688 lines
20 KiB
JavaScript
688 lines
20 KiB
JavaScript
import { isNumber } 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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* 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 = /* #__PURE__ */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 = /* #__PURE__ */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 = /* #__PURE__ */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 = /* #__PURE__ */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 = /* #__PURE__ */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); // 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 = /* #__PURE__ */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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} // 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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} // 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) {
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// determine notation from options
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if (options.notation) {
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notation = options.notation;
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} // determine precision from options
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if (isNumber(options)) {
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precision = options;
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} else if (isNumber(options.precision)) {
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precision = options.precision;
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}
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if (options.wordSize) {
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wordSize = options.wordSize;
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if (typeof wordSize !== 'number') {
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throw new Error('Option "wordSize" must be a number');
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}
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}
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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 && options).replace(/((\.\d*?)(0+))($|e)/, function () {
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var digits = arguments[2];
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var e = arguments[4];
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return digits !== '.' ? digits + e : e;
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});
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default:
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throw new Error('Unknown notation "' + notation + '". ' + 'Choose "auto", "exponential", "fixed", "bin", "oct", or "hex.');
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}
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}
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/**
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* Split a number into sign, coefficients, and exponent
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* @param {number | string} value
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* @return {SplitValue}
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* Returns an object containing sign, coefficients, and exponent
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*/
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export function splitNumber(value) {
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// parse the input value
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var match = String(value).toLowerCase().match(/^(-?)(\d+\.?\d*)(e([+-]?\d+))?$/);
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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: sign,
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coefficients: coefficients,
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exponent: 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; // 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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} // find difference in exponents
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var expDiff = Math.abs(e - newExp);
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var decimalIdx = 1; // 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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} // 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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} // 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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} // 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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} // 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; // 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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} // 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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} // determine lower and upper bound for exponential notation.
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var lowerExp = options && options.lowerExp !== undefined ? options.lowerExp : -3;
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var upperExp = options && options.upperExp !== undefined ? 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; // append trailing zeros
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if (c.length < precision) {
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c = c.concat(zeros(precision - c.length));
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} // append trailing zeros
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// TODO: simplify the next statement
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c = c.concat(zeros(e - c.length + 1 + (c.length < precision ? precision - c.length : 0))); // prepend zeros
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c = zeros(-e).concat(c);
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var dot = e > 0 ? e : 0;
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if (dot < c.length - 1) {
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c.splice(dot + 1, 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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/**
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* Round the number of digits of a number *
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* @param {SplitValue} split A value split with .splitNumber(value)
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* @param {number} precision A positive integer
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* @return {SplitValue}
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* Returns an object containing sign, coefficients, and exponent
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* with rounded digits
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*/
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export function roundDigits(split, precision) {
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// create a clone
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var rounded = {
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sign: split.sign,
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coefficients: split.coefficients,
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exponent: split.exponent
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};
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var c = rounded.coefficients; // prepend zeros if needed
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while (precision <= 0) {
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c.unshift(0);
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rounded.exponent++;
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precision++;
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}
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if (c.length > precision) {
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var removed = c.splice(precision, c.length - precision);
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if (removed[0] >= 5) {
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var i = precision - 1;
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c[i]++;
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|
|
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} x First value to compare
|
|
* @param {number} y Second value to compare
|
|
* @param {number} [epsilon] The maximum relative difference between x and y
|
|
* If epsilon is undefined or null, the function will
|
|
* test whether x and y are exactly equal.
|
|
* @return {boolean} whether the two numbers are nearly equal
|
|
*/
|
|
|
|
export function nearlyEqual(x, y, epsilon) {
|
|
// if epsilon is null or undefined, test whether x and y are exactly equal
|
|
if (epsilon === null || epsilon === undefined) {
|
|
return x === y;
|
|
}
|
|
|
|
if (x === y) {
|
|
return true;
|
|
} // NaN
|
|
|
|
|
|
if (isNaN(x) || isNaN(y)) {
|
|
return false;
|
|
} // at this point x and y should be finite
|
|
|
|
|
|
if (isFinite(x) && isFinite(y)) {
|
|
// check numbers are very close, needed when comparing numbers near zero
|
|
var diff = Math.abs(x - y);
|
|
|
|
if (diff < DBL_EPSILON) {
|
|
return true;
|
|
} else {
|
|
// use relative error
|
|
return diff <= Math.max(Math.abs(x), Math.abs(y)) * epsilon;
|
|
}
|
|
} // Infinite and Number or negative Infinite and positive Infinite cases
|
|
|
|
|
|
return false;
|
|
}
|
|
/**
|
|
* 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);
|
|
}; |