simple-squiggle

number.js (20473B)

---

 import { isNumber } from './is.js';
 /**
  * @typedef {{sign: '+' | '-' | '', coefficients: number[], exponent: number}} SplitValue
  */
 
 /**
  * Check if a number is integer
  * @param {number | boolean} value
  * @return {boolean} isInteger
  */
 
 export function isInteger(value) {
   if (typeof value === 'boolean') {
     return true;
   }
 
   return isFinite(value) ? value === Math.round(value) : false;
 }
 /**
  * Calculate the sign of a number
  * @param {number} x
  * @returns {number}
  */
 
 export var sign = /* #__PURE__ */Math.sign || function (x) {
   if (x > 0) {
     return 1;
   } else if (x < 0) {
     return -1;
   } else {
     return 0;
   }
 };
 /**
  * Calculate the base-2 logarithm of a number
  * @param {number} x
  * @returns {number}
  */
 
 export var log2 = /* #__PURE__ */Math.log2 || function log2(x) {
   return Math.log(x) / Math.LN2;
 };
 /**
  * Calculate the base-10 logarithm of a number
  * @param {number} x
  * @returns {number}
  */
 
 export var log10 = /* #__PURE__ */Math.log10 || function log10(x) {
   return Math.log(x) / Math.LN10;
 };
 /**
  * Calculate the natural logarithm of a number + 1
  * @param {number} x
  * @returns {number}
  */
 
 export var log1p = /* #__PURE__ */Math.log1p || function (x) {
   return Math.log(x + 1);
 };
 /**
  * Calculate cubic root for a number
  *
  * Code from es6-shim.js:
  *   https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1564-L1577
  *
  * @param {number} x
  * @returns {number} Returns the cubic root of x
  */
 
 export var cbrt = /* #__PURE__ */Math.cbrt || function cbrt(x) {
   if (x === 0) {
     return x;
   }
 
   var negate = x < 0;
   var result;
 
   if (negate) {
     x = -x;
   }
 
   if (isFinite(x)) {
     result = Math.exp(Math.log(x) / 3); // from https://en.wikipedia.org/wiki/Cube_root#Numerical_methods
 
     result = (x / (result * result) + 2 * result) / 3;
   } else {
     result = x;
   }
 
   return negate ? -result : result;
 };
 /**
  * Calculates exponentiation minus 1
  * @param {number} x
  * @return {number} res
  */
 
 export var expm1 = /* #__PURE__ */Math.expm1 || function expm1(x) {
   return x >= 2e-4 || x <= -2e-4 ? Math.exp(x) - 1 : x + x * x / 2 + x * x * x / 6;
 };
 /**
  * Formats a number in a given base
  * @param {number} n
  * @param {number} base
  * @param {number} size
  * @returns {string}
  */
 
 function formatNumberToBase(n, base, size) {
   var prefixes = {
     2: '0b',
     8: '0o',
     16: '0x'
   };
   var prefix = prefixes[base];
   var suffix = '';
 
   if (size) {
     if (size < 1) {
       throw new Error('size must be in greater than 0');
     }
 
     if (!isInteger(size)) {
       throw new Error('size must be an integer');
     }
 
     if (n > 2 ** (size - 1) - 1 || n < -(2 ** (size - 1))) {
       throw new Error("Value must be in range [-2^".concat(size - 1, ", 2^").concat(size - 1, "-1]"));
     }
 
     if (!isInteger(n)) {
       throw new Error('Value must be an integer');
     }
 
     if (n < 0) {
       n = n + 2 ** size;
     }
 
     suffix = "i".concat(size);
   }
 
   var sign = '';
 
   if (n < 0) {
     n = -n;
     sign = '-';
   }
 
   return "".concat(sign).concat(prefix).concat(n.toString(base)).concat(suffix);
 }
 /**
  * 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'
  *                         'engineering'    Always use engineering notation.
  *                                          For example '123.4e+0' and '14.0e+6'
  *                         'auto' (default) Regular number notation for numbers
  *                                          having an absolute value between
  *                                          `lowerExp` and `upperExp` bounds, and
  *                                          uses exponential notation elsewhere.
  *                                          Lower bound is included, upper bound
  *                                          is excluded.
  *                                          For example '123.4' and '1.4e7'.
  *                         'bin', 'oct, or
  *                         'hex'            Format the number using binary, octal,
  *                                          or hexadecimal notation.
  *                                          For example '0b1101' and '0x10fe'.
  *                     {number} wordSize    The word size in bits to use for formatting
  *                                          in binary, octal, or hexadecimal notation.
  *                                          To be used only with 'bin', 'oct', or 'hex'
  *                                          values for 'notation' option. When this option
  *                                          is defined the value is formatted as a signed
  *                                          twos complement integer of the given word size
  *                                          and the size suffix is appended to the output.
  *                                          For example
  *                                          format(-1, {notation: 'hex', wordSize: 8}) === '0xffi8'.
  *                                          Default value is undefined.
  *                     {number} precision   A number between 0 and 16 to round
  *                                          the digits of the number.
  *                                          In case of notations 'exponential',
  *                                          'engineering', and 'auto',
  *                                          `precision` defines the total
  *                                          number of significant digits returned.
  *                                          In case of notation 'fixed',
  *                                          `precision` defines the number of
  *                                          significant digits after the decimal
  *                                          point.
  *                                          `precision` is undefined by default,
  *                                          not rounding any digits.
  *                     {number} lowerExp    Exponent determining the lower boundary
  *                                          for formatting a value with an exponent
  *                                          when `notation='auto`.
  *                                          Default value is `-3`.
  *                     {number} upperExp    Exponent determining the upper boundary
  *                                          for formatting a value with an exponent
  *                                          when `notation='auto`.
  *                                          Default value is `5`.
  *    {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'
  *    format(12345678, {notation: 'engineering'})        // '12.345678e+6'
  *
  * @param {number} value
  * @param {Object | Function | number} [options]
  * @return {string} str The formatted value
  */
 
 
 export function format(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;
   var wordSize;
 
   if (options) {
     // determine notation from options
     if (options.notation) {
       notation = options.notation;
     } // determine precision from options
 
 
     if (isNumber(options)) {
       precision = options;
     } else if (isNumber(options.precision)) {
       precision = options.precision;
     }
 
     if (options.wordSize) {
       wordSize = options.wordSize;
 
       if (typeof wordSize !== 'number') {
         throw new Error('Option "wordSize" must be a number');
       }
     }
   } // handle the various notations
 
 
   switch (notation) {
     case 'fixed':
       return toFixed(value, precision);
 
     case 'exponential':
       return toExponential(value, precision);
 
     case 'engineering':
       return toEngineering(value, precision);
 
     case 'bin':
       return formatNumberToBase(value, 2, wordSize);
 
     case 'oct':
       return formatNumberToBase(value, 8, wordSize);
 
     case 'hex':
       return formatNumberToBase(value, 16, wordSize);
 
     case 'auto':
       // remove trailing zeros after the decimal point
       return toPrecision(value, precision, options && options).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", "fixed", "bin", "oct", or "hex.');
   }
 }
 /**
  * Split a number into sign, coefficients, and exponent
  * @param {number | string} value
  * @return {SplitValue}
  *              Returns an object containing sign, coefficients, and exponent
  */
 
 export function splitNumber(value) {
   // parse the input value
   var match = String(value).toLowerCase().match(/^(-?)(\d+\.?\d*)(e([+-]?\d+))?$/);
 
   if (!match) {
     throw new SyntaxError('Invalid number ' + value);
   }
 
   var sign = match[1];
   var digits = match[2];
   var exponent = parseFloat(match[4] || '0');
   var dot = digits.indexOf('.');
   exponent += dot !== -1 ? dot - 1 : digits.length - 1;
   var coefficients = digits.replace('.', '') // remove the dot (must be removed before removing leading zeros)
   .replace(/^0*/, function (zeros) {
     // remove leading zeros, add their count to the exponent
     exponent -= zeros.length;
     return '';
   }).replace(/0*$/, '') // remove trailing zeros
   .split('').map(function (d) {
     return parseInt(d);
   });
 
   if (coefficients.length === 0) {
     coefficients.push(0);
     exponent++;
   }
 
   return {
     sign: sign,
     coefficients: coefficients,
     exponent: exponent
   };
 }
 /**
  * Format a number in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'
  * @param {number | string} value
  * @param {number} [precision]        Optional number of significant figures to return.
  */
 
 export function toEngineering(value, precision) {
   if (isNaN(value) || !isFinite(value)) {
     return String(value);
   }
 
   var split = splitNumber(value);
   var rounded = roundDigits(split, precision);
   var e = rounded.exponent;
   var c = rounded.coefficients; // find nearest lower multiple of 3 for exponent
 
   var newExp = e % 3 === 0 ? e : e < 0 ? e - 3 - e % 3 : e - e % 3;
 
   if (isNumber(precision)) {
     // add zeroes to give correct sig figs
     while (precision > c.length || e - newExp + 1 > c.length) {
       c.push(0);
     }
   } else {
     // concatenate coefficients with necessary zeros
     // add zeros if necessary (for example: 1e+8 -> 100e+6)
     var missingZeros = Math.abs(e - newExp) - (c.length - 1);
 
     for (var i = 0; i < missingZeros; i++) {
       c.push(0);
     }
   } // find difference in exponents
 
 
   var expDiff = Math.abs(e - newExp);
   var decimalIdx = 1; // push decimal index over by expDiff times
 
   while (expDiff > 0) {
     decimalIdx++;
     expDiff--;
   } // if all coefficient values are zero after the decimal point and precision is unset, don't add a decimal value.
   // otherwise concat with the rest of the coefficients
 
 
   var decimals = c.slice(decimalIdx).join('');
   var decimalVal = isNumber(precision) && decimals.length || decimals.match(/[1-9]/) ? '.' + decimals : '';
   var str = c.slice(0, decimalIdx).join('') + decimalVal + 'e' + (e >= 0 ? '+' : '') + newExp.toString();
   return rounded.sign + str;
 }
 /**
  * Format a number with fixed notation.
  * @param {number | string} value
  * @param {number} [precision=undefined]  Optional number of decimals after the
  *                                        decimal point. null by default.
  */
 
 export function toFixed(value, precision) {
   if (isNaN(value) || !isFinite(value)) {
     return String(value);
   }
 
   var splitValue = splitNumber(value);
   var rounded = typeof precision === 'number' ? roundDigits(splitValue, splitValue.exponent + 1 + precision) : splitValue;
   var c = rounded.coefficients;
   var p = rounded.exponent + 1; // exponent may have changed
   // append zeros if needed
 
   var pp = p + (precision || 0);
 
   if (c.length < pp) {
     c = c.concat(zeros(pp - c.length));
   } // prepend zeros if needed
 
 
   if (p < 0) {
     c = zeros(-p + 1).concat(c);
     p = 1;
   } // insert a dot if needed
 
 
   if (p < c.length) {
     c.splice(p, 0, p === 0 ? '0.' : '.');
   }
 
   return rounded.sign + c.join('');
 }
 /**
  * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'
  * @param {number | string} value
  * @param {number} [precision]  Number of digits in formatted output.
  *                              If not provided, the maximum available digits
  *                              is used.
  */
 
 export function toExponential(value, precision) {
   if (isNaN(value) || !isFinite(value)) {
     return String(value);
   } // round if needed, else create a clone
 
 
   var split = splitNumber(value);
   var rounded = precision ? roundDigits(split, precision) : split;
   var c = rounded.coefficients;
   var e = rounded.exponent; // append zeros if needed
 
   if (c.length < precision) {
     c = c.concat(zeros(precision - c.length));
   } // format as `C.CCCe+EEE` or `C.CCCe-EEE`
 
 
   var first = c.shift();
   return rounded.sign + first + (c.length > 0 ? '.' + c.join('') : '') + 'e' + (e >= 0 ? '+' : '') + e;
 }
 /**
  * Format a number with a certain precision
  * @param {number | string} value
  * @param {number} [precision=undefined] Optional number of digits.
  * @param {{lowerExp: number | undefined, upperExp: number | undefined}} [options]
  *                                       By default:
  *                                         lowerExp = -3 (incl)
  *                                         upper = +5 (excl)
  * @return {string}
  */
 
 export function toPrecision(value, precision, options) {
   if (isNaN(value) || !isFinite(value)) {
     return String(value);
   } // determine lower and upper bound for exponential notation.
 
 
   var lowerExp = options && options.lowerExp !== undefined ? options.lowerExp : -3;
   var upperExp = options && options.upperExp !== undefined ? options.upperExp : 5;
   var split = splitNumber(value);
   var rounded = precision ? roundDigits(split, precision) : split;
 
   if (rounded.exponent < lowerExp || rounded.exponent >= upperExp) {
     // exponential notation
     return toExponential(value, precision);
   } else {
     var c = rounded.coefficients;
     var e = rounded.exponent; // append trailing zeros
 
     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} 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);
 };