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