mirror of
https://github.com/josdejong/mathjs.git
synced 2026-01-18 14:59:29 +00:00
262 lines
8.7 KiB
JavaScript
262 lines
8.7 KiB
JavaScript
'use strict';
|
|
|
|
var NumberFormatter = require('./NumberFormatter');
|
|
|
|
/**
|
|
* Test whether value is a number
|
|
* @param {*} value
|
|
* @return {boolean} isNumber
|
|
*/
|
|
exports.isNumber = function(value) {
|
|
return typeof value === 'number';
|
|
};
|
|
|
|
/**
|
|
* Check if a number is integer
|
|
* @param {number | boolean} value
|
|
* @return {boolean} isInteger
|
|
*/
|
|
exports.isInteger = function(value) {
|
|
return isFinite(value)
|
|
? (value == Math.round(value))
|
|
: false;
|
|
// Note: we use ==, not ===, as we can have Booleans as well
|
|
};
|
|
|
|
/**
|
|
* Calculate the sign of a number
|
|
* @param {number} x
|
|
* @returns {*}
|
|
*/
|
|
exports.sign = function(x) {
|
|
if (x > 0) {
|
|
return 1;
|
|
}
|
|
else if (x < 0) {
|
|
return -1;
|
|
}
|
|
else {
|
|
return 0;
|
|
}
|
|
};
|
|
|
|
/**
|
|
* Convert a number to a formatted string representation.
|
|
*
|
|
* Syntax:
|
|
*
|
|
* format(value)
|
|
* format(value, options)
|
|
* format(value, precision)
|
|
* format(value, fn)
|
|
*
|
|
* Where:
|
|
*
|
|
* {number} value The value to be formatted
|
|
* {Object} options An object with formatting options. Available options:
|
|
* {string} notation
|
|
* Number notation. Choose from:
|
|
* 'fixed' Always use regular number notation.
|
|
* For example '123.40' and '14000000'
|
|
* 'exponential' Always use exponential notation.
|
|
* For example '1.234e+2' and '1.4e+7'
|
|
* 'auto' (default) Regular number notation for numbers
|
|
* having an absolute value between
|
|
* `lower` and `upper` bounds, and uses
|
|
* exponential notation elsewhere.
|
|
* Lower bound is included, upper bound
|
|
* is excluded.
|
|
* For example '123.4' and '1.4e7'.
|
|
* {number} precision A number between 0 and 16 to round
|
|
* the digits of the number.
|
|
* In case of notations 'exponential' and
|
|
* 'auto', `precision` defines the total
|
|
* number of significant digits returned
|
|
* and is undefined by default.
|
|
* In case of notation 'fixed',
|
|
* `precision` defines the number of
|
|
* significant digits after the decimal
|
|
* point, and is 0 by default.
|
|
* {Object} exponential An object containing two parameters,
|
|
* {number} lower and {number} upper,
|
|
* used by notation 'auto' to determine
|
|
* when to return exponential notation.
|
|
* Default values are `lower=1e-3` and
|
|
* `upper=1e5`.
|
|
* Only applicable for notation `auto`.
|
|
* {Function} fn A custom formatting function. Can be used to override the
|
|
* built-in notations. Function `fn` is called with `value` as
|
|
* parameter and must return a string. Is useful for example to
|
|
* format all values inside a matrix in a particular way.
|
|
*
|
|
* Examples:
|
|
*
|
|
* format(6.4); // '6.4'
|
|
* format(1240000); // '1.24e6'
|
|
* format(1/3); // '0.3333333333333333'
|
|
* format(1/3, 3); // '0.333'
|
|
* format(21385, 2); // '21000'
|
|
* format(12.071, {notation: 'fixed'}); // '12'
|
|
* format(2.3, {notation: 'fixed', precision: 2}); // '2.30'
|
|
* format(52.8, {notation: 'exponential'}); // '5.28e+1'
|
|
*
|
|
* @param {number} value
|
|
* @param {Object | Function | number} [options]
|
|
* @return {string} str The formatted value
|
|
*/
|
|
exports.format = function(value, options) {
|
|
if (typeof options === 'function') {
|
|
// handle format(value, fn)
|
|
return options(value);
|
|
}
|
|
|
|
// handle special cases
|
|
if (value === Infinity) {
|
|
return 'Infinity';
|
|
}
|
|
else if (value === -Infinity) {
|
|
return '-Infinity';
|
|
}
|
|
else if (isNaN(value)) {
|
|
return 'NaN';
|
|
}
|
|
|
|
// default values for options
|
|
var notation = 'auto';
|
|
var precision = undefined;
|
|
|
|
if (options) {
|
|
// determine notation from options
|
|
if (options.notation) {
|
|
notation = options.notation;
|
|
}
|
|
|
|
// determine precision from options
|
|
if (exports.isNumber(options)) {
|
|
precision = options;
|
|
}
|
|
else if (options.precision) {
|
|
precision = options.precision;
|
|
}
|
|
}
|
|
|
|
// handle the various notations
|
|
switch (notation) {
|
|
case 'fixed':
|
|
return exports.toFixed(value, precision);
|
|
|
|
case 'exponential':
|
|
return exports.toExponential(value, precision);
|
|
|
|
case 'auto':
|
|
return exports
|
|
.toPrecision(value, precision, options && options.exponential)
|
|
|
|
// remove trailing zeros after the decimal point
|
|
.replace(/((\.\d*?)(0+))($|e)/, function () {
|
|
var digits = arguments[2];
|
|
var e = arguments[4];
|
|
return (digits !== '.') ? digits + e : e;
|
|
});
|
|
|
|
default:
|
|
throw new Error('Unknown notation "' + notation + '". ' +
|
|
'Choose "auto", "exponential", or "fixed".');
|
|
}
|
|
};
|
|
|
|
/**
|
|
* Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'
|
|
* @param {number} value
|
|
* @param {number} [precision] Number of digits in formatted output.
|
|
* If not provided, the maximum available digits
|
|
* is used.
|
|
* @returns {string} str
|
|
*/
|
|
exports.toExponential = function(value, precision) {
|
|
return new NumberFormatter(value).toExponential(precision);
|
|
};
|
|
|
|
/**
|
|
* Format a number with fixed notation.
|
|
* @param {number} value
|
|
* @param {number} [precision=0] Optional number of decimals after the
|
|
* decimal point. Zero by default.
|
|
*/
|
|
exports.toFixed = function(value, precision) {
|
|
return new NumberFormatter(value).toFixed(precision);
|
|
};
|
|
|
|
/**
|
|
* Format a number with a certain precision
|
|
* @param {number} value
|
|
* @param {number} [precision=undefined] Optional number of digits.
|
|
* @param {{lower: number, upper: number}} [options] By default:
|
|
* lower = 1e-3 (excl)
|
|
* upper = 1e+5 (incl)
|
|
* @return {string}
|
|
*/
|
|
exports.toPrecision = function(value, precision, options) {
|
|
return new NumberFormatter(value).toPrecision(precision, options);
|
|
};
|
|
|
|
/**
|
|
* Count the number of significant digits of a number.
|
|
*
|
|
* For example:
|
|
* 2.34 returns 3
|
|
* 0.0034 returns 2
|
|
* 120.5e+30 returns 4
|
|
*
|
|
* @param {number} value
|
|
* @return {number} digits Number of significant digits
|
|
*/
|
|
exports.digits = function(value) {
|
|
return value
|
|
.toExponential()
|
|
.replace(/e.*$/, '') // 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
|
|
*/
|
|
exports.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 equal
|
|
*/
|
|
exports.nearlyEqual = function(x, y, epsilon) {
|
|
// if epsilon is null or undefined, test whether x and y are exactly equal
|
|
if (epsilon == null) return x == y;
|
|
|
|
// use "==" operator, handles infinities
|
|
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 < exports.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;
|
|
};
|