1 | ;
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2 |
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3 | Object.defineProperty(exports, "__esModule", {
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4 | value: true
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5 | });
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6 | exports.isInteger = isInteger;
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7 | exports.format = format;
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8 | exports.splitNumber = splitNumber;
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9 | exports.toEngineering = toEngineering;
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10 | exports.toFixed = toFixed;
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11 | exports.toExponential = toExponential;
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12 | exports.toPrecision = toPrecision;
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13 | exports.roundDigits = roundDigits;
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14 | exports.digits = digits;
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15 | exports.nearlyEqual = nearlyEqual;
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16 | exports.tanh = exports.sinh = exports.cosh = exports.atanh = exports.asinh = exports.acosh = exports.DBL_EPSILON = exports.expm1 = exports.cbrt = exports.log1p = exports.log10 = exports.log2 = exports.sign = void 0;
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17 |
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18 | var _is = require("./is");
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19 |
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20 | /**
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21 | * @typedef {{sign: '+' | '-' | '', coefficients: number[], exponent: number}} SplitValue
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22 | */
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23 |
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24 | /**
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25 | * Check if a number is integer
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26 | * @param {number | boolean} value
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27 | * @return {boolean} isInteger
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28 | */
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29 | function isInteger(value) {
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30 | if (typeof value === 'boolean') {
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31 | return true;
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32 | }
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33 |
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34 | return isFinite(value) ? value === Math.round(value) : false; // Note: we use ==, not ===, as we can have Booleans as well
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35 | }
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36 | /**
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37 | * Calculate the sign of a number
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38 | * @param {number} x
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39 | * @returns {number}
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40 | */
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41 |
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42 |
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43 | var sign = /* #__PURE__ */Math.sign || function (x) {
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44 | if (x > 0) {
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45 | return 1;
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46 | } else if (x < 0) {
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47 | return -1;
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48 | } else {
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49 | return 0;
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50 | }
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51 | };
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52 | /**
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53 | * Calculate the base-2 logarithm of a number
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54 | * @param {number} x
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55 | * @returns {number}
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56 | */
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57 |
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58 |
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59 | exports.sign = sign;
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60 |
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61 | var log2 = /* #__PURE__ */Math.log2 || function log2(x) {
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62 | return Math.log(x) / Math.LN2;
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63 | };
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64 | /**
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65 | * Calculate the base-10 logarithm of a number
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66 | * @param {number} x
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67 | * @returns {number}
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68 | */
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69 |
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70 |
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71 | exports.log2 = log2;
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72 |
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73 | var log10 = /* #__PURE__ */Math.log10 || function log10(x) {
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74 | return Math.log(x) / Math.LN10;
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75 | };
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76 | /**
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77 | * Calculate the natural logarithm of a number + 1
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78 | * @param {number} x
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79 | * @returns {number}
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80 | */
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81 |
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82 |
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83 | exports.log10 = log10;
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84 |
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85 | var log1p = /* #__PURE__ */Math.log1p || function (x) {
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86 | return Math.log(x + 1);
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87 | };
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88 | /**
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89 | * Calculate cubic root for a number
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90 | *
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91 | * Code from es6-shim.js:
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92 | * https://github.com/paulmillr/es6-shim/blob/master/es6-shim.js#L1564-L1577
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93 | *
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94 | * @param {number} x
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95 | * @returns {number} Returns the cubic root of x
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96 | */
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97 |
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98 |
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99 | exports.log1p = log1p;
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100 |
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101 | var cbrt = /* #__PURE__ */Math.cbrt || function cbrt(x) {
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102 | if (x === 0) {
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103 | return x;
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104 | }
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105 |
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106 | var negate = x < 0;
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107 | var result;
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108 |
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109 | if (negate) {
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110 | x = -x;
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111 | }
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112 |
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113 | if (isFinite(x)) {
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114 | result = Math.exp(Math.log(x) / 3); // from https://en.wikipedia.org/wiki/Cube_root#Numerical_methods
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115 |
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116 | result = (x / (result * result) + 2 * result) / 3;
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117 | } else {
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118 | result = x;
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119 | }
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120 |
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121 | return negate ? -result : result;
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122 | };
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123 | /**
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124 | * Calculates exponentiation minus 1
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125 | * @param {number} x
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126 | * @return {number} res
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127 | */
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128 |
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129 |
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130 | exports.cbrt = cbrt;
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131 |
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132 | var expm1 = /* #__PURE__ */Math.expm1 || function expm1(x) {
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133 | return x >= 2e-4 || x <= -2e-4 ? Math.exp(x) - 1 : x + x * x / 2 + x * x * x / 6;
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134 | };
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135 | /**
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136 | * Convert a number to a formatted string representation.
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137 | *
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138 | * Syntax:
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139 | *
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140 | * format(value)
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141 | * format(value, options)
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142 | * format(value, precision)
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143 | * format(value, fn)
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144 | *
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145 | * Where:
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146 | *
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147 | * {number} value The value to be formatted
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148 | * {Object} options An object with formatting options. Available options:
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149 | * {string} notation
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150 | * Number notation. Choose from:
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151 | * 'fixed' Always use regular number notation.
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152 | * For example '123.40' and '14000000'
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153 | * 'exponential' Always use exponential notation.
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154 | * For example '1.234e+2' and '1.4e+7'
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155 | * 'engineering' Always use engineering notation.
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156 | * For example '123.4e+0' and '14.0e+6'
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157 | * 'auto' (default) Regular number notation for numbers
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158 | * having an absolute value between
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159 | * `lowerExp` and `upperExp` bounds, and
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160 | * uses exponential notation elsewhere.
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161 | * Lower bound is included, upper bound
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162 | * is excluded.
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163 | * For example '123.4' and '1.4e7'.
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164 | * {number} precision A number between 0 and 16 to round
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165 | * the digits of the number.
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166 | * In case of notations 'exponential',
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167 | * 'engineering', and 'auto',
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168 | * `precision` defines the total
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169 | * number of significant digits returned.
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170 | * In case of notation 'fixed',
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171 | * `precision` defines the number of
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172 | * significant digits after the decimal
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173 | * point.
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174 | * `precision` is undefined by default,
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175 | * not rounding any digits.
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176 | * {number} lowerExp Exponent determining the lower boundary
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177 | * for formatting a value with an exponent
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178 | * when `notation='auto`.
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179 | * Default value is `-3`.
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180 | * {number} upperExp Exponent determining the upper boundary
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181 | * for formatting a value with an exponent
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182 | * when `notation='auto`.
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183 | * Default value is `5`.
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184 | * {Function} fn A custom formatting function. Can be used to override the
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185 | * built-in notations. Function `fn` is called with `value` as
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186 | * parameter and must return a string. Is useful for example to
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187 | * format all values inside a matrix in a particular way.
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188 | *
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189 | * Examples:
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190 | *
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191 | * format(6.4) // '6.4'
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192 | * format(1240000) // '1.24e6'
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193 | * format(1/3) // '0.3333333333333333'
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194 | * format(1/3, 3) // '0.333'
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195 | * format(21385, 2) // '21000'
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196 | * format(12.071, {notation: 'fixed'}) // '12'
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197 | * format(2.3, {notation: 'fixed', precision: 2}) // '2.30'
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198 | * format(52.8, {notation: 'exponential'}) // '5.28e+1'
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199 | * format(12345678, {notation: 'engineering'}) // '12.345678e+6'
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200 | *
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201 | * @param {number} value
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202 | * @param {Object | Function | number} [options]
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203 | * @return {string} str The formatted value
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204 | */
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205 |
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206 |
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207 | exports.expm1 = expm1;
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208 |
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209 | function format(value, options) {
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210 | if (typeof options === 'function') {
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211 | // handle format(value, fn)
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212 | return options(value);
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213 | } // handle special cases
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214 |
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215 |
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216 | if (value === Infinity) {
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217 | return 'Infinity';
|
218 | } else if (value === -Infinity) {
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219 | return '-Infinity';
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220 | } else if (isNaN(value)) {
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221 | return 'NaN';
|
222 | } // default values for options
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223 |
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224 |
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225 | var notation = 'auto';
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226 | var precision;
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227 |
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228 | if (options) {
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229 | // determine notation from options
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230 | if (options.notation) {
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231 | notation = options.notation;
|
232 | } // determine precision from options
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233 |
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234 |
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235 | if ((0, _is.isNumber)(options)) {
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236 | precision = options;
|
237 | } else if ((0, _is.isNumber)(options.precision)) {
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238 | precision = options.precision;
|
239 | }
|
240 | } // handle the various notations
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241 |
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242 |
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243 | switch (notation) {
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244 | case 'fixed':
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245 | return toFixed(value, precision);
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246 |
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247 | case 'exponential':
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248 | return toExponential(value, precision);
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249 |
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250 | case 'engineering':
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251 | return toEngineering(value, precision);
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252 |
|
253 | case 'auto':
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254 | // remove trailing zeros after the decimal point
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255 | return toPrecision(value, precision, options && options).replace(/((\.\d*?)(0+))($|e)/, function () {
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256 | var digits = arguments[2];
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257 | var e = arguments[4];
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258 | return digits !== '.' ? digits + e : e;
|
259 | });
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260 |
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261 | default:
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262 | throw new Error('Unknown notation "' + notation + '". ' + 'Choose "auto", "exponential", or "fixed".');
|
263 | }
|
264 | }
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265 | /**
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266 | * Split a number into sign, coefficients, and exponent
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267 | * @param {number | string} value
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268 | * @return {SplitValue}
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269 | * Returns an object containing sign, coefficients, and exponent
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270 | */
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271 |
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272 |
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273 | function splitNumber(value) {
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274 | // parse the input value
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275 | var match = String(value).toLowerCase().match(/^0*?(-?)(\d+\.?\d*)(e([+-]?\d+))?$/);
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276 |
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277 | if (!match) {
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278 | throw new SyntaxError('Invalid number ' + value);
|
279 | }
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280 |
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281 | var sign = match[1];
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282 | var digits = match[2];
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283 | var exponent = parseFloat(match[4] || '0');
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284 | var dot = digits.indexOf('.');
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285 | exponent += dot !== -1 ? dot - 1 : digits.length - 1;
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286 | var coefficients = digits.replace('.', '') // remove the dot (must be removed before removing leading zeros)
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287 | .replace(/^0*/, function (zeros) {
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288 | // remove leading zeros, add their count to the exponent
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289 | exponent -= zeros.length;
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290 | return '';
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291 | }).replace(/0*$/, '') // remove trailing zeros
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292 | .split('').map(function (d) {
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293 | return parseInt(d);
|
294 | });
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295 |
|
296 | if (coefficients.length === 0) {
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297 | coefficients.push(0);
|
298 | exponent++;
|
299 | }
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300 |
|
301 | return {
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302 | sign: sign,
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303 | coefficients: coefficients,
|
304 | exponent: exponent
|
305 | };
|
306 | }
|
307 | /**
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308 | * Format a number in engineering notation. Like '1.23e+6', '2.3e+0', '3.500e-3'
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309 | * @param {number | string} value
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310 | * @param {number} [precision] Optional number of significant figures to return.
|
311 | */
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312 |
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313 |
|
314 | function toEngineering(value, precision) {
|
315 | if (isNaN(value) || !isFinite(value)) {
|
316 | return String(value);
|
317 | }
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318 |
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319 | var split = splitNumber(value);
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320 | var rounded = roundDigits(split, precision);
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321 | var e = rounded.exponent;
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322 | var c = rounded.coefficients; // find nearest lower multiple of 3 for exponent
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323 |
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324 | var newExp = e % 3 === 0 ? e : e < 0 ? e - 3 - e % 3 : e - e % 3;
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325 |
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326 | if ((0, _is.isNumber)(precision)) {
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327 | // add zeroes to give correct sig figs
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328 | while (precision > c.length || e - newExp + 1 > c.length) {
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329 | c.push(0);
|
330 | }
|
331 | } else {
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332 | // concatenate coefficients with necessary zeros
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333 | // add zeros if necessary (for example: 1e+8 -> 100e+6)
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334 | var missingZeros = Math.abs(e - newExp) - (c.length - 1);
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335 |
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336 | for (var i = 0; i < missingZeros; i++) {
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337 | c.push(0);
|
338 | }
|
339 | } // find difference in exponents
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340 |
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341 |
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342 | var expDiff = Math.abs(e - newExp);
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343 | var decimalIdx = 1; // push decimal index over by expDiff times
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344 |
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345 | while (expDiff > 0) {
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346 | decimalIdx++;
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347 | expDiff--;
|
348 | } // if all coefficient values are zero after the decimal point and precision is unset, don't add a decimal value.
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349 | // otherwise concat with the rest of the coefficients
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350 |
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351 |
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352 | var decimals = c.slice(decimalIdx).join('');
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353 | var decimalVal = (0, _is.isNumber)(precision) && decimals.length || decimals.match(/[1-9]/) ? '.' + decimals : '';
|
354 | var str = c.slice(0, decimalIdx).join('') + decimalVal + 'e' + (e >= 0 ? '+' : '') + newExp.toString();
|
355 | return rounded.sign + str;
|
356 | }
|
357 | /**
|
358 | * Format a number with fixed notation.
|
359 | * @param {number | string} value
|
360 | * @param {number} [precision=undefined] Optional number of decimals after the
|
361 | * decimal point. null by default.
|
362 | */
|
363 |
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364 |
|
365 | function toFixed(value, precision) {
|
366 | if (isNaN(value) || !isFinite(value)) {
|
367 | return String(value);
|
368 | }
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369 |
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370 | var splitValue = splitNumber(value);
|
371 | var rounded = typeof precision === 'number' ? roundDigits(splitValue, splitValue.exponent + 1 + precision) : splitValue;
|
372 | var c = rounded.coefficients;
|
373 | var p = rounded.exponent + 1; // exponent may have changed
|
374 | // append zeros if needed
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375 |
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376 | var pp = p + (precision || 0);
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377 |
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378 | if (c.length < pp) {
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379 | c = c.concat(zeros(pp - c.length));
|
380 | } // prepend zeros if needed
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381 |
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382 |
|
383 | if (p < 0) {
|
384 | c = zeros(-p + 1).concat(c);
|
385 | p = 1;
|
386 | } // insert a dot if needed
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387 |
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388 |
|
389 | if (p < c.length) {
|
390 | c.splice(p, 0, p === 0 ? '0.' : '.');
|
391 | }
|
392 |
|
393 | return rounded.sign + c.join('');
|
394 | }
|
395 | /**
|
396 | * Format a number in exponential notation. Like '1.23e+5', '2.3e+0', '3.500e-3'
|
397 | * @param {number | string} value
|
398 | * @param {number} [precision] Number of digits in formatted output.
|
399 | * If not provided, the maximum available digits
|
400 | * is used.
|
401 | */
|
402 |
|
403 |
|
404 | function toExponential(value, precision) {
|
405 | if (isNaN(value) || !isFinite(value)) {
|
406 | return String(value);
|
407 | } // round if needed, else create a clone
|
408 |
|
409 |
|
410 | var split = splitNumber(value);
|
411 | var rounded = precision ? roundDigits(split, precision) : split;
|
412 | var c = rounded.coefficients;
|
413 | var e = rounded.exponent; // append zeros if needed
|
414 |
|
415 | if (c.length < precision) {
|
416 | c = c.concat(zeros(precision - c.length));
|
417 | } // format as `C.CCCe+EEE` or `C.CCCe-EEE`
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418 |
|
419 |
|
420 | var first = c.shift();
|
421 | return rounded.sign + first + (c.length > 0 ? '.' + c.join('') : '') + 'e' + (e >= 0 ? '+' : '') + e;
|
422 | }
|
423 | /**
|
424 | * Format a number with a certain precision
|
425 | * @param {number | string} value
|
426 | * @param {number} [precision=undefined] Optional number of digits.
|
427 | * @param {{lowerExp: number | undefined, upperExp: number | undefined}} [options]
|
428 | * By default:
|
429 | * lowerExp = -3 (incl)
|
430 | * upper = +5 (excl)
|
431 | * @return {string}
|
432 | */
|
433 |
|
434 |
|
435 | function toPrecision(value, precision, options) {
|
436 | if (isNaN(value) || !isFinite(value)) {
|
437 | return String(value);
|
438 | } // determine lower and upper bound for exponential notation.
|
439 |
|
440 |
|
441 | var lowerExp = options && options.lowerExp !== undefined ? options.lowerExp : -3;
|
442 | var upperExp = options && options.upperExp !== undefined ? options.upperExp : 5;
|
443 | var split = splitNumber(value);
|
444 | var rounded = precision ? roundDigits(split, precision) : split;
|
445 |
|
446 | if (rounded.exponent < lowerExp || rounded.exponent >= upperExp) {
|
447 | // exponential notation
|
448 | return toExponential(value, precision);
|
449 | } else {
|
450 | var c = rounded.coefficients;
|
451 | var e = rounded.exponent; // append trailing zeros
|
452 |
|
453 | if (c.length < precision) {
|
454 | c = c.concat(zeros(precision - c.length));
|
455 | } // append trailing zeros
|
456 | // TODO: simplify the next statement
|
457 |
|
458 |
|
459 | c = c.concat(zeros(e - c.length + 1 + (c.length < precision ? precision - c.length : 0))); // prepend zeros
|
460 |
|
461 | c = zeros(-e).concat(c);
|
462 | var dot = e > 0 ? e : 0;
|
463 |
|
464 | if (dot < c.length - 1) {
|
465 | c.splice(dot + 1, 0, '.');
|
466 | }
|
467 |
|
468 | return rounded.sign + c.join('');
|
469 | }
|
470 | }
|
471 | /**
|
472 | * Round the number of digits of a number *
|
473 | * @param {SplitValue} split A value split with .splitNumber(value)
|
474 | * @param {number} precision A positive integer
|
475 | * @return {SplitValue}
|
476 | * Returns an object containing sign, coefficients, and exponent
|
477 | * with rounded digits
|
478 | */
|
479 |
|
480 |
|
481 | function roundDigits(split, precision) {
|
482 | // create a clone
|
483 | var rounded = {
|
484 | sign: split.sign,
|
485 | coefficients: split.coefficients,
|
486 | exponent: split.exponent
|
487 | };
|
488 | var c = rounded.coefficients; // prepend zeros if needed
|
489 |
|
490 | while (precision <= 0) {
|
491 | c.unshift(0);
|
492 | rounded.exponent++;
|
493 | precision++;
|
494 | }
|
495 |
|
496 | if (c.length > precision) {
|
497 | var removed = c.splice(precision, c.length - precision);
|
498 |
|
499 | if (removed[0] >= 5) {
|
500 | var i = precision - 1;
|
501 | c[i]++;
|
502 |
|
503 | while (c[i] === 10) {
|
504 | c.pop();
|
505 |
|
506 | if (i === 0) {
|
507 | c.unshift(0);
|
508 | rounded.exponent++;
|
509 | i++;
|
510 | }
|
511 |
|
512 | i--;
|
513 | c[i]++;
|
514 | }
|
515 | }
|
516 | }
|
517 |
|
518 | return rounded;
|
519 | }
|
520 | /**
|
521 | * Create an array filled with zeros.
|
522 | * @param {number} length
|
523 | * @return {Array}
|
524 | */
|
525 |
|
526 |
|
527 | function zeros(length) {
|
528 | var arr = [];
|
529 |
|
530 | for (var i = 0; i < length; i++) {
|
531 | arr.push(0);
|
532 | }
|
533 |
|
534 | return arr;
|
535 | }
|
536 | /**
|
537 | * Count the number of significant digits of a number.
|
538 | *
|
539 | * For example:
|
540 | * 2.34 returns 3
|
541 | * 0.0034 returns 2
|
542 | * 120.5e+30 returns 4
|
543 | *
|
544 | * @param {number} value
|
545 | * @return {number} digits Number of significant digits
|
546 | */
|
547 |
|
548 |
|
549 | function digits(value) {
|
550 | return value.toExponential().replace(/e.*$/, '') // remove exponential notation
|
551 | .replace(/^0\.?0*|\./, '') // remove decimal point and leading zeros
|
552 | .length;
|
553 | }
|
554 | /**
|
555 | * Minimum number added to one that makes the result different than one
|
556 | */
|
557 |
|
558 |
|
559 | var DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16;
|
560 | /**
|
561 | * Compares two floating point numbers.
|
562 | * @param {number} x First value to compare
|
563 | * @param {number} y Second value to compare
|
564 | * @param {number} [epsilon] The maximum relative difference between x and y
|
565 | * If epsilon is undefined or null, the function will
|
566 | * test whether x and y are exactly equal.
|
567 | * @return {boolean} whether the two numbers are nearly equal
|
568 | */
|
569 |
|
570 | exports.DBL_EPSILON = DBL_EPSILON;
|
571 |
|
572 | function nearlyEqual(x, y, epsilon) {
|
573 | // if epsilon is null or undefined, test whether x and y are exactly equal
|
574 | if (epsilon === null || epsilon === undefined) {
|
575 | return x === y;
|
576 | }
|
577 |
|
578 | if (x === y) {
|
579 | return true;
|
580 | } // NaN
|
581 |
|
582 |
|
583 | if (isNaN(x) || isNaN(y)) {
|
584 | return false;
|
585 | } // at this point x and y should be finite
|
586 |
|
587 |
|
588 | if (isFinite(x) && isFinite(y)) {
|
589 | // check numbers are very close, needed when comparing numbers near zero
|
590 | var diff = Math.abs(x - y);
|
591 |
|
592 | if (diff < DBL_EPSILON) {
|
593 | return true;
|
594 | } else {
|
595 | // use relative error
|
596 | return diff <= Math.max(Math.abs(x), Math.abs(y)) * epsilon;
|
597 | }
|
598 | } // Infinite and Number or negative Infinite and positive Infinite cases
|
599 |
|
600 |
|
601 | return false;
|
602 | }
|
603 | /**
|
604 | * Calculate the hyperbolic arccos of a number
|
605 | * @param {number} x
|
606 | * @return {number}
|
607 | */
|
608 |
|
609 |
|
610 | var acosh = Math.acosh || function (x) {
|
611 | return Math.log(Math.sqrt(x * x - 1) + x);
|
612 | };
|
613 |
|
614 | exports.acosh = acosh;
|
615 |
|
616 | var asinh = Math.asinh || function (x) {
|
617 | return Math.log(Math.sqrt(x * x + 1) + x);
|
618 | };
|
619 | /**
|
620 | * Calculate the hyperbolic arctangent of a number
|
621 | * @param {number} x
|
622 | * @return {number}
|
623 | */
|
624 |
|
625 |
|
626 | exports.asinh = asinh;
|
627 |
|
628 | var atanh = Math.atanh || function (x) {
|
629 | return Math.log((1 + x) / (1 - x)) / 2;
|
630 | };
|
631 | /**
|
632 | * Calculate the hyperbolic cosine of a number
|
633 | * @param {number} x
|
634 | * @returns {number}
|
635 | */
|
636 |
|
637 |
|
638 | exports.atanh = atanh;
|
639 |
|
640 | var cosh = Math.cosh || function (x) {
|
641 | return (Math.exp(x) + Math.exp(-x)) / 2;
|
642 | };
|
643 | /**
|
644 | * Calculate the hyperbolic sine of a number
|
645 | * @param {number} x
|
646 | * @returns {number}
|
647 | */
|
648 |
|
649 |
|
650 | exports.cosh = cosh;
|
651 |
|
652 | var sinh = Math.sinh || function (x) {
|
653 | return (Math.exp(x) - Math.exp(-x)) / 2;
|
654 | };
|
655 | /**
|
656 | * Calculate the hyperbolic tangent of a number
|
657 | * @param {number} x
|
658 | * @returns {number}
|
659 | */
|
660 |
|
661 |
|
662 | exports.sinh = sinh;
|
663 |
|
664 | var tanh = Math.tanh || function (x) {
|
665 | var e = Math.exp(2 * x);
|
666 | return (e - 1) / (e + 1);
|
667 | };
|
668 |
|
669 | exports.tanh = tanh; |
\ | No newline at end of file |