1 | import { mapObject } from './object';
|
2 | import { isNumber } from './is';
|
3 | /**
|
4 | * @typedef {{sign: '+' | '-' | '', coefficients: number[], exponent: number}} SplitValue
|
5 | */
|
6 |
|
7 | /**
|
8 | * Check if a number is integer
|
9 | * @param {number | boolean} value
|
10 | * @return {boolean} isInteger
|
11 | */
|
12 |
|
13 | export function isInteger(value) {
|
14 | if (typeof value === 'boolean') {
|
15 | return true;
|
16 | }
|
17 |
|
18 | return isFinite(value) ? value === Math.round(value) : false; // Note: we use ==, not ===, as we can have Booleans as well
|
19 | }
|
20 | /**
|
21 | * Calculate the sign of a number
|
22 | * @param {number} x
|
23 | * @returns {number}
|
24 | */
|
25 |
|
26 | export var sign =
|
27 | /* #__PURE__ */
|
28 | Math.sign || function (x) {
|
29 | if (x > 0) {
|
30 | return 1;
|
31 | } else if (x < 0) {
|
32 | return -1;
|
33 | } else {
|
34 | return 0;
|
35 | }
|
36 | };
|
37 | /**
|
38 | * Calculate the base-2 logarithm of a number
|
39 | * @param {number} x
|
40 | * @returns {number}
|
41 | */
|
42 |
|
43 | export var log2 =
|
44 | /* #__PURE__ */
|
45 | Math.log2 || function log2(x) {
|
46 | return Math.log(x) / Math.LN2;
|
47 | };
|
48 | /**
|
49 | * Calculate the base-10 logarithm of a number
|
50 | * @param {number} x
|
51 | * @returns {number}
|
52 | */
|
53 |
|
54 | export var log10 =
|
55 | /* #__PURE__ */
|
56 | Math.log10 || function log10(x) {
|
57 | return Math.log(x) / Math.LN10;
|
58 | };
|
59 | /**
|
60 | * Calculate the natural logarithm of a number + 1
|
61 | * @param {number} x
|
62 | * @returns {number}
|
63 | */
|
64 |
|
65 | export var log1p =
|
66 | /* #__PURE__ */
|
67 | Math.log1p || function (x) {
|
68 | return Math.log(x + 1);
|
69 | };
|
70 | /**
|
71 | * Calculate cubic root for a number
|
72 | *
|
73 | * Code from es6-shim.js:
|
74 | * https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1564-L1577
|
75 | *
|
76 | * @param {number} x
|
77 | * @returns {number} Returns the cubic root of x
|
78 | */
|
79 |
|
80 | export var cbrt =
|
81 | /* #__PURE__ */
|
82 | Math.cbrt || function cbrt(x) {
|
83 | if (x === 0) {
|
84 | return x;
|
85 | }
|
86 |
|
87 | var negate = x < 0;
|
88 | var result;
|
89 |
|
90 | if (negate) {
|
91 | x = -x;
|
92 | }
|
93 |
|
94 | if (isFinite(x)) {
|
95 | result = Math.exp(Math.log(x) / 3); // from https://en.wikipedia.org/wiki/Cube_root#Numerical_methods
|
96 |
|
97 | result = (x / (result * result) + 2 * result) / 3;
|
98 | } else {
|
99 | result = x;
|
100 | }
|
101 |
|
102 | return negate ? -result : result;
|
103 | };
|
104 | /**
|
105 | * Calculates exponentiation minus 1
|
106 | * @param {number} x
|
107 | * @return {number} res
|
108 | */
|
109 |
|
110 | export var expm1 =
|
111 | /* #__PURE__ */
|
112 | Math.expm1 || function expm1(x) {
|
113 | return x >= 2e-4 || x <= -2e-4 ? Math.exp(x) - 1 : x + x * x / 2 + x * x * x / 6;
|
114 | };
|
115 | /**
|
116 | * Convert a number to a formatted string representation.
|
117 | *
|
118 | * Syntax:
|
119 | *
|
120 | * format(value)
|
121 | * format(value, options)
|
122 | * format(value, precision)
|
123 | * format(value, fn)
|
124 | *
|
125 | * Where:
|
126 | *
|
127 | * {number} value The value to be formatted
|
128 | * {Object} options An object with formatting options. Available options:
|
129 | * {string} notation
|
130 | * Number notation. Choose from:
|
131 | * 'fixed' Always use regular number notation.
|
132 | * For example '123.40' and '14000000'
|
133 | * 'exponential' Always use exponential notation.
|
134 | * For example '1.234e+2' and '1.4e+7'
|
135 | * 'engineering' Always use engineering notation.
|
136 | * For example '123.4e+0' and '14.0e+6'
|
137 | * 'auto' (default) Regular number notation for numbers
|
138 | * having an absolute value between
|
139 | * `lowerExp` and `upperExp` bounds, and
|
140 | * uses exponential notation elsewhere.
|
141 | * Lower bound is included, upper bound
|
142 | * is excluded.
|
143 | * For example '123.4' and '1.4e7'.
|
144 | * {number} precision A number between 0 and 16 to round
|
145 | * the digits of the number.
|
146 | * In case of notations 'exponential',
|
147 | * 'engineering', and 'auto',
|
148 | * `precision` defines the total
|
149 | * number of significant digits returned.
|
150 | * In case of notation 'fixed',
|
151 | * `precision` defines the number of
|
152 | * significant digits after the decimal
|
153 | * point.
|
154 | * `precision` is undefined by default,
|
155 | * not rounding any digits.
|
156 | * {number} lowerExp Exponent determining the lower boundary
|
157 | * for formatting a value with an exponent
|
158 | * when `notation='auto`.
|
159 | * Default value is `-3`.
|
160 | * {number} upperExp Exponent determining the upper boundary
|
161 | * for formatting a value with an exponent
|
162 | * when `notation='auto`.
|
163 | * Default value is `5`.
|
164 | * {Function} fn A custom formatting function. Can be used to override the
|
165 | * built-in notations. Function `fn` is called with `value` as
|
166 | * parameter and must return a string. Is useful for example to
|
167 | * format all values inside a matrix in a particular way.
|
168 | *
|
169 | * Examples:
|
170 | *
|
171 | * format(6.4) // '6.4'
|
172 | * format(1240000) // '1.24e6'
|
173 | * format(1/3) // '0.3333333333333333'
|
174 | * format(1/3, 3) // '0.333'
|
175 | * format(21385, 2) // '21000'
|
176 | * format(12.071, {notation: 'fixed'}) // '12'
|
177 | * format(2.3, {notation: 'fixed', precision: 2}) // '2.30'
|
178 | * format(52.8, {notation: 'exponential'}) // '5.28e+1'
|
179 | * format(12345678, {notation: 'engineering'}) // '12.345678e+6'
|
180 | *
|
181 | * @param {number} value
|
182 | * @param {Object | Function | number} [options]
|
183 | * @return {string} str The formatted value
|
184 | */
|
185 |
|
186 | export function format(value, options) {
|
187 | if (typeof options === 'function') {
|
188 | // handle format(value, fn)
|
189 | return options(value);
|
190 | } // handle special cases
|
191 |
|
192 |
|
193 | if (value === Infinity) {
|
194 | return 'Infinity';
|
195 | } else if (value === -Infinity) {
|
196 | return '-Infinity';
|
197 | } else if (isNaN(value)) {
|
198 | return 'NaN';
|
199 | } // default values for options
|
200 |
|
201 |
|
202 | var notation = 'auto';
|
203 | var precision;
|
204 |
|
205 | if (options) {
|
206 | // determine notation from options
|
207 | if (options.notation) {
|
208 | notation = options.notation;
|
209 | } // determine precision from options
|
210 |
|
211 |
|
212 | if (isNumber(options)) {
|
213 | precision = options;
|
214 | } else if (isNumber(options.precision)) {
|
215 | precision = options.precision;
|
216 | }
|
217 | } // handle the various notations
|
218 |
|
219 |
|
220 | switch (notation) {
|
221 | case 'fixed':
|
222 | return toFixed(value, precision);
|
223 |
|
224 | case 'exponential':
|
225 | return toExponential(value, precision);
|
226 |
|
227 | case 'engineering':
|
228 | return toEngineering(value, precision);
|
229 |
|
230 | case 'auto':
|
231 | // TODO: clean up some day. Deprecated since: 2018-01-24
|
232 | // @deprecated upper and lower are replaced with upperExp and lowerExp since v4.0.0
|
233 | if (options && options.exponential && (options.exponential.lower !== undefined || options.exponential.upper !== undefined)) {
|
234 | var fixedOptions = mapObject(options, function (x) {
|
235 | return x;
|
236 | });
|
237 | fixedOptions.exponential = undefined;
|
238 |
|
239 | if (options.exponential.lower !== undefined) {
|
240 | fixedOptions.lowerExp = Math.round(Math.log(options.exponential.lower) / Math.LN10);
|
241 | }
|
242 |
|
243 | if (options.exponential.upper !== undefined) {
|
244 | fixedOptions.upperExp = Math.round(Math.log(options.exponential.upper) / Math.LN10);
|
245 | }
|
246 |
|
247 | console.warn('Deprecation warning: Formatting options exponential.lower and exponential.upper ' + '(minimum and maximum value) ' + 'are replaced with exponential.lowerExp and exponential.upperExp ' + '(minimum and maximum exponent) since version 4.0.0. ' + 'Replace ' + JSON.stringify(options) + ' with ' + JSON.stringify(fixedOptions));
|
248 | return toPrecision(value, precision, fixedOptions);
|
249 | } // remove trailing zeros after the decimal point
|
250 |
|
251 |
|
252 | return toPrecision(value, precision, options && options).replace(/((\.\d*?)(0+))($|e)/, function () {
|
253 | var digits = arguments[2];
|
254 | var e = arguments[4];
|
255 | return digits !== '.' ? digits + e : e;
|
256 | });
|
257 |
|
258 | default:
|
259 | throw new Error('Unknown notation "' + notation + '". ' + 'Choose "auto", "exponential", or "fixed".');
|
260 | }
|
261 | }
|
262 | /**
|
263 | * Split a number into sign, coefficients, and exponent
|
264 | * @param {number | string} value
|
265 | * @return {SplitValue}
|
266 | * Returns an object containing sign, coefficients, and exponent
|
267 | */
|
268 |
|
269 | export function splitNumber(value) {
|
270 | // parse the input value
|
271 | var match = String(value).toLowerCase().match(/^0*?(-?)(\d+\.?\d*)(e([+-]?\d+))?$/);
|
272 |
|
273 | if (!match) {
|
274 | throw new SyntaxError('Invalid number ' + value);
|
275 | }
|
276 |
|
277 | var sign = match[1];
|
278 | var digits = match[2];
|
279 | var exponent = parseFloat(match[4] || '0');
|
280 | var dot = digits.indexOf('.');
|
281 | exponent += dot !== -1 ? dot - 1 : digits.length - 1;
|
282 | var coefficients = digits.replace('.', '') // remove the dot (must be removed before removing leading zeros)
|
283 | .replace(/^0*/, function (zeros) {
|
284 | // remove leading zeros, add their count to the exponent
|
285 | exponent -= zeros.length;
|
286 | return '';
|
287 | }).replace(/0*$/, '') // remove trailing zeros
|
288 | .split('').map(function (d) {
|
289 | return parseInt(d);
|
290 | });
|
291 |
|
292 | if (coefficients.length === 0) {
|
293 | coefficients.push(0);
|
294 | exponent++;
|
295 | }
|
296 |
|
297 | return {
|
298 | sign: sign,
|
299 | coefficients: coefficients,
|
300 | exponent: exponent
|
301 | };
|
302 | }
|
303 | /**
|
304 | * Format a number in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'
|
305 | * @param {number | string} value
|
306 | * @param {number} [precision] Optional number of significant figures to return.
|
307 | */
|
308 |
|
309 | export function toEngineering(value, precision) {
|
310 | if (isNaN(value) || !isFinite(value)) {
|
311 | return String(value);
|
312 | }
|
313 |
|
314 | var rounded = roundDigits(splitNumber(value), precision);
|
315 | var e = rounded.exponent;
|
316 | var c = rounded.coefficients; // find nearest lower multiple of 3 for exponent
|
317 |
|
318 | var newExp = e % 3 === 0 ? e : e < 0 ? e - 3 - e % 3 : e - e % 3;
|
319 |
|
320 | if (isNumber(precision)) {
|
321 | // add zeroes to give correct sig figs
|
322 | while (precision > c.length || e - newExp + 1 > c.length) {
|
323 | c.push(0);
|
324 | }
|
325 | } else {
|
326 | // concatenate coefficients with necessary zeros
|
327 | var significandsDiff = e >= 0 ? e : Math.abs(newExp); // add zeros if necessary (for ex: 1e+8)
|
328 |
|
329 | while (c.length - 1 < significandsDiff) {
|
330 | c.push(0);
|
331 | }
|
332 | } // find difference in exponents
|
333 |
|
334 |
|
335 | var expDiff = Math.abs(e - newExp);
|
336 | var decimalIdx = 1; // push decimal index over by expDiff times
|
337 |
|
338 | while (expDiff > 0) {
|
339 | decimalIdx++;
|
340 | expDiff--;
|
341 | } // if all coefficient values are zero after the decimal point and precision is unset, don't add a decimal value.
|
342 | // otherwise concat with the rest of the coefficients
|
343 |
|
344 |
|
345 | var decimals = c.slice(decimalIdx).join('');
|
346 | var decimalVal = isNumber(precision) && decimals.length || decimals.match(/[1-9]/) ? '.' + decimals : '';
|
347 | var str = c.slice(0, decimalIdx).join('') + decimalVal + 'e' + (e >= 0 ? '+' : '') + newExp.toString();
|
348 | return rounded.sign + str;
|
349 | }
|
350 | /**
|
351 | * Format a number with fixed notation.
|
352 | * @param {number | string} value
|
353 | * @param {number} [precision=undefined] Optional number of decimals after the
|
354 | * decimal point. null by default.
|
355 | */
|
356 |
|
357 | export function toFixed(value, precision) {
|
358 | if (isNaN(value) || !isFinite(value)) {
|
359 | return String(value);
|
360 | }
|
361 |
|
362 | var splitValue = splitNumber(value);
|
363 | var rounded = typeof precision === 'number' ? roundDigits(splitValue, splitValue.exponent + 1 + precision) : splitValue;
|
364 | var c = rounded.coefficients;
|
365 | var p = rounded.exponent + 1; // exponent may have changed
|
366 | // append zeros if needed
|
367 |
|
368 | var pp = p + (precision || 0);
|
369 |
|
370 | if (c.length < pp) {
|
371 | c = c.concat(zeros(pp - c.length));
|
372 | } // prepend zeros if needed
|
373 |
|
374 |
|
375 | if (p < 0) {
|
376 | c = zeros(-p + 1).concat(c);
|
377 | p = 1;
|
378 | } // insert a dot if needed
|
379 |
|
380 |
|
381 | if (p < c.length) {
|
382 | c.splice(p, 0, p === 0 ? '0.' : '.');
|
383 | }
|
384 |
|
385 | return rounded.sign + c.join('');
|
386 | }
|
387 | /**
|
388 | * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'
|
389 | * @param {number | string} value
|
390 | * @param {number} [precision] Number of digits in formatted output.
|
391 | * If not provided, the maximum available digits
|
392 | * is used.
|
393 | */
|
394 |
|
395 | export function toExponential(value, precision) {
|
396 | if (isNaN(value) || !isFinite(value)) {
|
397 | return String(value);
|
398 | } // round if needed, else create a clone
|
399 |
|
400 |
|
401 | var split = splitNumber(value);
|
402 | var rounded = precision ? roundDigits(split, precision) : split;
|
403 | var c = rounded.coefficients;
|
404 | var e = rounded.exponent; // append zeros if needed
|
405 |
|
406 | if (c.length < precision) {
|
407 | c = c.concat(zeros(precision - c.length));
|
408 | } // format as `C.CCCe+EEE` or `C.CCCe-EEE`
|
409 |
|
410 |
|
411 | var first = c.shift();
|
412 | return rounded.sign + first + (c.length > 0 ? '.' + c.join('') : '') + 'e' + (e >= 0 ? '+' : '') + e;
|
413 | }
|
414 | /**
|
415 | * Format a number with a certain precision
|
416 | * @param {number | string} value
|
417 | * @param {number} [precision=undefined] Optional number of digits.
|
418 | * @param {{lowerExp: number | undefined, upperExp: number | undefined}} [options]
|
419 | * By default:
|
420 | * lowerExp = -3 (incl)
|
421 | * upper = +5 (excl)
|
422 | * @return {string}
|
423 | */
|
424 |
|
425 | export function toPrecision(value, precision, options) {
|
426 | if (isNaN(value) || !isFinite(value)) {
|
427 | return String(value);
|
428 | } // determine lower and upper bound for exponential notation.
|
429 |
|
430 |
|
431 | var lowerExp = options && options.lowerExp !== undefined ? options.lowerExp : -3;
|
432 | var upperExp = options && options.upperExp !== undefined ? options.upperExp : 5;
|
433 | var split = splitNumber(value);
|
434 | var rounded = precision ? roundDigits(split, precision) : split;
|
435 |
|
436 | if (rounded.exponent < lowerExp || rounded.exponent >= upperExp) {
|
437 | // exponential notation
|
438 | return toExponential(value, precision);
|
439 | } else {
|
440 | var c = rounded.coefficients;
|
441 | var e = rounded.exponent; // append trailing zeros
|
442 |
|
443 | if (c.length < precision) {
|
444 | c = c.concat(zeros(precision - c.length));
|
445 | } // append trailing zeros
|
446 | // TODO: simplify the next statement
|
447 |
|
448 |
|
449 | c = c.concat(zeros(e - c.length + 1 + (c.length < precision ? precision - c.length : 0))); // prepend zeros
|
450 |
|
451 | c = zeros(-e).concat(c);
|
452 | var dot = e > 0 ? e : 0;
|
453 |
|
454 | if (dot < c.length - 1) {
|
455 | c.splice(dot + 1, 0, '.');
|
456 | }
|
457 |
|
458 | return rounded.sign + c.join('');
|
459 | }
|
460 | }
|
461 | /**
|
462 | * Round the number of digits of a number *
|
463 | * @param {SplitValue} split A value split with .splitNumber(value)
|
464 | * @param {number} precision A positive integer
|
465 | * @return {SplitValue}
|
466 | * Returns an object containing sign, coefficients, and exponent
|
467 | * with rounded digits
|
468 | */
|
469 |
|
470 | export function roundDigits(split, precision) {
|
471 | // create a clone
|
472 | var rounded = {
|
473 | sign: split.sign,
|
474 | coefficients: split.coefficients,
|
475 | exponent: split.exponent
|
476 | };
|
477 | var c = rounded.coefficients; // prepend zeros if needed
|
478 |
|
479 | while (precision <= 0) {
|
480 | c.unshift(0);
|
481 | rounded.exponent++;
|
482 | precision++;
|
483 | }
|
484 |
|
485 | if (c.length > precision) {
|
486 | var removed = c.splice(precision, c.length - precision);
|
487 |
|
488 | if (removed[0] >= 5) {
|
489 | var i = precision - 1;
|
490 | c[i]++;
|
491 |
|
492 | while (c[i] === 10) {
|
493 | c.pop();
|
494 |
|
495 | if (i === 0) {
|
496 | c.unshift(0);
|
497 | rounded.exponent++;
|
498 | i++;
|
499 | }
|
500 |
|
501 | i--;
|
502 | c[i]++;
|
503 | }
|
504 | }
|
505 | }
|
506 |
|
507 | return rounded;
|
508 | }
|
509 | /**
|
510 | * Create an array filled with zeros.
|
511 | * @param {number} length
|
512 | * @return {Array}
|
513 | */
|
514 |
|
515 | function zeros(length) {
|
516 | var arr = [];
|
517 |
|
518 | for (var i = 0; i < length; i++) {
|
519 | arr.push(0);
|
520 | }
|
521 |
|
522 | return arr;
|
523 | }
|
524 | /**
|
525 | * Count the number of significant digits of a number.
|
526 | *
|
527 | * For example:
|
528 | * 2.34 returns 3
|
529 | * 0.0034 returns 2
|
530 | * 120.5e+30 returns 4
|
531 | *
|
532 | * @param {number} value
|
533 | * @return {number} digits Number of significant digits
|
534 | */
|
535 |
|
536 |
|
537 | export function digits(value) {
|
538 | return value.toExponential().replace(/e.*$/, '') // remove exponential notation
|
539 | .replace(/^0\.?0*|\./, '') // remove decimal point and leading zeros
|
540 | .length;
|
541 | }
|
542 | /**
|
543 | * Minimum number added to one that makes the result different than one
|
544 | */
|
545 |
|
546 | export var DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16;
|
547 | /**
|
548 | * Compares two floating point numbers.
|
549 | * @param {number} x First value to compare
|
550 | * @param {number} y Second value to compare
|
551 | * @param {number} [epsilon] The maximum relative difference between x and y
|
552 | * If epsilon is undefined or null, the function will
|
553 | * test whether x and y are exactly equal.
|
554 | * @return {boolean} whether the two numbers are nearly equal
|
555 | */
|
556 |
|
557 | export function nearlyEqual(x, y, epsilon) {
|
558 | // if epsilon is null or undefined, test whether x and y are exactly equal
|
559 | if (epsilon === null || epsilon === undefined) {
|
560 | return x === y;
|
561 | }
|
562 |
|
563 | if (x === y) {
|
564 | return true;
|
565 | } // NaN
|
566 |
|
567 |
|
568 | if (isNaN(x) || isNaN(y)) {
|
569 | return false;
|
570 | } // at this point x and y should be finite
|
571 |
|
572 |
|
573 | if (isFinite(x) && isFinite(y)) {
|
574 | // check numbers are very close, needed when comparing numbers near zero
|
575 | var diff = Math.abs(x - y);
|
576 |
|
577 | if (diff < DBL_EPSILON) {
|
578 | return true;
|
579 | } else {
|
580 | // use relative error
|
581 | return diff <= Math.max(Math.abs(x), Math.abs(y)) * epsilon;
|
582 | }
|
583 | } // Infinite and Number or negative Infinite and positive Infinite cases
|
584 |
|
585 |
|
586 | return false;
|
587 | }
|
588 | /**
|
589 | * Calculate the hyperbolic arccos of a number
|
590 | * @param {number} x
|
591 | * @return {number}
|
592 | */
|
593 |
|
594 | export var acosh = Math.acosh || function (x) {
|
595 | return Math.log(Math.sqrt(x * x - 1) + x);
|
596 | };
|
597 | export var asinh = Math.asinh || function (x) {
|
598 | return Math.log(Math.sqrt(x * x + 1) + x);
|
599 | };
|
600 | /**
|
601 | * Calculate the hyperbolic arctangent of a number
|
602 | * @param {number} x
|
603 | * @return {number}
|
604 | */
|
605 |
|
606 | export var atanh = Math.atanh || function (x) {
|
607 | return Math.log((1 + x) / (1 - x)) / 2;
|
608 | };
|
609 | /**
|
610 | * Calculate the hyperbolic cosine of a number
|
611 | * @param {number} x
|
612 | * @returns {number}
|
613 | */
|
614 |
|
615 | export var cosh = Math.cosh || function (x) {
|
616 | return (Math.exp(x) + Math.exp(-x)) / 2;
|
617 | };
|
618 | /**
|
619 | * Calculate the hyperbolic sine of a number
|
620 | * @param {number} x
|
621 | * @returns {number}
|
622 | */
|
623 |
|
624 | export var sinh = Math.sinh || function (x) {
|
625 | return (Math.exp(x) - Math.exp(-x)) / 2;
|
626 | };
|
627 | /**
|
628 | * Calculate the hyperbolic tangent of a number
|
629 | * @param {number} x
|
630 | * @returns {number}
|
631 | */
|
632 |
|
633 | export var tanh = Math.tanh || function (x) {
|
634 | var e = Math.exp(2 * x);
|
635 | return (e - 1) / (e + 1);
|
636 | }; |
\ | No newline at end of file |