737 lines
23 KiB
JavaScript
737 lines
23 KiB
JavaScript
import { isBigNumber, isNumber, isObject } from './is.js';
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/**
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* @typedef {{sign: '+' | '-' | '', coefficients: number[], exponent: number}} SplitValue
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*/
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/**
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* Check if a number is integer
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* @param {number | boolean} value
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* @return {boolean} isInteger
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*/
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export function isInteger(value) {
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if (typeof value === 'boolean') {
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return true;
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}
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return isFinite(value) ? value === Math.round(value) : false;
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}
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/**
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* Check if a string contains an integer
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* @param {string} str
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* @return {boolean} isInteger
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*/
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export function isIntegerStr(str) {
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// regex matching strings like "123" and "-123"
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return /^-?\d+$/.test(str);
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}
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/**
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* Ensure the number type is compatible with the provided value.
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* If not, return 'number' instead.
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*
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* For example:
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*
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* safeNumberType('2.3', { number: 'bigint', numberFallback: 'number' })
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*
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* will return 'number' and not 'bigint' because trying to create a bigint with
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* value 2.3 would throw an exception.
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*
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* @param {string} numberStr
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* @param {{
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* number: 'number' | 'BigNumber' | 'bigint' | 'Fraction'
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* numberFallback: 'number' | 'BigNumber'
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* }} config
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* @returns {'number' | 'BigNumber' | 'bigint' | 'Fraction'}
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*/
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export function safeNumberType(numberStr, config) {
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if (config.number === 'bigint' && !isIntegerStr(numberStr)) {
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return config.numberFallback;
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}
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return config.number;
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}
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/**
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* Calculate the sign of a number
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* @param {number} x
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* @returns {number}
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*/
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export var sign = Math.sign || function (x) {
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if (x > 0) {
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return 1;
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} else if (x < 0) {
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return -1;
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} else {
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return 0;
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}
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};
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/**
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* Calculate the base-2 logarithm of a number
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* @param {number} x
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* @returns {number}
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*/
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export var log2 = Math.log2 || function log2(x) {
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return Math.log(x) / Math.LN2;
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};
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/**
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* Calculate the base-10 logarithm of a number
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* @param {number} x
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* @returns {number}
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*/
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export var log10 = Math.log10 || function log10(x) {
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return Math.log(x) / Math.LN10;
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};
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/**
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* Calculate the natural logarithm of a number + 1
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* @param {number} x
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* @returns {number}
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*/
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export var log1p = Math.log1p || function (x) {
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return Math.log(x + 1);
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};
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/**
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* Calculate cubic root for a number
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*
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* Code from es6-shim.js:
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* https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1564-L1577
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*
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* @param {number} x
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* @returns {number} Returns the cubic root of x
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*/
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export var cbrt = Math.cbrt || function cbrt(x) {
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if (x === 0) {
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return x;
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}
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var negate = x < 0;
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var result;
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if (negate) {
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x = -x;
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}
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if (isFinite(x)) {
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result = Math.exp(Math.log(x) / 3);
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// from https://en.wikipedia.org/wiki/Cube_root#Numerical_methods
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result = (x / (result * result) + 2 * result) / 3;
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} else {
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result = x;
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}
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return negate ? -result : result;
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};
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/**
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* Calculates exponentiation minus 1
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* @param {number} x
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* @return {number} res
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*/
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export var expm1 = Math.expm1 || function expm1(x) {
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return x >= 2e-4 || x <= -2e-4 ? Math.exp(x) - 1 : x + x * x / 2 + x * x * x / 6;
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};
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/**
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* Formats a number in a given base
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* @param {number} n
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* @param {number} base
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* @param {number} size
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* @returns {string}
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*/
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function formatNumberToBase(n, base, size) {
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var prefixes = {
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2: '0b',
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8: '0o',
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16: '0x'
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};
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var prefix = prefixes[base];
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var suffix = '';
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if (size) {
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if (size < 1) {
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throw new Error('size must be in greater than 0');
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}
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if (!isInteger(size)) {
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throw new Error('size must be an integer');
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}
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if (n > 2 ** (size - 1) - 1 || n < -(2 ** (size - 1))) {
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throw new Error("Value must be in range [-2^".concat(size - 1, ", 2^").concat(size - 1, "-1]"));
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}
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if (!isInteger(n)) {
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throw new Error('Value must be an integer');
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}
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if (n < 0) {
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n = n + 2 ** size;
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}
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suffix = "i".concat(size);
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}
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var sign = '';
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if (n < 0) {
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n = -n;
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sign = '-';
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}
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return "".concat(sign).concat(prefix).concat(n.toString(base)).concat(suffix);
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}
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/**
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* Convert a number to a formatted string representation.
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*
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* Syntax:
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*
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* format(value)
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* format(value, options)
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* format(value, precision)
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* format(value, fn)
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*
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* Where:
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*
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* {number} value The value to be formatted
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* {Object} options An object with formatting options. Available options:
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* {string} notation
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* Number notation. Choose from:
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* 'fixed' Always use regular number notation.
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* For example '123.40' and '14000000'
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* 'exponential' Always use exponential notation.
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* For example '1.234e+2' and '1.4e+7'
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* 'engineering' Always use engineering notation.
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* For example '123.4e+0' and '14.0e+6'
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* 'auto' (default) Regular number notation for numbers
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* having an absolute value between
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* `lowerExp` and `upperExp` bounds, and
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* uses exponential notation elsewhere.
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* Lower bound is included, upper bound
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* is excluded.
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* For example '123.4' and '1.4e7'.
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* 'bin', 'oct, or
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* 'hex' Format the number using binary, octal,
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* or hexadecimal notation.
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* For example '0b1101' and '0x10fe'.
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* {number} wordSize The word size in bits to use for formatting
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* in binary, octal, or hexadecimal notation.
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* To be used only with 'bin', 'oct', or 'hex'
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* values for 'notation' option. When this option
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* is defined the value is formatted as a signed
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* twos complement integer of the given word size
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* and the size suffix is appended to the output.
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* For example
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* format(-1, {notation: 'hex', wordSize: 8}) === '0xffi8'.
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* Default value is undefined.
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* {number} precision A number between 0 and 16 to round
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* the digits of the number.
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* In case of notations 'exponential',
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* 'engineering', and 'auto',
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* `precision` defines the total
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* number of significant digits returned.
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* In case of notation 'fixed',
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* `precision` defines the number of
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* significant digits after the decimal
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* point.
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* `precision` is undefined by default,
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* not rounding any digits.
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* {number} lowerExp Exponent determining the lower boundary
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* for formatting a value with an exponent
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* when `notation='auto`.
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* Default value is `-3`.
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* {number} upperExp Exponent determining the upper boundary
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* for formatting a value with an exponent
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* when `notation='auto`.
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* Default value is `5`.
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* {Function} fn A custom formatting function. Can be used to override the
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* built-in notations. Function `fn` is called with `value` as
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* parameter and must return a string. Is useful for example to
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* format all values inside a matrix in a particular way.
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*
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* Examples:
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*
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* format(6.4) // '6.4'
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* format(1240000) // '1.24e6'
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* format(1/3) // '0.3333333333333333'
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* format(1/3, 3) // '0.333'
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* format(21385, 2) // '21000'
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* format(12.071, {notation: 'fixed'}) // '12'
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* format(2.3, {notation: 'fixed', precision: 2}) // '2.30'
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* format(52.8, {notation: 'exponential'}) // '5.28e+1'
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* format(12345678, {notation: 'engineering'}) // '12.345678e+6'
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*
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* @param {number} value
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* @param {Object | Function | number} [options]
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* @return {string} str The formatted value
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*/
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export function format(value, options) {
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if (typeof options === 'function') {
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// handle format(value, fn)
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return options(value);
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}
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// handle special cases
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if (value === Infinity) {
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return 'Infinity';
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} else if (value === -Infinity) {
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return '-Infinity';
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} else if (isNaN(value)) {
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return 'NaN';
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}
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var {
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notation,
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precision,
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wordSize
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} = normalizeFormatOptions(options);
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// handle the various notations
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switch (notation) {
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case 'fixed':
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return toFixed(value, precision);
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case 'exponential':
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return toExponential(value, precision);
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case 'engineering':
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return toEngineering(value, precision);
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case 'bin':
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return formatNumberToBase(value, 2, wordSize);
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case 'oct':
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return formatNumberToBase(value, 8, wordSize);
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case 'hex':
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return formatNumberToBase(value, 16, wordSize);
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case 'auto':
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// remove trailing zeros after the decimal point
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return toPrecision(value, precision, options).replace(/((\.\d*?)(0+))($|e)/, function () {
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var digits = arguments[2];
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var e = arguments[4];
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return digits !== '.' ? digits + e : e;
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});
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default:
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throw new Error('Unknown notation "' + notation + '". ' + 'Choose "auto", "exponential", "fixed", "bin", "oct", or "hex.');
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}
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}
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/**
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* Normalize format options into an object:
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* {
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* notation: string,
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* precision: number | undefined,
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* wordSize: number | undefined
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* }
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*/
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export function normalizeFormatOptions(options) {
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// default values for options
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var notation = 'auto';
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var precision;
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var wordSize;
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if (options !== undefined) {
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if (isNumber(options)) {
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precision = options;
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} else if (isBigNumber(options)) {
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precision = options.toNumber();
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} else if (isObject(options)) {
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if (options.precision !== undefined) {
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precision = _toNumberOrThrow(options.precision, () => {
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throw new Error('Option "precision" must be a number or BigNumber');
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});
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}
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if (options.wordSize !== undefined) {
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wordSize = _toNumberOrThrow(options.wordSize, () => {
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throw new Error('Option "wordSize" must be a number or BigNumber');
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});
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}
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if (options.notation) {
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notation = options.notation;
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}
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} else {
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throw new Error('Unsupported type of options, number, BigNumber, or object expected');
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}
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}
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return {
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notation,
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precision,
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wordSize
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};
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}
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/**
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* Split a number into sign, coefficients, and exponent
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* @param {number | string} value
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* @return {SplitValue}
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* Returns an object containing sign, coefficients, and exponent
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*/
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export function splitNumber(value) {
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// parse the input value
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var match = String(value).toLowerCase().match(/^(-?)(\d+\.?\d*)(e([+-]?\d+))?$/);
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if (!match) {
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throw new SyntaxError('Invalid number ' + value);
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}
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var sign = match[1];
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var digits = match[2];
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var exponent = parseFloat(match[4] || '0');
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var dot = digits.indexOf('.');
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exponent += dot !== -1 ? dot - 1 : digits.length - 1;
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var coefficients = digits.replace('.', '') // remove the dot (must be removed before removing leading zeros)
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.replace(/^0*/, function (zeros) {
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// remove leading zeros, add their count to the exponent
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exponent -= zeros.length;
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return '';
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}).replace(/0*$/, '') // remove trailing zeros
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.split('').map(function (d) {
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return parseInt(d);
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});
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if (coefficients.length === 0) {
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coefficients.push(0);
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exponent++;
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}
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return {
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sign,
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coefficients,
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exponent
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};
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}
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/**
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* Format a number in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'
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* @param {number | string} value
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* @param {number} [precision] Optional number of significant figures to return.
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*/
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export function toEngineering(value, precision) {
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if (isNaN(value) || !isFinite(value)) {
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return String(value);
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}
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var split = splitNumber(value);
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var rounded = roundDigits(split, precision);
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var e = rounded.exponent;
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var c = rounded.coefficients;
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// find nearest lower multiple of 3 for exponent
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var newExp = e % 3 === 0 ? e : e < 0 ? e - 3 - e % 3 : e - e % 3;
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if (isNumber(precision)) {
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// add zeroes to give correct sig figs
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while (precision > c.length || e - newExp + 1 > c.length) {
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c.push(0);
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}
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} else {
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// concatenate coefficients with necessary zeros
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// add zeros if necessary (for example: 1e+8 -> 100e+6)
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var missingZeros = Math.abs(e - newExp) - (c.length - 1);
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for (var i = 0; i < missingZeros; i++) {
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c.push(0);
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}
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}
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// find difference in exponents
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var expDiff = Math.abs(e - newExp);
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var decimalIdx = 1;
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// push decimal index over by expDiff times
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while (expDiff > 0) {
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decimalIdx++;
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expDiff--;
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}
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// if all coefficient values are zero after the decimal point and precision is unset, don't add a decimal value.
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// otherwise concat with the rest of the coefficients
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var decimals = c.slice(decimalIdx).join('');
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var decimalVal = isNumber(precision) && decimals.length || decimals.match(/[1-9]/) ? '.' + decimals : '';
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var str = c.slice(0, decimalIdx).join('') + decimalVal + 'e' + (e >= 0 ? '+' : '') + newExp.toString();
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return rounded.sign + str;
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}
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/**
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* Format a number with fixed notation.
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* @param {number | string} value
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* @param {number} [precision=undefined] Optional number of decimals after the
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* decimal point. null by default.
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*/
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export function toFixed(value, precision) {
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if (isNaN(value) || !isFinite(value)) {
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return String(value);
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}
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var splitValue = splitNumber(value);
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var rounded = typeof precision === 'number' ? roundDigits(splitValue, splitValue.exponent + 1 + precision) : splitValue;
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var c = rounded.coefficients;
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var p = rounded.exponent + 1; // exponent may have changed
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// append zeros if needed
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var pp = p + (precision || 0);
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if (c.length < pp) {
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c = c.concat(zeros(pp - c.length));
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}
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// prepend zeros if needed
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if (p < 0) {
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c = zeros(-p + 1).concat(c);
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p = 1;
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}
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// insert a dot if needed
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if (p < c.length) {
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c.splice(p, 0, p === 0 ? '0.' : '.');
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}
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return rounded.sign + c.join('');
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}
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/**
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* Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'
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* @param {number | string} value
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* @param {number} [precision] Number of digits in formatted output.
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* If not provided, the maximum available digits
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* is used.
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*/
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export function toExponential(value, precision) {
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if (isNaN(value) || !isFinite(value)) {
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return String(value);
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}
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// round if needed, else create a clone
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var split = splitNumber(value);
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var rounded = precision ? roundDigits(split, precision) : split;
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var c = rounded.coefficients;
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var e = rounded.exponent;
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// append zeros if needed
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if (c.length < precision) {
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c = c.concat(zeros(precision - c.length));
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}
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// format as `C.CCCe+EEE` or `C.CCCe-EEE`
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var first = c.shift();
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return rounded.sign + first + (c.length > 0 ? '.' + c.join('') : '') + 'e' + (e >= 0 ? '+' : '') + e;
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}
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/**
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* Format a number with a certain precision
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* @param {number | string} value
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* @param {number} [precision=undefined] Optional number of digits.
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* @param {{lowerExp: number | undefined, upperExp: number | undefined}} [options]
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* By default:
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* lowerExp = -3 (incl)
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* upper = +5 (excl)
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* @return {string}
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*/
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export function toPrecision(value, precision, options) {
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if (isNaN(value) || !isFinite(value)) {
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return String(value);
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}
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// determine lower and upper bound for exponential notation.
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var lowerExp = _toNumberOrDefault(options === null || options === void 0 ? void 0 : options.lowerExp, -3);
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var upperExp = _toNumberOrDefault(options === null || options === void 0 ? void 0 : options.upperExp, 5);
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var split = splitNumber(value);
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var rounded = precision ? roundDigits(split, precision) : split;
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if (rounded.exponent < lowerExp || rounded.exponent >= upperExp) {
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// exponential notation
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return toExponential(value, precision);
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} else {
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var c = rounded.coefficients;
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var e = rounded.exponent;
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// append trailing zeros
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|
if (c.length < precision) {
|
|
c = c.concat(zeros(precision - c.length));
|
|
}
|
|
|
|
// append trailing zeros
|
|
// TODO: simplify the next statement
|
|
c = c.concat(zeros(e - c.length + 1 + (c.length < precision ? precision - c.length : 0)));
|
|
|
|
// prepend zeros
|
|
c = zeros(-e).concat(c);
|
|
var dot = e > 0 ? e : 0;
|
|
if (dot < c.length - 1) {
|
|
c.splice(dot + 1, 0, '.');
|
|
}
|
|
return rounded.sign + c.join('');
|
|
}
|
|
}
|
|
|
|
/**
|
|
* Round the number of digits of a number *
|
|
* @param {SplitValue} split A value split with .splitNumber(value)
|
|
* @param {number} precision A positive integer
|
|
* @return {SplitValue}
|
|
* Returns an object containing sign, coefficients, and exponent
|
|
* with rounded digits
|
|
*/
|
|
export function roundDigits(split, precision) {
|
|
// create a clone
|
|
var rounded = {
|
|
sign: split.sign,
|
|
coefficients: split.coefficients,
|
|
exponent: split.exponent
|
|
};
|
|
var c = rounded.coefficients;
|
|
|
|
// prepend zeros if needed
|
|
while (precision <= 0) {
|
|
c.unshift(0);
|
|
rounded.exponent++;
|
|
precision++;
|
|
}
|
|
if (c.length > precision) {
|
|
var removed = c.splice(precision, c.length - precision);
|
|
if (removed[0] >= 5) {
|
|
var i = precision - 1;
|
|
c[i]++;
|
|
while (c[i] === 10) {
|
|
c.pop();
|
|
if (i === 0) {
|
|
c.unshift(0);
|
|
rounded.exponent++;
|
|
i++;
|
|
}
|
|
i--;
|
|
c[i]++;
|
|
}
|
|
}
|
|
}
|
|
return rounded;
|
|
}
|
|
|
|
/**
|
|
* Create an array filled with zeros.
|
|
* @param {number} length
|
|
* @return {Array}
|
|
*/
|
|
function zeros(length) {
|
|
var arr = [];
|
|
for (var i = 0; i < length; i++) {
|
|
arr.push(0);
|
|
}
|
|
return arr;
|
|
}
|
|
|
|
/**
|
|
* Count the number of significant digits of a number.
|
|
*
|
|
* For example:
|
|
* 2.34 returns 3
|
|
* 0.0034 returns 2
|
|
* 120.5e+30 returns 4
|
|
*
|
|
* @param {number} value
|
|
* @return {number} digits Number of significant digits
|
|
*/
|
|
export function digits(value) {
|
|
return value.toExponential().replace(/e.*$/, '') // remove exponential notation
|
|
.replace(/^0\.?0*|\./, '') // remove decimal point and leading zeros
|
|
.length;
|
|
}
|
|
|
|
/**
|
|
* Minimum number added to one that makes the result different than one
|
|
*/
|
|
export var DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16;
|
|
|
|
/**
|
|
* Compares two floating point numbers.
|
|
* @param {number} a - First value to compare
|
|
* @param {number} b - Second value to compare
|
|
* @param {number} [relTol=1e-09] - The relative tolerance, indicating the maximum allowed difference relative to the larger absolute value. Must be greater than 0.
|
|
* @param {number} [absTol=1e-12] - The minimum absolute tolerance, useful for comparisons near zero. Must be at least 0.
|
|
* @return {boolean} whether the two numbers are nearly equal
|
|
*
|
|
* @throws {Error} If `relTol` is less than or equal to 0.
|
|
* @throws {Error} If `absTol` is less than 0.
|
|
*
|
|
* @example
|
|
* nearlyEqual(1.000000001, 1.0, 1e-8); // true
|
|
* nearlyEqual(1.000000002, 1.0, 0); // false
|
|
* nearlyEqual(1.0, 1.009, undefined, 0.01); // true
|
|
* nearlyEqual(0.000000001, 0.0, undefined, 1e-8); // true
|
|
*/
|
|
export function nearlyEqual(a, b) {
|
|
var relTol = arguments.length > 2 && arguments[2] !== undefined ? arguments[2] : 1e-8;
|
|
var absTol = arguments.length > 3 && arguments[3] !== undefined ? arguments[3] : 0;
|
|
if (relTol <= 0) {
|
|
throw new Error('Relative tolerance must be greater than 0');
|
|
}
|
|
if (absTol < 0) {
|
|
throw new Error('Absolute tolerance must be at least 0');
|
|
}
|
|
|
|
// NaN
|
|
if (isNaN(a) || isNaN(b)) {
|
|
return false;
|
|
}
|
|
if (!isFinite(a) || !isFinite(b)) {
|
|
return a === b;
|
|
}
|
|
if (a === b) {
|
|
return true;
|
|
}
|
|
|
|
// abs(a-b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)
|
|
return Math.abs(a - b) <= Math.max(relTol * Math.max(Math.abs(a), Math.abs(b)), absTol);
|
|
}
|
|
|
|
/**
|
|
* Calculate the hyperbolic arccos of a number
|
|
* @param {number} x
|
|
* @return {number}
|
|
*/
|
|
export var acosh = Math.acosh || function (x) {
|
|
return Math.log(Math.sqrt(x * x - 1) + x);
|
|
};
|
|
export var asinh = Math.asinh || function (x) {
|
|
return Math.log(Math.sqrt(x * x + 1) + x);
|
|
};
|
|
|
|
/**
|
|
* Calculate the hyperbolic arctangent of a number
|
|
* @param {number} x
|
|
* @return {number}
|
|
*/
|
|
export var atanh = Math.atanh || function (x) {
|
|
return Math.log((1 + x) / (1 - x)) / 2;
|
|
};
|
|
|
|
/**
|
|
* Calculate the hyperbolic cosine of a number
|
|
* @param {number} x
|
|
* @returns {number}
|
|
*/
|
|
export var cosh = Math.cosh || function (x) {
|
|
return (Math.exp(x) + Math.exp(-x)) / 2;
|
|
};
|
|
|
|
/**
|
|
* Calculate the hyperbolic sine of a number
|
|
* @param {number} x
|
|
* @returns {number}
|
|
*/
|
|
export var sinh = Math.sinh || function (x) {
|
|
return (Math.exp(x) - Math.exp(-x)) / 2;
|
|
};
|
|
|
|
/**
|
|
* Calculate the hyperbolic tangent of a number
|
|
* @param {number} x
|
|
* @returns {number}
|
|
*/
|
|
export var tanh = Math.tanh || function (x) {
|
|
var e = Math.exp(2 * x);
|
|
return (e - 1) / (e + 1);
|
|
};
|
|
|
|
/**
|
|
* Returns a value with the magnitude of x and the sign of y.
|
|
* @param {number} x
|
|
* @param {number} y
|
|
* @returns {number}
|
|
*/
|
|
export function copysign(x, y) {
|
|
var signx = x > 0 ? true : x < 0 ? false : 1 / x === Infinity;
|
|
var signy = y > 0 ? true : y < 0 ? false : 1 / y === Infinity;
|
|
return signx ^ signy ? -x : x;
|
|
}
|
|
function _toNumberOrThrow(value, onError) {
|
|
if (isNumber(value)) {
|
|
return value;
|
|
} else if (isBigNumber(value)) {
|
|
return value.toNumber();
|
|
} else {
|
|
onError();
|
|
}
|
|
}
|
|
function _toNumberOrDefault(value, defaultValue) {
|
|
if (isNumber(value)) {
|
|
return value;
|
|
} else if (isBigNumber(value)) {
|
|
return value.toNumber();
|
|
} else {
|
|
return defaultValue;
|
|
}
|
|
} |