mathjs/lib/esm/utils/bignumber/bitwise.js

/**
 * Bitwise and for Bignumbers
 *
 * Special Cases:
 *   N &  n =  N
 *   n &  0 =  0
 *   n & -1 =  n
 *   n &  n =  n
 *   I &  I =  I
 *  -I & -I = -I
 *   I & -I =  0
 *   I &  n =  n
 *   I & -n =  I
 *  -I &  n =  0
 *  -I & -n = -I
 *
 * @param {BigNumber} x
 * @param {BigNumber} y
 * @return {BigNumber} Result of `x` & `y`, is fully precise
 * @private
 */
export function bitAndBigNumber(x, y) {
  if (x.isFinite() && !x.isInteger() || y.isFinite() && !y.isInteger()) {
    throw new Error('Integers expected in function bitAnd');
  }

  var BigNumber = x.constructor;

  if (x.isNaN() || y.isNaN()) {
    return new BigNumber(NaN);
  }

  if (x.isZero() || y.eq(-1) || x.eq(y)) {
    return x;
  }

  if (y.isZero() || x.eq(-1)) {
    return y;
  }

  if (!x.isFinite() || !y.isFinite()) {
    if (!x.isFinite() && !y.isFinite()) {
      if (x.isNegative() === y.isNegative()) {
        return x;
      }

      return new BigNumber(0);
    }

    if (!x.isFinite()) {
      if (y.isNegative()) {
        return x;
      }

      if (x.isNegative()) {
        return new BigNumber(0);
      }

      return y;
    }

    if (!y.isFinite()) {
      if (x.isNegative()) {
        return y;
      }

      if (y.isNegative()) {
        return new BigNumber(0);
      }

      return x;
    }
  }

  return bitwise(x, y, function (a, b) {
    return a & b;
  });
}
/**
 * Bitwise not
 * @param {BigNumber} x
 * @return {BigNumber} Result of ~`x`, fully precise
 *
 */

export function bitNotBigNumber(x) {
  if (x.isFinite() && !x.isInteger()) {
    throw new Error('Integer expected in function bitNot');
  }

  var BigNumber = x.constructor;
  var prevPrec = BigNumber.precision;
  BigNumber.config({
    precision: 1E9
  });
  var result = x.plus(new BigNumber(1));
  result.s = -result.s || null;
  BigNumber.config({
    precision: prevPrec
  });
  return result;
}
/**
 * Bitwise OR for BigNumbers
 *
 * Special Cases:
 *   N |  n =  N
 *   n |  0 =  n
 *   n | -1 = -1
 *   n |  n =  n
 *   I |  I =  I
 *  -I | -I = -I
 *   I | -n = -1
 *   I | -I = -1
 *   I |  n =  I
 *  -I |  n = -I
 *  -I | -n = -n
 *
 * @param {BigNumber} x
 * @param {BigNumber} y
 * @return {BigNumber} Result of `x` | `y`, fully precise
 */

export function bitOrBigNumber(x, y) {
  if (x.isFinite() && !x.isInteger() || y.isFinite() && !y.isInteger()) {
    throw new Error('Integers expected in function bitOr');
  }

  var BigNumber = x.constructor;

  if (x.isNaN() || y.isNaN()) {
    return new BigNumber(NaN);
  }

  var negOne = new BigNumber(-1);

  if (x.isZero() || y.eq(negOne) || x.eq(y)) {
    return y;
  }

  if (y.isZero() || x.eq(negOne)) {
    return x;
  }

  if (!x.isFinite() || !y.isFinite()) {
    if (!x.isFinite() && !x.isNegative() && y.isNegative() || x.isNegative() && !y.isNegative() && !y.isFinite()) {
      return negOne;
    }

    if (x.isNegative() && y.isNegative()) {
      return x.isFinite() ? x : y;
    }

    return x.isFinite() ? y : x;
  }

  return bitwise(x, y, function (a, b) {
    return a | b;
  });
}
/**
 * Applies bitwise function to numbers
 * @param {BigNumber} x
 * @param {BigNumber} y
 * @param {function (a, b)} func
 * @return {BigNumber}
 */

export function bitwise(x, y, func) {
  var BigNumber = x.constructor;
  var xBits, yBits;
  var xSign = +(x.s < 0);
  var ySign = +(y.s < 0);

  if (xSign) {
    xBits = decCoefficientToBinaryString(bitNotBigNumber(x));

    for (var i = 0; i < xBits.length; ++i) {
      xBits[i] ^= 1;
    }
  } else {
    xBits = decCoefficientToBinaryString(x);
  }

  if (ySign) {
    yBits = decCoefficientToBinaryString(bitNotBigNumber(y));

    for (var _i = 0; _i < yBits.length; ++_i) {
      yBits[_i] ^= 1;
    }
  } else {
    yBits = decCoefficientToBinaryString(y);
  }

  var minBits, maxBits, minSign;

  if (xBits.length <= yBits.length) {
    minBits = xBits;
    maxBits = yBits;
    minSign = xSign;
  } else {
    minBits = yBits;
    maxBits = xBits;
    minSign = ySign;
  }

  var shortLen = minBits.length;
  var longLen = maxBits.length;
  var expFuncVal = func(xSign, ySign) ^ 1;
  var outVal = new BigNumber(expFuncVal ^ 1);
  var twoPower = new BigNumber(1);
  var two = new BigNumber(2);
  var prevPrec = BigNumber.precision;
  BigNumber.config({
    precision: 1E9
  });

  while (shortLen > 0) {
    if (func(minBits[--shortLen], maxBits[--longLen]) === expFuncVal) {
      outVal = outVal.plus(twoPower);
    }

    twoPower = twoPower.times(two);
  }

  while (longLen > 0) {
    if (func(minSign, maxBits[--longLen]) === expFuncVal) {
      outVal = outVal.plus(twoPower);
    }

    twoPower = twoPower.times(two);
  }

  BigNumber.config({
    precision: prevPrec
  });

  if (expFuncVal === 0) {
    outVal.s = -outVal.s;
  }

  return outVal;
}
/* Extracted from decimal.js, and edited to specialize. */

function decCoefficientToBinaryString(x) {
  // Convert to string
  var a = x.d; // array with digits

  var r = a[0] + '';

  for (var i = 1; i < a.length; ++i) {
    var s = a[i] + '';

    for (var z = 7 - s.length; z--;) {
      s = '0' + s;
    }

    r += s;
  }

  var j = r.length;

  while (r.charAt(j) === '0') {
    j--;
  }

  var xe = x.e;
  var str = r.slice(0, j + 1 || 1);
  var strL = str.length;

  if (xe > 0) {
    if (++xe > strL) {
      // Append zeros.
      xe -= strL;

      while (xe--) {
        str += '0';
      }
    } else if (xe < strL) {
      str = str.slice(0, xe) + '.' + str.slice(xe);
    }
  } // Convert from base 10 (decimal) to base 2


  var arr = [0];

  for (var _i2 = 0; _i2 < str.length;) {
    var arrL = arr.length;

    while (arrL--) {
      arr[arrL] *= 10;
    }

    arr[0] += parseInt(str.charAt(_i2++)); // convert to int

    for (var _j = 0; _j < arr.length; ++_j) {
      if (arr[_j] > 1) {
        if (arr[_j + 1] === null || arr[_j + 1] === undefined) {
          arr[_j + 1] = 0;
        }

        arr[_j + 1] += arr[_j] >> 1;
        arr[_j] &= 1;
      }
    }
  }

  return arr.reverse();
}
/**
 * Bitwise XOR for BigNumbers
 *
 * Special Cases:
 *   N ^  n =  N
 *   n ^  0 =  n
 *   n ^  n =  0
 *   n ^ -1 = ~n
 *   I ^  n =  I
 *   I ^ -n = -I
 *   I ^ -I = -1
 *  -I ^  n = -I
 *  -I ^ -n =  I
 *
 * @param {BigNumber} x
 * @param {BigNumber} y
 * @return {BigNumber} Result of `x` ^ `y`, fully precise
 *
 */


export function bitXor(x, y) {
  if (x.isFinite() && !x.isInteger() || y.isFinite() && !y.isInteger()) {
    throw new Error('Integers expected in function bitXor');
  }

  var BigNumber = x.constructor;

  if (x.isNaN() || y.isNaN()) {
    return new BigNumber(NaN);
  }

  if (x.isZero()) {
    return y;
  }

  if (y.isZero()) {
    return x;
  }

  if (x.eq(y)) {
    return new BigNumber(0);
  }

  var negOne = new BigNumber(-1);

  if (x.eq(negOne)) {
    return bitNotBigNumber(y);
  }

  if (y.eq(negOne)) {
    return bitNotBigNumber(x);
  }

  if (!x.isFinite() || !y.isFinite()) {
    if (!x.isFinite() && !y.isFinite()) {
      return negOne;
    }

    return new BigNumber(x.isNegative() === y.isNegative() ? Infinity : -Infinity);
  }

  return bitwise(x, y, function (a, b) {
    return a ^ b;
  });
}
/**
 * Bitwise left shift
 *
 * Special Cases:
 *  n << -n = N
 *  n <<  N = N
 *  N <<  n = N
 *  n <<  0 = n
 *  0 <<  n = 0
 *  I <<  I = N
 *  I <<  n = I
 *  n <<  I = I
 *
 * @param {BigNumber} x
 * @param {BigNumber} y
 * @return {BigNumber} Result of `x` << `y`
 *
 */

export function leftShiftBigNumber(x, y) {
  if (x.isFinite() && !x.isInteger() || y.isFinite() && !y.isInteger()) {
    throw new Error('Integers expected in function leftShift');
  }

  var BigNumber = x.constructor;

  if (x.isNaN() || y.isNaN() || y.isNegative() && !y.isZero()) {
    return new BigNumber(NaN);
  }

  if (x.isZero() || y.isZero()) {
    return x;
  }

  if (!x.isFinite() && !y.isFinite()) {
    return new BigNumber(NaN);
  } // Math.pow(2, y) is fully precise for y < 55, and fast


  if (y.lt(55)) {
    return x.times(Math.pow(2, y.toNumber()) + '');
  }

  return x.times(new BigNumber(2).pow(y));
}
/*
 * Special Cases:
 *   n >> -n =  N
 *   n >>  N =  N
 *   N >>  n =  N
 *   I >>  I =  N
 *   n >>  0 =  n
 *   I >>  n =  I
 *  -I >>  n = -I
 *  -I >>  I = -I
 *   n >>  I =  I
 *  -n >>  I = -1
 *   0 >>  n =  0
 *
 * @param {BigNumber} value
 * @param {BigNumber} value
 * @return {BigNumber} Result of `x` >> `y`
 *
 */

export function rightArithShiftBigNumber(x, y) {
  if (x.isFinite() && !x.isInteger() || y.isFinite() && !y.isInteger()) {
    throw new Error('Integers expected in function rightArithShift');
  }

  var BigNumber = x.constructor;

  if (x.isNaN() || y.isNaN() || y.isNegative() && !y.isZero()) {
    return new BigNumber(NaN);
  }

  if (x.isZero() || y.isZero()) {
    return x;
  }

  if (!y.isFinite()) {
    if (x.isNegative()) {
      return new BigNumber(-1);
    }

    if (!x.isFinite()) {
      return new BigNumber(NaN);
    }

    return new BigNumber(0);
  } // Math.pow(2, y) is fully precise for y < 55, and fast


  if (y.lt(55)) {
    return x.div(Math.pow(2, y.toNumber()) + '').floor();
  }

  return x.div(new BigNumber(2).pow(y)).floor();
}