAG, undefined, partials, holders);
    });

    /**
     * This method is like `_.partial` except that partially applied arguments
     * are appended to the arguments it receives.
     *
     * The `_.partialRight.placeholder` value, which defaults to `_` in monolithic
     * builds, may be used as a placeholder for partially applied arguments.
     *
     * **Note:** This method doesn't set the "length" property of partially
     * applied functions.
     *
     * @static
     * @memberOf _
     * @since 1.0.0
     * @category Function
     * @param {Function} func The function to partially apply arguments to.
     * @param {...*} [partials] The arguments to be partially applied.
     * @returns {Function} Returns the new partially applied function.
     * @example
     *
     * function greet(greeting, name) {
     *   return greeting + ' ' + name;
     * }
     *
     * var greetFred = _.partialRight(greet, 'fred');
     * greetFred('hi');
     * // => 'hi fred'
     *
     * // Partially applied with placeholders.
     * var sayHelloTo = _.partialRight(greet, 'hello', _);
     * sayHelloTo('fred');
     * // => 'hello fred'
     */
    var partialRight = baseRest(function(func, partials) {
      var holders = replaceHolders(partials, getHolder(partialRight));
      return createWrap(func, PARTIAL_RIGHT_FLAG, undefined, partials, holders);
    });

    /**
     * Creates a function that invokes `func` with arguments arranged according
     * to the specified `indexes` where the argument value at the first index is
     * provided as the first argument, the argument value at the second index is
     * provided as the second argument, and so on.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Function
     * @param {Function} func The function to rearrange arguments for.
     * @param {...(number|number[])} indexes The arranged argument indexes.
     * @returns {Function} Returns the new function.
     * @example
     *
     * var rearged = _.rearg(function(a, b, c) {
     *   return [a, b, c];
     * }, [2, 0, 1]);
     *
     * rearged('b', 'c', 'a')
     * // => ['a', 'b', 'c']
     */
    var rearg = flatRest(function(func, indexes) {
      return createWrap(func, REARG_FLAG, undefined, undefined, undefined, indexes);
    });

    /**
     * Creates a function that invokes `func` with the `this` binding of the
     * created function and arguments from `start` and beyond provided as
     * an array.
     *
     * **Note:** This method is based on the
     * [rest parameter](https://mdn.io/rest_parameters).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Function
     * @param {Function} func The function to apply a rest parameter to.
     * @param {number} [start=func.length-1] The start position of the rest parameter.
     * @returns {Function} Returns the new function.
     * @example
     *
     * var say = _.rest(function(what, names) {
     *   return what + ' ' + _.initial(names).join(', ') +
     *     (_.size(names) > 1 ? ', & ' : '') + _.last(names);
     * });
     *
     * say('hello', 'fred', 'barney', 'pebbles');
     * // => 'hello fred, barney, & pebbles'
     */
    function rest(func, start) {
      if (typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      start = start === undefined ? start : toInteger(start);
      return baseRest(func, start);
    }

    /**
     * Creates a function that invokes `func` with the `this` binding of the
     * create function and an array of arguments much like
     * [`Function#apply`](http://www.ecma-international.org/ecma-262/7.0/#sec-function.prototype.apply).
     *
     * **Note:** This method is based on the
     * [spread operator](https://mdn.io/spread_operator).
     *
     * @static
     * @memberOf _
     * @since 3.2.0
     * @category Function
     * @param {Function} func The function to spread arguments over.
     * @param {number} [start=0] The start position of the spread.
     * @returns {Function} Returns the new function.
     * @example
     *
     * var say = _.spread(function(who, what) {
     *   return who + ' says ' + what;
     * });
     *
     * say(['fred', 'hello']);
     * // => 'fred says hello'
     *
     * var numbers = Promise.all([
     *   Promise.resolve(40),
     *   Promise.resolve(36)
     * ]);
     *
     * numbers.then(_.spread(function(x, y) {
     *   return x + y;
     * }));
     * // => a Promise of 76
     */
    function spread(func, start) {
      if (typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      start = start === undefined ? 0 : nativeMax(toInteger(start), 0);
      return baseRest(function(args) {
        var array = args[start],
            otherArgs = castSlice(args, 0, start);

        if (array) {
          arrayPush(otherArgs, array);
        }
        return apply(func, this, otherArgs);
      });
    }

    /**
     * Creates a throttled function that only invokes `func` at most once per
     * every `wait` milliseconds. The throttled function comes with a `cancel`
     * method to cancel delayed `func` invocations and a `flush` method to
     * immediately invoke them. Provide `options` to indicate whether `func`
     * should be invoked on the leading and/or trailing edge of the `wait`
     * timeout. The `func` is invoked with the last arguments provided to the
     * throttled function. Subsequent calls to the throttled function return the
     * result of the last `func` invocation.
     *
     * **Note:** If `leading` and `trailing` options are `true`, `func` is
     * invoked on the trailing edge of the timeout only if the throttled function
     * is invoked more than once during the `wait` timeout.
     *
     * If `wait` is `0` and `leading` is `false`, `func` invocation is deferred
     * until to the next tick, similar to `setTimeout` with a timeout of `0`.
     *
     * See [David Corbacho's article](https://css-tricks.com/debouncing-throttling-explained-examples/)
     * for details over the differences between `_.throttle` and `_.debounce`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {Function} func The function to throttle.
     * @param {number} [wait=0] The number of milliseconds to throttle invocations to.
     * @param {Object} [options={}] The options object.
     * @param {boolean} [options.leading=true]
     *  Specify invoking on the leading edge of the timeout.
     * @param {boolean} [options.trailing=true]
     *  Specify invoking on the trailing edge of the timeout.
     * @returns {Function} Returns the new throttled function.
     * @example
     *
     * // Avoid excessively updating the position while scrolling.
     * jQuery(window).on('scroll', _.throttle(updatePosition, 100));
     *
     * // Invoke `renewToken` when the click event is fired, but not more than once every 5 minutes.
     * var throttled = _.throttle(renewToken, 300000, { 'trailing': false });
     * jQuery(element).on('click', throttled);
     *
     * // Cancel the trailing throttled invocation.
     * jQuery(window).on('popstate', throttled.cancel);
     */
    function throttle(func, wait, options) {
      var leading = true,
          trailing = true;

      if (typeof func != 'function') {
        throw new TypeError(FUNC_ERROR_TEXT);
      }
      if (isObject(options)) {
        leading = 'leading' in options ? !!options.leading : leading;
        trailing = 'trailing' in options ? !!options.trailing : trailing;
      }
      return debounce(func, wait, {
        'leading': leading,
        'maxWait': wait,
        'trailing': trailing
      });
    }

    /**
     * Creates a function that accepts up to one argument, ignoring any
     * additional arguments.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Function
     * @param {Function} func The function to cap arguments for.
     * @returns {Function} Returns the new capped function.
     * @example
     *
     * _.map(['6', '8', '10'], _.unary(parseInt));
     * // => [6, 8, 10]
     */
    function unary(func) {
      return ary(func, 1);
    }

    /**
     * Creates a function that provides `value` to `wrapper` as its first
     * argument. Any additional arguments provided to the function are appended
     * to those provided to the `wrapper`. The wrapper is invoked with the `this`
     * binding of the created function.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Function
     * @param {*} value The value to wrap.
     * @param {Function} [wrapper=identity] The wrapper function.
     * @returns {Function} Returns the new function.
     * @example
     *
     * var p = _.wrap(_.escape, function(func, text) {
     *   return '<p>' + func(text) + '</p>';
     * });
     *
     * p('fred, barney, & pebbles');
     * // => '<p>fred, barney, &amp; pebbles</p>'
     */
    function wrap(value, wrapper) {
      wrapper = wrapper == null ? identity : wrapper;
      return partial(wrapper, value);
    }

    /*------------------------------------------------------------------------*/

    /**
     * Casts `value` as an array if it's not one.
     *
     * @static
     * @memberOf _
     * @since 4.4.0
     * @category Lang
     * @param {*} value The value to inspect.
     * @returns {Array} Returns the cast array.
     * @example
     *
     * _.castArray(1);
     * // => [1]
     *
     * _.castArray({ 'a': 1 });
     * // => [{ 'a': 1 }]
     *
     * _.castArray('abc');
     * // => ['abc']
     *
     * _.castArray(null);
     * // => [null]
     *
     * _.castArray(undefined);
     * // => [undefined]
     *
     * _.castArray();
     * // => []
     *
     * var array = [1, 2, 3];
     * console.log(_.castArray(array) === array);
     * // => true
     */
    function castArray() {
      if (!arguments.length) {
        return [];
      }
      var value = arguments[0];
      return isArray(value) ? value : [value];
    }

    /**
     * Creates a shallow clone of `value`.
     *
     * **Note:** This method is loosely based on the
     * [structured clone algorithm](https://mdn.io/Structured_clone_algorithm)
     * and supports cloning arrays, array buffers, booleans, date objects, maps,
     * numbers, `Object` objects, regexes, sets, strings, symbols, and typed
     * arrays. The own enumerable properties of `arguments` objects are cloned
     * as plain objects. An empty object is returned for uncloneable values such
     * as error objects, functions, DOM nodes, and WeakMaps.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to clone.
     * @returns {*} Returns the cloned value.
     * @see _.cloneDeep
     * @example
     *
     * var objects = [{ 'a': 1 }, { 'b': 2 }];
     *
     * var shallow = _.clone(objects);
     * console.log(shallow[0] === objects[0]);
     * // => true
     */
    function clone(value) {
      return baseClone(value, false, true);
    }

    /**
     * This method is like `_.clone` except that it accepts `customizer` which
     * is invoked to produce the cloned value. If `customizer` returns `undefined`,
     * cloning is handled by the method instead. The `customizer` is invoked with
     * up to four arguments; (value [, index|key, object, stack]).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to clone.
     * @param {Function} [customizer] The function to customize cloning.
     * @returns {*} Returns the cloned value.
     * @see _.cloneDeepWith
     * @example
     *
     * function customizer(value) {
     *   if (_.isElement(value)) {
     *     return value.cloneNode(false);
     *   }
     * }
     *
     * var el = _.cloneWith(document.body, customizer);
     *
     * console.log(el === document.body);
     * // => false
     * console.log(el.nodeName);
     * // => 'BODY'
     * console.log(el.childNodes.length);
     * // => 0
     */
    function cloneWith(value, customizer) {
      return baseClone(value, false, true, customizer);
    }

    /**
     * This method is like `_.clone` except that it recursively clones `value`.
     *
     * @static
     * @memberOf _
     * @since 1.0.0
     * @category Lang
     * @param {*} value The value to recursively clone.
     * @returns {*} Returns the deep cloned value.
     * @see _.clone
     * @example
     *
     * var objects = [{ 'a': 1 }, { 'b': 2 }];
     *
     * var deep = _.cloneDeep(objects);
     * console.log(deep[0] === objects[0]);
     * // => false
     */
    function cloneDeep(value) {
      return baseClone(value, true, true);
    }

    /**
     * This method is like `_.cloneWith` except that it recursively clones `value`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to recursively clone.
     * @param {Function} [customizer] The function to customize cloning.
     * @returns {*} Returns the deep cloned value.
     * @see _.cloneWith
     * @example
     *
     * function customizer(value) {
     *   if (_.isElement(value)) {
     *     return value.cloneNode(true);
     *   }
     * }
     *
     * var el = _.cloneDeepWith(document.body, customizer);
     *
     * console.log(el === document.body);
     * // => false
     * console.log(el.nodeName);
     * // => 'BODY'
     * console.log(el.childNodes.length);
     * // => 20
     */
    function cloneDeepWith(value, customizer) {
      return baseClone(value, true, true, customizer);
    }

    /**
     * Checks if `object` conforms to `source` by invoking the predicate
     * properties of `source` with the corresponding property values of `object`.
     *
     * **Note:** This method is equivalent to `_.conforms` when `source` is
     * partially applied.
     *
     * @static
     * @memberOf _
     * @since 4.14.0
     * @category Lang
     * @param {Object} object The object to inspect.
     * @param {Object} source The object of property predicates to conform to.
     * @returns {boolean} Returns `true` if `object` conforms, else `false`.
     * @example
     *
     * var object = { 'a': 1, 'b': 2 };
     *
     * _.conformsTo(object, { 'b': function(n) { return n > 1; } });
     * // => true
     *
     * _.conformsTo(object, { 'b': function(n) { return n > 2; } });
     * // => false
     */
    function conformsTo(object, source) {
      return source == null || baseConformsTo(object, source, keys(source));
    }

    /**
     * Performs a
     * [`SameValueZero`](http://ecma-international.org/ecma-262/7.0/#sec-samevaluezero)
     * comparison between two values to determine if they are equivalent.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if the values are equivalent, else `false`.
     * @example
     *
     * var object = { 'a': 1 };
     * var other = { 'a': 1 };
     *
     * _.eq(object, object);
     * // => true
     *
     * _.eq(object, other);
     * // => false
     *
     * _.eq('a', 'a');
     * // => true
     *
     * _.eq('a', Object('a'));
     * // => false
     *
     * _.eq(NaN, NaN);
     * // => true
     */
    function eq(value, other) {
      return value === other || (value !== value && other !== other);
    }

    /**
     * Checks if `value` is greater than `other`.
     *
     * @static
     * @memberOf _
     * @since 3.9.0
     * @category Lang
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if `value` is greater than `other`,
     *  else `false`.
     * @see _.lt
     * @example
     *
     * _.gt(3, 1);
     * // => true
     *
     * _.gt(3, 3);
     * // => false
     *
     * _.gt(1, 3);
     * // => false
     */
    var gt = createRelationalOperation(baseGt);

    /**
     * Checks if `value` is greater than or equal to `other`.
     *
     * @static
     * @memberOf _
     * @since 3.9.0
     * @category Lang
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if `value` is greater than or equal to
     *  `other`, else `false`.
     * @see _.lte
     * @example
     *
     * _.gte(3, 1);
     * // => true
     *
     * _.gte(3, 3);
     * // => true
     *
     * _.gte(1, 3);
     * // => false
     */
    var gte = createRelationalOperation(function(value, other) {
      return value >= other;
    });

    /**
     * Checks if `value` is likely an `arguments` object.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an `arguments` object,
     *  else `false`.
     * @example
     *
     * _.isArguments(function() { return arguments; }());
     * // => true
     *
     * _.isArguments([1, 2, 3]);
     * // => false
     */
    var isArguments = baseIsArguments(function() { return arguments; }()) ? baseIsArguments : function(value) {
      return isObjectLike(value) && hasOwnProperty.call(value, 'callee') &&
        !propertyIsEnumerable.call(value, 'callee');
    };

    /**
     * Checks if `value` is classified as an `Array` object.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an array, else `false`.
     * @example
     *
     * _.isArray([1, 2, 3]);
     * // => true
     *
     * _.isArray(document.body.children);
     * // => false
     *
     * _.isArray('abc');
     * // => false
     *
     * _.isArray(_.noop);
     * // => false
     */
    var isArray = Array.isArray;

    /**
     * Checks if `value` is classified as an `ArrayBuffer` object.
     *
     * @static
     * @memberOf _
     * @since 4.3.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an array buffer, else `false`.
     * @example
     *
     * _.isArrayBuffer(new ArrayBuffer(2));
     * // => true
     *
     * _.isArrayBuffer(new Array(2));
     * // => false
     */
    var isArrayBuffer = nodeIsArrayBuffer ? baseUnary(nodeIsArrayBuffer) : baseIsArrayBuffer;

    /**
     * Checks if `value` is array-like. A value is considered array-like if it's
     * not a function and has a `value.length` that's an integer greater than or
     * equal to `0` and less than or equal to `Number.MAX_SAFE_INTEGER`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is array-like, else `false`.
     * @example
     *
     * _.isArrayLike([1, 2, 3]);
     * // => true
     *
     * _.isArrayLike(document.body.children);
     * // => true
     *
     * _.isArrayLike('abc');
     * // => true
     *
     * _.isArrayLike(_.noop);
     * // => false
     */
    function isArrayLike(value) {
      return value != null && isLength(value.length) && !isFunction(value);
    }

    /**
     * This method is like `_.isArrayLike` except that it also checks if `value`
     * is an object.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an array-like object,
     *  else `false`.
     * @example
     *
     * _.isArrayLikeObject([1, 2, 3]);
     * // => true
     *
     * _.isArrayLikeObject(document.body.children);
     * // => true
     *
     * _.isArrayLikeObject('abc');
     * // => false
     *
     * _.isArrayLikeObject(_.noop);
     * // => false
     */
    function isArrayLikeObject(value) {
      return isObjectLike(value) && isArrayLike(value);
    }

    /**
     * Checks if `value` is classified as a boolean primitive or object.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a boolean, else `false`.
     * @example
     *
     * _.isBoolean(false);
     * // => true
     *
     * _.isBoolean(null);
     * // => false
     */
    function isBoolean(value) {
      return value === true || value === false ||
        (isObjectLike(value) && objectToString.call(value) == boolTag);
    }

    /**
     * Checks if `value` is a buffer.
     *
     * @static
     * @memberOf _
     * @since 4.3.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a buffer, else `false`.
     * @example
     *
     * _.isBuffer(new Buffer(2));
     * // => true
     *
     * _.isBuffer(new Uint8Array(2));
     * // => false
     */
    var isBuffer = nativeIsBuffer || stubFalse;

    /**
     * Checks if `value` is classified as a `Date` object.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a date object, else `false`.
     * @example
     *
     * _.isDate(new Date);
     * // => true
     *
     * _.isDate('Mon April 23 2012');
     * // => false
     */
    var isDate = nodeIsDate ? baseUnary(nodeIsDate) : baseIsDate;

    /**
     * Checks if `value` is likely a DOM element.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a DOM element, else `false`.
     * @example
     *
     * _.isElement(document.body);
     * // => true
     *
     * _.isElement('<body>');
     * // => false
     */
    function isElement(value) {
      return value != null && value.nodeType === 1 && isObjectLike(value) && !isPlainObject(value);
    }

    /**
     * Checks if `value` is an empty object, collection, map, or set.
     *
     * Objects are considered empty if they have no own enumerable string keyed
     * properties.
     *
     * Array-like values such as `arguments` objects, arrays, buffers, strings, or
     * jQuery-like collections are considered empty if they have a `length` of `0`.
     * Similarly, maps and sets are considered empty if they have a `size` of `0`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is empty, else `false`.
     * @example
     *
     * _.isEmpty(null);
     * // => true
     *
     * _.isEmpty(true);
     * // => true
     *
     * _.isEmpty(1);
     * // => true
     *
     * _.isEmpty([1, 2, 3]);
     * // => false
     *
     * _.isEmpty({ 'a': 1 });
     * // => false
     */
    function isEmpty(value) {
      if (isArrayLike(value) &&
          (isArray(value) || typeof value == 'string' || typeof value.splice == 'function' ||
            isBuffer(value) || isTypedArray(value) || isArguments(value))) {
        return !value.length;
      }
      var tag = getTag(value);
      if (tag == mapTag || tag == setTag) {
        return !value.size;
      }
      if (isPrototype(value)) {
        return !baseKeys(value).length;
      }
      for (var key in value) {
        if (hasOwnProperty.call(value, key)) {
          return false;
        }
      }
      return true;
    }

    /**
     * Performs a deep comparison between two values to determine if they are
     * equivalent.
     *
     * **Note:** This method supports comparing arrays, array buffers, booleans,
     * date objects, error objects, maps, numbers, `Object` objects, regexes,
     * sets, strings, symbols, and typed arrays. `Object` objects are compared
     * by their own, not inherited, enumerable properties. Functions and DOM
     * nodes are **not** supported.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if the values are equivalent, else `false`.
     * @example
     *
     * var object = { 'a': 1 };
     * var other = { 'a': 1 };
     *
     * _.isEqual(object, other);
     * // => true
     *
     * object === other;
     * // => false
     */
    function isEqual(value, other) {
      return baseIsEqual(value, other);
    }

    /**
     * This method is like `_.isEqual` except that it accepts `customizer` which
     * is invoked to compare values. If `customizer` returns `undefined`, comparisons
     * are handled by the method instead. The `customizer` is invoked with up to
     * six arguments: (objValue, othValue [, index|key, object, other, stack]).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @param {Function} [customizer] The function to customize comparisons.
     * @returns {boolean} Returns `true` if the values are equivalent, else `false`.
     * @example
     *
     * function isGreeting(value) {
     *   return /^h(?:i|ello)$/.test(value);
     * }
     *
     * function customizer(objValue, othValue) {
     *   if (isGreeting(objValue) && isGreeting(othValue)) {
     *     return true;
     *   }
     * }
     *
     * var array = ['hello', 'goodbye'];
     * var other = ['hi', 'goodbye'];
     *
     * _.isEqualWith(array, other, customizer);
     * // => true
     */
    function isEqualWith(value, other, customizer) {
      customizer = typeof customizer == 'function' ? customizer : undefined;
      var result = customizer ? customizer(value, other) : undefined;
      return result === undefined ? baseIsEqual(value, other, customizer) : !!result;
    }

    /**
     * Checks if `value` is an `Error`, `EvalError`, `RangeError`, `ReferenceError`,
     * `SyntaxError`, `TypeError`, or `URIError` object.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an error object, else `false`.
     * @example
     *
     * _.isError(new Error);
     * // => true
     *
     * _.isError(Error);
     * // => false
     */
    function isError(value) {
      if (!isObjectLike(value)) {
        return false;
      }
      return (objectToString.call(value) == errorTag) ||
        (typeof value.message == 'string' && typeof value.name == 'string');
    }

    /**
     * Checks if `value` is a finite primitive number.
     *
     * **Note:** This method is based on
     * [`Number.isFinite`](https://mdn.io/Number/isFinite).
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a finite number, else `false`.
     * @example
     *
     * _.isFinite(3);
     * // => true
     *
     * _.isFinite(Number.MIN_VALUE);
     * // => true
     *
     * _.isFinite(Infinity);
     * // => false
     *
     * _.isFinite('3');
     * // => false
     */
    function isFinite(value) {
      return typeof value == 'number' && nativeIsFinite(value);
    }

    /**
     * Checks if `value` is classified as a `Function` object.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a function, else `false`.
     * @example
     *
     * _.isFunction(_);
     * // => true
     *
     * _.isFunction(/abc/);
     * // => false
     */
    function isFunction(value) {
      // The use of `Object#toString` avoids issues with the `typeof` operator
      // in Safari 9 which returns 'object' for typed array and other constructors.
      var tag = isObject(value) ? objectToString.call(value) : '';
      return tag == funcTag || tag == genTag || tag == proxyTag;
    }

    /**
     * Checks if `value` is an integer.
     *
     * **Note:** This method is based on
     * [`Number.isInteger`](https://mdn.io/Number/isInteger).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an integer, else `false`.
     * @example
     *
     * _.isInteger(3);
     * // => true
     *
     * _.isInteger(Number.MIN_VALUE);
     * // => false
     *
     * _.isInteger(Infinity);
     * // => false
     *
     * _.isInteger('3');
     * // => false
     */
    function isInteger(value) {
      return typeof value == 'number' && value == toInteger(value);
    }

    /**
     * Checks if `value` is a valid array-like length.
     *
     * **Note:** This method is loosely based on
     * [`ToLength`](http://ecma-international.org/ecma-262/7.0/#sec-tolength).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a valid length, else `false`.
     * @example
     *
     * _.isLength(3);
     * // => true
     *
     * _.isLength(Number.MIN_VALUE);
     * // => false
     *
     * _.isLength(Infinity);
     * // => false
     *
     * _.isLength('3');
     * // => false
     */
    function isLength(value) {
      return typeof value == 'number' &&
        value > -1 && value % 1 == 0 && value <= MAX_SAFE_INTEGER;
    }

    /**
     * Checks if `value` is the
     * [language type](http://www.ecma-international.org/ecma-262/7.0/#sec-ecmascript-language-types)
     * of `Object`. (e.g. arrays, functions, objects, regexes, `new Number(0)`, and `new String('')`)
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is an object, else `false`.
     * @example
     *
     * _.isObject({});
     * // => true
     *
     * _.isObject([1, 2, 3]);
     * // => true
     *
     * _.isObject(_.noop);
     * // => true
     *
     * _.isObject(null);
     * // => false
     */
    function isObject(value) {
      var type = typeof value;
      return value != null && (type == 'object' || type == 'function');
    }

    /**
     * Checks if `value` is object-like. A value is object-like if it's not `null`
     * and has a `typeof` result of "object".
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is object-like, else `false`.
     * @example
     *
     * _.isObjectLike({});
     * // => true
     *
     * _.isObjectLike([1, 2, 3]);
     * // => true
     *
     * _.isObjectLike(_.noop);
     * // => false
     *
     * _.isObjectLike(null);
     * // => false
     */
    function isObjectLike(value) {
      return value != null && typeof value == 'object';
    }

    /**
     * Checks if `value` is classified as a `Map` object.
     *
     * @static
     * @memberOf _
     * @since 4.3.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a map, else `false`.
     * @example
     *
     * _.isMap(new Map);
     * // => true
     *
     * _.isMap(new WeakMap);
     * // => false
     */
    var isMap = nodeIsMap ? baseUnary(nodeIsMap) : baseIsMap;

    /**
     * Performs a partial deep comparison between `object` and `source` to
     * determine if `object` contains equivalent property values.
     *
     * **Note:** This method is equivalent to `_.matches` when `source` is
     * partially applied.
     *
     * Partial comparisons will match empty array and empty object `source`
     * values against any array or object value, respectively. See `_.isEqual`
     * for a list of supported value comparisons.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Lang
     * @param {Object} object The object to inspect.
     * @param {Object} source The object of property values to match.
     * @returns {boolean} Returns `true` if `object` is a match, else `false`.
     * @example
     *
     * var object = { 'a': 1, 'b': 2 };
     *
     * _.isMatch(object, { 'b': 2 });
     * // => true
     *
     * _.isMatch(object, { 'b': 1 });
     * // => false
     */
    function isMatch(object, source) {
      return object === source || baseIsMatch(object, source, getMatchData(source));
    }

    /**
     * This method is like `_.isMatch` except that it accepts `customizer` which
     * is invoked to compare values. If `customizer` returns `undefined`, comparisons
     * are handled by the method instead. The `customizer` is invoked with five
     * arguments: (objValue, srcValue, index|key, object, source).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {Object} object The object to inspect.
     * @param {Object} source The object of property values to match.
     * @param {Function} [customizer] The function to customize comparisons.
     * @returns {boolean} Returns `true` if `object` is a match, else `false`.
     * @example
     *
     * function isGreeting(value) {
     *   return /^h(?:i|ello)$/.test(value);
     * }
     *
     * function customizer(objValue, srcValue) {
     *   if (isGreeting(objValue) && isGreeting(srcValue)) {
     *     return true;
     *   }
     * }
     *
     * var object = { 'greeting': 'hello' };
     * var source = { 'greeting': 'hi' };
     *
     * _.isMatchWith(object, source, customizer);
     * // => true
     */
    function isMatchWith(object, source, customizer) {
      customizer = typeof customizer == 'function' ? customizer : undefined;
      return baseIsMatch(object, source, getMatchData(source), customizer);
    }

    /**
     * Checks if `value` is `NaN`.
     *
     * **Note:** This method is based on
     * [`Number.isNaN`](https://mdn.io/Number/isNaN) and is not the same as
     * global [`isNaN`](https://mdn.io/isNaN) which returns `true` for
     * `undefined` and other non-number values.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is `NaN`, else `false`.
     * @example
     *
     * _.isNaN(NaN);
     * // => true
     *
     * _.isNaN(new Number(NaN));
     * // => true
     *
     * isNaN(undefined);
     * // => true
     *
     * _.isNaN(undefined);
     * // => false
     */
    function isNaN(value) {
      // An `NaN` primitive is the only value that is not equal to itself.
      // Perform the `toStringTag` check first to avoid errors with some
      // ActiveX objects in IE.
      return isNumber(value) && value != +value;
    }

    /**
     * Checks if `value` is a pristine native function.
     *
     * **Note:** This method can't reliably detect native functions in the presence
     * of the core-js package because core-js circumvents this kind of detection.
     * Despite multiple requests, the core-js maintainer has made it clear: any
     * attempt to fix the detection will be obstructed. As a result, we're left
     * with little choice but to throw an error. Unfortunately, this also affects
     * packages, like [babel-polyfill](https://www.npmjs.com/package/babel-polyfill),
     * which rely on core-js.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a native function,
     *  else `false`.
     * @example
     *
     * _.isNative(Array.prototype.push);
     * // => true
     *
     * _.isNative(_);
     * // => false
     */
    function isNative(value) {
      if (isMaskable(value)) {
        throw new Error(CORE_ERROR_TEXT);
      }
      return baseIsNative(value);
    }

    /**
     * Checks if `value` is `null`.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is `null`, else `false`.
     * @example
     *
     * _.isNull(null);
     * // => true
     *
     * _.isNull(void 0);
     * // => false
     */
    function isNull(value) {
      return value === null;
    }

    /**
     * Checks if `value` is `null` or `undefined`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is nullish, else `false`.
     * @example
     *
     * _.isNil(null);
     * // => true
     *
     * _.isNil(void 0);
     * // => true
     *
     * _.isNil(NaN);
     * // => false
     */
    function isNil(value) {
      return value == null;
    }

    /**
     * Checks if `value` is classified as a `Number` primitive or object.
     *
     * **Note:** To exclude `Infinity`, `-Infinity`, and `NaN`, which are
     * classified as numbers, use the `_.isFinite` method.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a number, else `false`.
     * @example
     *
     * _.isNumber(3);
     * // => true
     *
     * _.isNumber(Number.MIN_VALUE);
     * // => true
     *
     * _.isNumber(Infinity);
     * // => true
     *
     * _.isNumber('3');
     * // => false
     */
    function isNumber(value) {
      return typeof value == 'number' ||
        (isObjectLike(value) && objectToString.call(value) == numberTag);
    }

    /**
     * Checks if `value` is a plain object, that is, an object created by the
     * `Object` constructor or one with a `[[Prototype]]` of `null`.
     *
     * @static
     * @memberOf _
     * @since 0.8.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a plain object, else `false`.
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     * }
     *
     * _.isPlainObject(new Foo);
     * // => false
     *
     * _.isPlainObject([1, 2, 3]);
     * // => false
     *
     * _.isPlainObject({ 'x': 0, 'y': 0 });
     * // => true
     *
     * _.isPlainObject(Object.create(null));
     * // => true
     */
    function isPlainObject(value) {
      if (!isObjectLike(value) || objectToString.call(value) != objectTag) {
        return false;
      }
      var proto = getPrototype(value);
      if (proto === null) {
        return true;
      }
      var Ctor = hasOwnProperty.call(proto, 'constructor') && proto.constructor;
      return (typeof Ctor == 'function' &&
        Ctor instanceof Ctor && funcToString.call(Ctor) == objectCtorString);
    }

    /**
     * Checks if `value` is classified as a `RegExp` object.
     *
     * @static
     * @memberOf _
     * @since 0.1.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a regexp, else `false`.
     * @example
     *
     * _.isRegExp(/abc/);
     * // => true
     *
     * _.isRegExp('/abc/');
     * // => false
     */
    var isRegExp = nodeIsRegExp ? baseUnary(nodeIsRegExp) : baseIsRegExp;

    /**
     * Checks if `value` is a safe integer. An integer is safe if it's an IEEE-754
     * double precision number which isn't the result of a rounded unsafe integer.
     *
     * **Note:** This method is based on
     * [`Number.isSafeInteger`](https://mdn.io/Number/isSafeInteger).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a safe integer, else `false`.
     * @example
     *
     * _.isSafeInteger(3);
     * // => true
     *
     * _.isSafeInteger(Number.MIN_VALUE);
     * // => false
     *
     * _.isSafeInteger(Infinity);
     * // => false
     *
     * _.isSafeInteger('3');
     * // => false
     */
    function isSafeInteger(value) {
      return isInteger(value) && value >= -MAX_SAFE_INTEGER && value <= MAX_SAFE_INTEGER;
    }

    /**
     * Checks if `value` is classified as a `Set` object.
     *
     * @static
     * @memberOf _
     * @since 4.3.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a set, else `false`.
     * @example
     *
     * _.isSet(new Set);
     * // => true
     *
     * _.isSet(new WeakSet);
     * // => false
     */
    var isSet = nodeIsSet ? baseUnary(nodeIsSet) : baseIsSet;

    /**
     * Checks if `value` is classified as a `String` primitive or object.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a string, else `false`.
     * @example
     *
     * _.isString('abc');
     * // => true
     *
     * _.isString(1);
     * // => false
     */
    function isString(value) {
      return typeof value == 'string' ||
        (!isArray(value) && isObjectLike(value) && objectToString.call(value) == stringTag);
    }

    /**
     * Checks if `value` is classified as a `Symbol` primitive or object.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a symbol, else `false`.
     * @example
     *
     * _.isSymbol(Symbol.iterator);
     * // => true
     *
     * _.isSymbol('abc');
     * // => false
     */
    function isSymbol(value) {
      return typeof value == 'symbol' ||
        (isObjectLike(value) && objectToString.call(value) == symbolTag);
    }

    /**
     * Checks if `value` is classified as a typed array.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a typed array, else `false`.
     * @example
     *
     * _.isTypedArray(new Uint8Array);
     * // => true
     *
     * _.isTypedArray([]);
     * // => false
     */
    var isTypedArray = nodeIsTypedArray ? baseUnary(nodeIsTypedArray) : baseIsTypedArray;

    /**
     * Checks if `value` is `undefined`.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.
     * @example
     *
     * _.isUndefined(void 0);
     * // => true
     *
     * _.isUndefined(null);
     * // => false
     */
    function isUndefined(value) {
      return value === undefined;
    }

    /**
     * Checks if `value` is classified as a `WeakMap` object.
     *
     * @static
     * @memberOf _
     * @since 4.3.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a weak map, else `false`.
     * @example
     *
     * _.isWeakMap(new WeakMap);
     * // => true
     *
     * _.isWeakMap(new Map);
     * // => false
     */
    function isWeakMap(value) {
      return isObjectLike(value) && getTag(value) == weakMapTag;
    }

    /**
     * Checks if `value` is classified as a `WeakSet` object.
     *
     * @static
     * @memberOf _
     * @since 4.3.0
     * @category Lang
     * @param {*} value The value to check.
     * @returns {boolean} Returns `true` if `value` is a weak set, else `false`.
     * @example
     *
     * _.isWeakSet(new WeakSet);
     * // => true
     *
     * _.isWeakSet(new Set);
     * // => false
     */
    function isWeakSet(value) {
      return isObjectLike(value) && objectToString.call(value) == weakSetTag;
    }

    /**
     * Checks if `value` is less than `other`.
     *
     * @static
     * @memberOf _
     * @since 3.9.0
     * @category Lang
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if `value` is less than `other`,
     *  else `false`.
     * @see _.gt
     * @example
     *
     * _.lt(1, 3);
     * // => true
     *
     * _.lt(3, 3);
     * // => false
     *
     * _.lt(3, 1);
     * // => false
     */
    var lt = createRelationalOperation(baseLt);

    /**
     * Checks if `value` is less than or equal to `other`.
     *
     * @static
     * @memberOf _
     * @since 3.9.0
     * @category Lang
     * @param {*} value The value to compare.
     * @param {*} other The other value to compare.
     * @returns {boolean} Returns `true` if `value` is less than or equal to
     *  `other`, else `false`.
     * @see _.gte
     * @example
     *
     * _.lte(1, 3);
     * // => true
     *
     * _.lte(3, 3);
     * // => true
     *
     * _.lte(3, 1);
     * // => false
     */
    var lte = createRelationalOperation(function(value, other) {
      return value <= other;
    });

    /**
     * Converts `value` to an array.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Lang
     * @param {*} value The value to convert.
     * @returns {Array} Returns the converted array.
     * @example
     *
     * _.toArray({ 'a': 1, 'b': 2 });
     * // => [1, 2]
     *
     * _.toArray('abc');
     * // => ['a', 'b', 'c']
     *
     * _.toArray(1);
     * // => []
     *
     * _.toArray(null);
     * // => []
     */
    function toArray(value) {
      if (!value) {
        return [];
      }
      if (isArrayLike(value)) {
        return isString(value) ? stringToArray(value) : copyArray(value);
      }
      if (iteratorSymbol && value[iteratorSymbol]) {
        return iteratorToArray(value[iteratorSymbol]());
      }
      var tag = getTag(value),
          func = tag == mapTag ? mapToArray : (tag == setTag ? setToArray : values);

      return func(value);
    }

    /**
     * Converts `value` to a finite number.
     *
     * @static
     * @memberOf _
     * @since 4.12.0
     * @category Lang
     * @param {*} value The value to convert.
     * @returns {number} Returns the converted number.
     * @example
     *
     * _.toFinite(3.2);
     * // => 3.2
     *
     * _.toFinite(Number.MIN_VALUE);
     * // => 5e-324
     *
     * _.toFinite(Infinity);
     * // => 1.7976931348623157e+308
     *
     * _.toFinite('3.2');
     * // => 3.2
     */
    function toFinite(value) {
      if (!value) {
        return value === 0 ? value : 0;
      }
      value = toNumber(value);
      if (value === INFINITY || value === -INFINITY) {
        var sign = (value < 0 ? -1 : 1);
        return sign * MAX_INTEGER;
      }
      return value === value ? value : 0;
    }

    /**
     * Converts `value` to an integer.
     *
     * **Note:** This method is loosely based on
     * [`ToInteger`](http://www.ecma-international.org/ecma-262/7.0/#sec-tointeger).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to convert.
     * @returns {number} Returns the converted integer.
     * @example
     *
     * _.toInteger(3.2);
     * // => 3
     *
     * _.toInteger(Number.MIN_VALUE);
     * // => 0
     *
     * _.toInteger(Infinity);
     * // => 1.7976931348623157e+308
     *
     * _.toInteger('3.2');
     * // => 3
     */
    function toInteger(value) {
      var result = toFinite(value),
          remainder = result % 1;

      return result === result ? (remainder ? result - remainder : result) : 0;
    }

    /**
     * Converts `value` to an integer suitable for use as the length of an
     * array-like object.
     *
     * **Note:** This method is based on
     * [`ToLength`](http://ecma-international.org/ecma-262/7.0/#sec-tolength).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to convert.
     * @returns {number} Returns the converted integer.
     * @example
     *
     * _.toLength(3.2);
     * // => 3
     *
     * _.toLength(Number.MIN_VALUE);
     * // => 0
     *
     * _.toLength(Infinity);
     * // => 4294967295
     *
     * _.toLength('3.2');
     * // => 3
     */
    function toLength(value) {
      return value ? baseClamp(toInteger(value), 0, MAX_ARRAY_LENGTH) : 0;
    }

    /**
     * Converts `value` to a number.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to process.
     * @returns {number} Returns the number.
     * @example
     *
     * _.toNumber(3.2);
     * // => 3.2
     *
     * _.toNumber(Number.MIN_VALUE);
     * // => 5e-324
     *
     * _.toNumber(Infinity);
     * // => Infinity
     *
     * _.toNumber('3.2');
     * // => 3.2
     */
    function toNumber(value) {
      if (typeof value == 'number') {
        return value;
      }
      if (isSymbol(value)) {
        return NAN;
      }
      if (isObject(value)) {
        var other = typeof value.valueOf == 'function' ? value.valueOf() : value;
        value = isObject(other) ? (other + '') : other;
      }
      if (typeof value != 'string') {
        return value === 0 ? value : +value;
      }
      value = value.replace(reTrim, '');
      var isBinary = reIsBinary.test(value);
      return (isBinary || reIsOctal.test(value))
        ? freeParseInt(value.slice(2), isBinary ? 2 : 8)
        : (reIsBadHex.test(value) ? NAN : +value);
    }

    /**
     * Converts `value` to a plain object flattening inherited enumerable string
     * keyed properties of `value` to own properties of the plain object.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Lang
     * @param {*} value The value to convert.
     * @returns {Object} Returns the converted plain object.
     * @example
     *
     * function Foo() {
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.assign({ 'a': 1 }, new Foo);
     * // => { 'a': 1, 'b': 2 }
     *
     * _.assign({ 'a': 1 }, _.toPlainObject(new Foo));
     * // => { 'a': 1, 'b': 2, 'c': 3 }
     */
    function toPlainObject(value) {
      return copyObject(value, keysIn(value));
    }

    /**
     * Converts `value` to a safe integer. A safe integer can be compared and
     * represented correctly.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to convert.
     * @returns {number} Returns the converted integer.
     * @example
     *
     * _.toSafeInteger(3.2);
     * // => 3
     *
     * _.toSafeInteger(Number.MIN_VALUE);
     * // => 0
     *
     * _.toSafeInteger(Infinity);
     * // => 9007199254740991
     *
     * _.toSafeInteger('3.2');
     * // => 3
     */
    function toSafeInteger(value) {
      return baseClamp(toInteger(value), -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER);
    }

    /**
     * Converts `value` to a string. An empty string is returned for `null`
     * and `undefined` values. The sign of `-0` is preserved.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Lang
     * @param {*} value The value to convert.
     * @returns {string} Returns the converted string.
     * @example
     *
     * _.toString(null);
     * // => ''
     *
     * _.toString(-0);
     * // => '-0'
     *
     * _.toString([1, 2, 3]);
     * // => '1,2,3'
     */
    function toString(value) {
      return value == null ? '' : baseToString(value);
    }

    /*------------------------------------------------------------------------*/

    /**
     * Assigns own enumerable string keyed properties of source objects to the
     * destination object. Source objects are applied from left to right.
     * Subsequent sources overwrite property assignments of previous sources.
     *
     * **Note:** This method mutates `object` and is loosely based on
     * [`Object.assign`](https://mdn.io/Object/assign).
     *
     * @static
     * @memberOf _
     * @since 0.10.0
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} [sources] The source objects.
     * @returns {Object} Returns `object`.
     * @see _.assignIn
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     * }
     *
     * function Bar() {
     *   this.c = 3;
     * }
     *
     * Foo.prototype.b = 2;
     * Bar.prototype.d = 4;
     *
     * _.assign({ 'a': 0 }, new Foo, new Bar);
     * // => { 'a': 1, 'c': 3 }
     */
    var assign = createAssigner(function(object, source) {
      if (isPrototype(source) || isArrayLike(source)) {
        copyObject(source, keys(source), object);
        return;
      }
      for (var key in source) {
        if (hasOwnProperty.call(source, key)) {
          assignValue(object, key, source[key]);
        }
      }
    });

    /**
     * This method is like `_.assign` except that it iterates over own and
     * inherited source properties.
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @alias extend
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} [sources] The source objects.
     * @returns {Object} Returns `object`.
     * @see _.assign
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     * }
     *
     * function Bar() {
     *   this.c = 3;
     * }
     *
     * Foo.prototype.b = 2;
     * Bar.prototype.d = 4;
     *
     * _.assignIn({ 'a': 0 }, new Foo, new Bar);
     * // => { 'a': 1, 'b': 2, 'c': 3, 'd': 4 }
     */
    var assignIn = createAssigner(function(object, source) {
      copyObject(source, keysIn(source), object);
    });

    /**
     * This method is like `_.assignIn` except that it accepts `customizer`
     * which is invoked to produce the assigned values. If `customizer` returns
     * `undefined`, assignment is handled by the method instead. The `customizer`
     * is invoked with five arguments: (objValue, srcValue, key, object, source).
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @alias extendWith
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} sources The source objects.
     * @param {Function} [customizer] The function to customize assigned values.
     * @returns {Object} Returns `object`.
     * @see _.assignWith
     * @example
     *
     * function customizer(objValue, srcValue) {
     *   return _.isUndefined(objValue) ? srcValue : objValue;
     * }
     *
     * var defaults = _.partialRight(_.assignInWith, customizer);
     *
     * defaults({ 'a': 1 }, { 'b': 2 }, { 'a': 3 });
     * // => { 'a': 1, 'b': 2 }
     */
    var assignInWith = createAssigner(function(object, source, srcIndex, customizer) {
      copyObject(source, keysIn(source), object, customizer);
    });

    /**
     * This method is like `_.assign` except that it accepts `customizer`
     * which is invoked to produce the assigned values. If `customizer` returns
     * `undefined`, assignment is handled by the method instead. The `customizer`
     * is invoked with five arguments: (objValue, srcValue, key, object, source).
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} sources The source objects.
     * @param {Function} [customizer] The function to customize assigned values.
     * @returns {Object} Returns `object`.
     * @see _.assignInWith
     * @example
     *
     * function customizer(objValue, srcValue) {
     *   return _.isUndefined(objValue) ? srcValue : objValue;
     * }
     *
     * var defaults = _.partialRight(_.assignWith, customizer);
     *
     * defaults({ 'a': 1 }, { 'b': 2 }, { 'a': 3 });
     * // => { 'a': 1, 'b': 2 }
     */
    var assignWith = createAssigner(function(object, source, srcIndex, customizer) {
      copyObject(source, keys(source), object, customizer);
    });

    /**
     * Creates an array of values corresponding to `paths` of `object`.
     *
     * @static
     * @memberOf _
     * @since 1.0.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {...(string|string[])} [paths] The property paths of elements to pick.
     * @returns {Array} Returns the picked values.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c': 3 } }, 4] };
     *
     * _.at(object, ['a[0].b.c', 'a[1]']);
     * // => [3, 4]
     */
    var at = flatRest(baseAt);

    /**
     * Creates an object that inherits from the `prototype` object. If a
     * `properties` object is given, its own enumerable string keyed properties
     * are assigned to the created object.
     *
     * @static
     * @memberOf _
     * @since 2.3.0
     * @category Object
     * @param {Object} prototype The object to inherit from.
     * @param {Object} [properties] The properties to assign to the object.
     * @returns {Object} Returns the new object.
     * @example
     *
     * function Shape() {
     *   this.x = 0;
     *   this.y = 0;
     * }
     *
     * function Circle() {
     *   Shape.call(this);
     * }
     *
     * Circle.prototype = _.create(Shape.prototype, {
     *   'constructor': Circle
     * });
     *
     * var circle = new Circle;
     * circle instanceof Circle;
     * // => true
     *
     * circle instanceof Shape;
     * // => true
     */
    function create(prototype, properties) {
      var result = baseCreate(prototype);
      return properties ? baseAssign(result, properties) : result;
    }

    /**
     * Assigns own and inherited enumerable string keyed properties of source
     * objects to the destination object for all destination properties that
     * resolve to `undefined`. Source objects are applied from left to right.
     * Once a property is set, additional values of the same property are ignored.
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} [sources] The source objects.
     * @returns {Object} Returns `object`.
     * @see _.defaultsDeep
     * @example
     *
     * _.defaults({ 'a': 1 }, { 'b': 2 }, { 'a': 3 });
     * // => { 'a': 1, 'b': 2 }
     */
    var defaults = baseRest(function(args) {
      args.push(undefined, assignInDefaults);
      return apply(assignInWith, undefined, args);
    });

    /**
     * This method is like `_.defaults` except that it recursively assigns
     * default properties.
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 3.10.0
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} [sources] The source objects.
     * @returns {Object} Returns `object`.
     * @see _.defaults
     * @example
     *
     * _.defaultsDeep({ 'a': { 'b': 2 } }, { 'a': { 'b': 1, 'c': 3 } });
     * // => { 'a': { 'b': 2, 'c': 3 } }
     */
    var defaultsDeep = baseRest(function(args) {
      args.push(undefined, mergeDefaults);
      return apply(mergeWith, undefined, args);
    });

    /**
     * This method is like `_.find` except that it returns the key of the first
     * element `predicate` returns truthy for instead of the element itself.
     *
     * @static
     * @memberOf _
     * @since 1.1.0
     * @category Object
     * @param {Object} object The object to inspect.
     * @param {Function} [predicate=_.identity] The function invoked per iteration.
     * @returns {string|undefined} Returns the key of the matched element,
     *  else `undefined`.
     * @example
     *
     * var users = {
     *   'barney':  { 'age': 36, 'active': true },
     *   'fred':    { 'age': 40, 'active': false },
     *   'pebbles': { 'age': 1,  'active': true }
     * };
     *
     * _.findKey(users, function(o) { return o.age < 40; });
     * // => 'barney' (iteration order is not guaranteed)
     *
     * // The `_.matches` iteratee shorthand.
     * _.findKey(users, { 'age': 1, 'active': true });
     * // => 'pebbles'
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.findKey(users, ['active', false]);
     * // => 'fred'
     *
     * // The `_.property` iteratee shorthand.
     * _.findKey(users, 'active');
     * // => 'barney'
     */
    function findKey(object, predicate) {
      return baseFindKey(object, getIteratee(predicate, 3), baseForOwn);
    }

    /**
     * This method is like `_.findKey` except that it iterates over elements of
     * a collection in the opposite order.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Object
     * @param {Object} object The object to inspect.
     * @param {Function} [predicate=_.identity] The function invoked per iteration.
     * @returns {string|undefined} Returns the key of the matched element,
     *  else `undefined`.
     * @example
     *
     * var users = {
     *   'barney':  { 'age': 36, 'active': true },
     *   'fred':    { 'age': 40, 'active': false },
     *   'pebbles': { 'age': 1,  'active': true }
     * };
     *
     * _.findLastKey(users, function(o) { return o.age < 40; });
     * // => returns 'pebbles' assuming `_.findKey` returns 'barney'
     *
     * // The `_.matches` iteratee shorthand.
     * _.findLastKey(users, { 'age': 36, 'active': true });
     * // => 'barney'
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.findLastKey(users, ['active', false]);
     * // => 'fred'
     *
     * // The `_.property` iteratee shorthand.
     * _.findLastKey(users, 'active');
     * // => 'pebbles'
     */
    function findLastKey(object, predicate) {
      return baseFindKey(object, getIteratee(predicate, 3), baseForOwnRight);
    }

    /**
     * Iterates over own and inherited enumerable string keyed properties of an
     * object and invokes `iteratee` for each property. The iteratee is invoked
     * with three arguments: (value, key, object). Iteratee functions may exit
     * iteration early by explicitly returning `false`.
     *
     * @static
     * @memberOf _
     * @since 0.3.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Object} Returns `object`.
     * @see _.forInRight
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.forIn(new Foo, function(value, key) {
     *   console.log(key);
     * });
     * // => Logs 'a', 'b', then 'c' (iteration order is not guaranteed).
     */
    function forIn(object, iteratee) {
      return object == null
        ? object
        : baseFor(object, getIteratee(iteratee, 3), keysIn);
    }

    /**
     * This method is like `_.forIn` except that it iterates over properties of
     * `object` in the opposite order.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Object} Returns `object`.
     * @see _.forIn
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.forInRight(new Foo, function(value, key) {
     *   console.log(key);
     * });
     * // => Logs 'c', 'b', then 'a' assuming `_.forIn` logs 'a', 'b', then 'c'.
     */
    function forInRight(object, iteratee) {
      return object == null
        ? object
        : baseForRight(object, getIteratee(iteratee, 3), keysIn);
    }

    /**
     * Iterates over own enumerable string keyed properties of an object and
     * invokes `iteratee` for each property. The iteratee is invoked with three
     * arguments: (value, key, object). Iteratee functions may exit iteration
     * early by explicitly returning `false`.
     *
     * @static
     * @memberOf _
     * @since 0.3.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Object} Returns `object`.
     * @see _.forOwnRight
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.forOwn(new Foo, function(value, key) {
     *   console.log(key);
     * });
     * // => Logs 'a' then 'b' (iteration order is not guaranteed).
     */
    function forOwn(object, iteratee) {
      return object && baseForOwn(object, getIteratee(iteratee, 3));
    }

    /**
     * This method is like `_.forOwn` except that it iterates over properties of
     * `object` in the opposite order.
     *
     * @static
     * @memberOf _
     * @since 2.0.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Object} Returns `object`.
     * @see _.forOwn
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.forOwnRight(new Foo, function(value, key) {
     *   console.log(key);
     * });
     * // => Logs 'b' then 'a' assuming `_.forOwn` logs 'a' then 'b'.
     */
    function forOwnRight(object, iteratee) {
      return object && baseForOwnRight(object, getIteratee(iteratee, 3));
    }

    /**
     * Creates an array of function property names from own enumerable properties
     * of `object`.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The object to inspect.
     * @returns {Array} Returns the function names.
     * @see _.functionsIn
     * @example
     *
     * function Foo() {
     *   this.a = _.constant('a');
     *   this.b = _.constant('b');
     * }
     *
     * Foo.prototype.c = _.constant('c');
     *
     * _.functions(new Foo);
     * // => ['a', 'b']
     */
    function functions(object) {
      return object == null ? [] : baseFunctions(object, keys(object));
    }

    /**
     * Creates an array of function property names from own and inherited
     * enumerable properties of `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The object to inspect.
     * @returns {Array} Returns the function names.
     * @see _.functions
     * @example
     *
     * function Foo() {
     *   this.a = _.constant('a');
     *   this.b = _.constant('b');
     * }
     *
     * Foo.prototype.c = _.constant('c');
     *
     * _.functionsIn(new Foo);
     * // => ['a', 'b', 'c']
     */
    function functionsIn(object) {
      return object == null ? [] : baseFunctions(object, keysIn(object));
    }

    /**
     * Gets the value at `path` of `object`. If the resolved value is
     * `undefined`, the `defaultValue` is returned in its place.
     *
     * @static
     * @memberOf _
     * @since 3.7.0
     * @category Object
     * @param {Object} object The object to query.
     * @param {Array|string} path The path of the property to get.
     * @param {*} [defaultValue] The value returned for `undefined` resolved values.
     * @returns {*} Returns the resolved value.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c': 3 } }] };
     *
     * _.get(object, 'a[0].b.c');
     * // => 3
     *
     * _.get(object, ['a', '0', 'b', 'c']);
     * // => 3
     *
     * _.get(object, 'a.b.c', 'default');
     * // => 'default'
     */
    function get(object, path, defaultValue) {
      var result = object == null ? undefined : baseGet(object, path);
      return result === undefined ? defaultValue : result;
    }

    /**
     * Checks if `path` is a direct property of `object`.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The object to query.
     * @param {Array|string} path The path to check.
     * @returns {boolean} Returns `true` if `path` exists, else `false`.
     * @example
     *
     * var object = { 'a': { 'b': 2 } };
     * var other = _.create({ 'a': _.create({ 'b': 2 }) });
     *
     * _.has(object, 'a');
     * // => true
     *
     * _.has(object, 'a.b');
     * // => true
     *
     * _.has(object, ['a', 'b']);
     * // => true
     *
     * _.has(other, 'a');
     * // => false
     */
    function has(object, path) {
      return object != null && hasPath(object, path, baseHas);
    }

    /**
     * Checks if `path` is a direct or inherited property of `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The object to query.
     * @param {Array|string} path The path to check.
     * @returns {boolean} Returns `true` if `path` exists, else `false`.
     * @example
     *
     * var object = _.create({ 'a': _.create({ 'b': 2 }) });
     *
     * _.hasIn(object, 'a');
     * // => true
     *
     * _.hasIn(object, 'a.b');
     * // => true
     *
     * _.hasIn(object, ['a', 'b']);
     * // => true
     *
     * _.hasIn(object, 'b');
     * // => false
     */
    function hasIn(object, path) {
      return object != null && hasPath(object, path, baseHasIn);
    }

    /**
     * Creates an object composed of the inverted keys and values of `object`.
     * If `object` contains duplicate values, subsequent values overwrite
     * property assignments of previous values.
     *
     * @static
     * @memberOf _
     * @since 0.7.0
     * @category Object
     * @param {Object} object The object to invert.
     * @returns {Object} Returns the new inverted object.
     * @example
     *
     * var object = { 'a': 1, 'b': 2, 'c': 1 };
     *
     * _.invert(object);
     * // => { '1': 'c', '2': 'b' }
     */
    var invert = createInverter(function(result, value, key) {
      result[value] = key;
    }, constant(identity));

    /**
     * This method is like `_.invert` except that the inverted object is generated
     * from the results of running each element of `object` thru `iteratee`. The
     * corresponding inverted value of each inverted key is an array of keys
     * responsible for generating the inverted value. The iteratee is invoked
     * with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.1.0
     * @category Object
     * @param {Object} object The object to invert.
     * @param {Function} [iteratee=_.identity] The iteratee invoked per element.
     * @returns {Object} Returns the new inverted object.
     * @example
     *
     * var object = { 'a': 1, 'b': 2, 'c': 1 };
     *
     * _.invertBy(object);
     * // => { '1': ['a', 'c'], '2': ['b'] }
     *
     * _.invertBy(object, function(value) {
     *   return 'group' + value;
     * });
     * // => { 'group1': ['a', 'c'], 'group2': ['b'] }
     */
    var invertBy = createInverter(function(result, value, key) {
      if (hasOwnProperty.call(result, value)) {
        result[value].push(key);
      } else {
        result[value] = [key];
      }
    }, getIteratee);

    /**
     * Invokes the method at `path` of `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The object to query.
     * @param {Array|string} path The path of the method to invoke.
     * @param {...*} [args] The arguments to invoke the method with.
     * @returns {*} Returns the result of the invoked method.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c': [1, 2, 3, 4] } }] };
     *
     * _.invoke(object, 'a[0].b.c.slice', 1, 3);
     * // => [2, 3]
     */
    var invoke = baseRest(baseInvoke);

    /**
     * Creates an array of the own enumerable property names of `object`.
     *
     * **Note:** Non-object values are coerced to objects. See the
     * [ES spec](http://ecma-international.org/ecma-262/7.0/#sec-object.keys)
     * for more details.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property names.
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.keys(new Foo);
     * // => ['a', 'b'] (iteration order is not guaranteed)
     *
     * _.keys('hi');
     * // => ['0', '1']
     */
    function keys(object) {
      return isArrayLike(object) ? arrayLikeKeys(object) : baseKeys(object);
    }

    /**
     * Creates an array of the own and inherited enumerable property names of `object`.
     *
     * **Note:** Non-object values are coerced to objects.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Object
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property names.
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.keysIn(new Foo);
     * // => ['a', 'b', 'c'] (iteration order is not guaranteed)
     */
    function keysIn(object) {
      return isArrayLike(object) ? arrayLikeKeys(object, true) : baseKeysIn(object);
    }

    /**
     * The opposite of `_.mapValues`; this method creates an object with the
     * same values as `object` and keys generated by running each own enumerable
     * string keyed property of `object` thru `iteratee`. The iteratee is invoked
     * with three arguments: (value, key, object).
     *
     * @static
     * @memberOf _
     * @since 3.8.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Object} Returns the new mapped object.
     * @see _.mapValues
     * @example
     *
     * _.mapKeys({ 'a': 1, 'b': 2 }, function(value, key) {
     *   return key + value;
     * });
     * // => { 'a1': 1, 'b2': 2 }
     */
    function mapKeys(object, iteratee) {
      var result = {};
      iteratee = getIteratee(iteratee, 3);

      baseForOwn(object, function(value, key, object) {
        baseAssignValue(result, iteratee(value, key, object), value);
      });
      return result;
    }

    /**
     * Creates an object with the same keys as `object` and values generated
     * by running each own enumerable string keyed property of `object` thru
     * `iteratee`. The iteratee is invoked with three arguments:
     * (value, key, object).
     *
     * @static
     * @memberOf _
     * @since 2.4.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Object} Returns the new mapped object.
     * @see _.mapKeys
     * @example
     *
     * var users = {
     *   'fred':    { 'user': 'fred',    'age': 40 },
     *   'pebbles': { 'user': 'pebbles', 'age': 1 }
     * };
     *
     * _.mapValues(users, function(o) { return o.age; });
     * // => { 'fred': 40, 'pebbles': 1 } (iteration order is not guaranteed)
     *
     * // The `_.property` iteratee shorthand.
     * _.mapValues(users, 'age');
     * // => { 'fred': 40, 'pebbles': 1 } (iteration order is not guaranteed)
     */
    function mapValues(object, iteratee) {
      var result = {};
      iteratee = getIteratee(iteratee, 3);

      baseForOwn(object, function(value, key, object) {
        baseAssignValue(result, key, iteratee(value, key, object));
      });
      return result;
    }

    /**
     * This method is like `_.assign` except that it recursively merges own and
     * inherited enumerable string keyed properties of source objects into the
     * destination object. Source properties that resolve to `undefined` are
     * skipped if a destination value exists. Array and plain object properties
     * are merged recursively. Other objects and value types are overridden by
     * assignment. Source objects are applied from left to right. Subsequent
     * sources overwrite property assignments of previous sources.
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 0.5.0
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} [sources] The source objects.
     * @returns {Object} Returns `object`.
     * @example
     *
     * var object = {
     *   'a': [{ 'b': 2 }, { 'd': 4 }]
     * };
     *
     * var other = {
     *   'a': [{ 'c': 3 }, { 'e': 5 }]
     * };
     *
     * _.merge(object, other);
     * // => { 'a': [{ 'b': 2, 'c': 3 }, { 'd': 4, 'e': 5 }] }
     */
    var merge = createAssigner(function(object, source, srcIndex) {
      baseMerge(object, source, srcIndex);
    });

    /**
     * This method is like `_.merge` except that it accepts `customizer` which
     * is invoked to produce the merged values of the destination and source
     * properties. If `customizer` returns `undefined`, merging is handled by the
     * method instead. The `customizer` is invoked with six arguments:
     * (objValue, srcValue, key, object, source, stack).
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The destination object.
     * @param {...Object} sources The source objects.
     * @param {Function} customizer The function to customize assigned values.
     * @returns {Object} Returns `object`.
     * @example
     *
     * function customizer(objValue, srcValue) {
     *   if (_.isArray(objValue)) {
     *     return objValue.concat(srcValue);
     *   }
     * }
     *
     * var object = { 'a': [1], 'b': [2] };
     * var other = { 'a': [3], 'b': [4] };
     *
     * _.mergeWith(object, other, customizer);
     * // => { 'a': [1, 3], 'b': [2, 4] }
     */
    var mergeWith = createAssigner(function(object, source, srcIndex, customizer) {
      baseMerge(object, source, srcIndex, customizer);
    });

    /**
     * The opposite of `_.pick`; this method creates an object composed of the
     * own and inherited enumerable string keyed properties of `object` that are
     * not omitted.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The source object.
     * @param {...(string|string[])} [props] The property identifiers to omit.
     * @returns {Object} Returns the new object.
     * @example
     *
     * var object = { 'a': 1, 'b': '2', 'c': 3 };
     *
     * _.omit(object, ['a', 'c']);
     * // => { 'b': '2' }
     */
    var omit = flatRest(function(object, props) {
      if (object == null) {
        return {};
      }
      props = arrayMap(props, toKey);
      return basePick(object, baseDifference(getAllKeysIn(object), props));
    });

    /**
     * The opposite of `_.pickBy`; this method creates an object composed of
     * the own and inherited enumerable string keyed properties of `object` that
     * `predicate` doesn't return truthy for. The predicate is invoked with two
     * arguments: (value, key).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The source object.
     * @param {Function} [predicate=_.identity] The function invoked per property.
     * @returns {Object} Returns the new object.
     * @example
     *
     * var object = { 'a': 1, 'b': '2', 'c': 3 };
     *
     * _.omitBy(object, _.isNumber);
     * // => { 'b': '2' }
     */
    function omitBy(object, predicate) {
      return pickBy(object, negate(getIteratee(predicate)));
    }

    /**
     * Creates an object composed of the picked `object` properties.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The source object.
     * @param {...(string|string[])} [props] The property identifiers to pick.
     * @returns {Object} Returns the new object.
     * @example
     *
     * var object = { 'a': 1, 'b': '2', 'c': 3 };
     *
     * _.pick(object, ['a', 'c']);
     * // => { 'a': 1, 'c': 3 }
     */
    var pick = flatRest(function(object, props) {
      return object == null ? {} : basePick(object, arrayMap(props, toKey));
    });

    /**
     * Creates an object composed of the `object` properties `predicate` returns
     * truthy for. The predicate is invoked with two arguments: (value, key).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The source object.
     * @param {Function} [predicate=_.identity] The function invoked per property.
     * @returns {Object} Returns the new object.
     * @example
     *
     * var object = { 'a': 1, 'b': '2', 'c': 3 };
     *
     * _.pickBy(object, _.isNumber);
     * // => { 'a': 1, 'c': 3 }
     */
    function pickBy(object, predicate) {
      return object == null ? {} : basePickBy(object, getAllKeysIn(object), getIteratee(predicate));
    }

    /**
     * This method is like `_.get` except that if the resolved value is a
     * function it's invoked with the `this` binding of its parent object and
     * its result is returned.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The object to query.
     * @param {Array|string} path The path of the property to resolve.
     * @param {*} [defaultValue] The value returned for `undefined` resolved values.
     * @returns {*} Returns the resolved value.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c1': 3, 'c2': _.constant(4) } }] };
     *
     * _.result(object, 'a[0].b.c1');
     * // => 3
     *
     * _.result(object, 'a[0].b.c2');
     * // => 4
     *
     * _.result(object, 'a[0].b.c3', 'default');
     * // => 'default'
     *
     * _.result(object, 'a[0].b.c3', _.constant('default'));
     * // => 'default'
     */
    function result(object, path, defaultValue) {
      path = isKey(path, object) ? [path] : castPath(path);

      var index = -1,
          length = path.length;

      // Ensure the loop is entered when path is empty.
      if (!length) {
        object = undefined;
        length = 1;
      }
      while (++index < length) {
        var value = object == null ? undefined : object[toKey(path[index])];
        if (value === undefined) {
          index = length;
          value = defaultValue;
        }
        object = isFunction(value) ? value.call(object) : value;
      }
      return object;
    }

    /**
     * Sets the value at `path` of `object`. If a portion of `path` doesn't exist,
     * it's created. Arrays are created for missing index properties while objects
     * are created for all other missing properties. Use `_.setWith` to customize
     * `path` creation.
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 3.7.0
     * @category Object
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to set.
     * @param {*} value The value to set.
     * @returns {Object} Returns `object`.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c': 3 } }] };
     *
     * _.set(object, 'a[0].b.c', 4);
     * console.log(object.a[0].b.c);
     * // => 4
     *
     * _.set(object, ['x', '0', 'y', 'z'], 5);
     * console.log(object.x[0].y.z);
     * // => 5
     */
    function set(object, path, value) {
      return object == null ? object : baseSet(object, path, value);
    }

    /**
     * This method is like `_.set` except that it accepts `customizer` which is
     * invoked to produce the objects of `path`.  If `customizer` returns `undefined`
     * path creation is handled by the method instead. The `customizer` is invoked
     * with three arguments: (nsValue, key, nsObject).
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to set.
     * @param {*} value The value to set.
     * @param {Function} [customizer] The function to customize assigned values.
     * @returns {Object} Returns `object`.
     * @example
     *
     * var object = {};
     *
     * _.setWith(object, '[0][1]', 'a', Object);
     * // => { '0': { '1': 'a' } }
     */
    function setWith(object, path, value, customizer) {
      customizer = typeof customizer == 'function' ? customizer : undefined;
      return object == null ? object : baseSet(object, path, value, customizer);
    }

    /**
     * Creates an array of own enumerable string keyed-value pairs for `object`
     * which can be consumed by `_.fromPairs`. If `object` is a map or set, its
     * entries are returned.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @alias entries
     * @category Object
     * @param {Object} object The object to query.
     * @returns {Array} Returns the key-value pairs.
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.toPairs(new Foo);
     * // => [['a', 1], ['b', 2]] (iteration order is not guaranteed)
     */
    var toPairs = createToPairs(keys);

    /**
     * Creates an array of own and inherited enumerable string keyed-value pairs
     * for `object` which can be consumed by `_.fromPairs`. If `object` is a map
     * or set, its entries are returned.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @alias entriesIn
     * @category Object
     * @param {Object} object The object to query.
     * @returns {Array} Returns the key-value pairs.
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.toPairsIn(new Foo);
     * // => [['a', 1], ['b', 2], ['c', 3]] (iteration order is not guaranteed)
     */
    var toPairsIn = createToPairs(keysIn);

    /**
     * An alternative to `_.reduce`; this method transforms `object` to a new
     * `accumulator` object which is the result of running each of its own
     * enumerable string keyed properties thru `iteratee`, with each invocation
     * potentially mutating the `accumulator` object. If `accumulator` is not
     * provided, a new object with the same `[[Prototype]]` will be used. The
     * iteratee is invoked with four arguments: (accumulator, value, key, object).
     * Iteratee functions may exit iteration early by explicitly returning `false`.
     *
     * @static
     * @memberOf _
     * @since 1.3.0
     * @category Object
     * @param {Object} object The object to iterate over.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @param {*} [accumulator] The custom accumulator value.
     * @returns {*} Returns the accumulated value.
     * @example
     *
     * _.transform([2, 3, 4], function(result, n) {
     *   result.push(n *= n);
     *   return n % 2 == 0;
     * }, []);
     * // => [4, 9]
     *
     * _.transform({ 'a': 1, 'b': 2, 'c': 1 }, function(result, value, key) {
     *   (result[value] || (result[value] = [])).push(key);
     * }, {});
     * // => { '1': ['a', 'c'], '2': ['b'] }
     */
    function transform(object, iteratee, accumulator) {
      var isArr = isArray(object),
          isArrLike = isArr || isBuffer(object) || isTypedArray(object);

      iteratee = getIteratee(iteratee, 4);
      if (accumulator == null) {
        var Ctor = object && object.constructor;
        if (isArrLike) {
          accumulator = isArr ? new Ctor : [];
        }
        else if (isObject(object)) {
          accumulator = isFunction(Ctor) ? baseCreate(getPrototype(object)) : {};
        }
        else {
          accumulator = {};
        }
      }
      (isArrLike ? arrayEach : baseForOwn)(object, function(value, index, object) {
        return iteratee(accumulator, value, index, object);
      });
      return accumulator;
    }

    /**
     * Removes the property at `path` of `object`.
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Object
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to unset.
     * @returns {boolean} Returns `true` if the property is deleted, else `false`.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c': 7 } }] };
     * _.unset(object, 'a[0].b.c');
     * // => true
     *
     * console.log(object);
     * // => { 'a': [{ 'b': {} }] };
     *
     * _.unset(object, ['a', '0', 'b', 'c']);
     * // => true
     *
     * console.log(object);
     * // => { 'a': [{ 'b': {} }] };
     */
    function unset(object, path) {
      return object == null ? true : baseUnset(object, path);
    }

    /**
     * This method is like `_.set` except that accepts `updater` to produce the
     * value to set. Use `_.updateWith` to customize `path` creation. The `updater`
     * is invoked with one argument: (value).
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.6.0
     * @category Object
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to set.
     * @param {Function} updater The function to produce the updated value.
     * @returns {Object} Returns `object`.
     * @example
     *
     * var object = { 'a': [{ 'b': { 'c': 3 } }] };
     *
     * _.update(object, 'a[0].b.c', function(n) { return n * n; });
     * console.log(object.a[0].b.c);
     * // => 9
     *
     * _.update(object, 'x[0].y.z', function(n) { return n ? n + 1 : 0; });
     * console.log(object.x[0].y.z);
     * // => 0
     */
    function update(object, path, updater) {
      return object == null ? object : baseUpdate(object, path, castFunction(updater));
    }

    /**
     * This method is like `_.update` except that it accepts `customizer` which is
     * invoked to produce the objects of `path`.  If `customizer` returns `undefined`
     * path creation is handled by the method instead. The `customizer` is invoked
     * with three arguments: (nsValue, key, nsObject).
     *
     * **Note:** This method mutates `object`.
     *
     * @static
     * @memberOf _
     * @since 4.6.0
     * @category Object
     * @param {Object} object The object to modify.
     * @param {Array|string} path The path of the property to set.
     * @param {Function} updater The function to produce the updated value.
     * @param {Function} [customizer] The function to customize assigned values.
     * @returns {Object} Returns `object`.
     * @example
     *
     * var object = {};
     *
     * _.updateWith(object, '[0][1]', _.constant('a'), Object);
     * // => { '0': { '1': 'a' } }
     */
    function updateWith(object, path, updater, customizer) {
      customizer = typeof customizer == 'function' ? customizer : undefined;
      return object == null ? object : baseUpdate(object, path, castFunction(updater), customizer);
    }

    /**
     * Creates an array of the own enumerable string keyed property values of `object`.
     *
     * **Note:** Non-object values are coerced to objects.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Object
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property values.
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.values(new Foo);
     * // => [1, 2] (iteration order is not guaranteed)
     *
     * _.values('hi');
     * // => ['h', 'i']
     */
    function values(object) {
      return object ? baseValues(object, keys(object)) : [];
    }

    /**
     * Creates an array of the own and inherited enumerable string keyed property
     * values of `object`.
     *
     * **Note:** Non-object values are coerced to objects.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Object
     * @param {Object} object The object to query.
     * @returns {Array} Returns the array of property values.
     * @example
     *
     * function Foo() {
     *   this.a = 1;
     *   this.b = 2;
     * }
     *
     * Foo.prototype.c = 3;
     *
     * _.valuesIn(new Foo);
     * // => [1, 2, 3] (iteration order is not guaranteed)
     */
    function valuesIn(object) {
      return object == null ? [] : baseValues(object, keysIn(object));
    }

    /*------------------------------------------------------------------------*/

    /**
     * Clamps `number` within the inclusive `lower` and `upper` bounds.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Number
     * @param {number} number The number to clamp.
     * @param {number} [lower] The lower bound.
     * @param {number} upper The upper bound.
     * @returns {number} Returns the clamped number.
     * @example
     *
     * _.clamp(-10, -5, 5);
     * // => -5
     *
     * _.clamp(10, -5, 5);
     * // => 5
     */
    function clamp(number, lower, upper) {
      if (upper === undefined) {
        upper = lower;
        lower = undefined;
      }
      if (upper !== undefined) {
        upper = toNumber(upper);
        upper = upper === upper ? upper : 0;
      }
      if (lower !== undefined) {
        lower = toNumber(lower);
        lower = lower === lower ? lower : 0;
      }
      return baseClamp(toNumber(number), lower, upper);
    }

    /**
     * Checks if `n` is between `start` and up to, but not including, `end`. If
     * `end` is not specified, it's set to `start` with `start` then set to `0`.
     * If `start` is greater than `end` the params are swapped to support
     * negative ranges.
     *
     * @static
     * @memberOf _
     * @since 3.3.0
     * @category Number
     * @param {number} number The number to check.
     * @param {number} [start=0] The start of the range.
     * @param {number} end The end of the range.
     * @returns {boolean} Returns `true` if `number` is in the range, else `false`.
     * @see _.range, _.rangeRight
     * @example
     *
     * _.inRange(3, 2, 4);
     * // => true
     *
     * _.inRange(4, 8);
     * // => true
     *
     * _.inRange(4, 2);
     * // => false
     *
     * _.inRange(2, 2);
     * // => false
     *
     * _.inRange(1.2, 2);
     * // => true
     *
     * _.inRange(5.2, 4);
     * // => false
     *
     * _.inRange(-3, -2, -6);
     * // => true
     */
    function inRange(number, start, end) {
      start = toFinite(start);
      if (end === undefined) {
        end = start;
        start = 0;
      } else {
        end = toFinite(end);
      }
      number = toNumber(number);
      return baseInRange(number, start, end);
    }

    /**
     * Produces a random number between the inclusive `lower` and `upper` bounds.
     * If only one argument is provided a number between `0` and the given number
     * is returned. If `floating` is `true`, or either `lower` or `upper` are
     * floats, a floating-point number is returned instead of an integer.
     *
     * **Note:** JavaScript follows the IEEE-754 standard for resolving
     * floating-point values which can produce unexpected results.
     *
     * @static
     * @memberOf _
     * @since 0.7.0
     * @category Number
     * @param {number} [lower=0] The lower bound.
     * @param {number} [upper=1] The upper bound.
     * @param {boolean} [floating] Specify returning a floating-point number.
     * @returns {number} Returns the random number.
     * @example
     *
     * _.random(0, 5);
     * // => an integer between 0 and 5
     *
     * _.random(5);
     * // => also an integer between 0 and 5
     *
     * _.random(5, true);
     * // => a floating-point number between 0 and 5
     *
     * _.random(1.2, 5.2);
     * // => a floating-point number between 1.2 and 5.2
     */
    function random(lower, upper, floating) {
      if (floating && typeof floating != 'boolean' && isIterateeCall(lower, upper, floating)) {
        upper = floating = undefined;
      }
      if (floating === undefined) {
        if (typeof upper == 'boolean') {
          floating = upper;
          upper = undefined;
        }
        else if (typeof lower == 'boolean') {
          floating = lower;
          lower = undefined;
        }
      }
      if (lower === undefined && upper === undefined) {
        lower = 0;
        upper = 1;
      }
      else {
        lower = toFinite(lower);
        if (upper === undefined) {
          upper = lower;
          lower = 0;
        } else {
          upper = toFinite(upper);
        }
      }
      if (lower > upper) {
        var temp = lower;
        lower = upper;
        upper = temp;
      }
      if (floating || lower % 1 || upper % 1) {
        var rand = nativeRandom();
        return nativeMin(lower + (rand * (upper - lower + freeParseFloat('1e-' + ((rand + '').length - 1)))), upper);
      }
      return baseRandom(lower, upper);
    }

    /*------------------------------------------------------------------------*/

    /**
     * Converts `string` to [camel case](https://en.wikipedia.org/wiki/CamelCase).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the camel cased string.
     * @example
     *
     * _.camelCase('Foo Bar');
     * // => 'fooBar'
     *
     * _.camelCase('--foo-bar--');
     * // => 'fooBar'
     *
     * _.camelCase('__FOO_BAR__');
     * // => 'fooBar'
     */
    var camelCase = createCompounder(function(result, word, index) {
      word = word.toLowerCase();
      return result + (index ? capitalize(word) : word);
    });

    /**
     * Converts the first character of `string` to upper case and the remaining
     * to lower case.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to capitalize.
     * @returns {string} Returns the capitalized string.
     * @example
     *
     * _.capitalize('FRED');
     * // => 'Fred'
     */
    function capitalize(string) {
      return upperFirst(toString(string).toLowerCase());
    }

    /**
     * Deburrs `string` by converting
     * [Latin-1 Supplement](https://en.wikipedia.org/wiki/Latin-1_Supplement_(Unicode_block)#Character_table)
     * and [Latin Extended-A](https://en.wikipedia.org/wiki/Latin_Extended-A)
     * letters to basic Latin letters and removing
     * [combining diacritical marks](https://en.wikipedia.org/wiki/Combining_Diacritical_Marks).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to deburr.
     * @returns {string} Returns the deburred string.
     * @example
     *
     * _.deburr('déjà vu');
     * // => 'deja vu'
     */
    function deburr(string) {
      string = toString(string);
      return string && string.replace(reLatin, deburrLetter).replace(reComboMark, '');
    }

    /**
     * Checks if `string` ends with the given target string.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to inspect.
     * @param {string} [target] The string to search for.
     * @param {number} [position=string.length] The position to search up to.
     * @returns {boolean} Returns `true` if `string` ends with `target`,
     *  else `false`.
     * @example
     *
     * _.endsWith('abc', 'c');
     * // => true
     *
     * _.endsWith('abc', 'b');
     * // => false
     *
     * _.endsWith('abc', 'b', 2);
     * // => true
     */
    function endsWith(string, target, position) {
      string = toString(string);
      target = baseToString(target);

      var length = string.length;
      position = position === undefined
        ? length
        : baseClamp(toInteger(position), 0, length);

      var end = position;
      position -= target.length;
      return position >= 0 && string.slice(position, end) == target;
    }

    /**
     * Converts the characters "&", "<", ">", '"', and "'" in `string` to their
     * corresponding HTML entities.
     *
     * **Note:** No other characters are escaped. To escape additional
     * characters use a third-party library like [_he_](https://mths.be/he).
     *
     * Though the ">" character is escaped for symmetry, characters like
     * ">" and "/" don't need escaping in HTML and have no special meaning
     * unless they're part of a tag or unquoted attribute value. See
     * [Mathias Bynens's article](https://mathiasbynens.be/notes/ambiguous-ampersands)
     * (under "semi-related fun fact") for more details.
     *
     * When working with HTML you should always
     * [quote attribute values](http://wonko.com/post/html-escaping) to reduce
     * XSS vectors.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category String
     * @param {string} [string=''] The string to escape.
     * @returns {string} Returns the escaped string.
     * @example
     *
     * _.escape('fred, barney, & pebbles');
     * // => 'fred, barney, &amp; pebbles'
     */
    function escape(string) {
      string = toString(string);
      return (string && reHasUnescapedHtml.test(string))
        ? string.replace(reUnescapedHtml, escapeHtmlChar)
        : string;
    }

    /**
     * Escapes the `RegExp` special characters "^", "$", "\", ".", "*", "+",
     * "?", "(", ")", "[", "]", "{", "}", and "|" in `string`.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to escape.
     * @returns {string} Returns the escaped string.
     * @example
     *
     * _.escapeRegExp('[lodash](https://lodash.com/)');
     * // => '\[lodash\]\(https://lodash\.com/\)'
     */
    function escapeRegExp(string) {
      string = toString(string);
      return (string && reHasRegExpChar.test(string))
        ? string.replace(reRegExpChar, '\\$&')
        : string;
    }

    /**
     * Converts `string` to
     * [kebab case](https://en.wikipedia.org/wiki/Letter_case#Special_case_styles).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the kebab cased string.
     * @example
     *
     * _.kebabCase('Foo Bar');
     * // => 'foo-bar'
     *
     * _.kebabCase('fooBar');
     * // => 'foo-bar'
     *
     * _.kebabCase('__FOO_BAR__');
     * // => 'foo-bar'
     */
    var kebabCase = createCompounder(function(result, word, index) {
      return result + (index ? '-' : '') + word.toLowerCase();
    });

    /**
     * Converts `string`, as space separated words, to lower case.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the lower cased string.
     * @example
     *
     * _.lowerCase('--Foo-Bar--');
     * // => 'foo bar'
     *
     * _.lowerCase('fooBar');
     * // => 'foo bar'
     *
     * _.lowerCase('__FOO_BAR__');
     * // => 'foo bar'
     */
    var lowerCase = createCompounder(function(result, word, index) {
      return result + (index ? ' ' : '') + word.toLowerCase();
    });

    /**
     * Converts the first character of `string` to lower case.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the converted string.
     * @example
     *
     * _.lowerFirst('Fred');
     * // => 'fred'
     *
     * _.lowerFirst('FRED');
     * // => 'fRED'
     */
    var lowerFirst = createCaseFirst('toLowerCase');

    /**
     * Pads `string` on the left and right sides if it's shorter than `length`.
     * Padding characters are truncated if they can't be evenly divided by `length`.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to pad.
     * @param {number} [length=0] The padding length.
     * @param {string} [chars=' '] The string used as padding.
     * @returns {string} Returns the padded string.
     * @example
     *
     * _.pad('abc', 8);
     * // => '  abc   '
     *
     * _.pad('abc', 8, '_-');
     * // => '_-abc_-_'
     *
     * _.pad('abc', 3);
     * // => 'abc'
     */
    function pad(string, length, chars) {
      string = toString(string);
      length = toInteger(length);

      var strLength = length ? stringSize(string) : 0;
      if (!length || strLength >= length) {
        return string;
      }
      var mid = (length - strLength) / 2;
      return (
        createPadding(nativeFloor(mid), chars) +
        string +
        createPadding(nativeCeil(mid), chars)
      );
    }

    /**
     * Pads `string` on the right side if it's shorter than `length`. Padding
     * characters are truncated if they exceed `length`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to pad.
     * @param {number} [length=0] The padding length.
     * @param {string} [chars=' '] The string used as padding.
     * @returns {string} Returns the padded string.
     * @example
     *
     * _.padEnd('abc', 6);
     * // => 'abc   '
     *
     * _.padEnd('abc', 6, '_-');
     * // => 'abc_-_'
     *
     * _.padEnd('abc', 3);
     * // => 'abc'
     */
    function padEnd(string, length, chars) {
      string = toString(string);
      length = toInteger(length);

      var strLength = length ? stringSize(string) : 0;
      return (length && strLength < length)
        ? (string + createPadding(length - strLength, chars))
        : string;
    }

    /**
     * Pads `string` on the left side if it's shorter than `length`. Padding
     * characters are truncated if they exceed `length`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to pad.
     * @param {number} [length=0] The padding length.
     * @param {string} [chars=' '] The string used as padding.
     * @returns {string} Returns the padded string.
     * @example
     *
     * _.padStart('abc', 6);
     * // => '   abc'
     *
     * _.padStart('abc', 6, '_-');
     * // => '_-_abc'
     *
     * _.padStart('abc', 3);
     * // => 'abc'
     */
    function padStart(string, length, chars) {
      string = toString(string);
      length = toInteger(length);

      var strLength = length ? stringSize(string) : 0;
      return (length && strLength < length)
        ? (createPadding(length - strLength, chars) + string)
        : string;
    }

    /**
     * Converts `string` to an integer of the specified radix. If `radix` is
     * `undefined` or `0`, a `radix` of `10` is used unless `value` is a
     * hexadecimal, in which case a `radix` of `16` is used.
     *
     * **Note:** This method aligns with the
     * [ES5 implementation](https://es5.github.io/#x15.1.2.2) of `parseInt`.
     *
     * @static
     * @memberOf _
     * @since 1.1.0
     * @category String
     * @param {string} string The string to convert.
     * @param {number} [radix=10] The radix to interpret `value` by.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {number} Returns the converted integer.
     * @example
     *
     * _.parseInt('08');
     * // => 8
     *
     * _.map(['6', '08', '10'], _.parseInt);
     * // => [6, 8, 10]
     */
    function parseInt(string, radix, guard) {
      if (guard || radix == null) {
        radix = 0;
      } else if (radix) {
        radix = +radix;
      }
      return nativeParseInt(toString(string).replace(reTrimStart, ''), radix || 0);
    }

    /**
     * Repeats the given string `n` times.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to repeat.
     * @param {number} [n=1] The number of times to repeat the string.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {string} Returns the repeated string.
     * @example
     *
     * _.repeat('*', 3);
     * // => '***'
     *
     * _.repeat('abc', 2);
     * // => 'abcabc'
     *
     * _.repeat('abc', 0);
     * // => ''
     */
    function repeat(string, n, guard) {
      if ((guard ? isIterateeCall(string, n, guard) : n === undefined)) {
        n = 1;
      } else {
        n = toInteger(n);
      }
      return baseRepeat(toString(string), n);
    }

    /**
     * Replaces matches for `pattern` in `string` with `replacement`.
     *
     * **Note:** This method is based on
     * [`String#replace`](https://mdn.io/String/replace).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to modify.
     * @param {RegExp|string} pattern The pattern to replace.
     * @param {Function|string} replacement The match replacement.
     * @returns {string} Returns the modified string.
     * @example
     *
     * _.replace('Hi Fred', 'Fred', 'Barney');
     * // => 'Hi Barney'
     */
    function replace() {
      var args = arguments,
          string = toString(args[0]);

      return args.length < 3 ? string : string.replace(args[1], args[2]);
    }

    /**
     * Converts `string` to
     * [snake case](https://en.wikipedia.org/wiki/Snake_case).
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the snake cased string.
     * @example
     *
     * _.snakeCase('Foo Bar');
     * // => 'foo_bar'
     *
     * _.snakeCase('fooBar');
     * // => 'foo_bar'
     *
     * _.snakeCase('--FOO-BAR--');
     * // => 'foo_bar'
     */
    var snakeCase = createCompounder(function(result, word, index) {
      return result + (index ? '_' : '') + word.toLowerCase();
    });

    /**
     * Splits `string` by `separator`.
     *
     * **Note:** This method is based on
     * [`String#split`](https://mdn.io/String/split).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to split.
     * @param {RegExp|string} separator The separator pattern to split by.
     * @param {number} [limit] The length to truncate results to.
     * @returns {Array} Returns the string segments.
     * @example
     *
     * _.split('a-b-c', '-', 2);
     * // => ['a', 'b']
     */
    function split(string, separator, limit) {
      if (limit && typeof limit != 'number' && isIterateeCall(string, separator, limit)) {
        separator = limit = undefined;
      }
      limit = limit === undefined ? MAX_ARRAY_LENGTH : limit >>> 0;
      if (!limit) {
        return [];
      }
      string = toString(string);
      if (string && (
            typeof separator == 'string' ||
            (separator != null && !isRegExp(separator))
          )) {
        separator = baseToString(separator);
        if (!separator && hasUnicode(string)) {
          return castSlice(stringToArray(string), 0, limit);
        }
      }
      return string.split(separator, limit);
    }

    /**
     * Converts `string` to
     * [start case](https://en.wikipedia.org/wiki/Letter_case#Stylistic_or_specialised_usage).
     *
     * @static
     * @memberOf _
     * @since 3.1.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the start cased string.
     * @example
     *
     * _.startCase('--foo-bar--');
     * // => 'Foo Bar'
     *
     * _.startCase('fooBar');
     * // => 'Foo Bar'
     *
     * _.startCase('__FOO_BAR__');
     * // => 'FOO BAR'
     */
    var startCase = createCompounder(function(result, word, index) {
      return result + (index ? ' ' : '') + upperFirst(word);
    });

    /**
     * Checks if `string` starts with the given target string.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to inspect.
     * @param {string} [target] The string to search for.
     * @param {number} [position=0] The position to search from.
     * @returns {boolean} Returns `true` if `string` starts with `target`,
     *  else `false`.
     * @example
     *
     * _.startsWith('abc', 'a');
     * // => true
     *
     * _.startsWith('abc', 'b');
     * // => false
     *
     * _.startsWith('abc', 'b', 1);
     * // => true
     */
    function startsWith(string, target, position) {
      string = toString(string);
      position = baseClamp(toInteger(position), 0, string.length);
      target = baseToString(target);
      return string.slice(position, position + target.length) == target;
    }

    /**
     * Creates a compiled template function that can interpolate data properties
     * in "interpolate" delimiters, HTML-escape interpolated data properties in
     * "escape" delimiters, and execute JavaScript in "evaluate" delimiters. Data
     * properties may be accessed as free variables in the template. If a setting
     * object is given, it takes precedence over `_.templateSettings` values.
     *
     * **Note:** In the development build `_.template` utilizes
     * [sourceURLs](http://www.html5rocks.com/en/tutorials/developertools/sourcemaps/#toc-sourceurl)
     * for easier debugging.
     *
     * For more information on precompiling templates see
     * [lodash's custom builds documentation](https://lodash.com/custom-builds).
     *
     * For more information on Chrome extension sandboxes see
     * [Chrome's extensions documentation](https://developer.chrome.com/extensions/sandboxingEval).
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category String
     * @param {string} [string=''] The template string.
     * @param {Object} [options={}] The options object.
     * @param {RegExp} [options.escape=_.templateSettings.escape]
     *  The HTML "escape" delimiter.
     * @param {RegExp} [options.evaluate=_.templateSettings.evaluate]
     *  The "evaluate" delimiter.
     * @param {Object} [options.imports=_.templateSettings.imports]
     *  An object to import into the template as free variables.
     * @param {RegExp} [options.interpolate=_.templateSettings.interpolate]
     *  The "interpolate" delimiter.
     * @param {string} [options.sourceURL='lodash.templateSources[n]']
     *  The sourceURL of the compiled template.
     * @param {string} [options.variable='obj']
     *  The data object variable name.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Function} Returns the compiled template function.
     * @example
     *
     * // Use the "interpolate" delimiter to create a compiled template.
     * var compiled = _.template('hello <%= user %>!');
     * compiled({ 'user': 'fred' });
     * // => 'hello fred!'
     *
     * // Use the HTML "escape" delimiter to escape data property values.
     * var compiled = _.template('<b><%- value %></b>');
     * compiled({ 'value': '<script>' });
     * // => '<b>&lt;script&gt;</b>'
     *
     * // Use the "evaluate" delimiter to execute JavaScript and generate HTML.
     * var compiled = _.template('<% _.forEach(users, function(user) { %><li><%- user %></li><% }); %>');
     * compiled({ 'users': ['fred', 'barney'] });
     * // => '<li>fred</li><li>barney</li>'
     *
     * // Use the internal `print` function in "evaluate" delimiters.
     * var compiled = _.template('<% print("hello " + user); %>!');
     * compiled({ 'user': 'barney' });
     * // => 'hello barney!'
     *
     * // Use the ES template literal delimiter as an "interpolate" delimiter.
     * // Disable support by replacing the "interpolate" delimiter.
     * var compiled = _.template('hello ${ user }!');
     * compiled({ 'user': 'pebbles' });
     * // => 'hello pebbles!'
     *
     * // Use backslashes to treat delimiters as plain text.
     * var compiled = _.template('<%= "\\<%- value %\\>" %>');
     * compiled({ 'value': 'ignored' });
     * // => '<%- value %>'
     *
     * // Use the `imports` option to import `jQuery` as `jq`.
     * var text = '<% jq.each(users, function(user) { %><li><%- user %></li><% }); %>';
     * var compiled = _.template(text, { 'imports': { 'jq': jQuery } });
     * compiled({ 'users': ['fred', 'barney'] });
     * // => '<li>fred</li><li>barney</li>'
     *
     * // Use the `sourceURL` option to specify a custom sourceURL for the template.
     * var compiled = _.template('hello <%= user %>!', { 'sourceURL': '/basic/greeting.jst' });
     * compiled(data);
     * // => Find the source of "greeting.jst" under the Sources tab or Resources panel of the web inspector.
     *
     * // Use the `variable` option to ensure a with-statement isn't used in the compiled template.
     * var compiled = _.template('hi <%= data.user %>!', { 'variable': 'data' });
     * compiled.source;
     * // => function(data) {
     * //   var __t, __p = '';
     * //   __p += 'hi ' + ((__t = ( data.user )) == null ? '' : __t) + '!';
     * //   return __p;
     * // }
     *
     * // Use custom template delimiters.
     * _.templateSettings.interpolate = /{{([\s\S]+?)}}/g;
     * var compiled = _.template('hello {{ user }}!');
     * compiled({ 'user': 'mustache' });
     * // => 'hello mustache!'
     *
     * // Use the `source` property to inline compiled templates for meaningful
     * // line numbers in error messages and stack traces.
     * fs.writeFileSync(path.join(process.cwd(), 'jst.js'), '\
     *   var JST = {\
     *     "main": ' + _.template(mainText).source + '\
     *   };\
     * ');
     */
    function template(string, options, guard) {
      // Based on John Resig's `tmpl` implementation
      // (http://ejohn.org/blog/javascript-micro-templating/)
      // and Laura Doktorova's doT.js (https://github.com/olado/doT).
      var settings = lodash.templateSettings;

      if (guard && isIterateeCall(string, options, guard)) {
        options = undefined;
      }
      string = toString(string);
      options = assignInWith({}, options, settings, assignInDefaults);

      var imports = assignInWith({}, options.imports, settings.imports, assignInDefaults),
          importsKeys = keys(imports),
          importsValues = baseValues(imports, importsKeys);

      var isEscaping,
          isEvaluating,
          index = 0,
          interpolate = options.interpolate || reNoMatch,
          source = "__p += '";

      // Compile the regexp to match each delimiter.
      var reDelimiters = RegExp(
        (options.escape || reNoMatch).source + '|' +
        interpolate.source + '|' +
        (interpolate === reInterpolate ? reEsTemplate : reNoMatch).source + '|' +
        (options.evaluate || reNoMatch).source + '|$'
      , 'g');

      // Use a sourceURL for easier debugging.
      var sourceURL = '//# sourceURL=' +
        ('sourceURL' in options
          ? options.sourceURL
          : ('lodash.templateSources[' + (++templateCounter) + ']')
        ) + '\n';

      string.replace(reDelimiters, function(match, escapeValue, interpolateValue, esTemplateValue, evaluateValue, offset) {
        interpolateValue || (interpolateValue = esTemplateValue);

        // Escape characters that can't be included in string literals.
        source += string.slice(index, offset).replace(reUnescapedString, escapeStringChar);

        // Replace delimiters with snippets.
        if (escapeValue) {
          isEscaping = true;
          source += "' +\n__e(" + escapeValue + ") +\n'";
        }
        if (evaluateValue) {
          isEvaluating = true;
          source += "';\n" + evaluateValue + ";\n__p += '";
        }
        if (interpolateValue) {
          source += "' +\n((__t = (" + interpolateValue + ")) == null ? '' : __t) +\n'";
        }
        index = offset + match.length;

        // The JS engine embedded in Adobe products needs `match` returned in
        // order to produce the correct `offset` value.
        return match;
      });

      source += "';\n";

      // If `variable` is not specified wrap a with-statement around the generated
      // code to add the data object to the top of the scope chain.
      var variable = options.variable;
      if (!variable) {
        source = 'with (obj) {\n' + source + '\n}\n';
      }
      // Cleanup code by stripping empty strings.
      source = (isEvaluating ? source.replace(reEmptyStringLeading, '') : source)
        .replace(reEmptyStringMiddle, '$1')
        .replace(reEmptyStringTrailing, '$1;');

      // Frame code as the function body.
      source = 'function(' + (variable || 'obj') + ') {\n' +
        (variable
          ? ''
          : 'obj || (obj = {});\n'
        ) +
        "var __t, __p = ''" +
        (isEscaping
           ? ', __e = _.escape'
           : ''
        ) +
        (isEvaluating
          ? ', __j = Array.prototype.join;\n' +
            "function print() { __p += __j.call(arguments, '') }\n"
          : ';\n'
        ) +
        source +
        'return __p\n}';

      var result = attempt(function() {
        return Function(importsKeys, sourceURL + 'return ' + source)
          .apply(undefined, importsValues);
      });

      // Provide the compiled function's source by its `toString` method or
      // the `source` property as a convenience for inlining compiled templates.
      result.source = source;
      if (isError(result)) {
        throw result;
      }
      return result;
    }

    /**
     * Converts `string`, as a whole, to lower case just like
     * [String#toLowerCase](https://mdn.io/toLowerCase).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the lower cased string.
     * @example
     *
     * _.toLower('--Foo-Bar--');
     * // => '--foo-bar--'
     *
     * _.toLower('fooBar');
     * // => 'foobar'
     *
     * _.toLower('__FOO_BAR__');
     * // => '__foo_bar__'
     */
    function toLower(value) {
      return toString(value).toLowerCase();
    }

    /**
     * Converts `string`, as a whole, to upper case just like
     * [String#toUpperCase](https://mdn.io/toUpperCase).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the upper cased string.
     * @example
     *
     * _.toUpper('--foo-bar--');
     * // => '--FOO-BAR--'
     *
     * _.toUpper('fooBar');
     * // => 'FOOBAR'
     *
     * _.toUpper('__foo_bar__');
     * // => '__FOO_BAR__'
     */
    function toUpper(value) {
      return toString(value).toUpperCase();
    }

    /**
     * Removes leading and trailing whitespace or specified characters from `string`.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to trim.
     * @param {string} [chars=whitespace] The characters to trim.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {string} Returns the trimmed string.
     * @example
     *
     * _.trim('  abc  ');
     * // => 'abc'
     *
     * _.trim('-_-abc-_-', '_-');
     * // => 'abc'
     *
     * _.map(['  foo  ', '  bar  '], _.trim);
     * // => ['foo', 'bar']
     */
    function trim(string, chars, guard) {
      string = toString(string);
      if (string && (guard || chars === undefined)) {
        return string.replace(reTrim, '');
      }
      if (!string || !(chars = baseToString(chars))) {
        return string;
      }
      var strSymbols = stringToArray(string),
          chrSymbols = stringToArray(chars),
          start = charsStartIndex(strSymbols, chrSymbols),
          end = charsEndIndex(strSymbols, chrSymbols) + 1;

      return castSlice(strSymbols, start, end).join('');
    }

    /**
     * Removes trailing whitespace or specified characters from `string`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to trim.
     * @param {string} [chars=whitespace] The characters to trim.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {string} Returns the trimmed string.
     * @example
     *
     * _.trimEnd('  abc  ');
     * // => '  abc'
     *
     * _.trimEnd('-_-abc-_-', '_-');
     * // => '-_-abc'
     */
    function trimEnd(string, chars, guard) {
      string = toString(string);
      if (string && (guard || chars === undefined)) {
        return string.replace(reTrimEnd, '');
      }
      if (!string || !(chars = baseToString(chars))) {
        return string;
      }
      var strSymbols = stringToArray(string),
          end = charsEndIndex(strSymbols, stringToArray(chars)) + 1;

      return castSlice(strSymbols, 0, end).join('');
    }

    /**
     * Removes leading whitespace or specified characters from `string`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to trim.
     * @param {string} [chars=whitespace] The characters to trim.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {string} Returns the trimmed string.
     * @example
     *
     * _.trimStart('  abc  ');
     * // => 'abc  '
     *
     * _.trimStart('-_-abc-_-', '_-');
     * // => 'abc-_-'
     */
    function trimStart(string, chars, guard) {
      string = toString(string);
      if (string && (guard || chars === undefined)) {
        return string.replace(reTrimStart, '');
      }
      if (!string || !(chars = baseToString(chars))) {
        return string;
      }
      var strSymbols = stringToArray(string),
          start = charsStartIndex(strSymbols, stringToArray(chars));

      return castSlice(strSymbols, start).join('');
    }

    /**
     * Truncates `string` if it's longer than the given maximum string length.
     * The last characters of the truncated string are replaced with the omission
     * string which defaults to "...".
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to truncate.
     * @param {Object} [options={}] The options object.
     * @param {number} [options.length=30] The maximum string length.
     * @param {string} [options.omission='...'] The string to indicate text is omitted.
     * @param {RegExp|string} [options.separator] The separator pattern to truncate to.
     * @returns {string} Returns the truncated string.
     * @example
     *
     * _.truncate('hi-diddly-ho there, neighborino');
     * // => 'hi-diddly-ho there, neighbo...'
     *
     * _.truncate('hi-diddly-ho there, neighborino', {
     *   'length': 24,
     *   'separator': ' '
     * });
     * // => 'hi-diddly-ho there,...'
     *
     * _.truncate('hi-diddly-ho there, neighborino', {
     *   'length': 24,
     *   'separator': /,? +/
     * });
     * // => 'hi-diddly-ho there...'
     *
     * _.truncate('hi-diddly-ho there, neighborino', {
     *   'omission': ' [...]'
     * });
     * // => 'hi-diddly-ho there, neig [...]'
     */
    function truncate(string, options) {
      var length = DEFAULT_TRUNC_LENGTH,
          omission = DEFAULT_TRUNC_OMISSION;

      if (isObject(options)) {
        var separator = 'separator' in options ? options.separator : separator;
        length = 'length' in options ? toInteger(options.length) : length;
        omission = 'omission' in options ? baseToString(options.omission) : omission;
      }
      string = toString(string);

      var strLength = string.length;
      if (hasUnicode(string)) {
        var strSymbols = stringToArray(string);
        strLength = strSymbols.length;
      }
      if (length >= strLength) {
        return string;
      }
      var end = length - stringSize(omission);
      if (end < 1) {
        return omission;
      }
      var result = strSymbols
        ? castSlice(strSymbols, 0, end).join('')
        : string.slice(0, end);

      if (separator === undefined) {
        return result + omission;
      }
      if (strSymbols) {
        end += (result.length - end);
      }
      if (isRegExp(separator)) {
        if (string.slice(end).search(separator)) {
          var match,
              substring = result;

          if (!separator.global) {
            separator = RegExp(separator.source, toString(reFlags.exec(separator)) + 'g');
          }
          separator.lastIndex = 0;
          while ((match = separator.exec(substring))) {
            var newEnd = match.index;
          }
          result = result.slice(0, newEnd === undefined ? end : newEnd);
        }
      } else if (string.indexOf(baseToString(separator), end) != end) {
        var index = result.lastIndexOf(separator);
        if (index > -1) {
          result = result.slice(0, index);
        }
      }
      return result + omission;
    }

    /**
     * The inverse of `_.escape`; this method converts the HTML entities
     * `&amp;`, `&lt;`, `&gt;`, `&quot;`, and `&#39;` in `string` to
     * their corresponding characters.
     *
     * **Note:** No other HTML entities are unescaped. To unescape additional
     * HTML entities use a third-party library like [_he_](https://mths.be/he).
     *
     * @static
     * @memberOf _
     * @since 0.6.0
     * @category String
     * @param {string} [string=''] The string to unescape.
     * @returns {string} Returns the unescaped string.
     * @example
     *
     * _.unescape('fred, barney, &amp; pebbles');
     * // => 'fred, barney, & pebbles'
     */
    function unescape(string) {
      string = toString(string);
      return (string && reHasEscapedHtml.test(string))
        ? string.replace(reEscapedHtml, unescapeHtmlChar)
        : string;
    }

    /**
     * Converts `string`, as space separated words, to upper case.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the upper cased string.
     * @example
     *
     * _.upperCase('--foo-bar');
     * // => 'FOO BAR'
     *
     * _.upperCase('fooBar');
     * // => 'FOO BAR'
     *
     * _.upperCase('__foo_bar__');
     * // => 'FOO BAR'
     */
    var upperCase = createCompounder(function(result, word, index) {
      return result + (index ? ' ' : '') + word.toUpperCase();
    });

    /**
     * Converts the first character of `string` to upper case.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category String
     * @param {string} [string=''] The string to convert.
     * @returns {string} Returns the converted string.
     * @example
     *
     * _.upperFirst('fred');
     * // => 'Fred'
     *
     * _.upperFirst('FRED');
     * // => 'FRED'
     */
    var upperFirst = createCaseFirst('toUpperCase');

    /**
     * Splits `string` into an array of its words.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category String
     * @param {string} [string=''] The string to inspect.
     * @param {RegExp|string} [pattern] The pattern to match words.
     * @param- {Object} [guard] Enables use as an iteratee for methods like `_.map`.
     * @returns {Array} Returns the words of `string`.
     * @example
     *
     * _.words('fred, barney, & pebbles');
     * // => ['fred', 'barney', 'pebbles']
     *
     * _.words('fred, barney, & pebbles', /[^, ]+/g);
     * // => ['fred', 'barney', '&', 'pebbles']
     */
    function words(string, pattern, guard) {
      string = toString(string);
      pattern = guard ? undefined : pattern;

      if (pattern === undefined) {
        return hasUnicodeWord(string) ? unicodeWords(string) : asciiWords(string);
      }
      return string.match(pattern) || [];
    }

    /*------------------------------------------------------------------------*/

    /**
     * Attempts to invoke `func`, returning either the result or the caught error
     * object. Any additional arguments are provided to `func` when it's invoked.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Util
     * @param {Function} func The function to attempt.
     * @param {...*} [args] The arguments to invoke `func` with.
     * @returns {*} Returns the `func` result or error object.
     * @example
     *
     * // Avoid throwing errors for invalid selectors.
     * var elements = _.attempt(function(selector) {
     *   return document.querySelectorAll(selector);
     * }, '>_>');
     *
     * if (_.isError(elements)) {
     *   elements = [];
     * }
     */
    var attempt = baseRest(function(func, args) {
      try {
        return apply(func, undefined, args);
      } catch (e) {
        return isError(e) ? e : new Error(e);
      }
    });

    /**
     * Binds methods of an object to the object itself, overwriting the existing
     * method.
     *
     * **Note:** This method doesn't set the "length" property of bound functions.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Util
     * @param {Object} object The object to bind and assign the bound methods to.
     * @param {...(string|string[])} methodNames The object method names to bind.
     * @returns {Object} Returns `object`.
     * @example
     *
     * var view = {
     *   'label': 'docs',
     *   'click': function() {
     *     console.log('clicked ' + this.label);
     *   }
     * };
     *
     * _.bindAll(view, ['click']);
     * jQuery(element).on('click', view.click);
     * // => Logs 'clicked docs' when clicked.
     */
    var bindAll = flatRest(function(object, methodNames) {
      arrayEach(methodNames, function(key) {
        key = toKey(key);
        baseAssignValue(object, key, bind(object[key], object));
      });
      return object;
    });

    /**
     * Creates a function that iterates over `pairs` and invokes the corresponding
     * function of the first predicate to return truthy. The predicate-function
     * pairs are invoked with the `this` binding and arguments of the created
     * function.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {Array} pairs The predicate-function pairs.
     * @returns {Function} Returns the new composite function.
     * @example
     *
     * var func = _.cond([
     *   [_.matches({ 'a': 1 }),           _.constant('matches A')],
     *   [_.conforms({ 'b': _.isNumber }), _.constant('matches B')],
     *   [_.stubTrue,                      _.constant('no match')]
     * ]);
     *
     * func({ 'a': 1, 'b': 2 });
     * // => 'matches A'
     *
     * func({ 'a': 0, 'b': 1 });
     * // => 'matches B'
     *
     * func({ 'a': '1', 'b': '2' });
     * // => 'no match'
     */
    function cond(pairs) {
      var length = pairs ? pairs.length : 0,
          toIteratee = getIteratee();

      pairs = !length ? [] : arrayMap(pairs, function(pair) {
        if (typeof pair[1] != 'function') {
          throw new TypeError(FUNC_ERROR_TEXT);
        }
        return [toIteratee(pair[0]), pair[1]];
      });

      return baseRest(function(args) {
        var index = -1;
        while (++index < length) {
          var pair = pairs[index];
          if (apply(pair[0], this, args)) {
            return apply(pair[1], this, args);
          }
        }
      });
    }

    /**
     * Creates a function that invokes the predicate properties of `source` with
     * the corresponding property values of a given object, returning `true` if
     * all predicates return truthy, else `false`.
     *
     * **Note:** The created function is equivalent to `_.conformsTo` with
     * `source` partially applied.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {Object} source The object of property predicates to conform to.
     * @returns {Function} Returns the new spec function.
     * @example
     *
     * var objects = [
     *   { 'a': 2, 'b': 1 },
     *   { 'a': 1, 'b': 2 }
     * ];
     *
     * _.filter(objects, _.conforms({ 'b': function(n) { return n > 1; } }));
     * // => [{ 'a': 1, 'b': 2 }]
     */
    function conforms(source) {
      return baseConforms(baseClone(source, true));
    }

    /**
     * Creates a function that returns `value`.
     *
     * @static
     * @memberOf _
     * @since 2.4.0
     * @category Util
     * @param {*} value The value to return from the new function.
     * @returns {Function} Returns the new constant function.
     * @example
     *
     * var objects = _.times(2, _.constant({ 'a': 1 }));
     *
     * console.log(objects);
     * // => [{ 'a': 1 }, { 'a': 1 }]
     *
     * console.log(objects[0] === objects[1]);
     * // => true
     */
    function constant(value) {
      return function() {
        return value;
      };
    }

    /**
     * Checks `value` to determine whether a default value should be returned in
     * its place. The `defaultValue` is returned if `value` is `NaN`, `null`,
     * or `undefined`.
     *
     * @static
     * @memberOf _
     * @since 4.14.0
     * @category Util
     * @param {*} value The value to check.
     * @param {*} defaultValue The default value.
     * @returns {*} Returns the resolved value.
     * @example
     *
     * _.defaultTo(1, 10);
     * // => 1
     *
     * _.defaultTo(undefined, 10);
     * // => 10
     */
    function defaultTo(value, defaultValue) {
      return (value == null || value !== value) ? defaultValue : value;
    }

    /**
     * Creates a function that returns the result of invoking the given functions
     * with the `this` binding of the created function, where each successive
     * invocation is supplied the return value of the previous.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Util
     * @param {...(Function|Function[])} [funcs] The functions to invoke.
     * @returns {Function} Returns the new composite function.
     * @see _.flowRight
     * @example
     *
     * function square(n) {
     *   return n * n;
     * }
     *
     * var addSquare = _.flow([_.add, square]);
     * addSquare(1, 2);
     * // => 9
     */
    var flow = createFlow();

    /**
     * This method is like `_.flow` except that it creates a function that
     * invokes the given functions from right to left.
     *
     * @static
     * @since 3.0.0
     * @memberOf _
     * @category Util
     * @param {...(Function|Function[])} [funcs] The functions to invoke.
     * @returns {Function} Returns the new composite function.
     * @see _.flow
     * @example
     *
     * function square(n) {
     *   return n * n;
     * }
     *
     * var addSquare = _.flowRight([square, _.add]);
     * addSquare(1, 2);
     * // => 9
     */
    var flowRight = createFlow(true);

    /**
     * This method returns the first argument it receives.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Util
     * @param {*} value Any value.
     * @returns {*} Returns `value`.
     * @example
     *
     * var object = { 'a': 1 };
     *
     * console.log(_.identity(object) === object);
     * // => true
     */
    function identity(value) {
      return value;
    }

    /**
     * Creates a function that invokes `func` with the arguments of the created
     * function. If `func` is a property name, the created function returns the
     * property value for a given element. If `func` is an array or object, the
     * created function returns `true` for elements that contain the equivalent
     * source properties, otherwise it returns `false`.
     *
     * @static
     * @since 4.0.0
     * @memberOf _
     * @category Util
     * @param {*} [func=_.identity] The value to convert to a callback.
     * @returns {Function} Returns the callback.
     * @example
     *
     * var users = [
     *   { 'user': 'barney', 'age': 36, 'active': true },
     *   { 'user': 'fred',   'age': 40, 'active': false }
     * ];
     *
     * // The `_.matches` iteratee shorthand.
     * _.filter(users, _.iteratee({ 'user': 'barney', 'active': true }));
     * // => [{ 'user': 'barney', 'age': 36, 'active': true }]
     *
     * // The `_.matchesProperty` iteratee shorthand.
     * _.filter(users, _.iteratee(['user', 'fred']));
     * // => [{ 'user': 'fred', 'age': 40 }]
     *
     * // The `_.property` iteratee shorthand.
     * _.map(users, _.iteratee('user'));
     * // => ['barney', 'fred']
     *
     * // Create custom iteratee shorthands.
     * _.iteratee = _.wrap(_.iteratee, function(iteratee, func) {
     *   return !_.isRegExp(func) ? iteratee(func) : function(string) {
     *     return func.test(string);
     *   };
     * });
     *
     * _.filter(['abc', 'def'], /ef/);
     * // => ['def']
     */
    function iteratee(func) {
      return baseIteratee(typeof func == 'function' ? func : baseClone(func, true));
    }

    /**
     * Creates a function that performs a partial deep comparison between a given
     * object and `source`, returning `true` if the given object has equivalent
     * property values, else `false`.
     *
     * **Note:** The created function is equivalent to `_.isMatch` with `source`
     * partially applied.
     *
     * Partial comparisons will match empty array and empty object `source`
     * values against any array or object value, respectively. See `_.isEqual`
     * for a list of supported value comparisons.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Util
     * @param {Object} source The object of property values to match.
     * @returns {Function} Returns the new spec function.
     * @example
     *
     * var objects = [
     *   { 'a': 1, 'b': 2, 'c': 3 },
     *   { 'a': 4, 'b': 5, 'c': 6 }
     * ];
     *
     * _.filter(objects, _.matches({ 'a': 4, 'c': 6 }));
     * // => [{ 'a': 4, 'b': 5, 'c': 6 }]
     */
    function matches(source) {
      return baseMatches(baseClone(source, true));
    }

    /**
     * Creates a function that performs a partial deep comparison between the
     * value at `path` of a given object to `srcValue`, returning `true` if the
     * object value is equivalent, else `false`.
     *
     * **Note:** Partial comparisons will match empty array and empty object
     * `srcValue` values against any array or object value, respectively. See
     * `_.isEqual` for a list of supported value comparisons.
     *
     * @static
     * @memberOf _
     * @since 3.2.0
     * @category Util
     * @param {Array|string} path The path of the property to get.
     * @param {*} srcValue The value to match.
     * @returns {Function} Returns the new spec function.
     * @example
     *
     * var objects = [
     *   { 'a': 1, 'b': 2, 'c': 3 },
     *   { 'a': 4, 'b': 5, 'c': 6 }
     * ];
     *
     * _.find(objects, _.matchesProperty('a', 4));
     * // => { 'a': 4, 'b': 5, 'c': 6 }
     */
    function matchesProperty(path, srcValue) {
      return baseMatchesProperty(path, baseClone(srcValue, true));
    }

    /**
     * Creates a function that invokes the method at `path` of a given object.
     * Any additional arguments are provided to the invoked method.
     *
     * @static
     * @memberOf _
     * @since 3.7.0
     * @category Util
     * @param {Array|string} path The path of the method to invoke.
     * @param {...*} [args] The arguments to invoke the method with.
     * @returns {Function} Returns the new invoker function.
     * @example
     *
     * var objects = [
     *   { 'a': { 'b': _.constant(2) } },
     *   { 'a': { 'b': _.constant(1) } }
     * ];
     *
     * _.map(objects, _.method('a.b'));
     * // => [2, 1]
     *
     * _.map(objects, _.method(['a', 'b']));
     * // => [2, 1]
     */
    var method = baseRest(function(path, args) {
      return function(object) {
        return baseInvoke(object, path, args);
      };
    });

    /**
     * The opposite of `_.method`; this method creates a function that invokes
     * the method at a given path of `object`. Any additional arguments are
     * provided to the invoked method.
     *
     * @static
     * @memberOf _
     * @since 3.7.0
     * @category Util
     * @param {Object} object The object to query.
     * @param {...*} [args] The arguments to invoke the method with.
     * @returns {Function} Returns the new invoker function.
     * @example
     *
     * var array = _.times(3, _.constant),
     *     object = { 'a': array, 'b': array, 'c': array };
     *
     * _.map(['a[2]', 'c[0]'], _.methodOf(object));
     * // => [2, 0]
     *
     * _.map([['a', '2'], ['c', '0']], _.methodOf(object));
     * // => [2, 0]
     */
    var methodOf = baseRest(function(object, args) {
      return function(path) {
        return baseInvoke(object, path, args);
      };
    });

    /**
     * Adds all own enumerable string keyed function properties of a source
     * object to the destination object. If `object` is a function, then methods
     * are added to its prototype as well.
     *
     * **Note:** Use `_.runInContext` to create a pristine `lodash` function to
     * avoid conflicts caused by modifying the original.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Util
     * @param {Function|Object} [object=lodash] The destination object.
     * @param {Object} source The object of functions to add.
     * @param {Object} [options={}] The options object.
     * @param {boolean} [options.chain=true] Specify whether mixins are chainable.
     * @returns {Function|Object} Returns `object`.
     * @example
     *
     * function vowels(string) {
     *   return _.filter(string, function(v) {
     *     return /[aeiou]/i.test(v);
     *   });
     * }
     *
     * _.mixin({ 'vowels': vowels });
     * _.vowels('fred');
     * // => ['e']
     *
     * _('fred').vowels().value();
     * // => ['e']
     *
     * _.mixin({ 'vowels': vowels }, { 'chain': false });
     * _('fred').vowels();
     * // => ['e']
     */
    function mixin(object, source, options) {
      var props = keys(source),
          methodNames = baseFunctions(source, props);

      if (options == null &&
          !(isObject(source) && (methodNames.length || !props.length))) {
        options = source;
        source = object;
        object = this;
        methodNames = baseFunctions(source, keys(source));
      }
      var chain = !(isObject(options) && 'chain' in options) || !!options.chain,
          isFunc = isFunction(object);

      arrayEach(methodNames, function(methodName) {
        var func = source[methodName];
        object[methodName] = func;
        if (isFunc) {
          object.prototype[methodName] = function() {
            var chainAll = this.__chain__;
            if (chain || chainAll) {
              var result = object(this.__wrapped__),
                  actions = result.__actions__ = copyArray(this.__actions__);

              actions.push({ 'func': func, 'args': arguments, 'thisArg': object });
              result.__chain__ = chainAll;
              return result;
            }
            return func.apply(object, arrayPush([this.value()], arguments));
          };
        }
      });

      return object;
    }

    /**
     * Reverts the `_` variable to its previous value and returns a reference to
     * the `lodash` function.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Util
     * @returns {Function} Returns the `lodash` function.
     * @example
     *
     * var lodash = _.noConflict();
     */
    function noConflict() {
      if (root._ === this) {
        root._ = oldDash;
      }
      return this;
    }

    /**
     * This method returns `undefined`.
     *
     * @static
     * @memberOf _
     * @since 2.3.0
     * @category Util
     * @example
     *
     * _.times(2, _.noop);
     * // => [undefined, undefined]
     */
    function noop() {
      // No operation performed.
    }

    /**
     * Creates a function that gets the argument at index `n`. If `n` is negative,
     * the nth argument from the end is returned.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {number} [n=0] The index of the argument to return.
     * @returns {Function} Returns the new pass-thru function.
     * @example
     *
     * var func = _.nthArg(1);
     * func('a', 'b', 'c', 'd');
     * // => 'b'
     *
     * var func = _.nthArg(-2);
     * func('a', 'b', 'c', 'd');
     * // => 'c'
     */
    function nthArg(n) {
      n = toInteger(n);
      return baseRest(function(args) {
        return baseNth(args, n);
      });
    }

    /**
     * Creates a function that invokes `iteratees` with the arguments it receives
     * and returns their results.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {...(Function|Function[])} [iteratees=[_.identity]]
     *  The iteratees to invoke.
     * @returns {Function} Returns the new function.
     * @example
     *
     * var func = _.over([Math.max, Math.min]);
     *
     * func(1, 2, 3, 4);
     * // => [4, 1]
     */
    var over = createOver(arrayMap);

    /**
     * Creates a function that checks if **all** of the `predicates` return
     * truthy when invoked with the arguments it receives.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {...(Function|Function[])} [predicates=[_.identity]]
     *  The predicates to check.
     * @returns {Function} Returns the new function.
     * @example
     *
     * var func = _.overEvery([Boolean, isFinite]);
     *
     * func('1');
     * // => true
     *
     * func(null);
     * // => false
     *
     * func(NaN);
     * // => false
     */
    var overEvery = createOver(arrayEvery);

    /**
     * Creates a function that checks if **any** of the `predicates` return
     * truthy when invoked with the arguments it receives.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {...(Function|Function[])} [predicates=[_.identity]]
     *  The predicates to check.
     * @returns {Function} Returns the new function.
     * @example
     *
     * var func = _.overSome([Boolean, isFinite]);
     *
     * func('1');
     * // => true
     *
     * func(null);
     * // => true
     *
     * func(NaN);
     * // => false
     */
    var overSome = createOver(arraySome);

    /**
     * Creates a function that returns the value at `path` of a given object.
     *
     * @static
     * @memberOf _
     * @since 2.4.0
     * @category Util
     * @param {Array|string} path The path of the property to get.
     * @returns {Function} Returns the new accessor function.
     * @example
     *
     * var objects = [
     *   { 'a': { 'b': 2 } },
     *   { 'a': { 'b': 1 } }
     * ];
     *
     * _.map(objects, _.property('a.b'));
     * // => [2, 1]
     *
     * _.map(_.sortBy(objects, _.property(['a', 'b'])), 'a.b');
     * // => [1, 2]
     */
    function property(path) {
      return isKey(path) ? baseProperty(toKey(path)) : basePropertyDeep(path);
    }

    /**
     * The opposite of `_.property`; this method creates a function that returns
     * the value at a given path of `object`.
     *
     * @static
     * @memberOf _
     * @since 3.0.0
     * @category Util
     * @param {Object} object The object to query.
     * @returns {Function} Returns the new accessor function.
     * @example
     *
     * var array = [0, 1, 2],
     *     object = { 'a': array, 'b': array, 'c': array };
     *
     * _.map(['a[2]', 'c[0]'], _.propertyOf(object));
     * // => [2, 0]
     *
     * _.map([['a', '2'], ['c', '0']], _.propertyOf(object));
     * // => [2, 0]
     */
    function propertyOf(object) {
      return function(path) {
        return object == null ? undefined : baseGet(object, path);
      };
    }

    /**
     * Creates an array of numbers (positive and/or negative) progressing from
     * `start` up to, but not including, `end`. A step of `-1` is used if a negative
     * `start` is specified without an `end` or `step`. If `end` is not specified,
     * it's set to `start` with `start` then set to `0`.
     *
     * **Note:** JavaScript follows the IEEE-754 standard for resolving
     * floating-point values which can produce unexpected results.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Util
     * @param {number} [start=0] The start of the range.
     * @param {number} end The end of the range.
     * @param {number} [step=1] The value to increment or decrement by.
     * @returns {Array} Returns the range of numbers.
     * @see _.inRange, _.rangeRight
     * @example
     *
     * _.range(4);
     * // => [0, 1, 2, 3]
     *
     * _.range(-4);
     * // => [0, -1, -2, -3]
     *
     * _.range(1, 5);
     * // => [1, 2, 3, 4]
     *
     * _.range(0, 20, 5);
     * // => [0, 5, 10, 15]
     *
     * _.range(0, -4, -1);
     * // => [0, -1, -2, -3]
     *
     * _.range(1, 4, 0);
     * // => [1, 1, 1]
     *
     * _.range(0);
     * // => []
     */
    var range = createRange();

    /**
     * This method is like `_.range` except that it populates values in
     * descending order.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {number} [start=0] The start of the range.
     * @param {number} end The end of the range.
     * @param {number} [step=1] The value to increment or decrement by.
     * @returns {Array} Returns the range of numbers.
     * @see _.inRange, _.range
     * @example
     *
     * _.rangeRight(4);
     * // => [3, 2, 1, 0]
     *
     * _.rangeRight(-4);
     * // => [-3, -2, -1, 0]
     *
     * _.rangeRight(1, 5);
     * // => [4, 3, 2, 1]
     *
     * _.rangeRight(0, 20, 5);
     * // => [15, 10, 5, 0]
     *
     * _.rangeRight(0, -4, -1);
     * // => [-3, -2, -1, 0]
     *
     * _.rangeRight(1, 4, 0);
     * // => [1, 1, 1]
     *
     * _.rangeRight(0);
     * // => []
     */
    var rangeRight = createRange(true);

    /**
     * This method returns a new empty array.
     *
     * @static
     * @memberOf _
     * @since 4.13.0
     * @category Util
     * @returns {Array} Returns the new empty array.
     * @example
     *
     * var arrays = _.times(2, _.stubArray);
     *
     * console.log(arrays);
     * // => [[], []]
     *
     * console.log(arrays[0] === arrays[1]);
     * // => false
     */
    function stubArray() {
      return [];
    }

    /**
     * This method returns `false`.
     *
     * @static
     * @memberOf _
     * @since 4.13.0
     * @category Util
     * @returns {boolean} Returns `false`.
     * @example
     *
     * _.times(2, _.stubFalse);
     * // => [false, false]
     */
    function stubFalse() {
      return false;
    }

    /**
     * This method returns a new empty object.
     *
     * @static
     * @memberOf _
     * @since 4.13.0
     * @category Util
     * @returns {Object} Returns the new empty object.
     * @example
     *
     * var objects = _.times(2, _.stubObject);
     *
     * console.log(objects);
     * // => [{}, {}]
     *
     * console.log(objects[0] === objects[1]);
     * // => false
     */
    function stubObject() {
      return {};
    }

    /**
     * This method returns an empty string.
     *
     * @static
     * @memberOf _
     * @since 4.13.0
     * @category Util
     * @returns {string} Returns the empty string.
     * @example
     *
     * _.times(2, _.stubString);
     * // => ['', '']
     */
    function stubString() {
      return '';
    }

    /**
     * This method returns `true`.
     *
     * @static
     * @memberOf _
     * @since 4.13.0
     * @category Util
     * @returns {boolean} Returns `true`.
     * @example
     *
     * _.times(2, _.stubTrue);
     * // => [true, true]
     */
    function stubTrue() {
      return true;
    }

    /**
     * Invokes the iteratee `n` times, returning an array of the results of
     * each invocation. The iteratee is invoked with one argument; (index).
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Util
     * @param {number} n The number of times to invoke `iteratee`.
     * @param {Function} [iteratee=_.identity] The function invoked per iteration.
     * @returns {Array} Returns the array of results.
     * @example
     *
     * _.times(3, String);
     * // => ['0', '1', '2']
     *
     *  _.times(4, _.constant(0));
     * // => [0, 0, 0, 0]
     */
    function times(n, iteratee) {
      n = toInteger(n);
      if (n < 1 || n > MAX_SAFE_INTEGER) {
        return [];
      }
      var index = MAX_ARRAY_LENGTH,
          length = nativeMin(n, MAX_ARRAY_LENGTH);

      iteratee = getIteratee(iteratee);
      n -= MAX_ARRAY_LENGTH;

      var result = baseTimes(length, iteratee);
      while (++index < n) {
        iteratee(index);
      }
      return result;
    }

    /**
     * Converts `value` to a property path array.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Util
     * @param {*} value The value to convert.
     * @returns {Array} Returns the new property path array.
     * @example
     *
     * _.toPath('a.b.c');
     * // => ['a', 'b', 'c']
     *
     * _.toPath('a[0].b.c');
     * // => ['a', '0', 'b', 'c']
     */
    function toPath(value) {
      if (isArray(value)) {
        return arrayMap(value, toKey);
      }
      return isSymbol(value) ? [value] : copyArray(stringToPath(value));
    }

    /**
     * Generates a unique ID. If `prefix` is given, the ID is appended to it.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Util
     * @param {string} [prefix=''] The value to prefix the ID with.
     * @returns {string} Returns the unique ID.
     * @example
     *
     * _.uniqueId('contact_');
     * // => 'contact_104'
     *
     * _.uniqueId();
     * // => '105'
     */
    function uniqueId(prefix) {
      var id = ++idCounter;
      return toString(prefix) + id;
    }

    /*------------------------------------------------------------------------*/

    /**
     * Adds two numbers.
     *
     * @static
     * @memberOf _
     * @since 3.4.0
     * @category Math
     * @param {number} augend The first number in an addition.
     * @param {number} addend The second number in an addition.
     * @returns {number} Returns the total.
     * @example
     *
     * _.add(6, 4);
     * // => 10
     */
    var add = createMathOperation(function(augend, addend) {
      return augend + addend;
    }, 0);

    /**
     * Computes `number` rounded up to `precision`.
     *
     * @static
     * @memberOf _
     * @since 3.10.0
     * @category Math
     * @param {number} number The number to round up.
     * @param {number} [precision=0] The precision to round up to.
     * @returns {number} Returns the rounded up number.
     * @example
     *
     * _.ceil(4.006);
     * // => 5
     *
     * _.ceil(6.004, 2);
     * // => 6.01
     *
     * _.ceil(6040, -2);
     * // => 6100
     */
    var ceil = createRound('ceil');

    /**
     * Divide two numbers.
     *
     * @static
     * @memberOf _
     * @since 4.7.0
     * @category Math
     * @param {number} dividend The first number in a division.
     * @param {number} divisor The second number in a division.
     * @returns {number} Returns the quotient.
     * @example
     *
     * _.divide(6, 4);
     * // => 1.5
     */
    var divide = createMathOperation(function(dividend, divisor) {
      return dividend / divisor;
    }, 1);

    /**
     * Computes `number` rounded down to `precision`.
     *
     * @static
     * @memberOf _
     * @since 3.10.0
     * @category Math
     * @param {number} number The number to round down.
     * @param {number} [precision=0] The precision to round down to.
     * @returns {number} Returns the rounded down number.
     * @example
     *
     * _.floor(4.006);
     * // => 4
     *
     * _.floor(0.046, 2);
     * // => 0.04
     *
     * _.floor(4060, -2);
     * // => 4000
     */
    var floor = createRound('floor');

    /**
     * Computes the maximum value of `array`. If `array` is empty or falsey,
     * `undefined` is returned.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Math
     * @param {Array} array The array to iterate over.
     * @returns {*} Returns the maximum value.
     * @example
     *
     * _.max([4, 2, 8, 6]);
     * // => 8
     *
     * _.max([]);
     * // => undefined
     */
    function max(array) {
      return (array && array.length)
        ? baseExtremum(array, identity, baseGt)
        : undefined;
    }

    /**
     * This method is like `_.max` except that it accepts `iteratee` which is
     * invoked for each element in `array` to generate the criterion by which
     * the value is ranked. The iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Math
     * @param {Array} array The array to iterate over.
     * @param {Function} [iteratee=_.identity] The iteratee invoked per element.
     * @returns {*} Returns the maximum value.
     * @example
     *
     * var objects = [{ 'n': 1 }, { 'n': 2 }];
     *
     * _.maxBy(objects, function(o) { return o.n; });
     * // => { 'n': 2 }
     *
     * // The `_.property` iteratee shorthand.
     * _.maxBy(objects, 'n');
     * // => { 'n': 2 }
     */
    function maxBy(array, iteratee) {
      return (array && array.length)
        ? baseExtremum(array, getIteratee(iteratee, 2), baseGt)
        : undefined;
    }

    /**
     * Computes the mean of the values in `array`.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Math
     * @param {Array} array The array to iterate over.
     * @returns {number} Returns the mean.
     * @example
     *
     * _.mean([4, 2, 8, 6]);
     * // => 5
     */
    function mean(array) {
      return baseMean(array, identity);
    }

    /**
     * This method is like `_.mean` except that it accepts `iteratee` which is
     * invoked for each element in `array` to generate the value to be averaged.
     * The iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.7.0
     * @category Math
     * @param {Array} array The array to iterate over.
     * @param {Function} [iteratee=_.identity] The iteratee invoked per element.
     * @returns {number} Returns the mean.
     * @example
     *
     * var objects = [{ 'n': 4 }, { 'n': 2 }, { 'n': 8 }, { 'n': 6 }];
     *
     * _.meanBy(objects, function(o) { return o.n; });
     * // => 5
     *
     * // The `_.property` iteratee shorthand.
     * _.meanBy(objects, 'n');
     * // => 5
     */
    function meanBy(array, iteratee) {
      return baseMean(array, getIteratee(iteratee, 2));
    }

    /**
     * Computes the minimum value of `array`. If `array` is empty or falsey,
     * `undefined` is returned.
     *
     * @static
     * @since 0.1.0
     * @memberOf _
     * @category Math
     * @param {Array} array The array to iterate over.
     * @returns {*} Returns the minimum value.
     * @example
     *
     * _.min([4, 2, 8, 6]);
     * // => 2
     *
     * _.min([]);
     * // => undefined
     */
    function min(array) {
      return (array && array.length)
        ? baseExtremum(array, identity, baseLt)
        : undefined;
    }

    /**
     * This method is like `_.min` except that it accepts `iteratee` which is
     * invoked for each element in `array` to generate the criterion by which
     * the value is ranked. The iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Math
     * @param {Array} array The array to iterate over.
     * @param {Function} [iteratee=_.identity] The iteratee invoked per element.
     * @returns {*} Returns the minimum value.
     * @example
     *
     * var objects = [{ 'n': 1 }, { 'n': 2 }];
     *
     * _.minBy(objects, function(o) { return o.n; });
     * // => { 'n': 1 }
     *
     * // The `_.property` iteratee shorthand.
     * _.minBy(objects, 'n');
     * // => { 'n': 1 }
     */
    function minBy(array, iteratee) {
      return (array && array.length)
        ? baseExtremum(array, getIteratee(iteratee, 2), baseLt)
        : undefined;
    }

    /**
     * Multiply two numbers.
     *
     * @static
     * @memberOf _
     * @since 4.7.0
     * @category Math
     * @param {number} multiplier The first number in a multiplication.
     * @param {number} multiplicand The second number in a multiplication.
     * @returns {number} Returns the product.
     * @example
     *
     * _.multiply(6, 4);
     * // => 24
     */
    var multiply = createMathOperation(function(multiplier, multiplicand) {
      return multiplier * multiplicand;
    }, 1);

    /**
     * Computes `number` rounded to `precision`.
     *
     * @static
     * @memberOf _
     * @since 3.10.0
     * @category Math
     * @param {number} number The number to round.
     * @param {number} [precision=0] The precision to round to.
     * @returns {number} Returns the rounded number.
     * @example
     *
     * _.round(4.006);
     * // => 4
     *
     * _.round(4.006, 2);
     * // => 4.01
     *
     * _.round(4060, -2);
     * // => 4100
     */
    var round = createRound('round');

    /**
     * Subtract two numbers.
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Math
     * @param {number} minuend The first number in a subtraction.
     * @param {number} subtrahend The second number in a subtraction.
     * @returns {number} Returns the difference.
     * @example
     *
     * _.subtract(6, 4);
     * // => 2
     */
    var subtract = createMathOperation(function(minuend, subtrahend) {
      return minuend - subtrahend;
    }, 0);

    /**
     * Computes the sum of the values in `array`.
     *
     * @static
     * @memberOf _
     * @since 3.4.0
     * @category Math
     * @param {Array} array The array to iterate over.
     * @returns {number} Returns the sum.
     * @example
     *
     * _.sum([4, 2, 8, 6]);
     * // => 20
     */
    function sum(array) {
      return (array && array.length)
        ? baseSum(array, identity)
        : 0;
    }

    /**
     * This method is like `_.sum` except that it accepts `iteratee` which is
     * invoked for each element in `array` to generate the value to be summed.
     * The iteratee is invoked with one argument: (value).
     *
     * @static
     * @memberOf _
     * @since 4.0.0
     * @category Math
     * @param {Array} array The array to iterate over.
     * @param {Function} [iteratee=_.identity] The iteratee invoked per element.
     * @returns {number} Returns the sum.
     * @example
     *
     * var objects = [{ 'n': 4 }, { 'n': 2 }, { 'n': 8 }, { 'n': 6 }];
     *
     * _.sumBy(objects, function(o) { return o.n; });
     * // => 20
     *
     * // The `_.property` iteratee shorthand.
     * _.sumBy(objects, 'n');
     * // => 20
     */
    function sumBy(array, iteratee) {
      return (array && array.length)
        ? baseSum(array, getIteratee(iteratee, 2))
        : 0;
    }

    /*------------------------------------------------------------------------*/

    // Add methods that return wrapped values in chain sequences.
    lodash.after = after;
    lodash.ary = ary;
    lodash.assign = assign;
    lodash.assignIn = assignIn;
    lodash.assignInWith = assignInWith;
    lodash.assignWith = assignWith;
    lodash.at = at;
    lodash.before = before;
    lodash.bind = bind;
    lodash.bindAll = bindAll;
    lodash.bindKey = bindKey;
    lodash.castArray = castArray;
    lodash.chain = chain;
    lodash.chunk = chunk;
    lodash.compact = compact;
    lodash.concat = concat;
    lodash.cond = cond;
    lodash.conforms = conforms;
    lodash.constant = constant;
    lodash.countBy = countBy;
    lodash.create = create;
    lodash.curry = curry;
    lodash.curryRight = curryRight;
    lodash.debounce = debounce;
    lodash.defaults = defaults;
    lodash.defaultsDeep = defaultsDeep;
    lodash.defer = defer;
    lodash.delay = delay;
    lodash.difference = difference;
    lodash.differenceBy = differenceBy;
    lodash.differenceWith = differenceWith;
    lodash.drop = drop;
    lodash.dropRight = dropRight;
    lodash.dropRightWhile = dropRightWhile;
    lodash.dropWhile = dropWhile;
    lodash.fill = fill;
    lodash.filter = filter;
    lodash.flatMap = flatMap;
    lodash.flatMapDeep = flatMapDeep;
    lodash.flatMapDepth = flatMapDepth;
    lodash.flatten = flatten;
    lodash.flattenDeep = flattenDeep;
    lodash.flattenDepth = flattenDepth;
    lodash.flip = flip;
    lodash.flow = flow;
    lodash.flowRight = flowRight;
    lodash.fromPairs = fromPairs;
    lodash.functions = functions;
    lodash.functionsIn = functionsIn;
    lodash.groupBy = groupBy;
    lodash.initial = initial;
    lodash.intersection = intersection;
    lodash.intersectionBy = intersectionBy;
    lodash.intersectionWith = intersectionWith;
    lodash.invert = invert;
    lodash.invertBy = invertBy;
    lodash.invokeMap = invokeMap;
    lodash.iteratee = iteratee;
    lodash.keyBy = keyBy;
    lodash.keys = keys;
    lodash.keysIn = keysIn;
    lodash.map = map;
    lodash.mapKeys = mapKeys;
    lodash.mapValues = mapValues;
    lodash.matches = matches;
    lodash.matchesProperty = matchesProperty;
    lodash.memoize = memoize;
    lodash.merge = merge;
    lodash.mergeWith = mergeWith;
    lodash.method = method;
    lodash.methodOf = methodOf;
    lodash.mixin = mixin;
    lodash.negate = negate;
    lodash.nthArg = nthArg;
    lodash.omit = omit;
    lodash.omitBy = omitBy;
    lodash.once = once;
    lodash.orderBy = orderBy;
    lodash.over = over;
    lodash.overArgs = overArgs;
    lodash.overEvery = overEvery;
    lodash.overSome = overSome;
    lodash.partial = partial;
    lodash.partialRight = partialRight;
    lodash.partition = partition;
    lodash.pick = pick;
    lodash.pickBy = pickBy;
    lodash.property = property;
    lodash.propertyOf = propertyOf;
    lodash.pull = pull;
    lodash.pullAll = pullAll;
    lodash.pullAllBy = pullAllBy;
    lodash.pullAllWith = pullAllWith;
    lodash.pullAt = pullAt;
    lodash.range = range;
    lodash.rangeRight = rangeRight;
    lodash.rearg = rearg;
    lodash.reject = reject;
    lodash.remove = remove;
    lodash.rest = rest;
    lodash.reverse = reverse;
    lodash.sampleSize = sampleSize;
    lodash.set = set;
    lodash.setWith = setWith;
    lodash.shuffle = shuffle;
    lodash.slice = slice;
    lodash.sortBy = sortBy;
    lodash.sortedUniq = sortedUniq;
    lodash.sortedUniqBy = sortedUniqBy;
    lodash.split = split;
    lodash.spread = spread;
    lodash.tail = tail;
    lodash.take = take;
    lodash.takeRight = takeRight;
    lodash.takeRightWhile = takeRightWhile;
    lodash.takeWhile = takeWhile;
    lodash.tap = tap;
    lodash.throttle = throttle;
    lodash.thru = thru;
    lodash.toArray = toArray;
    lodash.toPairs = toPairs;
    lodash.toPairsIn = toPairsIn;
    lodash.toPath = toPath;
    lodash.toPlainObject = toPlainObject;
    lodash.transform = transform;
    lodash.unary = unary;
    lodash.union = union;
    lodash.unionBy = unionBy;
    lodash.unionWith = unionWith;
    lodash.uniq = uniq;
    lodash.uniqBy = uniqBy;
    lodash.uniqWith = uniqWith;
    lodash.unset = unset;
    lodash.unzip = unzip;
    lodash.unzipWith = unzipWith;
    lodash.update = update;
    lodash.updateWith = updateWith;
    lodash.values = values;
    lodash.valuesIn = valuesIn;
    lodash.without = without;
    lodash.words = words;
    lodash.wrap = wrap;
    lodash.xor = xor;
    lodash.xorBy = xorBy;
    lodash.xorWith = xorWith;
    lodash.zip = zip;
    lodash.zipObject = zipObject;
    lodash.zipObjectDeep = zipObjectDeep;
    lodash.zipWith = zipWith;

    // Add aliases.
    lodash.entries = toPairs;
    lodash.entriesIn = toPairsIn;
    lodash.extend = assignIn;
    lodash.extendWith = assignInWith;

    // Add methods to `lodash.prototype`.
    mixin(lodash, lodash);

    /*------------------------------------------------------------------------*/

    // Add methods that return unwrapped values in chain sequences.
    lodash.add = add;
    lodash.attempt = attempt;
    lodash.camelCase = camelCase;
    lodash.capitalize = capitalize;
    lodash.ceil = ceil;
    lodash.clamp = clamp;
    lodash.clone = clone;
    lodash.cloneDeep = cloneDeep;
    lodash.cloneDeepWith = cloneDeepWith;
    lodash.cloneWith = cloneWith;
    lodash.conformsTo = conformsTo;
    lodash.deburr = deburr;
    lodash.defaultTo = defaultTo;
    lodash.divide = divide;
    lodash.endsWith = endsWith;
    lodash.eq = eq;
    lodash.escape = escape;
    lodash.escapeRegExp = escapeRegExp;
    lodash.every = every;
    lodash.find = find;
    lodash.findIndex = findIndex;
    lodash.findKey = findKey;
    lodash.findLast = findLast;
    lodash.findLastIndex = findLastIndex;
    lodash.findLastKey = findLastKey;
    lodash.floor = floor;
    lodash.forEach = forEach;
    lodash.forEachRight = forEachRight;
    lodash.forIn = forIn;
    lodash.forInRight = forInRight;
    lodash.forOwn = forOwn;
    lodash.forOwnRight = forOwnRight;
    lodash.get = get;
    lodash.gt = gt;
    lodash.gte = gte;
    lodash.has = has;
    lodash.hasIn = hasIn;
    lodash.head = head;
    lodash.identity = identity;
    lodash.includes = includes;
    lodash.indexOf = indexOf;
    lodash.inRange = inRange;
    lodash.invoke = invoke;
    lodash.isArguments = isArguments;
    lodash.isArray = isArray;
    lodash.isArrayBuffer = isArrayBuffer;
    lodash.isArrayLike = isArrayLike;
    lodash.isArrayLikeObject = isArrayLikeObject;
    lodash.isBoolean = isBoolean;
    lodash.isBuffer = isBuffer;
    lodash.isDate = isDate;
    lodash.isElement = isElement;
    lodash.isEmpty = isEmpty;
    lodash.isEqual = isEqual;
    lodash.isEqualWith = isEqualWith;
    lodash.isError = isError;
    lodash.isFinite = isFinite;
    lodash.isFunction = isFunction;
    lodash.isInteger = isInteger;
    lodash.isLength = isLength;
    lodash.isMap = isMap;
    lodash.isMatch = isMatch;
    lodash.isMatchWith = isMatchWith;
    lodash.isNaN = isNaN;
    lodash.isNative = isNative;
    lodash.isNil = isNil;
    lodash.isNull = isNull;
    lodash.isNumber = isNumber;
    lodash.isObject = isObject;
    lodash.isObjectLike = isObjectLike;
    lodash.isPlainObject = isPlainObject;
    lodash.isRegExp = isRegExp;
    lodash.isSafeInteger = isSafeInteger;
    lodash.isSet = isSet;
    lodash.isString = isString;
    lodash.isSymbol = isSymbol;
    lodash.isTypedArray = isTypedArray;
    lodash.isUndefined = isUndefined;
    lodash.isWeakMap = isWeakMap;
    lodash.isWeakSet = isWeakSet;
    lodash.join = join;
    lodash.kebabCase = kebabCase;
    lodash.last = last;
    lodash.lastIndexOf = lastIndexOf;
    lodash.lowerCase = lowerCase;
    lodash.lowerFirst = lowerFirst;
    lodash.lt = lt;
    lodash.lte = lte;
    lodash.max = max;
    lodash.maxBy = maxBy;
    lodash.mean = mean;
    lodash.meanBy = meanBy;
    lodash.min = min;
    lodash.minBy = minBy;
    lodash.stubArray = stubArray;
    lodash.stubFalse = stubFalse;
    lodash.stubObject = stubObject;
    lodash.stubString = stubString;
    lodash.stubTrue = stubTrue;
    lodash.multiply = multiply;
    lodash.nth = nth;
    lodash.noConflict = noConflict;
    lodash.noop = noop;
    lodash.now = now;
    lodash.pad = pad;
    lodash.padEnd = padEnd;
    lodash.padStart = padStart;
    lodash.parseInt = parseInt;
    lodash.random = random;
    lodash.reduce = reduce;
    lodash.reduceRight = reduceRight;
    lodash.repeat = repeat;
    lodash.replace = replace;
    lodash.result = result;
    lodash.round = round;
    lodash.runInContext = runInContext;
    lodash.sample = sample;
    lodash.size = size;
    lodash.snakeCase = snakeCase;
    lodash.some = some;
    lodash.sortedIndex = sortedIndex;
    lodash.sortedIndexBy = sortedIndexBy;
    lodash.sortedIndexOf = sortedIndexOf;
    lodash.sortedLastIndex = sortedLastIndex;
    lodash.sortedLastIndexBy = sortedLastIndexBy;
    lodash.sortedLastIndexOf = sortedLastIndexOf;
    lodash.startCase = startCase;
    lodash.startsWith = startsWith;
    lodash.subtract = subtract;
    lodash.sum = sum;
    lodash.sumBy = sumBy;
    lodash.template = template;
    lodash.times = times;
    lodash.toFinite = toFinite;
    lodash.toInteger = toInteger;
    lodash.toLength = toLength;
    lodash.toLower = toLower;
    lodash.toNumber = toNumber;
    lodash.toSafeInteger = toSafeInteger;
    lodash.toString = toString;
    lodash.toUpper = toUpper;
    lodash.trim = trim;
    lodash.trimEnd = trimEnd;
    lodash.trimStart = trimStart;
    lodash.truncate = truncate;
    lodash.unescape = unescape;
    lodash.uniqueId = uniqueId;
    lodash.upperCase = upperCase;
    lodash.upperFirst = upperFirst;

    // Add aliases.
    lodash.each = forEach;
    lodash.eachRight = forEachRight;
    lodash.first = head;

    mixin(lodash, (function() {
      var source = {};
      baseForOwn(lodash, function(func, methodName) {
        if (!hasOwnProperty.call(lodash.prototype, methodName)) {
          source[methodName] = func;
        }
      });
      return source;
    }()), { 'chain': false });

    /*------------------------------------------------------------------------*/

    /**
     * The semantic version number.
     *
     * @static
     * @memberOf _
     * @type {string}
     */
    lodash.VERSION = VERSION;

    // Assign default placeholders.
    arrayEach(['bind', 'bindKey', 'curry', 'curryRight', 'partial', 'partialRight'], function(methodName) {
      lodash[methodName].placeholder = lodash;
    });

    // Add `LazyWrapper` methods for `_.drop` and `_.take` variants.
    arrayEach(['drop', 'take'], function(methodName, index) {
      LazyWrapper.prototype[methodName] = function(n) {
        var filtered = this.__filtered__;
        if (filtered && !index) {
          return new LazyWrapper(this);
        }
        n = n === undefined ? 1 : nativeMax(toInteger(n), 0);

        var result = this.clone();
        if (filtered) {
          result.__takeCount__ = nativeMin(n, result.__takeCount__);
        } else {
          result.__views__.push({
            'size': nativeMin(n, MAX_ARRAY_LENGTH),
            'type': methodName + (result.__dir__ < 0 ? 'Right' : '')
          });
        }
        return result;
      };

      LazyWrapper.prototype[methodName + 'Right'] = function(n) {
        return this.reverse()[methodName](n).reverse();
      };
    });

    // Add `LazyWrapper` methods that accept an `iteratee` value.
    arrayEach(['filter', 'map', 'takeWhile'], function(methodName, index) {
      var type = index + 1,
          isFilter = type == LAZY_FILTER_FLAG || type == LAZY_WHILE_FLAG;

      LazyWrapper.prototype[methodName] = function(iteratee) {
        var result = this.clone();
        result.__iteratees__.push({
          'iteratee': getIteratee(iteratee, 3),
          'type': type
        });
        result.__filtered__ = result.__filtered__ || isFilter;
        return result;
      };
    });

    // Add `LazyWrapper` methods for `_.head` and `_.last`.
    arrayEach(['head', 'last'], function(methodName, index) {
      var takeName = 'take' + (index ? 'Right' : '');

      LazyWrapper.prototype[methodName] = function() {
        return this[takeName](1).value()[0];
      };
    });

    // Add `LazyWrapper` methods for `_.initial` and `_.tail`.
    arrayEach(['initial', 'tail'], function(methodName, index) {
      var dropName = 'drop' + (index ? '' : 'Right');

      LazyWrapper.prototype[methodName] = function() {
        return this.__filtered__ ? new LazyWrapper(this) : this[dropName](1);
      };
    });

    LazyWrapper.prototype.compact = function() {
      return this.filter(identity);
    };

    LazyWrapper.prototype.find = function(predicate) {
      return this.filter(predicate).head();
    };

    LazyWrapper.prototype.findLast = function(predicate) {
      return this.reverse().find(predicate);
    };

    LazyWrapper.prototype.invokeMap = baseRest(function(path, args) {
      if (typeof path == 'function') {
        return new LazyWrapper(this);
      }
      return this.map(function(value) {
        return baseInvoke(value, path, args);
      });
    });

    LazyWrapper.prototype.reject = function(predicate) {
      return this.filter(negate(getIteratee(predicate)));
    };

    LazyWrapper.prototype.slice = function(start, end) {
      start = toInteger(start);

      var result = this;
      if (result.__filtered__ && (start > 0 || end < 0)) {
        return new LazyWrapper(result);
      }
      if (start < 0) {
        result = result.takeRight(-start);
      } else if (start) {
        result = result.drop(start);
      }
      if (end !== undefined) {
        end = toInteger(end);
        result = end < 0 ? result.dropRight(-end) : result.take(end - start);
      }
      return result;
    };

    LazyWrapper.prototype.takeRightWhile = function(predicate) {
      return this.reverse().takeWhile(predicate).reverse();
    };

    LazyWrapper.prototype.toArray = function() {
      return this.take(MAX_ARRAY_LENGTH);
    };

    // Add `LazyWrapper` methods to `lodash.prototype`.
    baseForOwn(LazyWrapper.prototype, function(func, methodName) {
      var checkIteratee = /^(?:filter|find|map|reject)|While$/.test(methodName),
          isTaker = /^(?:head|last)$/.test(methodName),
          lodashFunc = lodash[isTaker ? ('take' + (methodName == 'last' ? 'Right' : '')) : methodName],
          retUnwrapped = isTaker || /^find/.test(methodName);

      if (!lodashFunc) {
        return;
      }
      lodash.prototype[methodName] = function() {
        var value = this.__wrapped__,
            args = isTaker ? [1] : arguments,
            isLazy = value instanceof LazyWrapper,
            iteratee = args[0],
            useLazy = isLazy || isArray(value);

        var interceptor = function(value) {
          var result = lodashFunc.apply(lodash, arrayPush([value], args));
          return (isTaker && chainAll) ? result[0] : result;
        };

        if (useLazy && checkIteratee && typeof iteratee == 'function' && iteratee.length != 1) {
          // Avoid lazy use if the iteratee has a "length" value other than `1`.
          isLazy = useLazy = false;
        }
        var chainAll = this.__chain__,
            isHybrid = !!this.__actions__.length,
            isUnwrapped = retUnwrapped && !chainAll,
            onlyLazy = isLazy && !isHybrid;

        if (!retUnwrapped && useLazy) {
          value = onlyLazy ? value : new LazyWrapper(this);
          var result = func.apply(value, args);
          result.__actions__.push({ 'func': thru, 'args': [interceptor], 'thisArg': undefined });
          return new LodashWrapper(result, chainAll);
        }
        if (isUnwrapped && onlyLazy) {
          return func.apply(this, args);
        }
        result = this.thru(interceptor);
        return isUnwrapped ? (isTaker ? result.value()[0] : result.value()) : result;
      };
    });

    // Add `Array` methods to `lodash.prototype`.
    arrayEach(['pop', 'push', 'shift', 'sort', 'splice', 'unshift'], function(methodName) {
      var func = arrayProto[methodName],
          chainName = /^(?:push|sort|unshift)$/.test(methodName) ? 'tap' : 'thru',
          retUnwrapped = /^(?:pop|shift)$/.test(methodName);

      lodash.prototype[methodName] = function() {
        var args = arguments;
        if (retUnwrapped && !this.__chain__) {
          var value = this.value();
          return func.apply(isArray(value) ? value : [], args);
        }
        return this[chainName](function(value) {
          return func.apply(isArray(value) ? value : [], args);
        });
      };
    });

    // Map minified method names to their real names.
    baseForOwn(LazyWrapper.prototype, function(func, methodName) {
      var lodashFunc = lodash[methodName];
      if (lodashFunc) {
        var key = (lodashFunc.name + ''),
            names = realNames[key] || (realNames[key] = []);

        names.push({ 'name': methodName, 'func': lodashFunc });
      }
    });

    realNames[createHybrid(undefined, BIND_KEY_FLAG).name] = [{
      'name': 'wrapper',
      'func': undefined
    }];

    // Add methods to `LazyWrapper`.
    LazyWrapper.prototype.clone = lazyClone;
    LazyWrapper.prototype.reverse = lazyReverse;
    LazyWrapper.prototype.value = lazyValue;

    // Add chain sequence methods to the `lodash` wrapper.
    lodash.prototype.at = wrapperAt;
    lodash.prototype.chain = wrapperChain;
    lodash.prototype.commit = wrapperCommit;
    lodash.prototype.next = wrapperNext;
    lodash.prototype.plant = wrapperPlant;
    lodash.prototype.reverse = wrapperReverse;
    lodash.prototype.toJSON = lodash.prototype.valueOf = lodash.prototype.value = wrapperValue;

    // Add lazy aliases.
    lodash.prototype.first = lodash.prototype.head;

    if (iteratorSymbol) {
      lodash.prototype[iteratorSymbol] = wrapperToIterator;
    }
    return lodash;
  });

  /*--------------------------------------------------------------------------*/

  // Export lodash.
  var _ = runInContext();

  // Some AMD build optimizers, like r.js, check for condition patterns like:
  if (typeof define == 'function' && typeof define.amd == 'object' && define.amd) {
    // Expose Lodash on the global object to prevent errors when Lodash is
    // loaded by a script tag in the presence of an AMD loader.
    // See http://requirejs.org/docs/errors.html#mismatch for more details.
    // Use `_.noConflict` to remove Lodash from the global object.
    root._ = _;

    // Define as an anonymous module so, through path mapping, it can be
    // referenced as the "underscore" module.
    define(function() {
      return _;
    });
  }
  // Check for `exports` after `define` in case a build optimizer adds it.
  else if (freeModule) {
    // Export for Node.js.
    (freeModule.exports = _)._ = _;
    // Export for CommonJS support.
    freeExports._ = _;
  }
  else {
    // Export to the global object.
    root._ = _;
  }
}.call(this));

}).call(this,typeof global !== "undefined" ? global : typeof self !== "undefined" ? self : typeof window !== "undefined" ? window : {})
},{}],16:[function(require,module,exports){
(function (global){
"use strict";

var numeric = (typeof exports === "undefined")?(function numeric() {}):(exports);
if(typeof global !== "undefined") { global.numeric = numeric; }

numeric.version = "1.2.6";

// 1. Utility functions
numeric.bench = function bench (f,interval) {
    var t1,t2,n,i;
    if(typeof interval === "undefined") { interval = 15; }
    n = 0.5;
    t1 = new Date();
    while(1) {
        n*=2;
        for(i=n;i>3;i-=4) { f(); f(); f(); f(); }
        while(i>0) { f(); i--; }
        t2 = new Date();
        if(t2-t1 > interval) break;
    }
    for(i=n;i>3;i-=4) { f(); f(); f(); f(); }
    while(i>0) { f(); i--; }
    t2 = new Date();
    return 1000*(3*n-1)/(t2-t1);
}

numeric._myIndexOf = (function _myIndexOf(w) {
    var n = this.length,k;
    for(k=0;k<n;++k) if(this[k]===w) return k;
    return -1;
});
numeric.myIndexOf = (Array.prototype.indexOf)?Array.prototype.indexOf:numeric._myIndexOf;

numeric.Function = Function;
numeric.precision = 4;
numeric.largeArray = 50;

numeric.prettyPrint = function prettyPrint(x) {
    function fmtnum(x) {
        if(x === 0) { return '0'; }
        if(isNaN(x)) { return 'NaN'; }
        if(x<0) { return '-'+fmtnum(-x); }
        if(isFinite(x)) {
            var scale = Math.floor(Math.log(x) / Math.log(10));
            var normalized = x / Math.pow(10,scale);
            var basic = normalized.toPrecision(numeric.precision);
            if(parseFloat(basic) === 10) { scale++; normalized = 1; basic = normalized.toPrecision(numeric.precision); }
            return parseFloat(basic).toString()+'e'+scale.toString();
        }
        return 'Infinity';
    }
    var ret = [];
    function foo(x) {
        var k;
        if(typeof x === "undefined") { ret.push(Array(numeric.precision+8).join(' ')); return false; }
        if(typeof x === "string") { ret.push('"'+x+'"'); return false; }
        if(typeof x === "boolean") { ret.push(x.toString()); return false; }
        if(typeof x === "number") {
            var a = fmtnum(x);
            var b = x.toPrecision(numeric.precision);
            var c = parseFloat(x.toString()).toString();
            var d = [a,b,c,parseFloat(b).toString(),parseFloat(c).toString()];
            for(k=1;k<d.length;k++) { if(d[k].length < a.length) a = d[k]; }
            ret.push(Array(numeric.precision+8-a.length).join(' ')+a);
            return false;
        }
        if(x === null) { ret.push("null"); return false; }
        if(typeof x === "function") { 
            ret.push(x.toString());
            var flag = false;
            for(k in x) { if(x.hasOwnProperty(k)) { 
                if(flag) ret.push(',\n');
                else ret.push('\n{');
                flag = true; 
                ret.push(k); 
                ret.push(': \n'); 
                foo(x[k]); 
            } }
            if(flag) ret.push('}\n');
            return true;
        }
        if(x instanceof Array) {
            if(x.length > numeric.largeArray) { ret.push('...Large Array...'); return true; }
            var flag = false;
            ret.push('[');
            for(k=0;k<x.length;k++) { if(k>0) { ret.push(','); if(flag) ret.push('\n '); } flag = foo(x[k]); }
            ret.push(']');
            return true;
        }
        ret.push('{');
        var flag = false;
        for(k in x) { if(x.hasOwnProperty(k)) { if(flag) ret.push(',\n'); flag = true; ret.push(k); ret.push(': \n'); foo(x[k]); } }
        ret.push('}');
        return true;
    }
    foo(x);
    return ret.join('');
}

numeric.parseDate = function parseDate(d) {
    function foo(d) {
        if(typeof d === 'string') { return Date.parse(d.replace(/-/g,'/')); }
        if(!(d instanceof Array)) { throw new Error("parseDate: parameter must be arrays of strings"); }
        var ret = [],k;
        for(k=0;k<d.length;k++) { ret[k] = foo(d[k]); }
        return ret;
    }
    return foo(d);
}

numeric.parseFloat = function parseFloat_(d) {
    function foo(d) {
        if(typeof d === 'string') { return parseFloat(d); }
        if(!(d instanceof Array)) { throw new Error("parseFloat: parameter must be arrays of strings"); }
        var ret = [],k;
        for(k=0;k<d.length;k++) { ret[k] = foo(d[k]); }
        return ret;
    }
    return foo(d);
}

numeric.parseCSV = function parseCSV(t) {
    var foo = t.split('\n');
    var j,k;
    var ret = [];
    var pat = /(([^'",]*)|('[^']*')|("[^"]*")),/g;
    var patnum = /^\s*(([+-]?[0-9]+(\.[0-9]*)?(e[+-]?[0-9]+)?)|([+-]?[0-9]*(\.[0-9]+)?(e[+-]?[0-9]+)?))\s*$/;
    var stripper = function(n) { return n.substr(0,n.length-1); }
    var count = 0;
    for(k=0;k<foo.length;k++) {
      var bar = (foo[k]+",").match(pat),baz;
      if(bar.length>0) {
          ret[count] = [];
          for(j=0;j<bar.length;j++) {
              baz = stripper(bar[j]);
              if(patnum.test(baz)) { ret[count][j] = parseFloat(baz); }
              else ret[count][j] = baz;
          }
          count++;
      }
    }
    return ret;
}

numeric.toCSV = function toCSV(A) {
    var s = numeric.dim(A);
    var i,j,m,n,row,ret;
    m = s[0];
    n = s[1];
    ret = [];
    for(i=0;i<m;i++) {
        row = [];
        for(j=0;j<m;j++) { row[j] = A[i][j].toString(); }
        ret[i] = row.join(', ');
    }
    return ret.join('\n')+'\n';
}

numeric.getURL = function getURL(url) {
    var client = new XMLHttpRequest();
    client.open("GET",url,false);
    client.send();
    return client;
}

numeric.imageURL = function imageURL(img) {
    function base64(A) {
        var n = A.length, i,x,y,z,p,q,r,s;
        var key = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=";
        var ret = "";
        for(i=0;i<n;i+=3) {
            x = A[i];
            y = A[i+1];
            z = A[i+2];
            p = x >> 2;
            q = ((x & 3) << 4) + (y >> 4);
            r = ((y & 15) << 2) + (z >> 6);
            s = z & 63;
            if(i+1>=n) { r = s = 64; }
            else if(i+2>=n) { s = 64; }
            ret += key.charAt(p) + key.charAt(q) + key.charAt(r) + key.charAt(s);
            }
        return ret;
    }
    function crc32Array (a,from,to) {
        if(typeof from === "undefined") { from = 0; }
        if(typeof to === "undefined") { to = a.length; }
        var table = [0x00000000, 0x77073096, 0xEE0E612C, 0x990951BA, 0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
                     0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988, 0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91, 
                     0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE, 0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
                     0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC, 0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5, 
                     0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172, 0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B, 
                     0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940, 0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59, 
                     0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116, 0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
                     0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924, 0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
                     0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A, 0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
                     0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818, 0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01, 
                     0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E, 0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457, 
                     0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C, 0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65, 
                     0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2, 0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB, 
                     0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0, 0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9, 
                     0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086, 0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F, 
                     0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4, 0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD, 
                     0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A, 0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683, 
                     0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8, 0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1, 
                     0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE, 0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7, 
                     0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC, 0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5, 
                     0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252, 0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B, 
                     0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60, 0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79, 
                     0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236, 0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F, 
                     0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04, 0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D, 
                     0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A, 0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713, 
                     0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38, 0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21, 
                     0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E, 0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777, 
                     0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C, 0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45, 
                     0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2, 0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB, 
                     0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0, 0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9, 
                     0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6, 0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF, 
                     0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94, 0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D];
     
        var crc = -1, y = 0, n = a.length,i;

        for (i = from; i < to; i++) {
            y = (crc ^ a[i]) & 0xFF;
            crc = (crc >>> 8) ^ table[y];
        }
     
        return crc ^ (-1);
    }

    var h = img[0].length, w = img[0][0].length, s1, s2, next,k,length,a,b,i,j,adler32,crc32;
    var stream = [
                  137, 80, 78, 71, 13, 10, 26, 10,                           //  0: PNG signature
                  0,0,0,13,                                                  //  8: IHDR Chunk length
                  73, 72, 68, 82,                                            // 12: "IHDR" 
                  (w >> 24) & 255, (w >> 16) & 255, (w >> 8) & 255, w&255,   // 16: Width
                  (h >> 24) & 255, (h >> 16) & 255, (h >> 8) & 255, h&255,   // 20: Height
                  8,                                                         // 24: bit depth
                  2,                                                         // 25: RGB
                  0,                                                         // 26: deflate
                  0,                                                         // 27: no filter
                  0,                                                         // 28: no interlace
                  -1,-2,-3,-4,                                               // 29: CRC
                  -5,-6,-7,-8,                                               // 33: IDAT Chunk length
                  73, 68, 65, 84,                                            // 37: "IDAT"
                  // RFC 1950 header starts here
                  8,                                                         // 41: RFC1950 CMF
                  29                                                         // 42: RFC1950 FLG
                  ];
    crc32 = crc32Array(stream,12,29);
    stream[29] = (crc32>>24)&255;
    stream[30] = (crc32>>16)&255;
    stream[31] = (crc32>>8)&255;
    stream[32] = (crc32)&255;
    s1 = 1;
    s2 = 0;
    for(i=0;i<h;i++) {
        if(i<h-1) { stream.push(0); }
        else { stream.push(1); }
        a = (3*w+1+(i===0))&255; b = ((3*w+1+(i===0))>>8)&255;
        stream.push(a); stream.push(b);
        stream.push((~a)&255); stream.push((~b)&255);
        if(i===0) stream.push(0);
        for(j=0;j<w;j++) {
            for(k=0;k<3;k++) {
                a = img[k][i][j];
                if(a>255) a = 255;
                else if(a<0) a=0;
                else a = Math.round(a);
                s1 = (s1 + a )%65521;
                s2 = (s2 + s1)%65521;
                stream.push(a);
            }
        }
        stream.push(0);
    }
    adler32 = (s2<<16)+s1;
    stream.push((adler32>>24)&255);
    stream.push((adler32>>16)&255);
    stream.push((adler32>>8)&255);
    stream.push((adler32)&255);
    length = stream.length - 41;
    stream[33] = (length>>24)&255;
    stream[34] = (length>>16)&255;
    stream[35] = (length>>8)&255;
    stream[36] = (length)&255;
    crc32 = crc32Array(stream,37);
    stream.push((crc32>>24)&255);
    stream.push((crc32>>16)&255);
    stream.push((crc32>>8)&255);
    stream.push((crc32)&255);
    stream.push(0);
    stream.push(0);
    stream.push(0);
    stream.push(0);
//    a = stream.length;
    stream.push(73);  // I
    stream.push(69);  // E
    stream.push(78);  // N
    stream.push(68);  // D
    stream.push(174); // CRC1
    stream.push(66);  // CRC2
    stream.push(96);  // CRC3
    stream.push(130); // CRC4
    return 'data:image/png;base64,'+base64(stream);
}

// 2. Linear algebra with Arrays.
numeric._dim = function _dim(x) {
    var ret = [];
    while(typeof x === "object") { ret.push(x.length); x = x[0]; }
    return ret;
}

numeric.dim = function dim(x) {
    var y,z;
    if(typeof x === "object") {
        y = x[0];
        if(typeof y === "object") {
            z = y[0];
            if(typeof z === "object") {
                return numeric._dim(x);
            }
            return [x.length,y.length];
        }
        return [x.length];
    }
    return [];
}

numeric.mapreduce = function mapreduce(body,init) {
    return Function('x','accum','_s','_k',
            'if(typeof accum === "undefined") accum = '+init+';\n'+
            'if(typeof x === "number") { var xi = x; '+body+'; return accum; }\n'+
            'if(typeof _s === "undefined") _s = numeric.dim(x);\n'+
            'if(typeof _k === "undefined") _k = 0;\n'+
            'var _n = _s[_k];\n'+
            'var i,xi;\n'+
            'if(_k < _s.length-1) {\n'+
            '    for(i=_n-1;i>=0;i--) {\n'+
            '        accum = arguments.callee(x[i],accum,_s,_k+1);\n'+
            '    }'+
            '    return accum;\n'+
            '}\n'+
            'for(i=_n-1;i>=1;i-=2) { \n'+
            '    xi = x[i];\n'+
            '    '+body+';\n'+
            '    xi = x[i-1];\n'+
            '    '+body+';\n'+
            '}\n'+
            'if(i === 0) {\n'+
            '    xi = x[i];\n'+
            '    '+body+'\n'+
            '}\n'+
            'return accum;'
            );
}
numeric.mapreduce2 = function mapreduce2(body,setup) {
    return Function('x',
            'var n = x.length;\n'+
            'var i,xi;\n'+setup+';\n'+
            'for(i=n-1;i!==-1;--i) { \n'+
            '    xi = x[i];\n'+
            '    '+body+';\n'+
            '}\n'+
            'return accum;'
            );
}


numeric.same = function same(x,y) {
    var i,n;
    if(!(x instanceof Array) || !(y instanceof Array)) { return false; }
    n = x.length;
    if(n !== y.length) { return false; }
    for(i=0;i<n;i++) {
        if(x[i] === y[i]) { continue; }
        if(typeof x[i] === "object") { if(!same(x[i],y[i])) return false; }
        else { return false; }
    }
    return true;
}

numeric.rep = function rep(s,v,k) {
    if(typeof k === "undefined") { k=0; }
    var n = s[k], ret = Array(n), i;
    if(k === s.length-1) {
        for(i=n-2;i>=0;i-=2) { ret[i+1] = v; ret[i] = v; }
        if(i===-1) { ret[0] = v; }
        return ret;
    }
    for(i=n-1;i>=0;i--) { ret[i] = numeric.rep(s,v,k+1); }
    return ret;
}


numeric.dotMMsmall = function dotMMsmall(x,y) {
    var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0;
    p = x.length; q = y.length; r = y[0].length;
    ret = Array(p);
    for(i=p-1;i>=0;i--) {
        foo = Array(r);
        bar = x[i];
        for(k=r-1;k>=0;k--) {
            woo = bar[q-1]*y[q-1][k];
            for(j=q-2;j>=1;j-=2) {
                i0 = j-1;
                woo += bar[j]*y[j][k] + bar[i0]*y[i0][k];
            }
            if(j===0) { woo += bar[0]*y[0][k]; }
            foo[k] = woo;
        }
        ret[i] = foo;
    }
    return ret;
}
numeric._getCol = function _getCol(A,j,x) {
    var n = A.length, i;
    for(i=n-1;i>0;--i) {
        x[i] = A[i][j];
        --i;
        x[i] = A[i][j];
    }
    if(i===0) x[0] = A[0][j];
}
numeric.dotMMbig = function dotMMbig(x,y){
    var gc = numeric._getCol, p = y.length, v = Array(p);
    var m = x.length, n = y[0].length, A = new Array(m), xj;
    var VV = numeric.dotVV;
    var i,j,k,z;
    --p;
    --m;
    for(i=m;i!==-1;--i) A[i] = Array(n);
    --n;
    for(i=n;i!==-1;--i) {
        gc(y,i,v);
        for(j=m;j!==-1;--j) {
            z=0;
            xj = x[j];
            A[j][i] = VV(xj,v);
        }
    }
    return A;
}

numeric.dotMV = function dotMV(x,y) {
    var p = x.length, q = y.length,i;
    var ret = Array(p), dotVV = numeric.dotVV;
    for(i=p-1;i>=0;i--) { ret[i] = dotVV(x[i],y); }
    return ret;
}

numeric.dotVM = function dotVM(x,y) {
    var i,j,k,p,q,r,ret,foo,bar,woo,i0,k0,p0,r0,s1,s2,s3,baz,accum;
    p = x.length; q = y[0].length;
    ret = Array(q);
    for(k=q-1;k>=0;k--) {
        woo = x[p-1]*y[p-1][k];
        for(j=p-2;j>=1;j-=2) {
            i0 = j-1;
            woo += x[j]*y[j][k] + x[i0]*y[i0][k];
        }
        if(j===0) { woo += x[0]*y[0][k]; }
        ret[k] = woo;
    }
    return ret;
}

numeric.dotVV = function dotVV(x,y) {
    var i,n=x.length,i1,ret = x[n-1]*y[n-1];
    for(i=n-2;i>=1;i-=2) {
        i1 = i-1;
        ret += x[i]*y[i] + x[i1]*y[i1];
    }
    if(i===0) { ret += x[0]*y[0]; }
    return ret;
}

numeric.dot = function dot(x,y) {
    var d = numeric.dim;
    switch(d(x).length*1000+d(y).length) {
    case 2002:
        if(y.length < 10) return numeric.dotMMsmall(x,y);
        else return numeric.dotMMbig(x,y);
    case 2001: return numeric.dotMV(x,y);
    case 1002: return numeric.dotVM(x,y);
    case 1001: return numeric.dotVV(x,y);
    case 1000: return numeric.mulVS(x,y);
    case 1: return numeric.mulSV(x,y);
    case 0: return x*y;
    default: throw new Error('numeric.dot only works on vectors and matrices');
    }
}

numeric.diag = function diag(d) {
    var i,i1,j,n = d.length, A = Array(n), Ai;
    for(i=n-1;i>=0;i--) {
        Ai = Array(n);
        i1 = i+2;
        for(j=n-1;j>=i1;j-=2) {
            Ai[j] = 0;
            Ai[j-1] = 0;
        }
        if(j>i) { Ai[j] = 0; }
        Ai[i] = d[i];
        for(j=i-1;j>=1;j-=2) {
            Ai[j] = 0;
            Ai[j-1] = 0;
        }
        if(j===0) { Ai[0] = 0; }
        A[i] = Ai;
    }
    return A;
}
numeric.getDiag = function(A) {
    var n = Math.min(A.length,A[0].length),i,ret = Array(n);
    for(i=n-1;i>=1;--i) {
        ret[i] = A[i][i];
        --i;
        ret[i] = A[i][i];
    }
    if(i===0) {
        ret[0] = A[0][0];
    }
    return ret;
}

numeric.identity = function identity(n) { return numeric.diag(numeric.rep([n],1)); }
numeric.pointwise = function pointwise(params,body,setup) {
    if(typeof setup === "undefined") { setup = ""; }
    var fun = [];
    var k;
    var avec = /\[i\]$/,p,thevec = '';
    var haveret = false;
    for(k=0;k<params.length;k++) {
        if(avec.test(params[k])) {
            p = params[k].substring(0,params[k].length-3);
            thevec = p;
        } else { p = params[k]; }
        if(p==='ret') haveret = true;
        fun.push(p);
    }
    fun[params.length] = '_s';
    fun[params.length+1] = '_k';
    fun[params.length+2] = (
            'if(typeof _s === "undefined") _s = numeric.dim('+thevec+');\n'+
            'if(typeof _k === "undefined") _k = 0;\n'+
            'var _n = _s[_k];\n'+
            'var i'+(haveret?'':', ret = Array(_n)')+';\n'+
            'if(_k < _s.length-1) {\n'+
            '    for(i=_n-1;i>=0;i--) ret[i] = arguments.callee('+params.join(',')+',_s,_k+1);\n'+
            '    return ret;\n'+
            '}\n'+
            setup+'\n'+
            'for(i=_n-1;i!==-1;--i) {\n'+
            '    '+body+'\n'+
            '}\n'+
            'return ret;'
            );
    return Function.apply(null,fun);
}
numeric.pointwise2 = function pointwise2(params,body,setup) {
    if(typeof setup === "undefined") { setup = ""; }
    var fun = [];
    var k;
    var avec = /\[i\]$/,p,thevec = '';
    var haveret = false;
    for(k=0;k<params.length;k++) {
        if(avec.test(params[k])) {
            p = params[k].substring(0,params[k].length-3);
            thevec = p;
        } else { p = params[k]; }
        if(p==='ret') haveret = true;
        fun.push(p);
    }
    fun[params.length] = (
            'var _n = '+thevec+'.length;\n'+
            'var i'+(haveret?'':', ret = Array(_n)')+';\n'+
            setup+'\n'+
            'for(i=_n-1;i!==-1;--i) {\n'+
            body+'\n'+
            '}\n'+
            'return ret;'
            );
    return Function.apply(null,fun);
}
numeric._biforeach = (function _biforeach(x,y,s,k,f) {
    if(k === s.length-1) { f(x,y); return; }
    var i,n=s[k];
    for(i=n-1;i>=0;i--) { _biforeach(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f); }
});
numeric._biforeach2 = (function _biforeach2(x,y,s,k,f) {
    if(k === s.length-1) { return f(x,y); }
    var i,n=s[k],ret = Array(n);
    for(i=n-1;i>=0;--i) { ret[i] = _biforeach2(typeof x==="object"?x[i]:x,typeof y==="object"?y[i]:y,s,k+1,f); }
    return ret;
});
numeric._foreach = (function _foreach(x,s,k,f) {
    if(k === s.length-1) { f(x); return; }
    var i,n=s[k];
    for(i=n-1;i>=0;i--) { _foreach(x[i],s,k+1,f); }
});
numeric._foreach2 = (function _foreach2(x,s,k,f) {
    if(k === s.length-1) { return f(x); }
    var i,n=s[k], ret = Array(n);
    for(i=n-1;i>=0;i--) { ret[i] = _foreach2(x[i],s,k+1,f); }
    return ret;
});

/*numeric.anyV = numeric.mapreduce('if(xi) return true;','false');
numeric.allV = numeric.mapreduce('if(!xi) return false;','true');
numeric.any = function(x) { if(typeof x.length === "undefined") return x; return numeric.anyV(x); }
numeric.all = function(x) { if(typeof x.length === "undefined") return x; return numeric.allV(x); }*/

numeric.ops2 = {
        add: '+',
        sub: '-',
        mul: '*',
        div: '/',
        mod: '%',
        and: '&&',
        or:  '||',
        eq:  '===',
        neq: '!==',
        lt:  '<',
        gt:  '>',
        leq: '<=',
        geq: '>=',
        band: '&',
        bor: '|',
        bxor: '^',
        lshift: '<<',
        rshift: '>>',
        rrshift: '>>>'
};
numeric.opseq = {
        addeq: '+=',
        subeq: '-=',
        muleq: '*=',
        diveq: '/=',
        modeq: '%=',
        lshifteq: '<<=',
        rshifteq: '>>=',
        rrshifteq: '>>>=',
        bandeq: '&=',
        boreq: '|=',
        bxoreq: '^='
};
numeric.mathfuns = ['abs','acos','asin','atan','ceil','cos',
                    'exp','floor','log','round','sin','sqrt','tan',
                    'isNaN','isFinite'];
numeric.mathfuns2 = ['atan2','pow','max','min'];
numeric.ops1 = {
        neg: '-',
        not: '!',
        bnot: '~',
        clone: ''
};
numeric.mapreducers = {
        any: ['if(xi) return true;','var accum = false;'],
        all: ['if(!xi) return false;','var accum = true;'],
        sum: ['accum += xi;','var accum = 0;'],
        prod: ['accum *= xi;','var accum = 1;'],
        norm2Squared: ['accum += xi*xi;','var accum = 0;'],
        norminf: ['accum = max(accum,abs(xi));','var accum = 0, max = Math.max, abs = Math.abs;'],
        norm1: ['accum += abs(xi)','var accum = 0, abs = Math.abs;'],
        sup: ['accum = max(accum,xi);','var accum = -Infinity, max = Math.max;'],
        inf: ['accum = min(accum,xi);','var accum = Infinity, min = Math.min;']
};

(function () {
    var i,o;
    for(i=0;i<numeric.mathfuns2.length;++i) {
        o = numeric.mathfuns2[i];
        numeric.ops2[o] = o;
    }
    for(i in numeric.ops2) {
        if(numeric.ops2.hasOwnProperty(i)) {
            o = numeric.ops2[i];
            var code, codeeq, setup = '';
            if(numeric.myIndexOf.call(numeric.mathfuns2,i)!==-1) {
                setup = 'var '+o+' = Math.'+o+';\n';
                code = function(r,x,y) { return r+' = '+o+'('+x+','+y+')'; };
                codeeq = function(x,y) { return x+' = '+o+'('+x+','+y+')'; };
            } else {
                code = function(r,x,y) { return r+' = '+x+' '+o+' '+y; };
                if(numeric.opseq.hasOwnProperty(i+'eq')) {
                    codeeq = function(x,y) { return x+' '+o+'= '+y; };
                } else {
                    codeeq = function(x,y) { return x+' = '+x+' '+o+' '+y; };                    
                }
            }
            numeric[i+'VV'] = numeric.pointwise2(['x[i]','y[i]'],code('ret[i]','x[i]','y[i]'),setup);
            numeric[i+'SV'] = numeric.pointwise2(['x','y[i]'],code('ret[i]','x','y[i]'),setup);
            numeric[i+'VS'] = numeric.pointwise2(['x[i]','y'],code('ret[i]','x[i]','y'),setup);
            numeric[i] = Function(
                    'var n = arguments.length, i, x = arguments[0], y;\n'+
                    'var VV = numeric.'+i+'VV, VS = numeric.'+i+'VS, SV = numeric.'+i+'SV;\n'+
                    'var dim = numeric.dim;\n'+
                    'for(i=1;i!==n;++i) { \n'+
                    '  y = arguments[i];\n'+
                    '  if(typeof x === "object") {\n'+
                    '      if(typeof y === "object") x = numeric._biforeach2(x,y,dim(x),0,VV);\n'+
                    '      else x = numeric._biforeach2(x,y,dim(x),0,VS);\n'+
                    '  } else if(typeof y === "object") x = numeric._biforeach2(x,y,dim(y),0,SV);\n'+
                    '  else '+codeeq('x','y')+'\n'+
                    '}\nreturn x;\n');
            numeric[o] = numeric[i];
            numeric[i+'eqV'] = numeric.pointwise2(['ret[i]','x[i]'], codeeq('ret[i]','x[i]'),setup);
            numeric[i+'eqS'] = numeric.pointwise2(['ret[i]','x'], codeeq('ret[i]','x'),setup);
            numeric[i+'eq'] = Function(
                    'var n = arguments.length, i, x = arguments[0], y;\n'+
                    'var V = numeric.'+i+'eqV, S = numeric.'+i+'eqS\n'+
                    'var s = numeric.dim(x);\n'+
                    'for(i=1;i!==n;++i) { \n'+
                    '  y = arguments[i];\n'+
                    '  if(typeof y === "object") numeric._biforeach(x,y,s,0,V);\n'+
                    '  else numeric._biforeach(x,y,s,0,S);\n'+
                    '}\nreturn x;\n');
        }
    }
    for(i=0;i<numeric.mathfuns2.length;++i) {
        o = numeric.mathfuns2[i];
        delete numeric.ops2[o];
    }
    for(i=0;i<numeric.mathfuns.length;++i) {
        o = numeric.mathfuns[i];
        numeric.ops1[o] = o;
    }
    for(i in numeric.ops1) {
        if(numeric.ops1.hasOwnProperty(i)) {
            setup = '';
            o = numeric.ops1[i];
            if(numeric.myIndexOf.call(numeric.mathfuns,i)!==-1) {
                if(Math.hasOwnProperty(o)) setup = 'var '+o+' = Math.'+o+';\n';
            }
            numeric[i+'eqV'] = numeric.pointwise2(['ret[i]'],'ret[i] = '+o+'(ret[i]);',setup);
            numeric[i+'eq'] = Function('x',
                    'if(typeof x !== "object") return '+o+'x\n'+
                    'var i;\n'+
                    'var V = numeric.'+i+'eqV;\n'+
                    'var s = numeric.dim(x);\n'+
                    'numeric._foreach(x,s,0,V);\n'+
                    'return x;\n');
            numeric[i+'V'] = numeric.pointwise2(['x[i]'],'ret[i] = '+o+'(x[i]);',setup);
            numeric[i] = Function('x',
                    'if(typeof x !== "object") return '+o+'(x)\n'+
                    'var i;\n'+
                    'var V = numeric.'+i+'V;\n'+
                    'var s = numeric.dim(x);\n'+
                    'return numeric._foreach2(x,s,0,V);\n');
        }
    }
    for(i=0;i<numeric.mathfuns.length;++i) {
        o = numeric.mathfuns[i];
        delete numeric.ops1[o];
    }
    for(i in numeric.mapreducers) {
        if(numeric.mapreducers.hasOwnProperty(i)) {
            o = numeric.mapreducers[i];
            numeric[i+'V'] = numeric.mapreduce2(o[0],o[1]);
            numeric[i] = Function('x','s','k',
                    o[1]+
                    'if(typeof x !== "object") {'+
                    '    xi = x;\n'+
                    o[0]+';\n'+
                    '    return accum;\n'+
                    '}'+
                    'if(typeof s === "undefined") s = numeric.dim(x);\n'+
                    'if(typeof k === "undefined") k = 0;\n'+
                    'if(k === s.length-1) return numeric.'+i+'V(x);\n'+
                    'var xi;\n'+
                    'var n = x.length, i;\n'+
                    'for(i=n-1;i!==-1;--i) {\n'+
                    '   xi = arguments.callee(x[i]);\n'+
                    o[0]+';\n'+
                    '}\n'+
                    'return accum;\n');
        }
    }
}());

numeric.truncVV = numeric.pointwise(['x[i]','y[i]'],'ret[i] = round(x[i]/y[i])*y[i];','var round = Math.round;');
numeric.truncVS = numeric.pointwise(['x[i]','y'],'ret[i] = round(x[i]/y)*y;','var round = Math.round;');
numeric.truncSV = numeric.pointwise(['x','y[i]'],'ret[i] = round(x/y[i])*y[i];','var round = Math.round;');
numeric.trunc = function trunc(x,y) {
    if(typeof x === "object") {
        if(typeof y === "object") return numeric.truncVV(x,y);
        return numeric.truncVS(x,y);
    }
    if (typeof y === "object") return numeric.truncSV(x,y);
    return Math.round(x/y)*y;
}

numeric.inv = function inv(x) {
    var s = numeric.dim(x), abs = Math.abs, m = s[0], n = s[1];
    var A = numeric.clone(x), Ai, Aj;
    var I = numeric.identity(m), Ii, Ij;
    var i,j,k,x;
    for(j=0;j<n;++j) {
        var i0 = -1;
        var v0 = -1;
        for(i=j;i!==m;++i) { k = abs(A[i][j]); if(k>v0) { i0 = i; v0 = k; } }
        Aj = A[i0]; A[i0] = A[j]; A[j] = Aj;
        Ij = I[i0]; I[i0] = I[j]; I[j] = Ij;
        x = Aj[j];
        for(k=j;k!==n;++k)    Aj[k] /= x; 
        for(k=n-1;k!==-1;--k) Ij[k] /= x;
        for(i=m-1;i!==-1;--i) {
            if(i!==j) {
                Ai = A[i];
                Ii = I[i];
                x = Ai[j];
                for(k=j+1;k!==n;++k)  Ai[k] -= Aj[k]*x;
                for(k=n-1;k>0;--k) { Ii[k] -= Ij[k]*x; --k; Ii[k] -= Ij[k]*x; }
                if(k===0) Ii[0] -= Ij[0]*x;
            }
        }
    }
    return I;
}

numeric.det = function det(x) {
    var s = numeric.dim(x);
    if(s.length !== 2 || s[0] !== s[1]) { throw new Error('numeric: det() only works on square matrices'); }
    var n = s[0], ret = 1,i,j,k,A = numeric.clone(x),Aj,Ai,alpha,temp,k1,k2,k3;
    for(j=0;j<n-1;j++) {
        k=j;
        for(i=j+1;i<n;i++) { if(Math.abs(A[i][j]) > Math.abs(A[k][j])) { k = i; } }
        if(k !== j) {
            temp = A[k]; A[k] = A[j]; A[j] = temp;
            ret *= -1;
        }
        Aj = A[j];
        for(i=j+1;i<n;i++) {
            Ai = A[i];
            alpha = Ai[j]/Aj[j];
            for(k=j+1;k<n-1;k+=2) {
                k1 = k+1;
                Ai[k] -= Aj[k]*alpha;
                Ai[k1] -= Aj[k1]*alpha;
            }
            if(k!==n) { Ai[k] -= Aj[k]*alpha; }
        }
        if(Aj[j] === 0) { return 0; }
        ret *= Aj[j];
    }
    return ret*A[j][j];
}

numeric.transpose = function transpose(x) {
    var i,j,m = x.length,n = x[0].length, ret=Array(n),A0,A1,Bj;
    for(j=0;j<n;j++) ret[j] = Array(m);
    for(i=m-1;i>=1;i-=2) {
        A1 = x[i];
        A0 = x[i-1];
        for(j=n-1;j>=1;--j) {
            Bj = ret[j]; Bj[i] = A1[j]; Bj[i-1] = A0[j];
            --j;
            Bj = ret[j]; Bj[i] = A1[j]; Bj[i-1] = A0[j];
        }
        if(j===0) {
            Bj = ret[0]; Bj[i] = A1[0]; Bj[i-1] = A0[0];
        }
    }
    if(i===0) {
        A0 = x[0];
        for(j=n-1;j>=1;--j) {
            ret[j][0] = A0[j];
            --j;
            ret[j][0] = A0[j];
        }
        if(j===0) { ret[0][0] = A0[0]; }
    }
    return ret;
}
numeric.negtranspose = function negtranspose(x) {
    var i,j,m = x.length,n = x[0].length, ret=Array(n),A0,A1,Bj;
    for(j=0;j<n;j++) ret[j] = Array(m);
    for(i=m-1;i>=1;i-=2) {
        A1 = x[i];
        A0 = x[i-1];
        for(j=n-1;j>=1;--j) {
            Bj = ret[j]; Bj[i] = -A1[j]; Bj[i-1] = -A0[j];
            --j;
            Bj = ret[j]; Bj[i] = -A1[j]; Bj[i-1] = -A0[j];
        }
        if(j===0) {
            Bj = ret[0]; Bj[i] = -A1[0]; Bj[i-1] = -A0[0];
        }
    }
    if(i===0) {
        A0 = x[0];
        for(j=n-1;j>=1;--j) {
            ret[j][0] = -A0[j];
            --j;
            ret[j][0] = -A0[j];
        }
        if(j===0) { ret[0][0] = -A0[0]; }
    }
    return ret;
}

numeric._random = function _random(s,k) {
    var i,n=s[k],ret=Array(n), rnd;
    if(k === s.length-1) {
        rnd = Math.random;
        for(i=n-1;i>=1;i-=2) {
            ret[i] = rnd();
            ret[i-1] = rnd();
        }
        if(i===0) { ret[0] = rnd(); }
        return ret;
    }
    for(i=n-1;i>=0;i--) ret[i] = _random(s,k+1);
    return ret;
}
numeric.random = function random(s) { return numeric._random(s,0); }

numeric.norm2 = function norm2(x) { return Math.sqrt(numeric.norm2Squared(x)); }

numeric.linspace = function linspace(a,b,n) {
    if(typeof n === "undefined") n = Math.max(Math.round(b-a)+1,1);
    if(n<2) { return n===1?[a]:[]; }
    var i,ret = Array(n);
    n--;
    for(i=n;i>=0;i--) { ret[i] = (i*b+(n-i)*a)/n; }
    return ret;
}

numeric.getBlock = function getBlock(x,from,to) {
    var s = numeric.dim(x);
    function foo(x,k) {
        var i,a = from[k], n = to[k]-a, ret = Array(n);
        if(k === s.length-1) {
            for(i=n;i>=0;i--) { ret[i] = x[i+a]; }
            return ret;
        }
        for(i=n;i>=0;i--) { ret[i] = foo(x[i+a],k+1); }
        return ret;
    }
    return foo(x,0);
}

numeric.setBlock = function setBlock(x,from,to,B) {
    var s = numeric.dim(x);
    function foo(x,y,k) {
        var i,a = from[k], n = to[k]-a;
        if(k === s.length-1) { for(i=n;i>=0;i--) { x[i+a] = y[i]; } }
        for(i=n;i>=0;i--) { foo(x[i+a],y[i],k+1); }
    }
    foo(x,B,0);
    return x;
}

numeric.getRange = function getRange(A,I,J) {
    var m = I.length, n = J.length;
    var i,j;
    var B = Array(m), Bi, AI;
    for(i=m-1;i!==-1;--i) {
        B[i] = Array(n);
        Bi = B[i];
        AI = A[I[i]];
        for(j=n-1;j!==-1;--j) Bi[j] = AI[J[j]];
    }
    return B;
}

numeric.blockMatrix = function blockMatrix(X) {
    var s = numeric.dim(X);
    if(s.length<4) return numeric.blockMatrix([X]);
    var m=s[0],n=s[1],M,N,i,j,Xij;
    M = 0; N = 0;
    for(i=0;i<m;++i) M+=X[i][0].length;
    for(j=0;j<n;++j) N+=X[0][j][0].length;
    var Z = Array(M);
    for(i=0;i<M;++i) Z[i] = Array(N);
    var I=0,J,ZI,k,l,Xijk;
    for(i=0;i<m;++i) {
        J=N;
        for(j=n-1;j!==-1;--j) {
            Xij = X[i][j];
            J -= Xij[0].length;
            for(k=Xij.length-1;k!==-1;--k) {
                Xijk = Xij[k];
                ZI = Z[I+k];
                for(l = Xijk.length-1;l!==-1;--l) ZI[J+l] = Xijk[l];
            }
        }
        I += X[i][0].length;
    }
    return Z;
}

numeric.tensor = function tensor(x,y) {
    if(typeof x === "number" || typeof y === "number") return numeric.mul(x,y);
    var s1 = numeric.dim(x), s2 = numeric.dim(y);
    if(s1.length !== 1 || s2.length !== 1) {
        throw new Error('numeric: tensor product is only defined for vectors');
    }
    var m = s1[0], n = s2[0], A = Array(m), Ai, i,j,xi;
    for(i=m-1;i>=0;i--) {
        Ai = Array(n);
        xi = x[i];
        for(j=n-1;j>=3;--j) {
            Ai[j] = xi * y[j];
            --j;
            Ai[j] = xi * y[j];
            --j;
            Ai[j] = xi * y[j];
            --j;
            Ai[j] = xi * y[j];
        }
        while(j>=0) { Ai[j] = xi * y[j]; --j; }
        A[i] = Ai;
    }
    return A;
}

// 3. The Tensor type T
numeric.T = function T(x,y) { this.x = x; this.y = y; }
numeric.t = function t(x,y) { return new numeric.T(x,y); }

numeric.Tbinop = function Tbinop(rr,rc,cr,cc,setup) {
    var io = numeric.indexOf;
    if(typeof setup !== "string") {
        var k;
        setup = '';
        for(k in numeric) {
            if(numeric.hasOwnProperty(k) && (rr.indexOf(k)>=0 || rc.indexOf(k)>=0 || cr.indexOf(k)>=0 || cc.indexOf(k)>=0) && k.length>1) {
                setup += 'var '+k+' = numeric.'+k+';\n';
            }
        }
    }
    return Function(['y'],
            'var x = this;\n'+
            'if(!(y instanceof numeric.T)) { y = new numeric.T(y); }\n'+
            setup+'\n'+
            'if(x.y) {'+
            '  if(y.y) {'+
            '    return new numeric.T('+cc+');\n'+
            '  }\n'+
            '  return new numeric.T('+cr+');\n'+
            '}\n'+
            'if(y.y) {\n'+
            '  return new numeric.T('+rc+');\n'+
            '}\n'+
            'return new numeric.T('+rr+');\n'
    );
}

numeric.T.prototype.add = numeric.Tbinop(
        'add(x.x,y.x)',
        'add(x.x,y.x),y.y',
        'add(x.x,y.x),x.y',
        'add(x.x,y.x),add(x.y,y.y)');
numeric.T.prototype.sub = numeric.Tbinop(
        'sub(x.x,y.x)',
        'sub(x.x,y.x),neg(y.y)',
        'sub(x.x,y.x),x.y',
        'sub(x.x,y.x),sub(x.y,y.y)');
numeric.T.prototype.mul = numeric.Tbinop(
        'mul(x.x,y.x)',
        'mul(x.x,y.x),mul(x.x,y.y)',
        'mul(x.x,y.x),mul(x.y,y.x)',
        'sub(mul(x.x,y.x),mul(x.y,y.y)),add(mul(x.x,y.y),mul(x.y,y.x))');

numeric.T.prototype.reciprocal = function reciprocal() {
    var mul = numeric.mul, div = numeric.div;
    if(this.y) {
        var d = numeric.add(mul(this.x,this.x),mul(this.y,this.y));
        return new numeric.T(div(this.x,d),div(numeric.neg(this.y),d));
    }
    return new T(div(1,this.x));
}
numeric.T.prototype.div = function div(y) {
    if(!(y instanceof numeric.T)) y = new numeric.T(y);
    if(y.y) { return this.mul(y.reciprocal()); }
    var div = numeric.div;
    if(this.y) { return new numeric.T(div(this.x,y.x),div(this.y,y.x)); }
    return new numeric.T(div(this.x,y.x));
}
numeric.T.prototype.dot = numeric.Tbinop(
        'dot(x.x,y.x)',
        'dot(x.x,y.x),dot(x.x,y.y)',
        'dot(x.x,y.x),dot(x.y,y.x)',
        'sub(dot(x.x,y.x),dot(x.y,y.y)),add(dot(x.x,y.y),dot(x.y,y.x))'
        );
numeric.T.prototype.transpose = function transpose() {
    var t = numeric.transpose, x = this.x, y = this.y;
    if(y) { return new numeric.T(t(x),t(y)); }
    return new numeric.T(t(x));
}
numeric.T.prototype.transjugate = function transjugate() {
    var t = numeric.transpose, x = this.x, y = this.y;
    if(y) { return new numeric.T(t(x),numeric.negtranspose(y)); }
    return new numeric.T(t(x));
}
numeric.Tunop = function Tunop(r,c,s) {
    if(typeof s !== "string") { s = ''; }
    return Function(
            'var x = this;\n'+
            s+'\n'+
            'if(x.y) {'+
            '  '+c+';\n'+
            '}\n'+
            r+';\n'
    );
}

numeric.T.prototype.exp = numeric.Tunop(
        'return new numeric.T(ex)',
        'return new numeric.T(mul(cos(x.y),ex),mul(sin(x.y),ex))',
        'var ex = numeric.exp(x.x), cos = numeric.cos, sin = numeric.sin, mul = numeric.mul;');
numeric.T.prototype.conj = numeric.Tunop(
        'return new numeric.T(x.x);',
        'return new numeric.T(x.x,numeric.neg(x.y));');
numeric.T.prototype.neg = numeric.Tunop(
        'return new numeric.T(neg(x.x));',
        'return new numeric.T(neg(x.x),neg(x.y));',
        'var neg = numeric.neg;');
numeric.T.prototype.sin = numeric.Tunop(
        'return new numeric.T(numeric.sin(x.x))',
        'return x.exp().sub(x.neg().exp()).div(new numeric.T(0,2));');
numeric.T.prototype.cos = numeric.Tunop(
        'return new numeric.T(numeric.cos(x.x))',
        'return x.exp().add(x.neg().exp()).div(2);');
numeric.T.prototype.abs = numeric.Tunop(
        'return new numeric.T(numeric.abs(x.x));',
        'return new numeric.T(numeric.sqrt(numeric.add(mul(x.x,x.x),mul(x.y,x.y))));',
        'var mul = numeric.mul;');
numeric.T.prototype.log = numeric.Tunop(
        'return new numeric.T(numeric.log(x.x));',
        'var theta = new numeric.T(numeric.atan2(x.y,x.x)), r = x.abs();\n'+
        'return new numeric.T(numeric.log(r.x),theta.x);');
numeric.T.prototype.norm2 = numeric.Tunop(
        'return numeric.norm2(x.x);',
        'var f = numeric.norm2Squared;\n'+
        'return Math.sqrt(f(x.x)+f(x.y));');
numeric.T.prototype.inv = function inv() {
    var A = this;
    if(typeof A.y === "undefined") { return new numeric.T(numeric.inv(A.x)); }
    var n = A.x.length, i, j, k;
    var Rx = numeric.identity(n),Ry = numeric.rep([n,n],0);
    var Ax = numeric.clone(A.x), Ay = numeric.clone(A.y);
    var Aix, Aiy, Ajx, Ajy, Rix, Riy, Rjx, Rjy;
    var i,j,k,d,d1,ax,ay,bx,by,temp;
    for(i=0;i<n;i++) {
        ax = Ax[i][i]; ay = Ay[i][i];
        d = ax*ax+ay*ay;
        k = i;
        for(j=i+1;j<n;j++) {
            ax = Ax[j][i]; ay = Ay[j][i];
            d1 = ax*ax+ay*ay;
            if(d1 > d) { k=j; d = d1; }
        }
        if(k!==i) {
            temp = Ax[i]; Ax[i] = Ax[k]; Ax[k] = temp;
            temp = Ay[i]; Ay[i] = Ay[k]; Ay[k] = temp;
            temp = Rx[i]; Rx[i] = Rx[k]; Rx[k] = temp;
            temp = Ry[i]; Ry[i] = Ry[k]; Ry[k] = temp;
        }
        Aix = Ax[i]; Aiy = Ay[i];
        Rix = Rx[i]; Riy = Ry[i];
        ax = Aix[i]; ay = Aiy[i];
        for(j=i+1;j<n;j++) {
            bx = Aix[j]; by = Aiy[j];
            Aix[j] = (bx*ax+by*ay)/d;
            Aiy[j] = (by*ax-bx*ay)/d;
        }
        for(j=0;j<n;j++) {
            bx = Rix[j]; by = Riy[j];
            Rix[j] = (bx*ax+by*ay)/d;
            Riy[j] = (by*ax-bx*ay)/d;
        }
        for(j=i+1;j<n;j++) {
            Ajx = Ax[j]; Ajy = Ay[j];
            Rjx = Rx[j]; Rjy = Ry[j];
            ax = Ajx[i]; ay = Ajy[i];
            for(k=i+1;k<n;k++) {
                bx = Aix[k]; by = Aiy[k];
                Ajx[k] -= bx*ax-by*ay;
                Ajy[k] -= by*ax+bx*ay;
            }
            for(k=0;k<n;k++) {
                bx = Rix[k]; by = Riy[k];
                Rjx[k] -= bx*ax-by*ay;
                Rjy[k] -= by*ax+bx*ay;
            }
        }
    }
    for(i=n-1;i>0;i--) {
        Rix = Rx[i]; Riy = Ry[i];
        for(j=i-1;j>=0;j--) {
            Rjx = Rx[j]; Rjy = Ry[j];
            ax = Ax[j][i]; ay = Ay[j][i];
            for(k=n-1;k>=0;k--) {
                bx = Rix[k]; by = Riy[k];
                Rjx[k] -= ax*bx - ay*by;
                Rjy[k] -= ax*by + ay*bx;
            }
        }
    }
    return new numeric.T(Rx,Ry);
}
numeric.T.prototype.get = function get(i) {
    var x = this.x, y = this.y, k = 0, ik, n = i.length;
    if(y) {
        while(k<n) {
            ik = i[k];
            x = x[ik];
            y = y[ik];
            k++;
        }
        return new numeric.T(x,y);
    }
    while(k<n) {
        ik = i[k];
        x = x[ik];
        k++;
    }
    return new numeric.T(x);
}
numeric.T.prototype.set = function set(i,v) {
    var x = this.x, y = this.y, k = 0, ik, n = i.length, vx = v.x, vy = v.y;
    if(n===0) {
        if(vy) { this.y = vy; }
        else if(y) { this.y = undefined; }
        this.x = x;
        return this;
    }
    if(vy) {
        if(y) { /* ok */ }
        else {
            y = numeric.rep(numeric.dim(x),0);
            this.y = y;
        }
        while(k<n-1) {
            ik = i[k];
            x = x[ik];
            y = y[ik];
            k++;
        }
        ik = i[k];
        x[ik] = vx;
        y[ik] = vy;
        return this;
    }
    if(y) {
        while(k<n-1) {
            ik = i[k];
            x = x[ik];
            y = y[ik];
            k++;
        }
        ik = i[k];
        x[ik] = vx;
        if(vx instanceof Array) y[ik] = numeric.rep(numeric.dim(vx),0);
        else y[ik] = 0;
        return this;
    }
    while(k<n-1) {
        ik = i[k];
        x = x[ik];
        k++;
    }
    ik = i[k];
    x[ik] = vx;
    return this;
}
numeric.T.prototype.getRows = function getRows(i0,i1) {
    var n = i1-i0+1, j;
    var rx = Array(n), ry, x = this.x, y = this.y;
    for(j=i0;j<=i1;j++) { rx[j-i0] = x[j]; }
    if(y) {
        ry = Array(n);
        for(j=i0;j<=i1;j++) { ry[j-i0] = y[j]; }
        return new numeric.T(rx,ry);
    }
    return new numeric.T(rx);
}
numeric.T.prototype.setRows = function setRows(i0,i1,A) {
    var j;
    var rx = this.x, ry = this.y, x = A.x, y = A.y;
    for(j=i0;j<=i1;j++) { rx[j] = x[j-i0]; }
    if(y) {
        if(!ry) { ry = numeric.rep(numeric.dim(rx),0); this.y = ry; }
        for(j=i0;j<=i1;j++) { ry[j] = y[j-i0]; }
    } else if(ry) {
        for(j=i0;j<=i1;j++) { ry[j] = numeric.rep([x[j-i0].length],0); }
    }
    return this;
}
numeric.T.prototype.getRow = function getRow(k) {
    var x = this.x, y = this.y;
    if(y) { return new numeric.T(x[k],y[k]); }
    return new numeric.T(x[k]);
}
numeric.T.prototype.setRow = function setRow(i,v) {
    var rx = this.x, ry = this.y, x = v.x, y = v.y;
    rx[i] = x;
    if(y) {
        if(!ry) { ry = numeric.rep(numeric.dim(rx),0); this.y = ry; }
        ry[i] = y;
    } else if(ry) {
        ry = numeric.rep([x.length],0);
    }
    return this;
}

numeric.T.prototype.getBlock = function getBlock(from,to) {
    var x = this.x, y = this.y, b = numeric.getBlock;
    if(y) { return new numeric.T(b(x,from,to),b(y,from,to)); }
    return new numeric.T(b(x,from,to));
}
numeric.T.prototype.setBlock = function setBlock(from,to,A) {
    if(!(A instanceof numeric.T)) A = new numeric.T(A);
    var x = this.x, y = this.y, b = numeric.setBlock, Ax = A.x, Ay = A.y;
    if(Ay) {
        if(!y) { this.y = numeric.rep(numeric.dim(this),0); y = this.y; }
        b(x,from,to,Ax);
        b(y,from,to,Ay);
        return this;
    }
    b(x,from,to,Ax);
    if(y) b(y,from,to,numeric.rep(numeric.dim(Ax),0));
}
numeric.T.rep = function rep(s,v) {
    var T = numeric.T;
    if(!(v instanceof T)) v = new T(v);
    var x = v.x, y = v.y, r = numeric.rep;
    if(y) return new T(r(s,x),r(s,y));
    return new T(r(s,x));
}
numeric.T.diag = function diag(d) {
    if(!(d instanceof numeric.T)) d = new numeric.T(d);
    var x = d.x, y = d.y, diag = numeric.diag;
    if(y) return new numeric.T(diag(x),diag(y));
    return new numeric.T(diag(x));
}
numeric.T.eig = function eig() {
    if(this.y) { throw new Error('eig: not implemented for complex matrices.'); }
    return numeric.eig(this.x);
}
numeric.T.identity = function identity(n) { return new numeric.T(numeric.identity(n)); }
numeric.T.prototype.getDiag = function getDiag() {
    var n = numeric;
    var x = this.x, y = this.y;
    if(y) { return new n.T(n.getDiag(x),n.getDiag(y)); }
    return new n.T(n.getDiag(x));
}

// 4. Eigenvalues of real matrices

numeric.house = function house(x) {
    var v = numeric.clone(x);
    var s = x[0] >= 0 ? 1 : -1;
    var alpha = s*numeric.norm2(x);
    v[0] += alpha;
    var foo = numeric.norm2(v);
    if(foo === 0) { /* this should not happen */ throw new Error('eig: internal error'); }
    return numeric.div(v,foo);
}

numeric.toUpperHessenberg = function toUpperHessenberg(me) {
    var s = numeric.dim(me);
    if(s.length !== 2 || s[0] !== s[1]) { throw new Error('numeric: toUpperHessenberg() only works on square matrices'); }
    var m = s[0], i,j,k,x,v,A = numeric.clone(me),B,C,Ai,Ci,Q = numeric.identity(m),Qi;
    for(j=0;j<m-2;j++) {
        x = Array(m-j-1);
        for(i=j+1;i<m;i++) { x[i-j-1] = A[i][j]; }
        if(numeric.norm2(x)>0) {
            v = numeric.house(x);
            B = numeric.getBlock(A,[j+1,j],[m-1,m-1]);
            C = numeric.tensor(v,numeric.dot(v,B));
            for(i=j+1;i<m;i++) { Ai = A[i]; Ci = C[i-j-1]; for(k=j;k<m;k++) Ai[k] -= 2*Ci[k-j]; }
            B = numeric.getBlock(A,[0,j+1],[m-1,m-1]);
            C = numeric.tensor(numeric.dot(B,v),v);
            for(i=0;i<m;i++) { Ai = A[i]; Ci = C[i]; for(k=j+1;k<m;k++) Ai[k] -= 2*Ci[k-j-1]; }
            B = Array(m-j-1);
            for(i=j+1;i<m;i++) B[i-j-1] = Q[i];
            C = numeric.tensor(v,numeric.dot(v,B));
            for(i=j+1;i<m;i++) { Qi = Q[i]; Ci = C[i-j-1]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
        }
    }
    return {H:A, Q:Q};
}

numeric.epsilon = 2.220446049250313e-16;

numeric.QRFrancis = function(H,maxiter) {
    if(typeof maxiter === "undefined") { maxiter = 10000; }
    H = numeric.clone(H);
    var H0 = numeric.clone(H);
    var s = numeric.dim(H),m=s[0],x,v,a,b,c,d,det,tr, Hloc, Q = numeric.identity(m), Qi, Hi, B, C, Ci,i,j,k,iter;
    if(m<3) { return {Q:Q, B:[ [0,m-1] ]}; }
    var epsilon = numeric.epsilon;
    for(iter=0;iter<maxiter;iter++) {
        for(j=0;j<m-1;j++) {
            if(Math.abs(H[j+1][j]) < epsilon*(Math.abs(H[j][j])+Math.abs(H[j+1][j+1]))) {
                var QH1 = numeric.QRFrancis(numeric.getBlock(H,[0,0],[j,j]),maxiter);
                var QH2 = numeric.QRFrancis(numeric.getBlock(H,[j+1,j+1],[m-1,m-1]),maxiter);
                B = Array(j+1);
                for(i=0;i<=j;i++) { B[i] = Q[i]; }
                C = numeric.dot(QH1.Q,B);
                for(i=0;i<=j;i++) { Q[i] = C[i]; }
                B = Array(m-j-1);
                for(i=j+1;i<m;i++) { B[i-j-1] = Q[i]; }
                C = numeric.dot(QH2.Q,B);
                for(i=j+1;i<m;i++) { Q[i] = C[i-j-1]; }
                return {Q:Q,B:QH1.B.concat(numeric.add(QH2.B,j+1))};
            }
        }
        a = H[m-2][m-2]; b = H[m-2][m-1];
        c = H[m-1][m-2]; d = H[m-1][m-1];
        tr = a+d;
        det = (a*d-b*c);
        Hloc = numeric.getBlock(H, [0,0], [2,2]);
        if(tr*tr>=4*det) {
            var s1,s2;
            s1 = 0.5*(tr+Math.sqrt(tr*tr-4*det));
            s2 = 0.5*(tr-Math.sqrt(tr*tr-4*det));
            Hloc = numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),
                                           numeric.mul(Hloc,s1+s2)),
                               numeric.diag(numeric.rep([3],s1*s2)));
        } else {
            Hloc = numeric.add(numeric.sub(numeric.dot(Hloc,Hloc),
                                           numeric.mul(Hloc,tr)),
                               numeric.diag(numeric.rep([3],det)));
        }
        x = [Hloc[0][0],Hloc[1][0],Hloc[2][0]];
        v = numeric.house(x);
        B = [H[0],H[1],H[2]];
        C = numeric.tensor(v,numeric.dot(v,B));
        for(i=0;i<3;i++) { Hi = H[i]; Ci = C[i]; for(k=0;k<m;k++) Hi[k] -= 2*Ci[k]; }
        B = numeric.getBlock(H, [0,0],[m-1,2]);
        C = numeric.tensor(numeric.dot(B,v),v);
        for(i=0;i<m;i++) { Hi = H[i]; Ci = C[i]; for(k=0;k<3;k++) Hi[k] -= 2*Ci[k]; }
        B = [Q[0],Q[1],Q[2]];
        C = numeric.tensor(v,numeric.dot(v,B));
        for(i=0;i<3;i++) { Qi = Q[i]; Ci = C[i]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
        var J;
        for(j=0;j<m-2;j++) {
            for(k=j;k<=j+1;k++) {
                if(Math.abs(H[k+1][k]) < epsilon*(Math.abs(H[k][k])+Math.abs(H[k+1][k+1]))) {
                    var QH1 = numeric.QRFrancis(numeric.getBlock(H,[0,0],[k,k]),maxiter);
                    var QH2 = numeric.QRFrancis(numeric.getBlock(H,[k+1,k+1],[m-1,m-1]),maxiter);
                    B = Array(k+1);
                    for(i=0;i<=k;i++) { B[i] = Q[i]; }
                    C = numeric.dot(QH1.Q,B);
                    for(i=0;i<=k;i++) { Q[i] = C[i]; }
                    B = Array(m-k-1);
                    for(i=k+1;i<m;i++) { B[i-k-1] = Q[i]; }
                    C = numeric.dot(QH2.Q,B);
                    for(i=k+1;i<m;i++) { Q[i] = C[i-k-1]; }
                    return {Q:Q,B:QH1.B.concat(numeric.add(QH2.B,k+1))};
                }
            }
            J = Math.min(m-1,j+3);
            x = Array(J-j);
            for(i=j+1;i<=J;i++) { x[i-j-1] = H[i][j]; }
            v = numeric.house(x);
            B = numeric.getBlock(H, [j+1,j],[J,m-1]);
            C = numeric.tensor(v,numeric.dot(v,B));
            for(i=j+1;i<=J;i++) { Hi = H[i]; Ci = C[i-j-1]; for(k=j;k<m;k++) Hi[k] -= 2*Ci[k-j]; }
            B = numeric.getBlock(H, [0,j+1],[m-1,J]);
            C = numeric.tensor(numeric.dot(B,v),v);
            for(i=0;i<m;i++) { Hi = H[i]; Ci = C[i]; for(k=j+1;k<=J;k++) Hi[k] -= 2*Ci[k-j-1]; }
            B = Array(J-j);
            for(i=j+1;i<=J;i++) B[i-j-1] = Q[i];
            C = numeric.tensor(v,numeric.dot(v,B));
            for(i=j+1;i<=J;i++) { Qi = Q[i]; Ci = C[i-j-1]; for(k=0;k<m;k++) Qi[k] -= 2*Ci[k]; }
        }
    }
    throw new Error('numeric: eigenvalue iteration does not converge -- increase maxiter?');
}

numeric.eig = function eig(A,maxiter) {
    var QH = numeric.toUpperHessenberg(A);
    var QB = numeric.QRFrancis(QH.H,maxiter);
    var T = numeric.T;
    var n = A.length,i,k,flag = false,B = QB.B,H = numeric.dot(QB.Q,numeric.dot(QH.H,numeric.transpose(QB.Q)));
    var Q = new T(numeric.dot(QB.Q,QH.Q)),Q0;
    var m = B.length,j;
    var a,b,c,d,p1,p2,disc,x,y,p,q,n1,n2;
    var sqrt = Math.sqrt;
    for(k=0;k<m;k++) {
        i = B[k][0];
        if(i === B[k][1]) {
            // nothing
        } else {
            j = i+1;
            a = H[i][i];
            b = H[i][j];
            c = H[j][i];
            d = H[j][j];
            if(b === 0 && c === 0) continue;
            p1 = -a-d;
            p2 = a*d-b*c;
            disc = p1*p1-4*p2;
            if(disc>=0) {
                if(p1<0) x = -0.5*(p1-sqrt(disc));
                else     x = -0.5*(p1+sqrt(disc));
                n1 = (a-x)*(a-x)+b*b;
                n2 = c*c+(d-x)*(d-x);
                if(n1>n2) {
                    n1 = sqrt(n1);
                    p = (a-x)/n1;
                    q = b/n1;
                } else {
                    n2 = sqrt(n2);
                    p = c/n2;
                    q = (d-x)/n2;
                }
                Q0 = new T([[q,-p],[p,q]]);
                Q.setRows(i,j,Q0.dot(Q.getRows(i,j)));
            } else {
                x = -0.5*p1;
                y = 0.5*sqrt(-disc);
                n1 = (a-x)*(a-x)+b*b;
                n2 = c*c+(d-x)*(d-x);
                if(n1>n2) {
                    n1 = sqrt(n1+y*y);
                    p = (a-x)/n1;
                    q = b/n1;
                    x = 0;
                    y /= n1;
                } else {
                    n2 = sqrt(n2+y*y);
                    p = c/n2;
                    q = (d-x)/n2;
                    x = y/n2;
                    y = 0;
                }
                Q0 = new T([[q,-p],[p,q]],[[x,y],[y,-x]]);
                Q.setRows(i,j,Q0.dot(Q.getRows(i,j)));
            }
        }
    }
    var R = Q.dot(A).dot(Q.transjugate()), n = A.length, E = numeric.T.identity(n);
    for(j=0;j<n;j++) {
        if(j>0) {
            for(k=j-1;k>=0;k--) {
                var Rk = R.get([k,k]), Rj = R.get([j,j]);
                if(numeric.neq(Rk.x,Rj.x) || numeric.neq(Rk.y,Rj.y)) {
                    x = R.getRow(k).getBlock([k],[j-1]);
                    y = E.getRow(j).getBlock([k],[j-1]);
                    E.set([j,k],(R.get([k,j]).neg().sub(x.dot(y))).div(Rk.sub(Rj)));
                } else {
                    E.setRow(j,E.getRow(k));
                    continue;
                }
            }
        }
    }
    for(j=0;j<n;j++) {
        x = E.getRow(j);
        E.setRow(j,x.div(x.norm2()));
    }
    E = E.transpose();
    E = Q.transjugate().dot(E);
    return { lambda:R.getDiag(), E:E };
};

// 5. Compressed Column Storage matrices
numeric.ccsSparse = function ccsSparse(A) {
    var m = A.length,n,foo, i,j, counts = [];
    for(i=m-1;i!==-1;--i) {
        foo = A[i];
        for(j in foo) {
            j = parseInt(j);
            while(j>=counts.length) counts[counts.length] = 0;
            if(foo[j]!==0) counts[j]++;
        }
    }
    var n = counts.length;
    var Ai = Array(n+1);
    Ai[0] = 0;
    for(i=0;i<n;++i) Ai[i+1] = Ai[i] + counts[i];
    var Aj = Array(Ai[n]), Av = Array(Ai[n]);
    for(i=m-1;i!==-1;--i) {
        foo = A[i];
        for(j in foo) {
            if(foo[j]!==0) {
                counts[j]--;
                Aj[Ai[j]+counts[j]] = i;
                Av[Ai[j]+counts[j]] = foo[j];
            }
        }
    }
    return [Ai,Aj,Av];
}
numeric.ccsFull = function ccsFull(A) {
    var Ai = A[0], Aj = A[1], Av = A[2], s = numeric.ccsDim(A), m = s[0], n = s[1], i,j,j0,j1,k;
    var B = numeric.rep([m,n],0);
    for(i=0;i<n;i++) {
        j0 = Ai[i];
        j1 = Ai[i+1];
        for(j=j0;j<j1;++j) { B[Aj[j]][i] = Av[j]; }
    }
    return B;
}
numeric.ccsTSolve = function ccsTSolve(A,b,x,bj,xj) {
    var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, max = Math.max,n=0;
    if(typeof bj === "undefined") x = numeric.rep([m],0);
    if(typeof bj === "undefined") bj = numeric.linspace(0,x.length-1);
    if(typeof xj === "undefined") xj = [];
    function dfs(j) {
        var k;
        if(x[j] !== 0) return;
        x[j] = 1;
        for(k=Ai[j];k<Ai[j+1];++k) dfs(Aj[k]);
        xj[n] = j;
        ++n;
    }
    var i,j,j0,j1,k,l,l0,l1,a;
    for(i=bj.length-1;i!==-1;--i) { dfs(bj[i]); }
    xj.length = n;
    for(i=xj.length-1;i!==-1;--i) { x[xj[i]] = 0; }
    for(i=bj.length-1;i!==-1;--i) { j = bj[i]; x[j] = b[j]; }
    for(i=xj.length-1;i!==-1;--i) {
        j = xj[i];
        j0 = Ai[j];
        j1 = max(Ai[j+1],j0);
        for(k=j0;k!==j1;++k) { if(Aj[k] === j) { x[j] /= Av[k]; break; } }
        a = x[j];
        for(k=j0;k!==j1;++k) {
            l = Aj[k];
            if(l !== j) x[l] -= a*Av[k];
        }
    }
    return x;
}
numeric.ccsDFS = function ccsDFS(n) {
    this.k = Array(n);
    this.k1 = Array(n);
    this.j = Array(n);
}
numeric.ccsDFS.prototype.dfs = function dfs(J,Ai,Aj,x,xj,Pinv) {
    var m = 0,foo,n=xj.length;
    var k = this.k, k1 = this.k1, j = this.j,km,k11;
    if(x[J]!==0) return;
    x[J] = 1;
    j[0] = J;
    k[0] = km = Ai[J];
    k1[0] = k11 = Ai[J+1];
    while(1) {
        if(km >= k11) {
            xj[n] = j[m];
            if(m===0) return;
            ++n;
            --m;
            km = k[m];
            k11 = k1[m];
        } else {
            foo = Pinv[Aj[km]];
            if(x[foo] === 0) {
                x[foo] = 1;
                k[m] = km;
                ++m;
                j[m] = foo;
                km = Ai[foo];
                k1[m] = k11 = Ai[foo+1];
            } else ++km;
        }
    }
}
numeric.ccsLPSolve = function ccsLPSolve(A,B,x,xj,I,Pinv,dfs) {
    var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, n=0;
    var Bi = B[0], Bj = B[1], Bv = B[2];
    
    var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;
    i0 = Bi[I];
    i1 = Bi[I+1];
    xj.length = 0;
    for(i=i0;i<i1;++i) { dfs.dfs(Pinv[Bj[i]],Ai,Aj,x,xj,Pinv); }
    for(i=xj.length-1;i!==-1;--i) { x[xj[i]] = 0; }
    for(i=i0;i!==i1;++i) { j = Pinv[Bj[i]]; x[j] = Bv[i]; }
    for(i=xj.length-1;i!==-1;--i) {
        j = xj[i];
        j0 = Ai[j];
        j1 = Ai[j+1];
        for(k=j0;k<j1;++k) { if(Pinv[Aj[k]] === j) { x[j] /= Av[k]; break; } }
        a = x[j];
        for(k=j0;k<j1;++k) {
            l = Pinv[Aj[k]];
            if(l !== j) x[l] -= a*Av[k];
        }
    }
    return x;
}
numeric.ccsLUP1 = function ccsLUP1(A,threshold) {
    var m = A[0].length-1;
    var L = [numeric.rep([m+1],0),[],[]], U = [numeric.rep([m+1], 0),[],[]];
    var Li = L[0], Lj = L[1], Lv = L[2], Ui = U[0], Uj = U[1], Uv = U[2];
    var x = numeric.rep([m],0), xj = numeric.rep([m],0);
    var i,j,k,j0,j1,a,e,c,d,K;
    var sol = numeric.ccsLPSolve, max = Math.max, abs = Math.abs;
    var P = numeric.linspace(0,m-1),Pinv = numeric.linspace(0,m-1);
    var dfs = new numeric.ccsDFS(m);
    if(typeof threshold === "undefined") { threshold = 1; }
    for(i=0;i<m;++i) {
        sol(L,A,x,xj,i,Pinv,dfs);
        a = -1;
        e = -1;
        for(j=xj.length-1;j!==-1;--j) {
            k = xj[j];
            if(k <= i) continue;
            c = abs(x[k]);
            if(c > a) { e = k; a = c; }
        }
        if(abs(x[i])<threshold*a) {
            j = P[i];
            a = P[e];
            P[i] = a; Pinv[a] = i;
            P[e] = j; Pinv[j] = e;
            a = x[i]; x[i] = x[e]; x[e] = a;
        }
        a = Li[i];
        e = Ui[i];
        d = x[i];
        Lj[a] = P[i];
        Lv[a] = 1;
        ++a;
        for(j=xj.length-1;j!==-1;--j) {
            k = xj[j];
            c = x[k];
            xj[j] = 0;
            x[k] = 0;
            if(k<=i) { Uj[e] = k; Uv[e] = c;   ++e; }
            else     { Lj[a] = P[k]; Lv[a] = c/d; ++a; }
        }
        Li[i+1] = a;
        Ui[i+1] = e;
    }
    for(j=Lj.length-1;j!==-1;--j) { Lj[j] = Pinv[Lj[j]]; }
    return {L:L, U:U, P:P, Pinv:Pinv};
}
numeric.ccsDFS0 = function ccsDFS0(n) {
    this.k = Array(n);
    this.k1 = Array(n);
    this.j = Array(n);
}
numeric.ccsDFS0.prototype.dfs = function dfs(J,Ai,Aj,x,xj,Pinv,P) {
    var m = 0,foo,n=xj.length;
    var k = this.k, k1 = this.k1, j = this.j,km,k11;
    if(x[J]!==0) return;
    x[J] = 1;
    j[0] = J;
    k[0] = km = Ai[Pinv[J]];
    k1[0] = k11 = Ai[Pinv[J]+1];
    while(1) {
        if(isNaN(km)) throw new Error("Ow!");
        if(km >= k11) {
            xj[n] = Pinv[j[m]];
            if(m===0) return;
            ++n;
            --m;
            km = k[m];
            k11 = k1[m];
        } else {
            foo = Aj[km];
            if(x[foo] === 0) {
                x[foo] = 1;
                k[m] = km;
                ++m;
                j[m] = foo;
                foo = Pinv[foo];
                km = Ai[foo];
                k1[m] = k11 = Ai[foo+1];
            } else ++km;
        }
    }
}
numeric.ccsLPSolve0 = function ccsLPSolve0(A,B,y,xj,I,Pinv,P,dfs) {
    var Ai = A[0], Aj = A[1], Av = A[2],m = Ai.length-1, n=0;
    var Bi = B[0], Bj = B[1], Bv = B[2];
    
    var i,i0,i1,j,J,j0,j1,k,l,l0,l1,a;
    i0 = Bi[I];
    i1 = Bi[I+1];
    xj.length = 0;
    for(i=i0;i<i1;++i) { dfs.dfs(Bj[i],Ai,Aj,y,xj,Pinv,P); }
    for(i=xj.length-1;i!==-1;--i) { j = xj[i]; y[P[j]] = 0; }
    for(i=i0;i!==i1;++i) { j = Bj[i]; y[j] = Bv[i]; }
    for(i=xj.length-1;i!==-1;--i) {
        j = xj[i];
        l = P[j];
        j0 = Ai[j];
        j1 = Ai[j+1];
        for(k=j0;k<j1;++k) { if(Aj[k] === l) { y[l] /= Av[k]; break; } }
        a = y[l];
        for(k=j0;k<j1;++k) y[Aj[k]] -= a*Av[k];
        y[l] = a;
    }
}
numeric.ccsLUP0 = function ccsLUP0(A,threshold) {
    var m = A[0].length-1;
    var L = [numeric.rep([m+1],0),[],[]], U = [numeric.rep([m+1], 0),[],[]];
    var Li = L[0], Lj = L[1], Lv = L[2], Ui = U[0], Uj = U[1], Uv = U[2];
    var y = numeric.rep([m],0), xj = numeric.rep([m],0);
    var i,j,k,j0,j1,a,e,c,d,K;
    var sol = numeric.ccsLPSolve0, max = Math.max, abs = Math.abs;
    var P = numeric.linspace(0,m-1),Pinv = numeric.linspace(0,m-1);
    var dfs = new numeric.ccsDFS0(m);
    if(typeof threshold === "undefined") { threshold = 1; }
    for(i=0;i<m;++i) {
        sol(L,A,y,xj,i,Pinv,P,dfs);
        a = -1;
        e = -1;
        for(j=xj.length-1;j!==-1;--j) {
            k = xj[j];
            if(k <= i) continue;
            c = abs(y[P[k]]);
            if(c > a) { e = k; a = c; }
        }
        if(abs(y[P[i]])<threshold*a) {
            j = P[i];
            a = P[e];
            P[i] = a; Pinv[a] = i;
            P[e] = j; Pinv[j] = e;
        }
        a = Li[i];
        e = Ui[i];
        d = y[P[i]];
        Lj[a] = P[i];
        Lv[a] = 1;
        ++a;
        for(j=xj.length-1;j!==-1;--j) {
            k = xj[j];
            c = y[P[k]];
            xj[j] = 0;
            y[P[k]] = 0;
            if(k<=i) { Uj[e] = k; Uv[e] = c;   ++e; }
            else     { Lj[a] = P[k]; Lv[a] = c/d; ++a; }
        }
        Li[i+1] = a;
        Ui[i+1] = e;
    }
    for(j=Lj.length-1;j!==-1;--j) { Lj[j] = Pinv[Lj[j]]; }
    return {L:L, U:U, P:P, Pinv:Pinv};
}
numeric.ccsLUP = numeric.ccsLUP0;

numeric.ccsDim = function ccsDim(A) { return [numeric.sup(A[1])+1,A[0].length-1]; }
numeric.ccsGetBlock = function ccsGetBlock(A,i,j) {
    var s = numeric.ccsDim(A),m=s[0],n=s[1];
    if(typeof i === "undefined") { i = numeric.linspace(0,m-1); }
    else if(typeof i === "number") { i = [i]; }
    if(typeof j === "undefined") { j = numeric.linspace(0,n-1); }
    else if(typeof j === "number") { j = [j]; }
    var p,p0,p1,P = i.length,q,Q = j.length,r,jq,ip;
    var Bi = numeric.rep([n],0), Bj=[], Bv=[], B = [Bi,Bj,Bv];
    var Ai = A[0], Aj = A[1], Av = A[2];
    var x = numeric.rep([m],0),count=0,flags = numeric.rep([m],0);
    for(q=0;q<Q;++q) {
        jq = j[q];
        var q0 = Ai[jq];
        var q1 = Ai[jq+1];
        for(p=q0;p<q1;++p) {
            r = Aj[p];
            flags[r] = 1;
            x[r] = Av[p];
        }
        for(p=0;p<P;++p) {
            ip = i[p];
            if(flags[ip]) {
                Bj[count] = p;
                Bv[count] = x[i[p]];
                ++count;
            }
        }
        for(p=q0;p<q1;++p) {
            r = Aj[p];
            flags[r] = 0;
        }
        Bi[q+1] = count;
    }
    return B;
}

numeric.ccsDot = function ccsDot(A,B) {
    var Ai = A[0], Aj = A[1], Av = A[2];
    var Bi = B[0], Bj = B[1], Bv = B[2];
    var sA = numeric.ccsDim(A), sB = numeric.ccsDim(B);
    var m = sA[0], n = sA[1], o = sB[1];
    var x = numeric.rep([m],0), flags = numeric.rep([m],0), xj = Array(m);
    var Ci = numeric.rep([o],0), Cj = [], Cv = [], C = [Ci,Cj,Cv];
    var i,j,k,j0,j1,i0,i1,l,p,a,b;
    for(k=0;k!==o;++k) {
        j0 = Bi[k];
        j1 = Bi[k+1];
        p = 0;
        for(j=j0;j<j1;++j) {
            a = Bj[j];
            b = Bv[j];
            i0 = Ai[a];
            i1 = Ai[a+1];
            for(i=i0;i<i1;++i) {
                l = Aj[i];
                if(flags[l]===0) {
                    xj[p] = l;
                    flags[l] = 1;
                    p = p+1;
                }
                x[l] = x[l] + Av[i]*b;
            }
        }
        j0 = Ci[k];
        j1 = j0+p;
        Ci[k+1] = j1;
        for(j=p-1;j!==-1;--j) {
            b = j0+j;
            i = xj[j];
            Cj[b] = i;
            Cv[b] = x[i];
            flags[i] = 0;
            x[i] = 0;
        }
        Ci[k+1] = Ci[k]+p;
    }
    return C;
}

numeric.ccsLUPSolve = function ccsLUPSolve(LUP,B) {
    var L = LUP.L, U = LUP.U, P = LUP.P;
    var Bi = B[0];
    var flag = false;
    if(typeof Bi !== "object") { B = [[0,B.length],numeric.linspace(0,B.length-1),B]; Bi = B[0]; flag = true; }
    var Bj = B[1], Bv = B[2];
    var n = L[0].length-1, m = Bi.length-1;
    var x = numeric.rep([n],0), xj = Array(n);
    var b = numeric.rep([n],0), bj = Array(n);
    var Xi = numeric.rep([m+1],0), Xj = [], Xv = [];
    var sol = numeric.ccsTSolve;
    var i,j,j0,j1,k,J,N=0;
    for(i=0;i<m;++i) {
        k = 0;
        j0 = Bi[i];
        j1 = Bi[i+1];
        for(j=j0;j<j1;++j) { 
            J = LUP.Pinv[Bj[j]];
            bj[k] = J;
            b[J] = Bv[j];
            ++k;
        }
        bj.length = k;
        sol(L,b,x,bj,xj);
        for(j=bj.length-1;j!==-1;--j) b[bj[j]] = 0;
        sol(U,x,b,xj,bj);
        if(flag) return b;
        for(j=xj.length-1;j!==-1;--j) x[xj[j]] = 0;
        for(j=bj.length-1;j!==-1;--j) {
            J = bj[j];
            Xj[N] = J;
            Xv[N] = b[J];
            b[J] = 0;
            ++N;
        }
        Xi[i+1] = N;
    }
    return [Xi,Xj,Xv];
}

numeric.ccsbinop = function ccsbinop(body,setup) {
    if(typeof setup === "undefined") setup='';
    return Function('X','Y',
            'var Xi = X[0], Xj = X[1], Xv = X[2];\n'+
            'var Yi = Y[0], Yj = Y[1], Yv = Y[2];\n'+
            'var n = Xi.length-1,m = Math.max(numeric.sup(Xj),numeric.sup(Yj))+1;\n'+
            'var Zi = numeric.rep([n+1],0), Zj = [], Zv = [];\n'+
            'var x = numeric.rep([m],0),y = numeric.rep([m],0);\n'+
            'var xk,yk,zk;\n'+
            'var i,j,j0,j1,k,p=0;\n'+
            setup+
            'for(i=0;i<n;++i) {\n'+
            '  j0 = Xi[i]; j1 = Xi[i+1];\n'+
            '  for(j=j0;j!==j1;++j) {\n'+
            '    k = Xj[j];\n'+
            '    x[k] = 1;\n'+
            '    Zj[p] = k;\n'+
            '    ++p;\n'+
            '  }\n'+
            '  j0 = Yi[i]; j1 = Yi[i+1];\n'+
            '  for(j=j0;j!==j1;++j) {\n'+
            '    k = Yj[j];\n'+
            '    y[k] = Yv[j];\n'+
            '    if(x[k] === 0) {\n'+
            '      Zj[p] = k;\n'+
            '      ++p;\n'+
            '    }\n'+
            '  }\n'+
            '  Zi[i+1] = p;\n'+
            '  j0 = Xi[i]; j1 = Xi[i+1];\n'+
            '  for(j=j0;j!==j1;++j) x[Xj[j]] = Xv[j];\n'+
            '  j0 = Zi[i]; j1 = Zi[i+1];\n'+
            '  for(j=j0;j!==j1;++j) {\n'+
            '    k = Zj[j];\n'+
            '    xk = x[k];\n'+
            '    yk = y[k];\n'+
            body+'\n'+
            '    Zv[j] = zk;\n'+
            '  }\n'+
            '  j0 = Xi[i]; j1 = Xi[i+1];\n'+
            '  for(j=j0;j!==j1;++j) x[Xj[j]] = 0;\n'+
            '  j0 = Yi[i]; j1 = Yi[i+1];\n'+
            '  for(j=j0;j!==j1;++j) y[Yj[j]] = 0;\n'+
            '}\n'+
            'return [Zi,Zj,Zv];'
            );
};

(function() {
    var k,A,B,C;
    for(k in numeric.ops2) {
        if(isFinite(eval('1'+numeric.ops2[k]+'0'))) A = '[Y[0],Y[1],numeric.'+k+'(X,Y[2])]';
        else A = 'NaN';
        if(isFinite(eval('0'+numeric.ops2[k]+'1'))) B = '[X[0],X[1],numeric.'+k+'(X[2],Y)]';
        else B = 'NaN';
        if(isFinite(eval('1'+numeric.ops2[k]+'0')) && isFinite(eval('0'+numeric.ops2[k]+'1'))) C = 'numeric.ccs'+k+'MM(X,Y)';
        else C = 'NaN';
        numeric['ccs'+k+'MM'] = numeric.ccsbinop('zk = xk '+numeric.ops2[k]+'yk;');
        numeric['ccs'+k] = Function('X','Y',
                'if(typeof X === "number") return '+A+';\n'+
                'if(typeof Y === "number") return '+B+';\n'+
                'return '+C+';\n'
                );
    }
}());

numeric.ccsScatter = function ccsScatter(A) {
    var Ai = A[0], Aj = A[1], Av = A[2];
    var n = numeric.sup(Aj)+1,m=Ai.length;
    var Ri = numeric.rep([n],0),Rj=Array(m), Rv = Array(m);
    var counts = numeric.rep([n],0),i;
    for(i=0;i<m;++i) counts[Aj[i]]++;
    for(i=0;i<n;++i) Ri[i+1] = Ri[i] + counts[i];
    var ptr = Ri.slice(0),k,Aii;
    for(i=0;i<m;++i) {
        Aii = Aj[i];
        k = ptr[Aii];
        Rj[k] = Ai[i];
        Rv[k] = Av[i];
        ptr[Aii]=ptr[Aii]+1;
    }
    return [Ri,Rj,Rv];
}

numeric.ccsGather = function ccsGather(A) {
    var Ai = A[0], Aj = A[1], Av = A[2];
    var n = Ai.length-1,m = Aj.length;
    var Ri = Array(m), Rj = Array(m), Rv = Array(m);
    var i,j,j0,j1,p;
    p=0;
    for(i=0;i<n;++i) {
        j0 = Ai[i];
        j1 = Ai[i+1];
        for(j=j0;j!==j1;++j) {
            Rj[p] = i;
            Ri[p] = Aj[j];
            Rv[p] = Av[j];
            ++p;
        }
    }
    return [Ri,Rj,Rv];
}

// The following sparse linear algebra routines are deprecated.

numeric.sdim = function dim(A,ret,k) {
    if(typeof ret === "undefined") { ret = []; }
    if(typeof A !== "object") return ret;
    if(typeof k === "undefined") { k=0; }
    if(!(k in ret)) { ret[k] = 0; }
    if(A.length > ret[k]) ret[k] = A.length;
    var i;
    for(i in A) {
        if(A.hasOwnProperty(i)) dim(A[i],ret,k+1);
    }
    return ret;
};

numeric.sclone = function clone(A,k,n) {
    if(typeof k === "undefined") { k=0; }
    if(typeof n === "undefined") { n = numeric.sdim(A).length; }
    var i,ret = Array(A.length);
    if(k === n-1) {
        for(i in A) { if(A.hasOwnProperty(i)) ret[i] = A[i]; }
        return ret;
    }
    for(i in A) {
        if(A.hasOwnProperty(i)) ret[i] = clone(A[i],k+1,n);
    }
    return ret;
}

numeric.sdiag = function diag(d) {
    var n = d.length,i,ret = Array(n),i1,i2,i3;
    for(i=n-1;i>=1;i-=2) {
        i1 = i-1;
        ret[i] = []; ret[i][i] = d[i];
        ret[i1] = []; ret[i1][i1] = d[i1];
    }
    if(i===0) { ret[0] = []; ret[0][0] = d[i]; }
    return ret;
}

numeric.sidentity = function identity(n) { return numeric.sdiag(numeric.rep([n],1)); }

numeric.stranspose = function transpose(A) {
    var ret = [], n = A.length, i,j,Ai;
    for(i in A) {
        if(!(A.hasOwnProperty(i))) continue;
        Ai = A[i];
        for(j in Ai) {
            if(!(Ai.hasOwnProperty(j))) continue;
            if(typeof ret[j] !== "object") { ret[j] = []; }
            ret[j][i] = Ai[j];
        }
    }
    return ret;
}

numeric.sLUP = function LUP(A,tol) {
    throw new Error("The function numeric.sLUP had a bug in it and has been removed. Please use the new numeric.ccsLUP function instead.");
};

numeric.sdotMM = function dotMM(A,B) {
    var p = A.length, q = B.length, BT = numeric.stranspose(B), r = BT.length, Ai, BTk;
    var i,j,k,accum;
    var ret = Array(p),reti;
    for(i=p-1;i>=0;i--) {
        reti = [];
        Ai = A[i];
        for(k=r-1;k>=0;k--) {
            accum = 0;
            BTk = BT[k];
            for(j in Ai) {
                if(!(Ai.hasOwnProperty(j))) continue;
                if(j in BTk) { accum += Ai[j]*BTk[j]; }
            }
            if(accum) reti[k] = accum;
        }
        ret[i] = reti;
    }
    return ret;
}

numeric.sdotMV = function dotMV(A,x) {
    var p = A.length, Ai, i,j;
    var ret = Array(p), accum;
    for(i=p-1;i>=0;i--) {
        Ai = A[i];
        accum = 0;
        for(j in Ai) {
            if(!(Ai.hasOwnProperty(j))) continue;
            if(x[j]) accum += Ai[j]*x[j];
        }
        if(accum) ret[i] = accum;
    }
    return ret;
}

numeric.sdotVM = function dotMV(x,A) {
    var i,j,Ai,alpha;
    var ret = [], accum;
    for(i in x) {
        if(!x.hasOwnProperty(i)) continue;
        Ai = A[i];
        alpha = x[i];
        for(j in Ai) {
            if(!Ai.hasOwnProperty(j)) continue;
            if(!ret[j]) { ret[j] = 0; }
            ret[j] += alpha*Ai[j];
        }
    }
    return ret;
}

numeric.sdotVV = function dotVV(x,y) {
    var i,ret=0;
    for(i in x) { if(x[i] && y[i]) ret+= x[i]*y[i]; }
    return ret;
}

numeric.sdot = function dot(A,B) {
    var m = numeric.sdim(A).length, n = numeric.sdim(B).length;
    var k = m*1000+n;
    switch(k) {
    case 0: return A*B;
    case 1001: return numeric.sdotVV(A,B);
    case 2001: return numeric.sdotMV(A,B);
    case 1002: return numeric.sdotVM(A,B);
    case 2002: return numeric.sdotMM(A,B);
    default: throw new Error('numeric.sdot not implemented for tensors of order '+m+' and '+n);
    }
}

numeric.sscatter = function scatter(V) {
    var n = V[0].length, Vij, i, j, m = V.length, A = [], Aj;
    for(i=n-1;i>=0;--i) {
        if(!V[m-1][i]) continue;
        Aj = A;
        for(j=0;j<m-2;j++) {
            Vij = V[j][i];
            if(!Aj[Vij]) Aj[Vij] = [];
            Aj = Aj[Vij];
        }
        Aj[V[j][i]] = V[j+1][i];
    }
    return A;
}

numeric.sgather = function gather(A,ret,k) {
    if(typeof ret === "undefined") ret = [];
    if(typeof k === "undefined") k = [];
    var n,i,Ai;
    n = k.length;
    for(i in A) {
        if(A.hasOwnProperty(i)) {
            k[n] = parseInt(i);
            Ai = A[i];
            if(typeof Ai === "number") {
                if(Ai) {
                    if(ret.length === 0) {
                        for(i=n+1;i>=0;--i) ret[i] = [];
                    }
                    for(i=n;i>=0;--i) ret[i].push(k[i]);
                    ret[n+1].push(Ai);
                }
            } else gather(Ai,ret,k);
        }
    }
    if(k.length>n) k.pop();
    return ret;
}

// 6. Coordinate matrices
numeric.cLU = function LU(A) {
    var I = A[0], J = A[1], V = A[2];
    var p = I.length, m=0, i,j,k,a,b,c;
    for(i=0;i<p;i++) if(I[i]>m) m=I[i];
    m++;
    var L = Array(m), U = Array(m), left = numeric.rep([m],Infinity), right = numeric.rep([m],-Infinity);
    var Ui, Uj,alpha;
    for(k=0;k<p;k++) {
        i = I[k];
        j = J[k];
        if(j<left[i]) left[i] = j;
        if(j>right[i]) right[i] = j;
    }
    for(i=0;i<m-1;i++) { if(right[i] > right[i+1]) right[i+1] = right[i]; }
    for(i=m-1;i>=1;i--) { if(left[i]<left[i-1]) left[i-1] = left[i]; }
    var countL = 0, countU = 0;
    for(i=0;i<m;i++) {
        U[i] = numeric.rep([right[i]-left[i]+1],0);
        L[i] = numeric.rep([i-left[i]],0);
        countL += i-left[i]+1;
        countU += right[i]-i+1;
    }
    for(k=0;k<p;k++) { i = I[k]; U[i][J[k]-left[i]] = V[k]; }
    for(i=0;i<m-1;i++) {
        a = i-left[i];
        Ui = U[i];
        for(j=i+1;left[j]<=i && j<m;j++) {
            b = i-left[j];
            c = right[i]-i;
            Uj = U[j];
            alpha = Uj[b]/Ui[a];
            if(alpha) {
                for(k=1;k<=c;k++) { Uj[k+b] -= alpha*Ui[k+a]; }
                L[j][i-left[j]] = alpha;
            }
        }
    }
    var Ui = [], Uj = [], Uv = [], Li = [], Lj = [], Lv = [];
    var p,q,foo;
    p=0; q=0;
    for(i=0;i<m;i++) {
        a = left[i];
        b = right[i];
        foo = U[i];
        for(j=i;j<=b;j++) {
            if(foo[j-a]) {
                Ui[p] = i;
                Uj[p] = j;
                Uv[p] = foo[j-a];
                p++;
            }
        }
        foo = L[i];
        for(j=a;j<i;j++) {
            if(foo[j-a]) {
                Li[q] = i;
                Lj[q] = j;
                Lv[q] = foo[j-a];
                q++;
            }
        }
        Li[q] = i;
        Lj[q] = i;
        Lv[q] = 1;
        q++;
    }
    return {U:[Ui,Uj,Uv], L:[Li,Lj,Lv]};
};

numeric.cLUsolve = function LUsolve(lu,b) {
    var L = lu.L, U = lu.U, ret = numeric.clone(b);
    var Li = L[0], Lj = L[1], Lv = L[2];
    var Ui = U[0], Uj = U[1], Uv = U[2];
    var p = Ui.length, q = Li.length;
    var m = ret.length,i,j,k;
    k = 0;
    for(i=0;i<m;i++) {
        while(Lj[k] < i) {
            ret[i] -= Lv[k]*ret[Lj[k]];
            k++;
        }
        k++;
    }
    k = p-1;
    for(i=m-1;i>=0;i--) {
        while(Uj[k] > i) {
            ret[i] -= Uv[k]*ret[Uj[k]];
            k--;
        }
        ret[i] /= Uv[k];
        k--;
    }
    return ret;
};

numeric.cgrid = function grid(n,shape) {
    if(typeof n === "number") n = [n,n];
    var ret = numeric.rep(n,-1);
    var i,j,count;
    if(typeof shape !== "function") {
        switch(shape) {
        case 'L':
            shape = function(i,j) { return (i>=n[0]/2 || j<n[1]/2); }
            break;
        default:
            shape = function(i,j) { return true; };
            break;
        }
    }
    count=0;
    for(i=1;i<n[0]-1;i++) for(j=1;j<n[1]-1;j++) 
        if(shape(i,j)) {
            ret[i][j] = count;
            count++;
        }
    return ret;
}

numeric.cdelsq = function delsq(g) {
    var dir = [[-1,0],[0,-1],[0,1],[1,0]];
    var s = numeric.dim(g), m = s[0], n = s[1], i,j,k,p,q;
    var Li = [], Lj = [], Lv = [];
    for(i=1;i<m-1;i++) for(j=1;j<n-1;j++) {
        if(g[i][j]<0) continue;
        for(k=0;k<4;k++) {
            p = i+dir[k][0];
            q = j+dir[k][1];
            if(g[p][q]<0) continue;
            Li.push(g[i][j]);
            Lj.push(g[p][q]);
            Lv.push(-1);
        }
        Li.push(g[i][j]);
        Lj.push(g[i][j]);
        Lv.push(4);
    }
    return [Li,Lj,Lv];
}

numeric.cdotMV = function dotMV(A,x) {
    var ret, Ai = A[0], Aj = A[1], Av = A[2],k,p=Ai.length,N;
    N=0;
    for(k=0;k<p;k++) { if(Ai[k]>N) N = Ai[k]; }
    N++;
    ret = numeric.rep([N],0);
    for(k=0;k<p;k++) { ret[Ai[k]]+=Av[k]*x[Aj[k]]; }
    return ret;
}

// 7. Splines

numeric.Spline = function Spline(x,yl,yr,kl,kr) { this.x = x; this.yl = yl; this.yr = yr; this.kl = kl; this.kr = kr; }
numeric.Spline.prototype._at = function _at(x1,p) {
    var x = this.x;
    var yl = this.yl;
    var yr = this.yr;
    var kl = this.kl;
    var kr = this.kr;
    var x1,a,b,t;
    var add = numeric.add, sub = numeric.sub, mul = numeric.mul;
    a = sub(mul(kl[p],x[p+1]-x[p]),sub(yr[p+1],yl[p]));
    b = add(mul(kr[p+1],x[p]-x[p+1]),sub(yr[p+1],yl[p]));
    t = (x1-x[p])/(x[p+1]-x[p]);
    var s = t*(1-t);
    return add(add(add(mul(1-t,yl[p]),mul(t,yr[p+1])),mul(a,s*(1-t))),mul(b,s*t));
}
numeric.Spline.prototype.at = function at(x0) {
    if(typeof x0 === "number") {
        var x = this.x;
        var n = x.length;
        var p,q,mid,floor = Math.floor,a,b,t;
        p = 0;
        q = n-1;
        while(q-p>1) {
            mid = floor((p+q)/2);
            if(x[mid] <= x0) p = mid;
            else q = mid;
        }
        return this._at(x0,p);
    }
    var n = x0.length, i, ret = Array(n);
    for(i=n-1;i!==-1;--i) ret[i] = this.at(x0[i]);
    return ret;
}
numeric.Spline.prototype.diff = function diff() {
    var x = this.x;
    var yl = this.yl;
    var yr = this.yr;
    var kl = this.kl;
    var kr = this.kr;
    var n = yl.length;
    var i,dx,dy;
    var zl = kl, zr = kr, pl = Array(n), pr = Array(n);
    var add = numeric.add, mul = numeric.mul, div = numeric.div, sub = numeric.sub;
    for(i=n-1;i!==-1;--i) {
        dx = x[i+1]-x[i];
        dy = sub(yr[i+1],yl[i]);
        pl[i] = div(add(mul(dy, 6),mul(kl[i],-4*dx),mul(kr[i+1],-2*dx)),dx*dx);
        pr[i+1] = div(add(mul(dy,-6),mul(kl[i], 2*dx),mul(kr[i+1], 4*dx)),dx*dx);
    }
    return new numeric.Spline(x,zl,zr,pl,pr);
}
numeric.Spline.prototype.roots = function roots() {
    function sqr(x) { return x*x; }
    function heval(y0,y1,k0,k1,x) {
        var A = k0*2-(y1-y0);
        var B = -k1*2+(y1-y0);
        var t = (x+1)*0.5;
        var s = t*(1-t);
        return (1-t)*y0+t*y1+A*s*(1-t)+B*s*t;
    }
    var ret = [];
    var x = this.x, yl = this.yl, yr = this.yr, kl = this.kl, kr = this.kr;
    if(typeof yl[0] === "number") {
        yl = [yl];
        yr = [yr];
        kl = [kl];
        kr = [kr];
    }
    var m = yl.length,n=x.length-1,i,j,k,y,s,t;
    var ai,bi,ci,di, ret = Array(m),ri,k0,k1,y0,y1,A,B,D,dx,cx,stops,z0,z1,zm,t0,t1,tm;
    var sqrt = Math.sqrt;
    for(i=0;i!==m;++i) {
        ai = yl[i];
        bi = yr[i];
        ci = kl[i];
        di = kr[i];
        ri = [];
        for(j=0;j!==n;j++) {
            if(j>0 && bi[j]*ai[j]<0) ri.push(x[j]);
            dx = (x[j+1]-x[j]);
            cx = x[j];
            y0 = ai[j];
            y1 = bi[j+1];
            k0 = ci[j]/dx;
            k1 = di[j+1]/dx;
            D = sqr(k0-k1+3*(y0-y1)) + 12*k1*y0;
            A = k1+3*y0+2*k0-3*y1;
            B = 3*(k1+k0+2*(y0-y1));
            if(D<=0) {
                z0 = A/B;
                if(z0>x[j] && z0<x[j+1]) stops = [x[j],z0,x[j+1]];
                else stops = [x[j],x[j+1]];
            } else {
                z0 = (A-sqrt(D))/B;
                z1 = (A+sqrt(D))/B;
                stops = [x[j]];
                if(z0>x[j] && z0<x[j+1]) stops.push(z0);
                if(z1>x[j] && z1<x[j+1]) stops.push(z1);
                stops.push(x[j+1]);
            }
            t0 = stops[0];
            z0 = this._at(t0,j);
            for(k=0;k<stops.length-1;k++) {
                t1 = stops[k+1];
                z1 = this._at(t1,j);
                if(z0 === 0) {
                    ri.push(t0); 
                    t0 = t1;
                    z0 = z1;
                    continue;
                }
                if(z1 === 0 || z0*z1>0) {
                    t0 = t1;
                    z0 = z1;
                    continue;
                }
                var side = 0;
                while(1) {
                    tm = (z0*t1-z1*t0)/(z0-z1);
                    if(tm <= t0 || tm >= t1) { break; }
                    zm = this._at(tm,j);
                    if(zm*z1>0) {
                        t1 = tm;
                        z1 = zm;
                        if(side === -1) z0*=0.5;
                        side = -1;
                    } else if(zm*z0>0) {
                        t0 = tm;
                        z0 = zm;
                        if(side === 1) z1*=0.5;
                        side = 1;
                    } else break;
                }
                ri.push(tm);
                t0 = stops[k+1];
                z0 = this._at(t0, j);
            }
            if(z1 === 0) ri.push(t1);
        }
        ret[i] = ri;
    }
    if(typeof this.yl[0] === "number") return ret[0];
    return ret;
}
numeric.spline = function spline(x,y,k1,kn) {
    var n = x.length, b = [], dx = [], dy = [];
    var i;
    var sub = numeric.sub,mul = numeric.mul,add = numeric.add;
    for(i=n-2;i>=0;i--) { dx[i] = x[i+1]-x[i]; dy[i] = sub(y[i+1],y[i]); }
    if(typeof k1 === "string" || typeof kn === "string") { 
        k1 = kn = "periodic";
    }
    // Build sparse tridiagonal system
    var T = [[],[],[]];
    switch(typeof k1) {
    case "undefined":
        b[0] = mul(3/(dx[0]*dx[0]),dy[0]);
        T[0].push(0,0);
        T[1].push(0,1);
        T[2].push(2/dx[0],1/dx[0]);
        break;
    case "string":
        b[0] = add(mul(3/(dx[n-2]*dx[n-2]),dy[n-2]),mul(3/(dx[0]*dx[0]),dy[0]));
        T[0].push(0,0,0);
        T[1].push(n-2,0,1);
        T[2].push(1/dx[n-2],2/dx[n-2]+2/dx[0],1/dx[0]);
        break;
    default:
        b[0] = k1;
        T[0].push(0);
        T[1].push(0);
        T[2].push(1);
        break;
    }
    for(i=1;i<n-1;i++) {
        b[i] = add(mul(3/(dx[i-1]*dx[i-1]),dy[i-1]),mul(3/(dx[i]*dx[i]),dy[i]));
        T[0].push(i,i,i);
        T[1].push(i-1,i,i+1);
        T[2].push(1/dx[i-1],2/dx[i-1]+2/dx[i],1/dx[i]);
    }
    switch(typeof kn) {
    case "undefined":
        b[n-1] = mul(3/(dx[n-2]*dx[n-2]),dy[n-2]);
        T[0].push(n-1,n-1);
        T[1].push(n-2,n-1);
        T[2].push(1/dx[n-2],2/dx[n-2]);
        break;
    case "string":
        T[1][T[1].length-1] = 0;
        break;
    default:
        b[n-1] = kn;
        T[0].push(n-1);
        T[1].push(n-1);
        T[2].push(1);
        break;
    }
    if(typeof b[0] !== "number") b = numeric.transpose(b);
    else b = [b];
    var k = Array(b.length);
    if(typeof k1 === "string") {
        for(i=k.length-1;i!==-1;--i) {
            k[i] = numeric.ccsLUPSolve(numeric.ccsLUP(numeric.ccsScatter(T)),b[i]);
            k[i][n-1] = k[i][0];
        }
    } else {
        for(i=k.length-1;i!==-1;--i) {
            k[i] = numeric.cLUsolve(numeric.cLU(T),b[i]);
        }
    }
    if(typeof y[0] === "number") k = k[0];
    else k = numeric.transpose(k);
    return new numeric.Spline(x,y,y,k,k);
}

// 8. FFT
numeric.fftpow2 = function fftpow2(x,y) {
    var n = x.length;
    if(n === 1) return;
    var cos = Math.cos, sin = Math.sin, i,j;
    var xe = Array(n/2), ye = Array(n/2), xo = Array(n/2), yo = Array(n/2);
    j = n/2;
    for(i=n-1;i!==-1;--i) {
        --j;
        xo[j] = x[i];
        yo[j] = y[i];
        --i;
        xe[j] = x[i];
        ye[j] = y[i];
    }
    fftpow2(xe,ye);
    fftpow2(xo,yo);
    j = n/2;
    var t,k = (-6.2831853071795864769252867665590057683943387987502116419/n),ci,si;
    for(i=n-1;i!==-1;--i) {
        --j;
        if(j === -1) j = n/2-1;
        t = k*i;
        ci = cos(t);
        si = sin(t);
        x[i] = xe[j] + ci*xo[j] - si*yo[j];
        y[i] = ye[j] + ci*yo[j] + si*xo[j];
    }
}
numeric._ifftpow2 = function _ifftpow2(x,y) {
    var n = x.length;
    if(n === 1) return;
    var cos = Math.cos, sin = Math.sin, i,j;
    var xe = Array(n/2), ye = Array(n/2), xo = Array(n/2), yo = Array(n/2);
    j = n/2;
    for(i=n-1;i!==-1;--i) {
        --j;
        xo[j] = x[i];
        yo[j] = y[i];
        --i;
        xe[j] = x[i];
        ye[j] = y[i];
    }
    _ifftpow2(xe,ye);
    _ifftpow2(xo,yo);
    j = n/2;
    var t,k = (6.2831853071795864769252867665590057683943387987502116419/n),ci,si;
    for(i=n-1;i!==-1;--i) {
        --j;
        if(j === -1) j = n/2-1;
        t = k*i;
        ci = cos(t);
        si = sin(t);
        x[i] = xe[j] + ci*xo[j] - si*yo[j];
        y[i] = ye[j] + ci*yo[j] + si*xo[j];
    }
}
numeric.ifftpow2 = function ifftpow2(x,y) {
    numeric._ifftpow2(x,y);
    numeric.diveq(x,x.length);
    numeric.diveq(y,y.length);
}
numeric.convpow2 = function convpow2(ax,ay,bx,by) {
    numeric.fftpow2(ax,ay);
    numeric.fftpow2(bx,by);
    var i,n = ax.length,axi,bxi,ayi,byi;
    for(i=n-1;i!==-1;--i) {
        axi = ax[i]; ayi = ay[i]; bxi = bx[i]; byi = by[i];
        ax[i] = axi*bxi-ayi*byi;
        ay[i] = axi*byi+ayi*bxi;
    }
    numeric.ifftpow2(ax,ay);
}
numeric.T.prototype.fft = function fft() {
    var x = this.x, y = this.y;
    var n = x.length, log = Math.log, log2 = log(2),
        p = Math.ceil(log(2*n-1)/log2), m = Math.pow(2,p);
    var cx = numeric.rep([m],0), cy = numeric.rep([m],0), cos = Math.cos, sin = Math.sin;
    var k, c = (-3.141592653589793238462643383279502884197169399375105820/n),t;
    var a = numeric.rep([m],0), b = numeric.rep([m],0),nhalf = Math.floor(n/2);
    for(k=0;k<n;k++) a[k] = x[k];
    if(typeof y !== "undefined") for(k=0;k<n;k++) b[k] = y[k];
    cx[0] = 1;
    for(k=1;k<=m/2;k++) {
        t = c*k*k;
        cx[k] = cos(t);
        cy[k] = sin(t);
        cx[m-k] = cos(t);
        cy[m-k] = sin(t)
    }
    var X = new numeric.T(a,b), Y = new numeric.T(cx,cy);
    X = X.mul(Y);
    numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));
    X = X.mul(Y);
    X.x.length = n;
    X.y.length = n;
    return X;
}
numeric.T.prototype.ifft = function ifft() {
    var x = this.x, y = this.y;
    var n = x.length, log = Math.log, log2 = log(2),
        p = Math.ceil(log(2*n-1)/log2), m = Math.pow(2,p);
    var cx = numeric.rep([m],0), cy = numeric.rep([m],0), cos = Math.cos, sin = Math.sin;
    var k, c = (3.141592653589793238462643383279502884197169399375105820/n),t;
    var a = numeric.rep([m],0), b = numeric.rep([m],0),nhalf = Math.floor(n/2);
    for(k=0;k<n;k++) a[k] = x[k];
    if(typeof y !== "undefined") for(k=0;k<n;k++) b[k] = y[k];
    cx[0] = 1;
    for(k=1;k<=m/2;k++) {
        t = c*k*k;
        cx[k] = cos(t);
        cy[k] = sin(t);
        cx[m-k] = cos(t);
        cy[m-k] = sin(t)
    }
    var X = new numeric.T(a,b), Y = new numeric.T(cx,cy);
    X = X.mul(Y);
    numeric.convpow2(X.x,X.y,numeric.clone(Y.x),numeric.neg(Y.y));
    X = X.mul(Y);
    X.x.length = n;
    X.y.length = n;
    return X.div(n);
}

//9. Unconstrained optimization
numeric.gradient = function gradient(f,x) {
    var n = x.length;
    var f0 = f(x);
    if(isNaN(f0)) throw new Error('gradient: f(x) is a NaN!');
    var max = Math.max;
    var i,x0 = numeric.clone(x),f1,f2, J = Array(n);
    var div = numeric.div, sub = numeric.sub,errest,roundoff,max = Math.max,eps = 1e-3,abs = Math.abs, min = Math.min;
    var t0,t1,t2,it=0,d1,d2,N;
    for(i=0;i<n;i++) {
        var h = max(1e-6*f0,1e-8);
        while(1) {
            ++it;
            if(it>20) { throw new Error("Numerical gradient fails"); }
            x0[i] = x[i]+h;
            f1 = f(x0);
            x0[i] = x[i]-h;
            f2 = f(x0);
            x0[i] = x[i];
            if(isNaN(f1) || isNaN(f2)) { h/=16; continue; }
            J[i] = (f1-f2)/(2*h);
            t0 = x[i]-h;
            t1 = x[i];
            t2 = x[i]+h;
            d1 = (f1-f0)/h;
            d2 = (f0-f2)/h;
            N = max(abs(J[i]),abs(f0),abs(f1),abs(f2),abs(t0),abs(t1),abs(t2),1e-8);
            errest = min(max(abs(d1-J[i]),abs(d2-J[i]),abs(d1-d2))/N,h/N);
            if(errest>eps) { h/=16; }
            else break;
            }
    }
    return J;
}

numeric.uncmin = function uncmin(f,x0,tol,gradient,maxit,callback,options) {
    var grad = numeric.gradient;
    if(typeof options === "undefined") { options = {}; }
    if(typeof tol === "undefined") { tol = 1e-8; }
    if(typeof gradient === "undefined") { gradient = function(x) { return grad(f,x); }; }
    if(typeof maxit === "undefined") maxit = 1000;
    x0 = numeric.clone(x0);
    var n = x0.length;
    var f0 = f(x0),f1,df0;
    if(isNaN(f0)) throw new Error('uncmin: f(x0) is a NaN!');
    var max = Math.max, norm2 = numeric.norm2;
    tol = max(tol,numeric.epsilon);
    var step,g0,g1,H1 = options.Hinv || numeric.identity(n);
    var dot = numeric.dot, inv = numeric.inv, sub = numeric.sub, add = numeric.add, ten = numeric.tensor, div = numeric.div, mul = numeric.mul;
    var all = numeric.all, isfinite = numeric.isFinite, neg = numeric.neg;
    var it=0,i,s,x1,y,Hy,Hs,ys,i0,t,nstep,t1,t2;
    var msg = "";
    g0 = gradient(x0);
    while(it<maxit) {
        if(typeof callback === "function") { if(callback(it,x0,f0,g0,H1)) { msg = "Callback returned true"; break; } }
        if(!all(isfinite(g0))) { msg = "Gradient has Infinity or NaN"; break; }
        step = neg(dot(H1,g0));
        if(!all(isfinite(step))) { msg = "Search direction has Infinity or NaN"; break; }
        nstep = norm2(step);
        if(nstep < tol) { msg="Newton step smaller than tol"; break; }
        t = 1;
        df0 = dot(g0,step);
        // line search
        x1 = x0;
        while(it < maxit) {
            if(t*nstep < tol) { break; }
            s = mul(step,t);
            x1 = add(x0,s);
            f1 = f(x1);
            if(f1-f0 >= 0.1*t*df0 || isNaN(f1)) {
                t *= 0.5;
                ++it;
                continue;
            }
            break;
        }
        if(t*nstep < tol) { msg = "Line search step size smaller than tol"; break; }
        if(it === maxit) { msg = "maxit reached during line search"; break; }
        g1 = gradient(x1);
        y = sub(g1,g0);
        ys = dot(y,s);
        Hy = dot(H1,y);
        H1 = sub(add(H1,
                mul(
                        (ys+dot(y,Hy))/(ys*ys),
                        ten(s,s)    )),
                div(add(ten(Hy,s),ten(s,Hy)),ys));
        x0 = x1;
        f0 = f1;
        g0 = g1;
        ++it;
    }
    return {solution: x0, f: f0, gradient: g0, invHessian: H1, iterations:it, message: msg};
}

// 10. Ode solver (Dormand-Prince)
numeric.Dopri = function Dopri(x,y,f,ymid,iterations,msg,events) {
    this.x = x;
    this.y = y;
    this.f = f;
    this.ymid = ymid;
    this.iterations = iterations;
    this.events = events;
    this.message = msg;
}
numeric.Dopri.prototype._at = function _at(xi,j) {
    function sqr(x) { return x*x; }
    var sol = this;
    var xs = sol.x;
    var ys = sol.y;
    var k1 = sol.f;
    var ymid = sol.ymid;
    var n = xs.length;
    var x0,x1,xh,y0,y1,yh,xi;
    var floor = Math.floor,h;
    var c = 0.5;
    var add = numeric.add, mul = numeric.mul,sub = numeric.sub, p,q,w;
    x0 = xs[j];
    x1 = xs[j+1];
    y0 = ys[j];
    y1 = ys[j+1];
    h  = x1-x0;
    xh = x0+c*h;
    yh = ymid[j];
    p = sub(k1[j  ],mul(y0,1/(x0-xh)+2/(x0-x1)));
    q = sub(k1[j+1],mul(y1,1/(x1-xh)+2/(x1-x0)));
    w = [sqr(xi - x1) * (xi - xh) / sqr(x0 - x1) / (x0 - xh),
         sqr(xi - x0) * sqr(xi - x1) / sqr(x0 - xh) / sqr(x1 - xh),
         sqr(xi - x0) * (xi - xh) / sqr(x1 - x0) / (x1 - xh),
         (xi - x0) * sqr(xi - x1) * (xi - xh) / sqr(x0-x1) / (x0 - xh),
         (xi - x1) * sqr(xi - x0) * (xi - xh) / sqr(x0-x1) / (x1 - xh)];
    return add(add(add(add(mul(y0,w[0]),
                           mul(yh,w[1])),
                           mul(y1,w[2])),
                           mul( p,w[3])),
                           mul( q,w[4]));
}
numeric.Dopri.prototype.at = function at(x) {
    var i,j,k,floor = Math.floor;
    if(typeof x !== "number") {
        var n = x.length, ret = Array(n);
        for(i=n-1;i!==-1;--i) {
            ret[i] = this.at(x[i]);
        }
        return ret;
    }
    var x0 = this.x;
    i = 0; j = x0.length-1;
    while(j-i>1) {
        k = floor(0.5*(i+j));
        if(x0[k] <= x) i = k;
        else j = k;
    }
    return this._at(x,i);
}

numeric.dopri = function dopri(x0,x1,y0,f,tol,maxit,event) {
    if(typeof tol === "undefined") { tol = 1e-6; }
    if(typeof maxit === "undefined") { maxit = 1000; }
    var xs = [x0], ys = [y0], k1 = [f(x0,y0)], k2,k3,k4,k5,k6,k7, ymid = [];
    var A2 = 1/5;
    var A3 = [3/40,9/40];
    var A4 = [44/45,-56/15,32/9];
    var A5 = [19372/6561,-25360/2187,64448/6561,-212/729];
    var A6 = [9017/3168,-355/33,46732/5247,49/176,-5103/18656];
    var b = [35/384,0,500/1113,125/192,-2187/6784,11/84];
    var bm = [0.5*6025192743/30085553152,
              0,
              0.5*51252292925/65400821598,
              0.5*-2691868925/45128329728,
              0.5*187940372067/1594534317056,
              0.5*-1776094331/19743644256,
              0.5*11237099/235043384];
    var c = [1/5,3/10,4/5,8/9,1,1];
    var e = [-71/57600,0,71/16695,-71/1920,17253/339200,-22/525,1/40];
    var i = 0,er,j;
    var h = (x1-x0)/10;
    var it = 0;
    var add = numeric.add, mul = numeric.mul, y1,erinf;
    var max = Math.max, min = Math.min, abs = Math.abs, norminf = numeric.norminf,pow = Math.pow;
    var any = numeric.any, lt = numeric.lt, and = numeric.and, sub = numeric.sub;
    var e0, e1, ev;
    var ret = new numeric.Dopri(xs,ys,k1,ymid,-1,"");
    if(typeof event === "function") e0 = event(x0,y0);
    while(x0<x1 && it<maxit) {
        ++it;
        if(x0+h>x1) h = x1-x0;
        k2 = f(x0+c[0]*h,                add(y0,mul(   A2*h,k1[i])));
        k3 = f(x0+c[1]*h,            add(add(y0,mul(A3[0]*h,k1[i])),mul(A3[1]*h,k2)));
        k4 = f(x0+c[2]*h,        add(add(add(y0,mul(A4[0]*h,k1[i])),mul(A4[1]*h,k2)),mul(A4[2]*h,k3)));
        k5 = f(x0+c[3]*h,    add(add(add(add(y0,mul(A5[0]*h,k1[i])),mul(A5[1]*h,k2)),mul(A5[2]*h,k3)),mul(A5[3]*h,k4)));
        k6 = f(x0+c[4]*h,add(add(add(add(add(y0,mul(A6[0]*h,k1[i])),mul(A6[1]*h,k2)),mul(A6[2]*h,k3)),mul(A6[3]*h,k4)),mul(A6[4]*h,k5)));
        y1 = add(add(add(add(add(y0,mul(k1[i],h*b[0])),mul(k3,h*b[2])),mul(k4,h*b[3])),mul(k5,h*b[4])),mul(k6,h*b[5]));
        k7 = f(x0+h,y1);
        er = add(add(add(add(add(mul(k1[i],h*e[0]),mul(k3,h*e[2])),mul(k4,h*e[3])),mul(k5,h*e[4])),mul(k6,h*e[5])),mul(k7,h*e[6]));
        if(typeof er === "number") erinf = abs(er);
        else erinf = norminf(er);
        if(erinf > tol) { // reject
            h = 0.2*h*pow(tol/erinf,0.25);
            if(x0+h === x0) {
                ret.msg = "Step size became too small";
                break;
            }
            continue;
        }
        ymid[i] = add(add(add(add(add(add(y0,
                mul(k1[i],h*bm[0])),
                mul(k3   ,h*bm[2])),
                mul(k4   ,h*bm[3])),
                mul(k5   ,h*bm[4])),
                mul(k6   ,h*bm[5])),
                mul(k7   ,h*bm[6]));
        ++i;
        xs[i] = x0+h;
        ys[i] = y1;
        k1[i] = k7;
        if(typeof event === "function") {
            var yi,xl = x0,xr = x0+0.5*h,xi;
            e1 = event(xr,ymid[i-1]);
            ev = and(lt(e0,0),lt(0,e1));
            if(!any(ev)) { xl = xr; xr = x0+h; e0 = e1; e1 = event(xr,y1); ev = and(lt(e0,0),lt(0,e1)); }
            if(any(ev)) {
                var xc, yc, en,ei;
                var side=0, sl = 1.0, sr = 1.0;
                while(1) {
                    if(typeof e0 === "number") xi = (sr*e1*xl-sl*e0*xr)/(sr*e1-sl*e0);
                    else {
                        xi = xr;
                        for(j=e0.length-1;j!==-1;--j) {
                            if(e0[j]<0 && e1[j]>0) xi = min(xi,(sr*e1[j]*xl-sl*e0[j]*xr)/(sr*e1[j]-sl*e0[j]));
                        }
                    }
                    if(xi <= xl || xi >= xr) break;
                    yi = ret._at(xi, i-1);
                    ei = event(xi,yi);
                    en = and(lt(e0,0),lt(0,ei));
                    if(any(en)) {
                        xr = xi;
                        e1 = ei;
                        ev = en;
                        sr = 1.0;
                        if(side === -1) sl *= 0.5;
                        else sl = 1.0;
                        side = -1;
                    } else {
                        xl = xi;
                        e0 = ei;
                        sl = 1.0;
                        if(side === 1) sr *= 0.5;
                        else sr = 1.0;
                        side = 1;
                    }
                }
                y1 = ret._at(0.5*(x0+xi),i-1);
                ret.f[i] = f(xi,yi);
                ret.x[i] = xi;
                ret.y[i] = yi;
                ret.ymid[i-1] = y1;
                ret.events = ev;
                ret.iterations = it;
                return ret;
            }
        }
        x0 += h;
        y0 = y1;
        e0 = e1;
        h = min(0.8*h*pow(tol/erinf,0.25),4*h);
    }
    ret.iterations = it;
    return ret;
}

// 11. Ax = b
numeric.LU = function(A, fast) {
  fast = fast || false;

  var abs = Math.abs;
  var i, j, k, absAjk, Akk, Ak, Pk, Ai;
  var max;
  var n = A.length, n1 = n-1;
  var P = new Array(n);
  if(!fast) A = numeric.clone(A);

  for (k = 0; k < n; ++k) {
    Pk = k;
    Ak = A[k];
    max = abs(Ak[k]);
    for (j = k + 1; j < n; ++j) {
      absAjk = abs(A[j][k]);
      if (max < absAjk) {
        max = absAjk;
        Pk = j;
      }
    }
    P[k] = Pk;

    if (Pk != k) {
      A[k] = A[Pk];
      A[Pk] = Ak;
      Ak = A[k];
    }

    Akk = Ak[k];

    for (i = k + 1; i < n; ++i) {
      A[i][k] /= Akk;
    }

    for (i = k + 1; i < n; ++i) {
      Ai = A[i];
      for (j = k + 1; j < n1; ++j) {
        Ai[j] -= Ai[k] * Ak[j];
        ++j;
        Ai[j] -= Ai[k] * Ak[j];
      }
      if(j===n1) Ai[j] -= Ai[k] * Ak[j];
    }
  }

  return {
    LU: A,
    P:  P
  };
}

numeric.LUsolve = function LUsolve(LUP, b) {
  var i, j;
  var LU = LUP.LU;
  var n   = LU.length;
  var x = numeric.clone(b);
  var P   = LUP.P;
  var Pi, LUi, LUii, tmp;

  for (i=n-1;i!==-1;--i) x[i] = b[i];
  for (i = 0; i < n; ++i) {
    Pi = P[i];
    if (P[i] !== i) {
      tmp = x[i];
      x[i] = x[Pi];
      x[Pi] = tmp;
    }

    LUi = LU[i];
    for (j = 0; j < i; ++j) {
      x[i] -= x[j] * LUi[j];
    }
  }

  for (i = n - 1; i >= 0; --i) {
    LUi = LU[i];
    for (j = i + 1; j < n; ++j) {
      x[i] -= x[j] * LUi[j];
    }

    x[i] /= LUi[i];
  }

  return x;
}

numeric.solve = function solve(A,b,fast) { return numeric.LUsolve(numeric.LU(A,fast), b); }

// 12. Linear programming
numeric.echelonize = function echelonize(A) {
    var s = numeric.dim(A), m = s[0], n = s[1];
    var I = numeric.identity(m);
    var P = Array(m);
    var i,j,k,l,Ai,Ii,Z,a;
    var abs = Math.abs;
    var diveq = numeric.diveq;
    A = numeric.clone(A);
    for(i=0;i<m;++i) {
        k = 0;
        Ai = A[i];
        Ii = I[i];
        for(j=1;j<n;++j) if(abs(Ai[k])<abs(Ai[j])) k=j;
        P[i] = k;
        diveq(Ii,Ai[k]);
        diveq(Ai,Ai[k]);
        for(j=0;j<m;++j) if(j!==i) {
            Z = A[j]; a = Z[k];
            for(l=n-1;l!==-1;--l) Z[l] -= Ai[l]*a;
            Z = I[j];
            for(l=m-1;l!==-1;--l) Z[l] -= Ii[l]*a;
        }
    }
    return {I:I, A:A, P:P};
}

numeric.__solveLP = function __solveLP(c,A,b,tol,maxit,x,flag) {
    var sum = numeric.sum, log = numeric.log, mul = numeric.mul, sub = numeric.sub, dot = numeric.dot, div = numeric.div, add = numeric.add;
    var m = c.length, n = b.length,y;
    var unbounded = false, cb,i0=0;
    var alpha = 1.0;
    var f0,df0,AT = numeric.transpose(A), svd = numeric.svd,transpose = numeric.transpose,leq = numeric.leq, sqrt = Math.sqrt, abs = Math.abs;
    var muleq = numeric.muleq;
    var norm = numeric.norminf, any = numeric.any,min = Math.min;
    var all = numeric.all, gt = numeric.gt;
    var p = Array(m), A0 = Array(n),e=numeric.rep([n],1), H;
    var solve = numeric.solve, z = sub(b,dot(A,x)),count;
    var dotcc = dot(c,c);
    var g;
    for(count=i0;count<maxit;++count) {
        var i,j,d;
        for(i=n-1;i!==-1;--i) A0[i] = div(A[i],z[i]);
        var A1 = transpose(A0);
        for(i=m-1;i!==-1;--i) p[i] = (/*x[i]+*/sum(A1[i]));
        alpha = 0.25*abs(dotcc/dot(c,p));
        var a1 = 100*sqrt(dotcc/dot(p,p));
        if(!isFinite(alpha) || alpha>a1) alpha = a1;
        g = add(c,mul(alpha,p));
        H = dot(A1,A0);
        for(i=m-1;i!==-1;--i) H[i][i] += 1;
        d = solve(H,div(g,alpha),true);
        var t0 = div(z,dot(A,d));
        var t = 1.0;
        for(i=n-1;i!==-1;--i) if(t0[i]<0) t = min(t,-0.999*t0[i]);
        y = sub(x,mul(d,t));
        z = sub(b,dot(A,y));
        if(!all(gt(z,0))) return { solution: x, message: "", iterations: count };
        x = y;
        if(alpha<tol) return { solution: y, message: "", iterations: count };
        if(flag) {
            var s = dot(c,g), Ag = dot(A,g);
            unbounded = true;
            for(i=n-1;i!==-1;--i) if(s*Ag[i]<0) { unbounded = false; break; }
        } else {
            if(x[m-1]>=0) unbounded = false;
            else unbounded = true;
        }
        if(unbounded) return { solution: y, message: "Unbounded", iterations: count };
    }
    return { solution: x, message: "maximum iteration count exceeded", iterations:count };
}

numeric._solveLP = function _solveLP(c,A,b,tol,maxit) {
    var m = c.length, n = b.length,y;
    var sum = numeric.sum, log = numeric.log, mul = numeric.mul, sub = numeric.sub, dot = numeric.dot, div = numeric.div, add = numeric.add;
    var c0 = numeric.rep([m],0).concat([1]);
    var J = numeric.rep([n,1],-1);
    var A0 = numeric.blockMatrix([[A                   ,   J  ]]);
    var b0 = b;
    var y = numeric.rep([m],0).concat(Math.max(0,numeric.sup(numeric.neg(b)))+1);
    var x0 = numeric.__solveLP(c0,A0,b0,tol,maxit,y,false);
    var x = numeric.clone(x0.solution);
    x.length = m;
    var foo = numeric.inf(sub(b,dot(A,x)));
    if(foo<0) { return { solution: NaN, message: "Infeasible", iterations: x0.iterations }; }
    var ret = numeric.__solveLP(c, A, b, tol, maxit-x0.iterations, x, true);
    ret.iterations += x0.iterations;
    return ret;
};

numeric.solveLP = function solveLP(c,A,b,Aeq,beq,tol,maxit) {
    if(typeof maxit === "undefined") maxit = 1000;
    if(typeof tol === "undefined") tol = numeric.epsilon;
    if(typeof Aeq === "undefined") return numeric._solveLP(c,A,b,tol,maxit);
    var m = Aeq.length, n = Aeq[0].length, o = A.length;
    var B = numeric.echelonize(Aeq);
    var flags = numeric.rep([n],0);
    var P = B.P;
    var Q = [];
    var i;
    for(i=P.length-1;i!==-1;--i) flags[P[i]] = 1;
    for(i=n-1;i!==-1;--i) if(flags[i]===0) Q.push(i);
    var g = numeric.getRange;
    var I = numeric.linspace(0,m-1), J = numeric.linspace(0,o-1);
    var Aeq2 = g(Aeq,I,Q), A1 = g(A,J,P), A2 = g(A,J,Q), dot = numeric.dot, sub = numeric.sub;
    var A3 = dot(A1,B.I);
    var A4 = sub(A2,dot(A3,Aeq2)), b4 = sub(b,dot(A3,beq));
    var c1 = Array(P.length), c2 = Array(Q.length);
    for(i=P.length-1;i!==-1;--i) c1[i] = c[P[i]];
    for(i=Q.length-1;i!==-1;--i) c2[i] = c[Q[i]];
    var c4 = sub(c2,dot(c1,dot(B.I,Aeq2)));
    var S = numeric._solveLP(c4,A4,b4,tol,maxit);
    var x2 = S.solution;
    if(x2!==x2) return S;
    var x1 = dot(B.I,sub(beq,dot(Aeq2,x2)));
    var x = Array(c.length);
    for(i=P.length-1;i!==-1;--i) x[P[i]] = x1[i];
    for(i=Q.length-1;i!==-1;--i) x[Q[i]] = x2[i];
    return { solution: x, message:S.message, iterations: S.iterations };
}

numeric.MPStoLP = function MPStoLP(MPS) {
    if(MPS instanceof String) { MPS.split('\n'); }
    var state = 0;
    var states = ['Initial state','NAME','ROWS','COLUMNS','RHS','BOUNDS','ENDATA'];
    var n = MPS.length;
    var i,j,z,N=0,rows = {}, sign = [], rl = 0, vars = {}, nv = 0;
    var name;
    var c = [], A = [], b = [];
    function err(e) { throw new Error('MPStoLP: '+e+'\nLine '+i+': '+MPS[i]+'\nCurrent state: '+states[state]+'\n'); }
    for(i=0;i<n;++i) {
        z = MPS[i];
        var w0 = z.match(/\S*/g);
        var w = [];
        for(j=0;j<w0.length;++j) if(w0[j]!=="") w.push(w0[j]);
        if(w.length === 0) continue;
        for(j=0;j<states.length;++j) if(z.substr(0,states[j].length) === states[j]) break;
        if(j<states.length) {
            state = j;
            if(j===1) { name = w[1]; }
            if(j===6) return { name:name, c:c, A:numeric.transpose(A), b:b, rows:rows, vars:vars };
            continue;
        }
        switch(state) {
        case 0: case 1: err('Unexpected line');
        case 2: 
            switch(w[0]) {
            case 'N': if(N===0) N = w[1]; else err('Two or more N rows'); break;
            case 'L': rows[w[1]] = rl; sign[rl] = 1; b[rl] = 0; ++rl; break;
            case 'G': rows[w[1]] = rl; sign[rl] = -1;b[rl] = 0; ++rl; break;
            case 'E': rows[w[1]] = rl; sign[rl] = 0;b[rl] = 0; ++rl; break;
            default: err('Parse error '+numeric.prettyPrint(w));
            }
            break;
        case 3:
            if(!vars.hasOwnProperty(w[0])) { vars[w[0]] = nv; c[nv] = 0; A[nv] = numeric.rep([rl],0); ++nv; }
            var p = vars[w[0]];
            for(j=1;j<w.length;j+=2) {
                if(w[j] === N) { c[p] = parseFloat(w[j+1]); continue; }
                var q = rows[w[j]];
                A[p][q] = (sign[q]<0?-1:1)*parseFloat(w[j+1]);
            }
            break;
        case 4:
            for(j=1;j<w.length;j+=2) b[rows[w[j]]] = (sign[rows[w[j]]]<0?-1:1)*parseFloat(w[j+1]);
            break;
        case 5: /*FIXME*/ break;
        case 6: err('Internal error');
        }
    }
    err('Reached end of file without ENDATA');
}
// seedrandom.js version 2.0.
// Author: David Bau 4/2/2011
//
// Defines a method Math.seedrandom() that, when called, substitutes
// an explicitly seeded RC4-based algorithm for Math.random().  Also
// supports automatic seeding from local or network sources of entropy.
//
// Usage:
//
//   <script src=http://davidbau.com/encode/seedrandom-min.js></script>
//
//   Math.seedrandom('yipee'); Sets Math.random to a function that is
//                             initialized using the given explicit seed.
//
//   Math.seedrandom();        Sets Math.random to a function that is
//                             seeded using the current time, dom state,
//                             and other accumulated local entropy.
//                             The generated seed string is returned.
//
//   Math.seedrandom('yowza', true);
//                             Seeds using the given explicit seed mixed
//                             together with accumulated entropy.
//
//   <script src="http://bit.ly/srandom-512"></script>
//                             Seeds using physical random bits downloaded
//                             from random.org.
//
//   <script src="https://jsonlib.appspot.com/urandom?callback=Math.seedrandom">
//   </script>                 Seeds using urandom bits from call.jsonlib.com,
//                             which is faster than random.org.
//
// Examples:
//
//   Math.seedrandom("hello");            // Use "hello" as the seed.
//   document.write(Math.random());       // Always 0.5463663768140734
//   document.write(Math.random());       // Always 0.43973793770592234
//   var rng1 = Math.random;              // Remember the current prng.
//
//   var autoseed = Math.seedrandom();    // New prng with an automatic seed.
//   document.write(Math.random());       // Pretty much unpredictable.
//
//   Math.random = rng1;                  // Continue "hello" prng sequence.
//   document.write(Math.random());       // Always 0.554769432473455
//
//   Math.seedrandom(autoseed);           // Restart at the previous seed.
//   document.write(Math.random());       // Repeat the 'unpredictable' value.
//
// Notes:
//
// Each time seedrandom('arg') is called, entropy from the passed seed
// is accumulated in a pool to help generate future seeds for the
// zero-argument form of Math.seedrandom, so entropy can be injected over
// time by calling seedrandom with explicit data repeatedly.
//
// On speed - This javascript implementation of Math.random() is about
// 3-10x slower than the built-in Math.random() because it is not native
// code, but this is typically fast enough anyway.  Seeding is more expensive,
// especially if you use auto-seeding.  Some details (timings on Chrome 4):
//
// Our Math.random()            - avg less than 0.002 milliseconds per call
// seedrandom('explicit')       - avg less than 0.5 milliseconds per call
// seedrandom('explicit', true) - avg less than 2 milliseconds per call
// seedrandom()                 - avg about 38 milliseconds per call
//
// LICENSE (BSD):
//
// Copyright 2010 David Bau, all rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
// 
//   1. Redistributions of source code must retain the above copyright
//      notice, this list of conditions and the following disclaimer.
//
//   2. Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in the
//      documentation and/or other materials provided with the distribution.
// 
//   3. Neither the name of this module nor the names of its contributors may
//      be used to endorse or promote products derived from this software
//      without specific prior written permission.
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
/**
 * All code is in an anonymous closure to keep the global namespace clean.
 *
 * @param {number=} overflow 
 * @param {number=} startdenom
 */

// Patched by Seb so that seedrandom.js does not pollute the Math object.
// My tests suggest that doing Math.trouble = 1 makes Math lookups about 5%
// slower.
numeric.seedrandom = { pow:Math.pow, random:Math.random };

(function (pool, math, width, chunks, significance, overflow, startdenom) {


//
// seedrandom()
// This is the seedrandom function described above.
//
math['seedrandom'] = function seedrandom(seed, use_entropy) {
  var key = [];
  var arc4;

  // Flatten the seed string or build one from local entropy if needed.
  seed = mixkey(flatten(
    use_entropy ? [seed, pool] :
    arguments.length ? seed :
    [new Date().getTime(), pool, window], 3), key);

  // Use the seed to initialize an ARC4 generator.
  arc4 = new ARC4(key);

  // Mix the randomness into accumulated entropy.
  mixkey(arc4.S, pool);

  // Override Math.random

  // This function returns a random double in [0, 1) that contains
  // randomness in every bit of the mantissa of the IEEE 754 value.

  math['random'] = function random() {  // Closure to return a random double:
    var n = arc4.g(chunks);             // Start with a numerator n < 2 ^ 48
    var d = startdenom;                 //   and denominator d = 2 ^ 48.
    var x = 0;                          //   and no 'extra last byte'.
    while (n < significance) {          // Fill up all significant digits by
      n = (n + x) * width;              //   shifting numerator and
      d *= width;                       //   denominator and generating a
      x = arc4.g(1);                    //   new least-significant-byte.
    }
    while (n >= overflow) {             // To avoid rounding up, before adding
      n /= 2;                           //   last byte, shift everything
      d /= 2;                           //   right using integer math until
      x >>>= 1;                         //   we have exactly the desired bits.
    }
    return (n + x) / d;                 // Form the number within [0, 1).
  };

  // Return the seed that was used
  return seed;
};

//
// ARC4
//
// An ARC4 implementation.  The constructor takes a key in the form of
// an array of at most (width) integers that should be 0 <= x < (width).
//
// The g(count) method returns a pseudorandom integer that concatenates
// the next (count) outputs from ARC4.  Its return value is a number x
// that is in the range 0 <= x < (width ^ count).
//
/** @constructor */
function ARC4(key) {
  var t, u, me = this, keylen = key.length;
  var i = 0, j = me.i = me.j = me.m = 0;
  me.S = [];
  me.c = [];

  // The empty key [] is treated as [0].
  if (!keylen) { key = [keylen++]; }

  // Set up S using the standard key scheduling algorithm.
  while (i < width) { me.S[i] = i++; }
  for (i = 0; i < width; i++) {
    t = me.S[i];
    j = lowbits(j + t + key[i % keylen]);
    u = me.S[j];
    me.S[i] = u;
    me.S[j] = t;
  }

  // The "g" method returns the next (count) outputs as one number.
  me.g = function getnext(count) {
    var s = me.S;
    var i = lowbits(me.i + 1); var t = s[i];
    var j = lowbits(me.j + t); var u = s[j];
    s[i] = u;
    s[j] = t;
    var r = s[lowbits(t + u)];
    while (--count) {
      i = lowbits(i + 1); t = s[i];
      j = lowbits(j + t); u = s[j];
      s[i] = u;
      s[j] = t;
      r = r * width + s[lowbits(t + u)];
    }
    me.i = i;
    me.j = j;
    return r;
  };
  // For robust unpredictability discard an initial batch of values.
  // See http://www.rsa.com/rsalabs/node.asp?id=2009
  me.g(width);
}

//
// flatten()
// Converts an object tree to nested arrays of strings.
//
/** @param {Object=} result 
  * @param {string=} prop
  * @param {string=} typ */
function flatten(obj, depth, result, prop, typ) {
  result = [];
  typ = typeof(obj);
  if (depth && typ == 'object') {
    for (prop in obj) {
      if (prop.indexOf('S') < 5) {    // Avoid FF3 bug (local/sessionStorage)
        try { result.push(flatten(obj[prop], depth - 1)); } catch (e) {}
      }
    }
  }
  return (result.length ? result : obj + (typ != 'string' ? '\0' : ''));
}

//
// mixkey()
// Mixes a string seed into a key that is an array of integers, and
// returns a shortened string seed that is equivalent to the result key.
//
/** @param {number=} smear 
  * @param {number=} j */
function mixkey(seed, key, smear, j) {
  seed += '';                         // Ensure the seed is a string
  smear = 0;
  for (j = 0; j < seed.length; j++) {
    key[lowbits(j)] =
      lowbits((smear ^= key[lowbits(j)] * 19) + seed.charCodeAt(j));
  }
  seed = '';
  for (j in key) { seed += String.fromCharCode(key[j]); }
  return seed;
}

//
// lowbits()
// A quick "n mod width" for width a power of 2.
//
function lowbits(n) { return n & (width - 1); }

//
// The following constants are related to IEEE 754 limits.
//
startdenom = math.pow(width, chunks);
significance = math.pow(2, significance);
overflow = significance * 2;

//
// When seedrandom.js is loaded, we immediately mix a few bits
// from the built-in RNG into the entropy pool.  Because we do
// not want to intefere with determinstic PRNG state later,
// seedrandom will not call math.random on its own again after
// initialization.
//
mixkey(math.random(), pool);

// End anonymous scope, and pass initial values.
}(
  [],   // pool: entropy pool starts empty
  numeric.seedrandom, // math: package containing random, pow, and seedrandom
  256,  // width: each RC4 output is 0 <= x < 256
  6,    // chunks: at least six RC4 outputs for each double
  52    // significance: there are 52 significant digits in a double
  ));
/* This file is a slightly modified version of quadprog.js from Alberto Santini.
 * It has been slightly modified by Sébastien Loisel to make sure that it handles
 * 0-based Arrays instead of 1-based Arrays.
 * License is in resources/LICENSE.quadprog */
(function(exports) {

function base0to1(A) {
    if(typeof A !== "object") { return A; }
    var ret = [], i,n=A.length;
    for(i=0;i<n;i++) ret[i+1] = base0to1(A[i]);
    return ret;
}
function base1to0(A) {
    if(typeof A !== "object") { return A; }
    var ret = [], i,n=A.length;
    for(i=1;i<n;i++) ret[i-1] = base1to0(A[i]);
    return ret;
}

function dpori(a, lda, n) {
    var i, j, k, kp1, t;

    for (k = 1; k <= n; k = k + 1) {
        a[k][k] = 1 / a[k][k];
        t = -a[k][k];
        //~ dscal(k - 1, t, a[1][k], 1);
        for (i = 1; i < k; i = i + 1) {
            a[i][k] = t * a[i][k];
        }

        kp1 = k + 1;
        if (n < kp1) {
            break;
        }
        for (j = kp1; j <= n; j = j + 1) {
            t = a[k][j];
            a[k][j] = 0;
            //~ daxpy(k, t, a[1][k], 1, a[1][j], 1);
            for (i = 1; i <= k; i = i + 1) {
                a[i][j] = a[i][j] + (t * a[i][k]);
            }
        }
    }

}

function dposl(a, lda, n, b) {
    var i, k, kb, t;

    for (k = 1; k <= n; k = k + 1) {
        //~ t = ddot(k - 1, a[1][k], 1, b[1], 1);
        t = 0;
        for (i = 1; i < k; i = i + 1) {
            t = t + (a[i][k] * b[i]);
        }

        b[k] = (b[k] - t) / a[k][k];
    }

    for (kb = 1; kb <= n; kb = kb + 1) {
        k = n + 1 - kb;
        b[k] = b[k] / a[k][k];
        t = -b[k];
        //~ daxpy(k - 1, t, a[1][k], 1, b[1], 1);
        for (i = 1; i < k; i = i + 1) {
            b[i] = b[i] + (t * a[i][k]);
        }
    }
}

function dpofa(a, lda, n, info) {
    var i, j, jm1, k, t, s;

    for (j = 1; j <= n; j = j + 1) {
        info[1] = j;
        s = 0;
        jm1 = j - 1;
        if (jm1 < 1) {
            s = a[j][j] - s;
            if (s <= 0) {
                break;
            }
            a[j][j] = Math.sqrt(s);
        } else {
            for (k = 1; k <= jm1; k = k + 1) {
                //~ t = a[k][j] - ddot(k - 1, a[1][k], 1, a[1][j], 1);
                t = a[k][j];
                for (i = 1; i < k; i = i + 1) {
                    t = t - (a[i][j] * a[i][k]);
                }
                t = t / a[k][k];
                a[k][j] = t;
                s = s + t * t;
            }
            s = a[j][j] - s;
            if (s <= 0) {
                break;
            }
            a[j][j] = Math.sqrt(s);
        }
        info[1] = 0;
    }
}

function qpgen2(dmat, dvec, fddmat, n, sol, crval, amat,
    bvec, fdamat, q, meq, iact, nact, iter, work, ierr) {

    var i, j, l, l1, info, it1, iwzv, iwrv, iwrm, iwsv, iwuv, nvl, r, iwnbv,
        temp, sum, t1, tt, gc, gs, nu,
        t1inf, t2min,
        vsmall, tmpa, tmpb,
        go;

    r = Math.min(n, q);
    l = 2 * n + (r * (r + 5)) / 2 + 2 * q + 1;

    vsmall = 1.0e-60;
    do {
        vsmall = vsmall + vsmall;
        tmpa = 1 + 0.1 * vsmall;
        tmpb = 1 + 0.2 * vsmall;
    } while (tmpa <= 1 || tmpb <= 1);

    for (i = 1; i <= n; i = i + 1) {
        work[i] = dvec[i];
    }
    for (i = n + 1; i <= l; i = i + 1) {
        work[i] = 0;
    }
    for (i = 1; i <= q; i = i + 1) {
        iact[i] = 0;
    }

    info = [];

    if (ierr[1] === 0) {
        dpofa(dmat, fddmat, n, info);
        if (info[1] !== 0) {
            ierr[1] = 2;
            return;
        }
        dposl(dmat, fddmat, n, dvec);
        dpori(dmat, fddmat, n);
    } else {
        for (j = 1; j <= n; j = j + 1) {
            sol[j] = 0;
            for (i = 1; i <= j; i = i + 1) {
                sol[j] = sol[j] + dmat[i][j] * dvec[i];
            }
        }
        for (j = 1; j <= n; j = j + 1) {
            dvec[j] = 0;
            for (i = j; i <= n; i = i + 1) {
                dvec[j] = dvec[j] + dmat[j][i] * sol[i];
            }
        }
    }

    crval[1] = 0;
    for (j = 1; j <= n; j = j + 1) {
        sol[j] = dvec[j];
        crval[1] = crval[1] + work[j] * sol[j];
        work[j] = 0;
        for (i = j + 1; i <= n; i = i + 1) {
            dmat[i][j] = 0;
        }
    }
    crval[1] = -crval[1] / 2;
    ierr[1] = 0;

    iwzv = n;
    iwrv = iwzv + n;
    iwuv = iwrv + r;
    iwrm = iwuv + r + 1;
    iwsv = iwrm + (r * (r + 1)) / 2;
    iwnbv = iwsv + q;

    for (i = 1; i <= q; i = i + 1) {
        sum = 0;
        for (j = 1; j <= n; j = j + 1) {
            sum = sum + amat[j][i] * amat[j][i];
        }
        work[iwnbv + i] = Math.sqrt(sum);
    }
    nact = 0;
    iter[1] = 0;
    iter[2] = 0;

    function fn_goto_50() {
        iter[1] = iter[1] + 1;

        l = iwsv;
        for (i = 1; i <= q; i = i + 1) {
            l = l + 1;
            sum = -bvec[i];
            for (j = 1; j <= n; j = j + 1) {
                sum = sum + amat[j][i] * sol[j];
            }
            if (Math.abs(sum) < vsmall) {
                sum = 0;
            }
            if (i > meq) {
                work[l] = sum;
            } else {
                work[l] = -Math.abs(sum);
                if (sum > 0) {
                    for (j = 1; j <= n; j = j + 1) {
                        amat[j][i] = -amat[j][i];
                    }
                    bvec[i] = -bvec[i];
                }
            }
        }

        for (i = 1; i <= nact; i = i + 1) {
            work[iwsv + iact[i]] = 0;
        }

        nvl = 0;
        temp = 0;
        for (i = 1; i <= q; i = i + 1) {
            if (work[iwsv + i] < temp * work[iwnbv + i]) {
                nvl = i;
                temp = work[iwsv + i] / work[iwnbv + i];
            }
        }
        if (nvl === 0) {
            return 999;
        }

        return 0;
    }

    function fn_goto_55() {
        for (i = 1; i <= n; i = i + 1) {
            sum = 0;
            for (j = 1; j <= n; j = j + 1) {
                sum = sum + dmat[j][i] * amat[j][nvl];
            }
            work[i] = sum;
        }

        l1 = iwzv;
        for (i = 1; i <= n; i = i + 1) {
            work[l1 + i] = 0;
        }
        for (j = nact + 1; j <= n; j = j + 1) {
            for (i = 1; i <= n; i = i + 1) {
                work[l1 + i] = work[l1 + i] + dmat[i][j] * work[j];
            }
        }

        t1inf = true;
        for (i = nact; i >= 1; i = i - 1) {
            sum = work[i];
            l = iwrm + (i * (i + 3)) / 2;
            l1 = l - i;
            for (j = i + 1; j <= nact; j = j + 1) {
                sum = sum - work[l] * work[iwrv + j];
                l = l + j;
            }
            sum = sum / work[l1];
            work[iwrv + i] = sum;
            if (iact[i] < meq) {
                // continue;
                break;
            }
            if (sum < 0) {
                // continue;
                break;
            }
            t1inf = false;
            it1 = i;
        }

        if (!t1inf) {
            t1 = work[iwuv + it1] / work[iwrv + it1];
            for (i = 1; i <= nact; i = i + 1) {
                if (iact[i] < meq) {
                    // continue;
                    break;
                }
                if (work[iwrv + i] < 0) {
                    // continue;
                    break;
                }
                temp = work[iwuv + i] / work[iwrv + i];
                if (temp < t1) {
                    t1 = temp;
                    it1 = i;
                }
            }
        }

        sum = 0;
        for (i = iwzv + 1; i <= iwzv + n; i = i + 1) {
            sum = sum + work[i] * work[i];
        }
        if (Math.abs(sum) <= vsmall) {
            if (t1inf) {
                ierr[1] = 1;
                // GOTO 999
                return 999;
            } else {
                for (i = 1; i <= nact; i = i + 1) {
                    work[iwuv + i] = work[iwuv + i] - t1 * work[iwrv + i];
                }
                work[iwuv + nact + 1] = work[iwuv + nact + 1] + t1;
                // GOTO 700
                return 700;
            }
        } else {
            sum = 0;
            for (i = 1; i <= n; i = i + 1) {
                sum = sum + work[iwzv + i] * amat[i][nvl];
            }
            tt = -work[iwsv + nvl] / sum;
            t2min = true;
            if (!t1inf) {
                if (t1 < tt) {
                    tt = t1;
                    t2min = false;
                }
            }

            for (i = 1; i <= n; i = i + 1) {
                sol[i] = sol[i] + tt * work[iwzv + i];
                if (Math.abs(sol[i]) < vsmall) {
                    sol[i] = 0;
                }
            }

            crval[1] = crval[1] + tt * sum * (tt / 2 + work[iwuv + nact + 1]);
            for (i = 1; i <= nact; i = i + 1) {
                work[iwuv + i] = work[iwuv + i] - tt * work[iwrv + i];
            }
            work[iwuv + nact + 1] = work[iwuv + nact + 1] + tt;

            if (t2min) {
                nact = nact + 1;
                iact[nact] = nvl;

                l = iwrm + ((nact - 1) * nact) / 2 + 1;
                for (i = 1; i <= nact - 1; i = i + 1) {
                    work[l] = work[i];
                    l = l + 1;
                }

                if (nact === n) {
                    work[l] = work[n];
                } else {
                    for (i = n; i >= nact + 1; i = i - 1) {
                        if (work[i] === 0) {
                            // continue;
                            break;
                        }
                        gc = Math.max(Math.abs(work[i - 1]), Math.abs(work[i]));
                        gs = Math.min(Math.abs(work[i - 1]), Math.abs(work[i]));
                        if (work[i - 1] >= 0) {
                            temp = Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
                        } else {
                            temp = -Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
                        }
                        gc = work[i - 1] / temp;
                        gs = work[i] / temp;

                        if (gc === 1) {
                            // continue;
                            break;
                        }
                        if (gc === 0) {
                            work[i - 1] = gs * temp;
                            for (j = 1; j <= n; j = j + 1) {
                                temp = dmat[j][i - 1];
                                dmat[j][i - 1] = dmat[j][i];
                                dmat[j][i] = temp;
                            }
                        } else {
                            work[i - 1] = temp;
                            nu = gs / (1 + gc);
                            for (j = 1; j <= n; j = j + 1) {
                                temp = gc * dmat[j][i - 1] + gs * dmat[j][i];
                                dmat[j][i] = nu * (dmat[j][i - 1] + temp) - dmat[j][i];
                                dmat[j][i - 1] = temp;

                            }
                        }
                    }
                    work[l] = work[nact];
                }
            } else {
                sum = -bvec[nvl];
                for (j = 1; j <= n; j = j + 1) {
                    sum = sum + sol[j] * amat[j][nvl];
                }
                if (nvl > meq) {
                    work[iwsv + nvl] = sum;
                } else {
                    work[iwsv + nvl] = -Math.abs(sum);
                    if (sum > 0) {
                        for (j = 1; j <= n; j = j + 1) {
                            amat[j][nvl] = -amat[j][nvl];
                        }
                        bvec[nvl] = -bvec[nvl];
                    }
                }
                // GOTO 700
                return 700;
            }
        }

        return 0;
    }

    function fn_goto_797() {
        l = iwrm + (it1 * (it1 + 1)) / 2 + 1;
        l1 = l + it1;
        if (work[l1] === 0) {
            // GOTO 798
            return 798;
        }
        gc = Math.max(Math.abs(work[l1 - 1]), Math.abs(work[l1]));
        gs = Math.min(Math.abs(work[l1 - 1]), Math.abs(work[l1]));
        if (work[l1 - 1] >= 0) {
            temp = Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
        } else {
            temp = -Math.abs(gc * Math.sqrt(1 + gs * gs / (gc * gc)));
        }
        gc = work[l1 - 1] / temp;
        gs = work[l1] / temp;

        if (gc === 1) {
            // GOTO 798
            return 798;
        }
        if (gc === 0) {
            for (i = it1 + 1; i <= nact; i = i + 1) {
                temp = work[l1 - 1];
                work[l1 - 1] = work[l1];
                work[l1] = temp;
                l1 = l1 + i;
            }
            for (i = 1; i <= n; i = i + 1) {
                temp = dmat[i][it1];
                dmat[i][it1] = dmat[i][it1 + 1];
                dmat[i][it1 + 1] = temp;
            }
        } else {
            nu = gs / (1 + gc);
            for (i = it1 + 1; i <= nact; i = i + 1) {
                temp = gc * work[l1 - 1] + gs * work[l1];
                work[l1] = nu * (work[l1 - 1] + temp) - work[l1];
                work[l1 - 1] = temp;
                l1 = l1 + i;
            }
            for (i = 1; i <= n; i = i + 1) {
                temp = gc * dmat[i][it1] + gs * dmat[i][it1 + 1];
                dmat[i][it1 + 1] = nu * (dmat[i][it1] + temp) - dmat[i][it1 + 1];
                dmat[i][it1] = temp;
            }
        }

        return 0;
    }

    function fn_goto_798() {
        l1 = l - it1;
        for (i = 1; i <= it1; i = i + 1) {
            work[l1] = work[l];
            l = l + 1;
            l1 = l1 + 1;
        }

        work[iwuv + it1] = work[iwuv + it1 + 1];
        iact[it1] = iact[it1 + 1];
        it1 = it1 + 1;
        if (it1 < nact) {
            // GOTO 797
            return 797;
        }

        return 0;
    }

    function fn_goto_799() {
        work[iwuv + nact] = work[iwuv + nact + 1];
        work[iwuv + nact + 1] = 0;
        iact[nact] = 0;
        nact = nact - 1;
        iter[2] = iter[2] + 1;

        return 0;
    }

    go = 0;
    while (true) {
        go = fn_goto_50();
        if (go === 999) {
            return;
        }
        while (true) {
            go = fn_goto_55();
            if (go === 0) {
                break;
            }
            if (go === 999) {
                return;
            }
            if (go === 700) {
                if (it1 === nact) {
                    fn_goto_799();
                } else {
                    while (true) {
                        fn_goto_797();
                        go = fn_goto_798();
                        if (go !== 797) {
                            break;
                        }
                    }
                    fn_goto_799();
                }
            }
        }
    }

}

function solveQP(Dmat, dvec, Amat, bvec, meq, factorized) {
    Dmat = base0to1(Dmat);
    dvec = base0to1(dvec);
    Amat = base0to1(Amat);
    var i, n, q,
        nact, r,
        crval = [], iact = [], sol = [], work = [], iter = [],
        message;

    meq = meq || 0;
    factorized = factorized ? base0to1(factorized) : [undefined, 0];
    bvec = bvec ? base0to1(bvec) : [];

    // In Fortran the array index starts from 1
    n = Dmat.length - 1;
    q = Amat[1].length - 1;

    if (!bvec) {
        for (i = 1; i <= q; i = i + 1) {
            bvec[i] = 0;
        }
    }
    for (i = 1; i <= q; i = i + 1) {
        iact[i] = 0;
    }
    nact = 0;
    r = Math.min(n, q);
    for (i = 1; i <= n; i = i + 1) {
        sol[i] = 0;
    }
    crval[1] = 0;
    for (i = 1; i <= (2 * n + (r * (r + 5)) / 2 + 2 * q + 1); i = i + 1) {
        work[i] = 0;
    }
    for (i = 1; i <= 2; i = i + 1) {
        iter[i] = 0;
    }

    qpgen2(Dmat, dvec, n, n, sol, crval, Amat,
        bvec, n, q, meq, iact, nact, iter, work, factorized);

    message = "";
    if (factorized[1] === 1) {
        message = "constraints are inconsistent, no solution!";
    }
    if (factorized[1] === 2) {
        message = "matrix D in quadratic function is not positive definite!";
    }

    return {
        solution: base1to0(sol),
        value: base1to0(crval),
        unconstrained_solution: base1to0(dvec),
        iterations: base1to0(iter),
        iact: base1to0(iact),
        message: message
    };
}
exports.solveQP = solveQP;
}(numeric));
/*
Shanti Rao sent me this routine by private email. I had to modify it
slightly to work on Arrays instead of using a Matrix object.
It is apparently translated from http://stitchpanorama.sourceforge.net/Python/svd.py
*/

numeric.svd= function svd(A) {
    var temp;
//Compute the thin SVD from G. H. Golub and C. Reinsch, Numer. Math. 14, 403-420 (1970)
	var prec= numeric.epsilon; //Math.pow(2,-52) // assumes double prec
	var tolerance= 1.e-64/prec;
	var itmax= 50;
	var c=0;
	var i=0;
	var j=0;
	var k=0;
	var l=0;
	
	var u= numeric.clone(A);
	var m= u.length;
	
	var n= u[0].length;
	
	if (m < n) throw "Need more rows than columns"
	
	var e = new Array(n);
	var q = new Array(n);
	for (i=0; i<n; i++) e[i] = q[i] = 0.0;
	var v = numeric.rep([n,n],0);
//	v.zero();
	
 	function pythag(a,b)
 	{
		a = Math.abs(a)
		b = Math.abs(b)
		if (a > b)
			return a*Math.sqrt(1.0+(b*b/a/a))
		else if (b == 0.0) 
			return a
		return b*Math.sqrt(1.0+(a*a/b/b))
	}

	//Householder's reduction to bidiagonal form

	var f= 0.0;
	var g= 0.0;
	var h= 0.0;
	var x= 0.0;
	var y= 0.0;
	var z= 0.0;
	var s= 0.0;
	
	for (i=0; i < n; i++)
	{	
		e[i]= g;
		s= 0.0;
		l= i+1;
		for (j=i; j < m; j++) 
			s += (u[j][i]*u[j][i]);
		if (s <= tolerance)
			g= 0.0;
		else
		{	
			f= u[i][i];
			g= Math.sqrt(s);
			if (f >= 0.0) g= -g;
			h= f*g-s
			u[i][i]=f-g;
			for (j=l; j < n; j++)
			{
				s= 0.0
				for (k=i; k < m; k++) 
					s += u[k][i]*u[k][j]
				f= s/h
				for (k=i; k < m; k++) 
					u[k][j]+=f*u[k][i]
			}
		}
		q[i]= g
		s= 0.0
		for (j=l; j < n; j++) 
			s= s + u[i][j]*u[i][j]
		if (s <= tolerance)
			g= 0.0
		else
		{	
			f= u[i][i+1]
			g= Math.sqrt(s)
			if (f >= 0.0) g= -g
			h= f*g - s
			u[i][i+1] = f-g;
			for (j=l; j < n; j++) e[j]= u[i][j]/h
			for (j=l; j < m; j++)
			{	
				s=0.0
				for (k=l; k < n; k++) 
					s += (u[j][k]*u[i][k])
				for (k=l; k < n; k++) 
					u[j][k]+=s*e[k]
			}	
		}
		y= Math.abs(q[i])+Math.abs(e[i])
		if (y>x) 
			x=y
	}
	
	// accumulation of right hand gtransformations
	for (i=n-1; i != -1; i+= -1)
	{	
		if (g != 0.0)
		{
		 	h= g*u[i][i+1]
			for (j=l; j < n; j++) 
				v[j][i]=u[i][j]/h
			for (j=l; j < n; j++)
			{	
				s=0.0
				for (k=l; k < n; k++) 
					s += u[i][k]*v[k][j]
				for (k=l; k < n; k++) 
					v[k][j]+=(s*v[k][i])
			}	
		}
		for (j=l; j < n; j++)
		{
			v[i][j] = 0;
			v[j][i] = 0;
		}
		v[i][i] = 1;
		g= e[i]
		l= i
	}
	
	// accumulation of left hand transformations
	for (i=n-1; i != -1; i+= -1)
	{	
		l= i+1
		g= q[i]
		for (j=l; j < n; j++) 
			u[i][j] = 0;
		if (g != 0.0)
		{
			h= u[i][i]*g
			for (j=l; j < n; j++)
			{
				s=0.0
				for (k=l; k < m; k++) s += u[k][i]*u[k][j];
				f= s/h
				for (k=i; k < m; k++) u[k][j]+=f*u[k][i];
			}
			for (j=i; j < m; j++) u[j][i] = u[j][i]/g;
		}
		else
			for (j=i; j < m; j++) u[j][i] = 0;
		u[i][i] += 1;
	}
	
	// diagonalization of the bidiagonal form
	prec= prec*x
	for (k=n-1; k != -1; k+= -1)
	{
		for (var iteration=0; iteration < itmax; iteration++)
		{	// test f splitting
			var test_convergence = false
			for (l=k; l != -1; l+= -1)
			{	
				if (Math.abs(e[l]) <= prec)
				{	test_convergence= true
					break 
				}
				if (Math.abs(q[l-1]) <= prec)
					break 
			}
			if (!test_convergence)
			{	// cancellation of e[l] if l>0
				c= 0.0
				s= 1.0
				var l1= l-1
				for (i =l; i<k+1; i++)
				{	
					f= s*e[i]
					e[i]= c*e[i]
					if (Math.abs(f) <= prec)
						break
					g= q[i]
					h= pythag(f,g)
					q[i]= h
					c= g/h
					s= -f/h
					for (j=0; j < m; j++)
					{	
						y= u[j][l1]
						z= u[j][i]
						u[j][l1] =  y*c+(z*s)
						u[j][i] = -y*s+(z*c)
					} 
				}	
			}
			// test f convergence
			z= q[k]
			if (l== k)
			{	//convergence
				if (z<0.0)
				{	//q[k] is made non-negative
					q[k]= -z
					for (j=0; j < n; j++)
						v[j][k] = -v[j][k]
				}
				break  //break out of iteration loop and move on to next k value
			}
			if (iteration >= itmax-1)
				throw 'Error: no convergence.'
			// shift from bottom 2x2 minor
			x= q[l]
			y= q[k-1]
			g= e[k-1]
			h= e[k]
			f= ((y-z)*(y+z)+(g-h)*(g+h))/(2.0*h*y)
			g= pythag(f,1.0)
			if (f < 0.0)
				f= ((x-z)*(x+z)+h*(y/(f-g)-h))/x
			else
				f= ((x-z)*(x+z)+h*(y/(f+g)-h))/x
			// next QR transformation
			c= 1.0
			s= 1.0
			for (i=l+1; i< k+1; i++)
			{	
				g= e[i]
				y= q[i]
				h= s*g
				g= c*g
				z= pythag(f,h)
				e[i-1]= z
				c= f/z
				s= h/z
				f= x*c+g*s
				g= -x*s+g*c
				h= y*s
				y= y*c
				for (j=0; j < n; j++)
				{	
					x= v[j][i-1]
					z= v[j][i]
					v[j][i-1] = x*c+z*s
					v[j][i] = -x*s+z*c
				}
				z= pythag(f,h)
				q[i-1]= z
				c= f/z
				s= h/z
				f= c*g+s*y
				x= -s*g+c*y
				for (j=0; j < m; j++)
				{
					y= u[j][i-1]
					z= u[j][i]
					u[j][i-1] = y*c+z*s
					u[j][i] = -y*s+z*c
				}
			}
			e[l]= 0.0
			e[k]= f
			q[k]= x
		} 
	}
		
	//vt= transpose(v)
	//return (u,q,vt)
	for (i=0;i<q.length; i++) 
	  if (q[i] < prec) q[i] = 0
	  
	//sort eigenvalues	
	for (i=0; i< n; i++)
	{	 
	//writeln(q)
	 for (j=i-1; j >= 0; j--)
	 {
	  if (q[j] < q[i])
	  {
	//  writeln(i,'-',j)
	   c = q[j]
	   q[j] = q[i]
	   q[i] = c
	   for(k=0;k<u.length;k++) { temp = u[k][i]; u[k][i] = u[k][j]; u[k][j] = temp; }
	   for(k=0;k<v.length;k++) { temp = v[k][i]; v[k][i] = v[k][j]; v[k][j] = temp; }
//	   u.swapCols(i,j)
//	   v.swapCols(i,j)
	   i = j	   
	  }
	 }	
	}
	
	return {U:u,S:q,V:v}
};


}).call(this,typeof global !== "undefined" ? global : typeof self !== "undefined" ? self : typeof window !== "undefined" ? window : {})
},{}],17:[function(require,module,exports){
// http://cs.stanford.edu/people/karpathy/convnetjs/
// https://github.com/junku901/dnn
var NN = {};

NN.sigmoid = function(x) {
	var sigmoid = (1. / (1 + Math.exp(-x)))
	if(sigmoid ==1) {
	 //   console.warn("Something Wrong!! Sigmoid Function returns 1. Probably javascript float precision problem?\nSlightly Controlled value to 1 - 1e-14")
			sigmoid = 0.99999999999999; // Javascript Float Precision Problem.. This is a limit of javascript.
	} else if(sigmoid ==0) {
		//  console.warn("Something Wrong!! Sigmoid Function returns 0. Probably javascript float precision problem?\nSlightly Controlled value to 1e-14")
			sigmoid = 1e-14;
	}
	return sigmoid; // sigmoid cannot be 0 or 1;;
}

NN.dSigmoid = function(x){
	a = B.sigmoid(x);
	return a * (1. - a);
}

module.exports = NN;
},{}],18:[function(require,module,exports){
var NN = require("../neural");
var R, M;

var RBM = function (rlab, settings) {
  R = rlab;
  M = R.M;
  Object.assign(this, settings);
	this.settings = {
			'log level' : 1 // 0 : nothing, 1 : info, 2: warn
	};
	var a = 1. / this.nVisible;
	this.W = this.W || M.randomM(this.nVisible,this.nHidden,-a,a);
	this.hbias = this.hbias || M.newV(this.nHidden);
  this.vbias = this.vbias || M.newV(this.nVisible);
}

RBM.prototype.train = function(settings) {
	var lr = settings.lr||0.8;
	var k  = settings.k||1;
	var epochs = settings.epochs||1500;
	this.input = settings.input||this.input;

	var i,j;
	var currentProgress = 1;
	for(i=0;i<epochs;i++) {
			/* CD - k . Contrastive Divergence */
		var ph = this.sampleHgivenV(this.input);
		var phMean = ph[0], phSample = ph[1];
		var chainStart = phSample;
		var nvMeans, nvSamples, nhMeans, nhSamples;

		for(j=0 ; j<k ; j++) {
			if (j==0) {
				var gibbsVH = this.gibbsHVH(chainStart);
				nvMeans = gibbsVH[0], nvSamples = gibbsVH[1], nhMeans = gibbsVH[2], nhSamples = gibbsVH[3];
			} else {
				var gibbsVH = this.gibbsHVH(nhSamples);
				nvMeans = gibbsVH[0], nvSamples = gibbsVH[1], nhMeans = gibbsVH[2], nhSamples = gibbsVH[3];
			}
		}
    // ((input^t*phMean)-(nvSample^t*nhMeans))*1/input.length
	  var deltaW = this.input.tr().dot(phMean).sub(nvSamples.tr().dot(nhMeans)).mul(1./this.input.length);
    // deltaW = (input*phMean)-(nvSample^t * nhMeans)*1/input.length
		var deltaVbias = this.input.sub(nvSamples).colMean();
    // deltaHbias = (phSample - nhMeans).mean(row)
    var deltaHbias = phSample.sub(nhMeans).colMean();
    // W += deltaW*lr
		this.W = this.W.add(deltaW.mul(lr));
    // vbias += deltaVbias*lr
		this.vbias = this.vbias.add(deltaVbias.dot(lr));
    // hbias += deltaHbias*lr
		this.hbias = this.hbias.add(deltaHbias.dot(lr));
		if(this.settings['log level'] > 0) {
			var progress = (1.*i/epochs)*100;
			if(progress > currentProgress) {
				console.log("RBM",progress.toFixed(0),"% Completed.");
				currentProgress+=8;
			}
		}
	}
	if(this.settings['log level'] > 0)
		console.log("RBM Final Cross Entropy : ",this.getReconstructionCrossEntropy())
};

RBM.prototype.propup = function(v) {
  // sigmoid(v*W+hbias)
	return v.dot(this.W).addMV(this.hbias).mapM(NN.sigmoid);
};

RBM.prototype.probToBinaryMat = function(m) {
	return M.mapM(m, (x)=>(Math.random() < m[i][j])?1:0);
};

RBM.prototype.propdown = function(h) {
	return h.dot(this.W.tr()).addMV(this.vbias).mapM(NN.sigmoid);
};

RBM.prototype.sampleHgivenV = function(v0_sample) {
	var h1_mean = this.propup(v0_sample);
	var h1_sample = this.probToBinaryMat(h1_mean);
	return [h1_mean,h1_sample];
};

RBM.prototype.sampleVgivenH = function(h0_sample) {
	var v1_mean = this.propdown(h0_sample);
	var v1_sample = this.probToBinaryMat(v1_mean);
	return [v1_mean,v1_sample];
};

RBM.prototype.gibbsHVH = function(h0_sample) {
	var v1 = this.sampleVgivenH(h0_sample);
	var h1 = this.sampleHgivenV(v1[1]);
	return [v1[0],v1[1],h1[0],h1[1]];
};

RBM.prototype.reconstruct = function(v) {
	var h = v.dot(this.W).addMV(this.hbias).mapM(NN.sigmoid);
	return h.dot(this.W.tr()).addMV(this.vbias).mapM(NN.sigmoid);
};

RBM.prototype.getReconstructionCrossEntropy = function() {
	var reconstructedV = this.reconstruct(this.input);
	var a = M.mapMM(this.input, reconstructedV, function(x,y){
		return x*Math.log(y);
	});

	var b = M.mapMM(this.input,reconstructedV,function(x,y){
		return (1-x)*Math.log(1-y);
	});
  var crossEntropy = -a.add(b).rowSum().mean();
	return crossEntropy

};

RBM.prototype.set = function(property,value) {
	this.settings[property] = value;
}

module.exports = RBM;
},{"../neural":17}],19:[function(require,module,exports){
var R    = require("./lib/math");
var _ = R._ = require("lodash");
R.Symbol = require("./lib/symbolic");
R.NN     = require("./plugin/neural");
R.NN.RBM = require("./plugin/neural/rbm");

// space 沒有加上機率參數 , 不能指定機率
R.samples = function(space, size, arg) {
	var arg = _.defaults(arg, {replace:true});
	if (arg.replace)
		return _.times(size, ()=>_.sample(space));
	else
		return _.sampleSize(space, size);
}

// Global
R.debug = debug = function() {
	var arg = _.slice(arguments);
	console.debug.apply(console, arg);
}

R.print = print = function() {
	var arg = _.slice(arguments);
	console.log.apply(console, arg);
}

p = R.parse;
be = R.be;

R.mixThisMap(Array.prototype, R, {
lu:"lu",
luSolve:"luSolve",
svd:"svd",
// "cdelsq",
// "clone",
rows:"rows",
cols:"cols",
row:"row",
col:"col",
tr:"tr",
inv:"inv",
// "all",
// "any",
// "same",
// "isFinite",
// "isNaN",
// "mapreduce",
// "complex",
det:"det",
// "norm2",
// "norm2Squared",
// "norm2inf",
dot:"dot",
// "dim",
eig:"eig",
// "sum",
rowSum:"rowSum",
colSum:"colSum",
rowMean:"rowMean",
colMean:"colMean",
addMV:"addMV",
mapM:"mapM",
mapMM:"mapMM",
flatM:"flatM",
fillVM:"fillVM",
fillMM:"fillMM",
getBlock:"getBlock",
setBlock:"setBlock",
getDiag:"getDiag",
diag:"diag",
// "parseFloat",
// "parseDate",
// "parseCSV",
// "toCSV",
mstr:"mstr",
// "sumM",
str:'astr',
print:'print',
});

R.mixThis(Array.prototype, R, [
"max",
"min",
"sum",
"product",
"norm",
"mean",
"range",
"median",
"variance",
"deviation",
"sd",
"cov",
"cor",
"normalize",
"curve",
"hist",
"ihist",
"eval",
// +-*/%
"add",
"sub",
"mul",
"div",
"mod",
"neg",
// "inv", 和矩陣相衝
// logical
"and",
"or",
"xor",
"not",
// bits operation
"bnot",
"band",
"bor",
"bxor",
// function
"power",
// "dot", 和矩陣相衝
"sqrt",
"log",
"exp",
"abs",
"sin",
"cos",
"tan",
"asin",
"acos",
"atan",
"ceil",
"floor",
"round",
]);

R.mixThisMap(Number.prototype, R, {
	str:'nstr',
	print:'print',
});

R.mixThis(Number.prototype, R, [
	'eval',
	'add',
	'sub',
	'mul',
	'div',
	'mod',
	'power',
	'neg',
	'inv',
	'sqrt',
	'log',
	'exp',
	'abs',
	'sin',
	'cos',
	'tan',
	'asin',
	'acos',
	'atan',
	'ceil',
	'floor',
	'round',
]);
R.mixThisMap(Function.prototype, R, {
	add:'fadd',
	sub:'fsub',
	mul:'fmul',
	div:'fdiv',
	compose:'fcompose',
	eval:'feval',
	diff:'fdiff',
	integral:'fintegral',
});
R.mixThisMap(String.prototype, R, {str:'sstr',print:'print'});
R.mixThisMap(Object.prototype, R, {str:'ostr',print:'print'});
R.mixThisMap(Object.prototype, R, {
	proto:'proto',
	eq:'eq',
	neq:'neq',
	geq:'geq',
	leq:'leq',
	gt:'gt',
	lt:'lt',
});

R.mixThisMap(Array.prototype, R._, {
// lodash
_chunk:'chunk',
_compact:'compact',
_concat:'concat',
_difference:'difference',
_differenceBy:'differenceBy',
_differenceWith:'differenceWith',
_drop:'drop',
_dropRight:'dropRight',
_dropRightWhile:'dropRightWhile',
_dropWhile:'dropWhile',
_fill:'fill',
_findIndex:'findIndex',
_findLastIndex:'findLastIndex',
_flatten:'flatten',
_flattenDeep:'flattenDeep',
_flattenDepth:'flattenDepth',
_fromPairs:'flattenPairs',
_head:'head',
_indexOf:'indexOf',
_initial:'initial',
_intersection:'intersection',
_intersectionBy:'intersectonBy',
_intersectionWith:'intersectionWith',
_join:'join',
_last:'last',
_lastIndexOf:'lastIndexOf',
_nth:'nth',
_pull:'pull',
_pullAll:'pullAll',
_pullAllBy:'pullAllBy',
_pullAllWith:'pullAllWith',
_pullAt:'pullAt',
_remove:'remove',
_reverse:'reverse',
_slice:'slice',
_sortedIndex:'sortedIndex',
_sortedIndexBy:'sortedIndexBy',
_sortedIndexOf:'sortedIndexOf',
_sortedLastIndex:'sortedLastIndex',
_sortedLastIndexBy:'sortedLastIndexBy',
_sortedLastIndexOf:'sortedLastIndexOf',
_sortedUniq:'sortedUniq',
_sortedUniqBy:'sortedUniqBy',
_tail:'tail',
_take:'take',
_takeRight:'takeRight',
_takeRightWhile:'takeRightWhile',
_takeWhile:'takeWhile',
_union:'union',
_unionBy:'unionBy',
_unionWith:'unionWith',
_uniq:'uniq',
_uniqBy:'uniqBy',
_uniqWith:'uniqWith',
_unzip:'unzip',
_unzipWith:'unzipWith',
_without:'without',
_xor:'xor',
_xorBy:'xorBy',
_xorWith:'xorWith',
_zip:'zip',
_zipObject:'zipObject',
_zipObjectDeep:'zipObjectDeep',
_zipWith:'zipWith',
// Collection
_countBy:'countBy',
// each→ forEach
// _eachRight → forEachRight
_every:'every',
_filter:'filter',
_find:'find',
_findLast:'findLast',
_flatMap:'flatMap',
_flatMapDeep:'flatMapDeep',
_flatMapDepth:'flatMapDepth',
_forEach:'forEach',
_forEachRight:'forEachRight',
_groupBy:'groupBy',
_includes:'includes',
_invokeMap:'invokeMap',
_keyBy:'keyBy',
_map:'map',
_orderBy:'orderBy',
_partition:'partition',
_reduce:'reduce',
_reduceRight:'reduceRight',
_reject:'reject',
_sample:'sample',
_sampleSize:'sampleSize',
_shuffle:'shuffle',
_size:'size',
_some:'some',
_sortBy:'sortBy',
});

module.exports = R;

// R.mixThis(Array.prototype,  {str:R.astr}, ['str']);
// R.mixThisMap(Array.prototype, R, {str:'astr',print:'print'});
// R.mixThisMap(Object.prototype, R, {strM:'strM'});
// ==== Copy functions to R ======
// R.copyFunctions(R, D, "differential,integral".split(","));
// R.copyFunctions(R, Math, "abs,acos,asin,atan,ceil,cos,exp,floor,log,pow,random,round,sin,sqrt,tan".split(","));

// R.copyFunctions(R, M, "solveLP,solveMP,ODE,minimize,complex,spline,linspace".split(","));

// not include : bench, xxxeq, ccsXXX, cgrid, 
// Complex = R.Complex;
// Ratio = R.Ratio;

},{"./lib/math":7,"./lib/symbolic":11,"./plugin/neural":17,"./plugin/neural/rbm":18,"lodash":15}],20:[function(require,module,exports){
R=rlab=require("../rlab");
},{"../rlab":19}]},{},[20]);