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<!DOCTYPE html><meta charset="UTF-8"><meta http-equiv="Content-Language" content="en" /><title>math.js</title><link href="../../../../dossier.css" rel="stylesheet" type="text/css"><div id="main-wrapper"><input type="checkbox" id="sidenav-toggle" /><main><header><h1>lib/goog/math/math.js</h1></header><pre><table class="srcfile"><tbody><tr><td><a name="l1" href="#l1">1</a><td>// Copyright 2006 The Closure Library Authors. All Rights Reserved.<tr><td><a name="l2" href="#l2">2</a><td>//<tr><td><a name="l3" href="#l3">3</a><td>// Licensed under the Apache License, Version 2.0 (the "License");<tr><td><a name="l4" href="#l4">4</a><td>// you may not use this file except in compliance with the License.<tr><td><a name="l5" href="#l5">5</a><td>// You may obtain a copy of the License at<tr><td><a name="l6" href="#l6">6</a><td>//<tr><td><a name="l7" href="#l7">7</a><td>// http://www.apache.org/licenses/LICENSE-2.0<tr><td><a name="l8" href="#l8">8</a><td>//<tr><td><a name="l9" href="#l9">9</a><td>// Unless required by applicable law or agreed to in writing, software<tr><td><a name="l10" href="#l10">10</a><td>// distributed under the License is distributed on an "AS-IS" BASIS,<tr><td><a name="l11" href="#l11">11</a><td>// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<tr><td><a name="l12" href="#l12">12</a><td>// See the License for the specific language governing permissions and<tr><td><a name="l13" href="#l13">13</a><td>// limitations under the License.<tr><td><a name="l14" href="#l14">14</a><td><tr><td><a name="l15" href="#l15">15</a><td>/**<tr><td><a name="l16" href="#l16">16</a><td> * @fileoverview Additional mathematical functions.<tr><td><a name="l17" href="#l17">17</a><td> */<tr><td><a name="l18" href="#l18">18</a><td><tr><td><a name="l19" href="#l19">19</a><td>goog.provide('goog.math');<tr><td><a name="l20" href="#l20">20</a><td><tr><td><a name="l21" href="#l21">21</a><td>goog.require('goog.array');<tr><td><a name="l22" href="#l22">22</a><td>goog.require('goog.asserts');<tr><td><a name="l23" href="#l23">23</a><td><tr><td><a name="l24" href="#l24">24</a><td><tr><td><a name="l25" href="#l25">25</a><td>/**<tr><td><a name="l26" href="#l26">26</a><td> * Returns a random integer greater than or equal to 0 and less than {@code a}.<tr><td><a name="l27" href="#l27">27</a><td> * @param {number} a The upper bound for the random integer (exclusive).<tr><td><a name="l28" href="#l28">28</a><td> * @return {number} A random integer N such that 0 <= N < a.<tr><td><a name="l29" href="#l29">29</a><td> */<tr><td><a name="l30" href="#l30">30</a><td>goog.math.randomInt = function(a) {<tr><td><a name="l31" href="#l31">31</a><td> return Math.floor(Math.random() * a);<tr><td><a name="l32" href="#l32">32</a><td>};<tr><td><a name="l33" href="#l33">33</a><td><tr><td><a name="l34" href="#l34">34</a><td><tr><td><a name="l35" href="#l35">35</a><td>/**<tr><td><a name="l36" href="#l36">36</a><td> * Returns a random number greater than or equal to {@code a} and less than<tr><td><a name="l37" href="#l37">37</a><td> * {@code b}.<tr><td><a name="l38" href="#l38">38</a><td> * @param {number} a The lower bound for the random number (inclusive).<tr><td><a name="l39" href="#l39">39</a><td> * @param {number} b The upper bound for the random number (exclusive).<tr><td><a name="l40" href="#l40">40</a><td> * @return {number} A random number N such that a <= N < b.<tr><td><a name="l41" href="#l41">41</a><td> */<tr><td><a name="l42" href="#l42">42</a><td>goog.math.uniformRandom = function(a, b) {<tr><td><a name="l43" href="#l43">43</a><td> return a + Math.random() * (b - a);<tr><td><a name="l44" href="#l44">44</a><td>};<tr><td><a name="l45" href="#l45">45</a><td><tr><td><a name="l46" href="#l46">46</a><td><tr><td><a name="l47" href="#l47">47</a><td>/**<tr><td><a name="l48" href="#l48">48</a><td> * Takes a number and clamps it to within the provided bounds.<tr><td><a name="l49" href="#l49">49</a><td> * @param {number} value The input number.<tr><td><a name="l50" href="#l50">50</a><td> * @param {number} min The minimum value to return.<tr><td><a name="l51" href="#l51">51</a><td> * @param {number} max The maximum value to return.<tr><td><a name="l52" href="#l52">52</a><td> * @return {number} The input number if it is within bounds, or the nearest<tr><td><a name="l53" href="#l53">53</a><td> * number within the bounds.<tr><td><a name="l54" href="#l54">54</a><td> */<tr><td><a name="l55" href="#l55">55</a><td>goog.math.clamp = function(value, min, max) {<tr><td><a name="l56" href="#l56">56</a><td> return Math.min(Math.max(value, min), max);<tr><td><a name="l57" href="#l57">57</a><td>};<tr><td><a name="l58" href="#l58">58</a><td><tr><td><a name="l59" href="#l59">59</a><td><tr><td><a name="l60" href="#l60">60</a><td>/**<tr><td><a name="l61" href="#l61">61</a><td> * The % operator in JavaScript returns the remainder of a / b, but differs from<tr><td><a name="l62" href="#l62">62</a><td> * some other languages in that the result will have the same sign as the<tr><td><a name="l63" href="#l63">63</a><td> * dividend. For example, -1 % 8 == -1, whereas in some other languages<tr><td><a name="l64" href="#l64">64</a><td> * (such as Python) the result would be 7. This function emulates the more<tr><td><a name="l65" href="#l65">65</a><td> * correct modulo behavior, which is useful for certain applications such as<tr><td><a name="l66" href="#l66">66</a><td> * calculating an offset index in a circular list.<tr><td><a name="l67" href="#l67">67</a><td> *<tr><td><a name="l68" href="#l68">68</a><td> * @param {number} a The dividend.<tr><td><a name="l69" href="#l69">69</a><td> * @param {number} b The divisor.<tr><td><a name="l70" href="#l70">70</a><td> * @return {number} a % b where the result is between 0 and b (either 0 <= x < b<tr><td><a name="l71" href="#l71">71</a><td> * or b < x <= 0, depending on the sign of b).<tr><td><a name="l72" href="#l72">72</a><td> */<tr><td><a name="l73" href="#l73">73</a><td>goog.math.modulo = function(a, b) {<tr><td><a name="l74" href="#l74">74</a><td> var r = a % b;<tr><td><a name="l75" href="#l75">75</a><td> // If r and b differ in sign, add b to wrap the result to the correct sign.<tr><td><a name="l76" href="#l76">76</a><td> return (r * b < 0) ? r + b : r;<tr><td><a name="l77" href="#l77">77</a><td>};<tr><td><a name="l78" href="#l78">78</a><td><tr><td><a name="l79" href="#l79">79</a><td><tr><td><a name="l80" href="#l80">80</a><td>/**<tr><td><a name="l81" href="#l81">81</a><td> * Performs linear interpolation between values a and b. Returns the value<tr><td><a name="l82" href="#l82">82</a><td> * between a and b proportional to x (when x is between 0 and 1. When x is<tr><td><a name="l83" href="#l83">83</a><td> * outside this range, the return value is a linear extrapolation).<tr><td><a name="l84" href="#l84">84</a><td> * @param {number} a A number.<tr><td><a name="l85" href="#l85">85</a><td> * @param {number} b A number.<tr><td><a name="l86" href="#l86">86</a><td> * @param {number} x The proportion between a and b.<tr><td><a name="l87" href="#l87">87</a><td> * @return {number} The interpolated value between a and b.<tr><td><a name="l88" href="#l88">88</a><td> */<tr><td><a name="l89" href="#l89">89</a><td>goog.math.lerp = function(a, b, x) {<tr><td><a name="l90" href="#l90">90</a><td> return a + x * (b - a);<tr><td><a name="l91" href="#l91">91</a><td>};<tr><td><a name="l92" href="#l92">92</a><td><tr><td><a name="l93" href="#l93">93</a><td><tr><td><a name="l94" href="#l94">94</a><td>/**<tr><td><a name="l95" href="#l95">95</a><td> * Tests whether the two values are equal to each other, within a certain<tr><td><a name="l96" href="#l96">96</a><td> * tolerance to adjust for floating point errors.<tr><td><a name="l97" href="#l97">97</a><td> * @param {number} a A number.<tr><td><a name="l98" href="#l98">98</a><td> * @param {number} b A number.<tr><td><a name="l99" href="#l99">99</a><td> * @param {number=} opt_tolerance Optional tolerance range. Defaults<tr><td><a name="l100" href="#l100">100</a><td> * to 0.000001. If specified, should be greater than 0.<tr><td><a name="l101" href="#l101">101</a><td> * @return {boolean} Whether {@code a} and {@code b} are nearly equal.<tr><td><a name="l102" href="#l102">102</a><td> */<tr><td><a name="l103" href="#l103">103</a><td>goog.math.nearlyEquals = function(a, b, opt_tolerance) {<tr><td><a name="l104" href="#l104">104</a><td> return Math.abs(a - b) <= (opt_tolerance || 0.000001);<tr><td><a name="l105" href="#l105">105</a><td>};<tr><td><a name="l106" href="#l106">106</a><td><tr><td><a name="l107" href="#l107">107</a><td><tr><td><a name="l108" href="#l108">108</a><td>// TODO(user): Rename to normalizeAngle, retaining old name as deprecated<tr><td><a name="l109" href="#l109">109</a><td>// alias.<tr><td><a name="l110" href="#l110">110</a><td>/**<tr><td><a name="l111" href="#l111">111</a><td> * Normalizes an angle to be in range [0-360). Angles outside this range will<tr><td><a name="l112" href="#l112">112</a><td> * be normalized to be the equivalent angle with that range.<tr><td><a name="l113" href="#l113">113</a><td> * @param {number} angle Angle in degrees.<tr><td><a name="l114" href="#l114">114</a><td> * @return {number} Standardized angle.<tr><td><a name="l115" href="#l115">115</a><td> */<tr><td><a name="l116" href="#l116">116</a><td>goog.math.standardAngle = function(angle) {<tr><td><a name="l117" href="#l117">117</a><td> return goog.math.modulo(angle, 360);<tr><td><a name="l118" href="#l118">118</a><td>};<tr><td><a name="l119" href="#l119">119</a><td><tr><td><a name="l120" href="#l120">120</a><td><tr><td><a name="l121" href="#l121">121</a><td>/**<tr><td><a name="l122" href="#l122">122</a><td> * Normalizes an angle to be in range [0-2*PI). Angles outside this range will<tr><td><a name="l123" href="#l123">123</a><td> * be normalized to be the equivalent angle with that range.<tr><td><a name="l124" href="#l124">124</a><td> * @param {number} angle Angle in radians.<tr><td><a name="l125" href="#l125">125</a><td> * @return {number} Standardized angle.<tr><td><a name="l126" href="#l126">126</a><td> */<tr><td><a name="l127" href="#l127">127</a><td>goog.math.standardAngleInRadians = function(angle) {<tr><td><a name="l128" href="#l128">128</a><td> return goog.math.modulo(angle, 2 * Math.PI);<tr><td><a name="l129" href="#l129">129</a><td>};<tr><td><a name="l130" href="#l130">130</a><td><tr><td><a name="l131" href="#l131">131</a><td><tr><td><a name="l132" href="#l132">132</a><td>/**<tr><td><a name="l133" href="#l133">133</a><td> * Converts degrees to radians.<tr><td><a name="l134" href="#l134">134</a><td> * @param {number} angleDegrees Angle in degrees.<tr><td><a name="l135" href="#l135">135</a><td> * @return {number} Angle in radians.<tr><td><a name="l136" href="#l136">136</a><td> */<tr><td><a name="l137" href="#l137">137</a><td>goog.math.toRadians = function(angleDegrees) {<tr><td><a name="l138" href="#l138">138</a><td> return angleDegrees * Math.PI / 180;<tr><td><a name="l139" href="#l139">139</a><td>};<tr><td><a name="l140" href="#l140">140</a><td><tr><td><a name="l141" href="#l141">141</a><td><tr><td><a name="l142" href="#l142">142</a><td>/**<tr><td><a name="l143" href="#l143">143</a><td> * Converts radians to degrees.<tr><td><a name="l144" href="#l144">144</a><td> * @param {number} angleRadians Angle in radians.<tr><td><a name="l145" href="#l145">145</a><td> * @return {number} Angle in degrees.<tr><td><a name="l146" href="#l146">146</a><td> */<tr><td><a name="l147" href="#l147">147</a><td>goog.math.toDegrees = function(angleRadians) {<tr><td><a name="l148" href="#l148">148</a><td> return angleRadians * 180 / Math.PI;<tr><td><a name="l149" href="#l149">149</a><td>};<tr><td><a name="l150" href="#l150">150</a><td><tr><td><a name="l151" href="#l151">151</a><td><tr><td><a name="l152" href="#l152">152</a><td>/**<tr><td><a name="l153" href="#l153">153</a><td> * For a given angle and radius, finds the X portion of the offset.<tr><td><a name="l154" href="#l154">154</a><td> * @param {number} degrees Angle in degrees (zero points in +X direction).<tr><td><a name="l155" href="#l155">155</a><td> * @param {number} radius Radius.<tr><td><a name="l156" href="#l156">156</a><td> * @return {number} The x-distance for the angle and radius.<tr><td><a name="l157" href="#l157">157</a><td> */<tr><td><a name="l158" href="#l158">158</a><td>goog.math.angleDx = function(degrees, radius) {<tr><td><a name="l159" href="#l159">159</a><td> return radius * Math.cos(goog.math.toRadians(degrees));<tr><td><a name="l160" href="#l160">160</a><td>};<tr><td><a name="l161" href="#l161">161</a><td><tr><td><a name="l162" href="#l162">162</a><td><tr><td><a name="l163" href="#l163">163</a><td>/**<tr><td><a name="l164" href="#l164">164</a><td> * For a given angle and radius, finds the Y portion of the offset.<tr><td><a name="l165" href="#l165">165</a><td> * @param {number} degrees Angle in degrees (zero points in +X direction).<tr><td><a name="l166" href="#l166">166</a><td> * @param {number} radius Radius.<tr><td><a name="l167" href="#l167">167</a><td> * @return {number} The y-distance for the angle and radius.<tr><td><a name="l168" href="#l168">168</a><td> */<tr><td><a name="l169" href="#l169">169</a><td>goog.math.angleDy = function(degrees, radius) {<tr><td><a name="l170" href="#l170">170</a><td> return radius * Math.sin(goog.math.toRadians(degrees));<tr><td><a name="l171" href="#l171">171</a><td>};<tr><td><a name="l172" href="#l172">172</a><td><tr><td><a name="l173" href="#l173">173</a><td><tr><td><a name="l174" href="#l174">174</a><td>/**<tr><td><a name="l175" href="#l175">175</a><td> * Computes the angle between two points (x1,y1) and (x2,y2).<tr><td><a name="l176" href="#l176">176</a><td> * Angle zero points in the +X direction, 90 degrees points in the +Y<tr><td><a name="l177" href="#l177">177</a><td> * direction (down) and from there we grow clockwise towards 360 degrees.<tr><td><a name="l178" href="#l178">178</a><td> * @param {number} x1 x of first point.<tr><td><a name="l179" href="#l179">179</a><td> * @param {number} y1 y of first point.<tr><td><a name="l180" href="#l180">180</a><td> * @param {number} x2 x of second point.<tr><td><a name="l181" href="#l181">181</a><td> * @param {number} y2 y of second point.<tr><td><a name="l182" href="#l182">182</a><td> * @return {number} Standardized angle in degrees of the vector from<tr><td><a name="l183" href="#l183">183</a><td> * x1,y1 to x2,y2.<tr><td><a name="l184" href="#l184">184</a><td> */<tr><td><a name="l185" href="#l185">185</a><td>goog.math.angle = function(x1, y1, x2, y2) {<tr><td><a name="l186" href="#l186">186</a><td> return goog.math.standardAngle(goog.math.toDegrees(Math.atan2(y2 - y1,<tr><td><a name="l187" href="#l187">187</a><td> x2 - x1)));<tr><td><a name="l188" href="#l188">188</a><td>};<tr><td><a name="l189" href="#l189">189</a><td><tr><td><a name="l190" href="#l190">190</a><td><tr><td><a name="l191" href="#l191">191</a><td>/**<tr><td><a name="l192" href="#l192">192</a><td> * Computes the difference between startAngle and endAngle (angles in degrees).<tr><td><a name="l193" href="#l193">193</a><td> * @param {number} startAngle Start angle in degrees.<tr><td><a name="l194" href="#l194">194</a><td> * @param {number} endAngle End angle in degrees.<tr><td><a name="l195" href="#l195">195</a><td> * @return {number} The number of degrees that when added to<tr><td><a name="l196" href="#l196">196</a><td> * startAngle will result in endAngle. Positive numbers mean that the<tr><td><a name="l197" href="#l197">197</a><td> * direction is clockwise. Negative numbers indicate a counter-clockwise<tr><td><a name="l198" href="#l198">198</a><td> * direction.<tr><td><a name="l199" href="#l199">199</a><td> * The shortest route (clockwise vs counter-clockwise) between the angles<tr><td><a name="l200" href="#l200">200</a><td> * is used.<tr><td><a name="l201" href="#l201">201</a><td> * When the difference is 180 degrees, the function returns 180 (not -180)<tr><td><a name="l202" href="#l202">202</a><td> * angleDifference(30, 40) is 10, and angleDifference(40, 30) is -10.<tr><td><a name="l203" href="#l203">203</a><td> * angleDifference(350, 10) is 20, and angleDifference(10, 350) is -20.<tr><td><a name="l204" href="#l204">204</a><td> */<tr><td><a name="l205" href="#l205">205</a><td>goog.math.angleDifference = function(startAngle, endAngle) {<tr><td><a name="l206" href="#l206">206</a><td> var d = goog.math.standardAngle(endAngle) -<tr><td><a name="l207" href="#l207">207</a><td> goog.math.standardAngle(startAngle);<tr><td><a name="l208" href="#l208">208</a><td> if (d > 180) {<tr><td><a name="l209" href="#l209">209</a><td> d = d - 360;<tr><td><a name="l210" href="#l210">210</a><td> } else if (d <= -180) {<tr><td><a name="l211" href="#l211">211</a><td> d = 360 + d;<tr><td><a name="l212" href="#l212">212</a><td> }<tr><td><a name="l213" href="#l213">213</a><td> return d;<tr><td><a name="l214" href="#l214">214</a><td>};<tr><td><a name="l215" href="#l215">215</a><td><tr><td><a name="l216" href="#l216">216</a><td><tr><td><a name="l217" href="#l217">217</a><td>/**<tr><td><a name="l218" href="#l218">218</a><td> * Returns the sign of a number as per the "sign" or "signum" function.<tr><td><a name="l219" href="#l219">219</a><td> * @param {number} x The number to take the sign of.<tr><td><a name="l220" href="#l220">220</a><td> * @return {number} -1 when negative, 1 when positive, 0 when 0.<tr><td><a name="l221" href="#l221">221</a><td> */<tr><td><a name="l222" href="#l222">222</a><td>goog.math.sign = function(x) {<tr><td><a name="l223" href="#l223">223</a><td> return x == 0 ? 0 : (x < 0 ? -1 : 1);<tr><td><a name="l224" href="#l224">224</a><td>};<tr><td><a name="l225" href="#l225">225</a><td><tr><td><a name="l226" href="#l226">226</a><td><tr><td><a name="l227" href="#l227">227</a><td>/**<tr><td><a name="l228" href="#l228">228</a><td> * JavaScript implementation of Longest Common Subsequence problem.<tr><td><a name="l229" href="#l229">229</a><td> * http://en.wikipedia.org/wiki/Longest_common_subsequence<tr><td><a name="l230" href="#l230">230</a><td> *<tr><td><a name="l231" href="#l231">231</a><td> * Returns the longest possible array that is subarray of both of given arrays.<tr><td><a name="l232" href="#l232">232</a><td> *<tr><td><a name="l233" href="#l233">233</a><td> * @param {Array.<Object>} array1 First array of objects.<tr><td><a name="l234" href="#l234">234</a><td> * @param {Array.<Object>} array2 Second array of objects.<tr><td><a name="l235" href="#l235">235</a><td> * @param {Function=} opt_compareFn Function that acts as a custom comparator<tr><td><a name="l236" href="#l236">236</a><td> * for the array ojects. Function should return true if objects are equal,<tr><td><a name="l237" href="#l237">237</a><td> * otherwise false.<tr><td><a name="l238" href="#l238">238</a><td> * @param {Function=} opt_collectorFn Function used to decide what to return<tr><td><a name="l239" href="#l239">239</a><td> * as a result subsequence. It accepts 2 arguments: index of common element<tr><td><a name="l240" href="#l240">240</a><td> * in the first array and index in the second. The default function returns<tr><td><a name="l241" href="#l241">241</a><td> * element from the first array.<tr><td><a name="l242" href="#l242">242</a><td> * @return {!Array.<Object>} A list of objects that are common to both arrays<tr><td><a name="l243" href="#l243">243</a><td> * such that there is no common subsequence with size greater than the<tr><td><a name="l244" href="#l244">244</a><td> * length of the list.<tr><td><a name="l245" href="#l245">245</a><td> */<tr><td><a name="l246" href="#l246">246</a><td>goog.math.longestCommonSubsequence = function(<tr><td><a name="l247" href="#l247">247</a><td> array1, array2, opt_compareFn, opt_collectorFn) {<tr><td><a name="l248" href="#l248">248</a><td><tr><td><a name="l249" href="#l249">249</a><td> var compare = opt_compareFn || function(a, b) {<tr><td><a name="l250" href="#l250">250</a><td> return a == b;<tr><td><a name="l251" href="#l251">251</a><td> };<tr><td><a name="l252" href="#l252">252</a><td><tr><td><a name="l253" href="#l253">253</a><td> var collect = opt_collectorFn || function(i1, i2) {<tr><td><a name="l254" href="#l254">254</a><td> return array1[i1];<tr><td><a name="l255" href="#l255">255</a><td> };<tr><td><a name="l256" href="#l256">256</a><td><tr><td><a name="l257" href="#l257">257</a><td> var length1 = array1.length;<tr><td><a name="l258" href="#l258">258</a><td> var length2 = array2.length;<tr><td><a name="l259" href="#l259">259</a><td><tr><td><a name="l260" href="#l260">260</a><td> var arr = [];<tr><td><a name="l261" href="#l261">261</a><td> for (var i = 0; i < length1 + 1; i++) {<tr><td><a name="l262" href="#l262">262</a><td> arr[i] = [];<tr><td><a name="l263" href="#l263">263</a><td> arr[i][0] = 0;<tr><td><a name="l264" href="#l264">264</a><td> }<tr><td><a name="l265" href="#l265">265</a><td><tr><td><a name="l266" href="#l266">266</a><td> for (var j = 0; j < length2 + 1; j++) {<tr><td><a name="l267" href="#l267">267</a><td> arr[0][j] = 0;<tr><td><a name="l268" href="#l268">268</a><td> }<tr><td><a name="l269" href="#l269">269</a><td><tr><td><a name="l270" href="#l270">270</a><td> for (i = 1; i <= length1; i++) {<tr><td><a name="l271" href="#l271">271</a><td> for (j = 1; j <= length2; j++) {<tr><td><a name="l272" href="#l272">272</a><td> if (compare(array1[i - 1], array2[j - 1])) {<tr><td><a name="l273" href="#l273">273</a><td> arr[i][j] = arr[i - 1][j - 1] + 1;<tr><td><a name="l274" href="#l274">274</a><td> } else {<tr><td><a name="l275" href="#l275">275</a><td> arr[i][j] = Math.max(arr[i - 1][j], arr[i][j - 1]);<tr><td><a name="l276" href="#l276">276</a><td> }<tr><td><a name="l277" href="#l277">277</a><td> }<tr><td><a name="l278" href="#l278">278</a><td> }<tr><td><a name="l279" href="#l279">279</a><td><tr><td><a name="l280" href="#l280">280</a><td> // Backtracking<tr><td><a name="l281" href="#l281">281</a><td> var result = [];<tr><td><a name="l282" href="#l282">282</a><td> var i = length1, j = length2;<tr><td><a name="l283" href="#l283">283</a><td> while (i > 0 && j > 0) {<tr><td><a name="l284" href="#l284">284</a><td> if (compare(array1[i - 1], array2[j - 1])) {<tr><td><a name="l285" href="#l285">285</a><td> result.unshift(collect(i - 1, j - 1));<tr><td><a name="l286" href="#l286">286</a><td> i--;<tr><td><a name="l287" href="#l287">287</a><td> j--;<tr><td><a name="l288" href="#l288">288</a><td> } else {<tr><td><a name="l289" href="#l289">289</a><td> if (arr[i - 1][j] > arr[i][j - 1]) {<tr><td><a name="l290" href="#l290">290</a><td> i--;<tr><td><a name="l291" href="#l291">291</a><td> } else {<tr><td><a name="l292" href="#l292">292</a><td> j--;<tr><td><a name="l293" href="#l293">293</a><td> }<tr><td><a name="l294" href="#l294">294</a><td> }<tr><td><a name="l295" href="#l295">295</a><td> }<tr><td><a name="l296" href="#l296">296</a><td><tr><td><a name="l297" href="#l297">297</a><td> return result;<tr><td><a name="l298" href="#l298">298</a><td>};<tr><td><a name="l299" href="#l299">299</a><td><tr><td><a name="l300" href="#l300">300</a><td><tr><td><a name="l301" href="#l301">301</a><td>/**<tr><td><a name="l302" href="#l302">302</a><td> * Returns the sum of the arguments.<tr><td><a name="l303" href="#l303">303</a><td> * @param {...number} var_args Numbers to add.<tr><td><a name="l304" href="#l304">304</a><td> * @return {number} The sum of the arguments (0 if no arguments were provided,<tr><td><a name="l305" href="#l305">305</a><td> * {@code NaN} if any of the arguments is not a valid number).<tr><td><a name="l306" href="#l306">306</a><td> */<tr><td><a name="l307" href="#l307">307</a><td>goog.math.sum = function(var_args) {<tr><td><a name="l308" href="#l308">308</a><td> return /** @type {number} */ (goog.array.reduce(arguments,<tr><td><a name="l309" href="#l309">309</a><td> function(sum, value) {<tr><td><a name="l310" href="#l310">310</a><td> return sum + value;<tr><td><a name="l311" href="#l311">311</a><td> }, 0));<tr><td><a name="l312" href="#l312">312</a><td>};<tr><td><a name="l313" href="#l313">313</a><td><tr><td><a name="l314" href="#l314">314</a><td><tr><td><a name="l315" href="#l315">315</a><td>/**<tr><td><a name="l316" href="#l316">316</a><td> * Returns the arithmetic mean of the arguments.<tr><td><a name="l317" href="#l317">317</a><td> * @param {...number} var_args Numbers to average.<tr><td><a name="l318" href="#l318">318</a><td> * @return {number} The average of the arguments ({@code NaN} if no arguments<tr><td><a name="l319" href="#l319">319</a><td> * were provided or any of the arguments is not a valid number).<tr><td><a name="l320" href="#l320">320</a><td> */<tr><td><a name="l321" href="#l321">321</a><td>goog.math.average = function(var_args) {<tr><td><a name="l322" href="#l322">322</a><td> return goog.math.sum.apply(null, arguments) / arguments.length;<tr><td><a name="l323" href="#l323">323</a><td>};<tr><td><a name="l324" href="#l324">324</a><td><tr><td><a name="l325" href="#l325">325</a><td><tr><td><a name="l326" href="#l326">326</a><td>/**<tr><td><a name="l327" href="#l327">327</a><td> * Returns the unbiased sample variance of the arguments. For a definition,<tr><td><a name="l328" href="#l328">328</a><td> * see e.g. http://en.wikipedia.org/wiki/Variance<tr><td><a name="l329" href="#l329">329</a><td> * @param {...number} var_args Number samples to analyze.<tr><td><a name="l330" href="#l330">330</a><td> * @return {number} The unbiased sample variance of the arguments (0 if fewer<tr><td><a name="l331" href="#l331">331</a><td> * than two samples were provided, or {@code NaN} if any of the samples is<tr><td><a name="l332" href="#l332">332</a><td> * not a valid number).<tr><td><a name="l333" href="#l333">333</a><td> */<tr><td><a name="l334" href="#l334">334</a><td>goog.math.sampleVariance = function(var_args) {<tr><td><a name="l335" href="#l335">335</a><td> var sampleSize = arguments.length;<tr><td><a name="l336" href="#l336">336</a><td> if (sampleSize < 2) {<tr><td><a name="l337" href="#l337">337</a><td> return 0;<tr><td><a name="l338" href="#l338">338</a><td> }<tr><td><a name="l339" href="#l339">339</a><td><tr><td><a name="l340" href="#l340">340</a><td> var mean = goog.math.average.apply(null, arguments);<tr><td><a name="l341" href="#l341">341</a><td> var variance = goog.math.sum.apply(null, goog.array.map(arguments,<tr><td><a name="l342" href="#l342">342</a><td> function(val) {<tr><td><a name="l343" href="#l343">343</a><td> return Math.pow(val - mean, 2);<tr><td><a name="l344" href="#l344">344</a><td> })) / (sampleSize - 1);<tr><td><a name="l345" href="#l345">345</a><td><tr><td><a name="l346" href="#l346">346</a><td> return variance;<tr><td><a name="l347" href="#l347">347</a><td>};<tr><td><a name="l348" href="#l348">348</a><td><tr><td><a name="l349" href="#l349">349</a><td><tr><td><a name="l350" href="#l350">350</a><td>/**<tr><td><a name="l351" href="#l351">351</a><td> * Returns the sample standard deviation of the arguments. For a definition of<tr><td><a name="l352" href="#l352">352</a><td> * sample standard deviation, see e.g.<tr><td><a name="l353" href="#l353">353</a><td> * http://en.wikipedia.org/wiki/Standard_deviation<tr><td><a name="l354" href="#l354">354</a><td> * @param {...number} var_args Number samples to analyze.<tr><td><a name="l355" href="#l355">355</a><td> * @return {number} The sample standard deviation of the arguments (0 if fewer<tr><td><a name="l356" href="#l356">356</a><td> * than two samples were provided, or {@code NaN} if any of the samples is<tr><td><a name="l357" href="#l357">357</a><td> * not a valid number).<tr><td><a name="l358" href="#l358">358</a><td> */<tr><td><a name="l359" href="#l359">359</a><td>goog.math.standardDeviation = function(var_args) {<tr><td><a name="l360" href="#l360">360</a><td> return Math.sqrt(goog.math.sampleVariance.apply(null, arguments));<tr><td><a name="l361" href="#l361">361</a><td>};<tr><td><a name="l362" href="#l362">362</a><td><tr><td><a name="l363" href="#l363">363</a><td><tr><td><a name="l364" href="#l364">364</a><td>/**<tr><td><a name="l365" href="#l365">365</a><td> * Returns whether the supplied number represents an integer, i.e. that is has<tr><td><a name="l366" href="#l366">366</a><td> * no fractional component. No range-checking is performed on the number.<tr><td><a name="l367" href="#l367">367</a><td> * @param {number} num The number to test.<tr><td><a name="l368" href="#l368">368</a><td> * @return {boolean} Whether {@code num} is an integer.<tr><td><a name="l369" href="#l369">369</a><td> */<tr><td><a name="l370" href="#l370">370</a><td>goog.math.isInt = function(num) {<tr><td><a name="l371" href="#l371">371</a><td> return isFinite(num) && num % 1 == 0;<tr><td><a name="l372" href="#l372">372</a><td>};<tr><td><a name="l373" href="#l373">373</a><td><tr><td><a name="l374" href="#l374">374</a><td><tr><td><a name="l375" href="#l375">375</a><td>/**<tr><td><a name="l376" href="#l376">376</a><td> * Returns whether the supplied number is finite and not NaN.<tr><td><a name="l377" href="#l377">377</a><td> * @param {number} num The number to test.<tr><td><a name="l378" href="#l378">378</a><td> * @return {boolean} Whether {@code num} is a finite number.<tr><td><a name="l379" href="#l379">379</a><td> */<tr><td><a name="l380" href="#l380">380</a><td>goog.math.isFiniteNumber = function(num) {<tr><td><a name="l381" href="#l381">381</a><td> return isFinite(num) && !isNaN(num);<tr><td><a name="l382" href="#l382">382</a><td>};<tr><td><a name="l383" href="#l383">383</a><td><tr><td><a name="l384" href="#l384">384</a><td><tr><td><a name="l385" href="#l385">385</a><td>/**<tr><td><a name="l386" href="#l386">386</a><td> * Returns the precise value of floor(log10(num)).<tr><td><a name="l387" href="#l387">387</a><td> * Simpler implementations didn't work because of floating point rounding<tr><td><a name="l388" href="#l388">388</a><td> * errors. For example<tr><td><a name="l389" href="#l389">389</a><td> * <ul><tr><td><a name="l390" href="#l390">390</a><td> * <li>Math.floor(Math.log(num) / Math.LN10) is off by one for num == 1e+3.<tr><td><a name="l391" href="#l391">391</a><td> * <li>Math.floor(Math.log(num) * Math.LOG10E) is off by one for num == 1e+15.<tr><td><a name="l392" href="#l392">392</a><td> * <li>Math.floor(Math.log10(num)) is off by one for num == 1e+15 - 1.<tr><td><a name="l393" href="#l393">393</a><td> * </ul><tr><td><a name="l394" href="#l394">394</a><td> * @param {number} num A floating point number.<tr><td><a name="l395" href="#l395">395</a><td> * @return {number} Its logarithm to base 10 rounded down to the nearest<tr><td><a name="l396" href="#l396">396</a><td> * integer if num > 0. -Infinity if num == 0. NaN if num < 0.<tr><td><a name="l397" href="#l397">397</a><td> */<tr><td><a name="l398" href="#l398">398</a><td>goog.math.log10Floor = function(num) {<tr><td><a name="l399" href="#l399">399</a><td> if (num > 0) {<tr><td><a name="l400" href="#l400">400</a><td> var x = Math.round(Math.log(num) * Math.LOG10E);<tr><td><a name="l401" href="#l401">401</a><td> return x - (parseFloat('1e' + x) > num);<tr><td><a name="l402" href="#l402">402</a><td> }<tr><td><a name="l403" href="#l403">403</a><td> return num == 0 ? -Infinity : NaN;<tr><td><a name="l404" href="#l404">404</a><td>};<tr><td><a name="l405" href="#l405">405</a><td><tr><td><a name="l406" href="#l406">406</a><td><tr><td><a name="l407" href="#l407">407</a><td>/**<tr><td><a name="l408" href="#l408">408</a><td> * A tweaked variant of {@code Math.floor} which tolerates if the passed number<tr><td><a name="l409" href="#l409">409</a><td> * is infinitesimally smaller than the closest integer. It often happens with<tr><td><a name="l410" href="#l410">410</a><td> * the results of floating point calculations because of the finite precision<tr><td><a name="l411" href="#l411">411</a><td> * of the intermediate results. For example {@code Math.floor(Math.log(1000) /<tr><td><a name="l412" href="#l412">412</a><td> * Math.LN10) == 2}, not 3 as one would expect.<tr><td><a name="l413" href="#l413">413</a><td> * @param {number} num A number.<tr><td><a name="l414" href="#l414">414</a><td> * @param {number=} opt_epsilon An infinitesimally small positive number, the<tr><td><a name="l415" href="#l415">415</a><td> * rounding error to tolerate.<tr><td><a name="l416" href="#l416">416</a><td> * @return {number} The largest integer less than or equal to {@code num}.<tr><td><a name="l417" href="#l417">417</a><td> */<tr><td><a name="l418" href="#l418">418</a><td>goog.math.safeFloor = function(num, opt_epsilon) {<tr><td><a name="l419" href="#l419">419</a><td> goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);<tr><td><a name="l420" href="#l420">420</a><td> return Math.floor(num + (opt_epsilon || 2e-15));<tr><td><a name="l421" href="#l421">421</a><td>};<tr><td><a name="l422" href="#l422">422</a><td><tr><td><a name="l423" href="#l423">423</a><td><tr><td><a name="l424" href="#l424">424</a><td>/**<tr><td><a name="l425" href="#l425">425</a><td> * A tweaked variant of {@code Math.ceil}. See {@code goog.math.safeFloor} for<tr><td><a name="l426" href="#l426">426</a><td> * details.<tr><td><a name="l427" href="#l427">427</a><td> * @param {number} num A number.<tr><td><a name="l428" href="#l428">428</a><td> * @param {number=} opt_epsilon An infinitesimally small positive number, the<tr><td><a name="l429" href="#l429">429</a><td> * rounding error to tolerate.<tr><td><a name="l430" href="#l430">430</a><td> * @return {number} The smallest integer greater than or equal to {@code num}.<tr><td><a name="l431" href="#l431">431</a><td> */<tr><td><a name="l432" href="#l432">432</a><td>goog.math.safeCeil = function(num, opt_epsilon) {<tr><td><a name="l433" href="#l433">433</a><td> goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);<tr><td><a name="l434" href="#l434">434</a><td> return Math.ceil(num - (opt_epsilon || 2e-15));<tr><td><a name="l435" href="#l435">435</a><td>};</table></pre></main><nav id="topnav"><div><div id="menubutton"><label for="sidenav-toggle">Menu</label></div><form id="searchbox"><div><input type="search" placeholder="Search" tabindex="1"></div></form></div></nav><nav id="sidenav"><input type="checkbox" id="sidenav-types-ctrl" /><input type="checkbox" id="sidenav-files-ctrl" /><input type="checkbox" id="sidenav-modules-ctrl" /><a id="sidenav-overview"><div><h4>Overview</h4></div></a><div id="sidenav-types"><label for="sidenav-types-ctrl"><h4>Types</h4></label><i>No data</i></div><div id="sidenav-modules"><label for="sidenav-modules-ctrl"><h4>Modules</h4></label><i>No data</i></div><div id="sidenav-files"><label for="sidenav-files-ctrl"><h4>Files</h4></label><i>No data</i></div><a href="license.html"><div><h4>License</h4></div></a></nav><div id="push-footer"></div></div><footer><a href="https://github.com/jleyba/js-dossier">Generated by dossier</a></footer><script src="../../../../types.js"></script><script src="../../../../dossier.js"></script> |