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<!DOCTYPE html><meta charset="UTF-8"><meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"><meta http-equiv="Content-Language" content="en"><meta http-equiv="X-UA-Compatible" content="IE=edge"><title>math.js</title><link href="../../../../dossier.css" rel="stylesheet" type="text/css"><header><div><form><div><input type="search" placeholder="Search" tabindex="1"></div></form></div></header><main><article class="srcfile"><h1>lib/goog/math/math.js</h1><div><table><tr><td><a id="l1"></a><a href="#l1">1</a><td>// Copyright 2006 The Closure Library Authors. All Rights Reserved.<tr><td><a id="l2"></a><a href="#l2">2</a><td>//<tr><td><a id="l3"></a><a href="#l3">3</a><td>// Licensed under the Apache License, Version 2.0 (the "License");<tr><td><a id="l4"></a><a href="#l4">4</a><td>// you may not use this file except in compliance with the License.<tr><td><a id="l5"></a><a href="#l5">5</a><td>// You may obtain a copy of the License at<tr><td><a id="l6"></a><a href="#l6">6</a><td>//<tr><td><a id="l7"></a><a href="#l7">7</a><td>// http://www.apache.org/licenses/LICENSE-2.0<tr><td><a id="l8"></a><a href="#l8">8</a><td>//<tr><td><a id="l9"></a><a href="#l9">9</a><td>// Unless required by applicable law or agreed to in writing, software<tr><td><a id="l10"></a><a href="#l10">10</a><td>// distributed under the License is distributed on an "AS-IS" BASIS,<tr><td><a id="l11"></a><a href="#l11">11</a><td>// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<tr><td><a id="l12"></a><a href="#l12">12</a><td>// See the License for the specific language governing permissions and<tr><td><a id="l13"></a><a href="#l13">13</a><td>// limitations under the License.<tr><td><a id="l14"></a><a href="#l14">14</a><td><tr><td><a id="l15"></a><a href="#l15">15</a><td>/**<tr><td><a id="l16"></a><a href="#l16">16</a><td> * @fileoverview Additional mathematical functions.<tr><td><a id="l17"></a><a href="#l17">17</a><td> */<tr><td><a id="l18"></a><a href="#l18">18</a><td><tr><td><a id="l19"></a><a href="#l19">19</a><td>goog.provide('goog.math');<tr><td><a id="l20"></a><a href="#l20">20</a><td><tr><td><a id="l21"></a><a href="#l21">21</a><td>goog.require('goog.array');<tr><td><a id="l22"></a><a href="#l22">22</a><td>goog.require('goog.asserts');<tr><td><a id="l23"></a><a href="#l23">23</a><td><tr><td><a id="l24"></a><a href="#l24">24</a><td><tr><td><a id="l25"></a><a href="#l25">25</a><td>/**<tr><td><a id="l26"></a><a href="#l26">26</a><td> * Returns a random integer greater than or equal to 0 and less than {@code a}.<tr><td><a id="l27"></a><a href="#l27">27</a><td> * @param {number} a The upper bound for the random integer (exclusive).<tr><td><a id="l28"></a><a href="#l28">28</a><td> * @return {number} A random integer N such that 0 <= N < a.<tr><td><a id="l29"></a><a href="#l29">29</a><td> */<tr><td><a id="l30"></a><a href="#l30">30</a><td>goog.math.randomInt = function(a) {<tr><td><a id="l31"></a><a href="#l31">31</a><td> return Math.floor(Math.random() * a);<tr><td><a id="l32"></a><a href="#l32">32</a><td>};<tr><td><a id="l33"></a><a href="#l33">33</a><td><tr><td><a id="l34"></a><a href="#l34">34</a><td><tr><td><a id="l35"></a><a href="#l35">35</a><td>/**<tr><td><a id="l36"></a><a href="#l36">36</a><td> * Returns a random number greater than or equal to {@code a} and less than<tr><td><a id="l37"></a><a href="#l37">37</a><td> * {@code b}.<tr><td><a id="l38"></a><a href="#l38">38</a><td> * @param {number} a The lower bound for the random number (inclusive).<tr><td><a id="l39"></a><a href="#l39">39</a><td> * @param {number} b The upper bound for the random number (exclusive).<tr><td><a id="l40"></a><a href="#l40">40</a><td> * @return {number} A random number N such that a <= N < b.<tr><td><a id="l41"></a><a href="#l41">41</a><td> */<tr><td><a id="l42"></a><a href="#l42">42</a><td>goog.math.uniformRandom = function(a, b) {<tr><td><a id="l43"></a><a href="#l43">43</a><td> return a + Math.random() * (b - a);<tr><td><a id="l44"></a><a href="#l44">44</a><td>};<tr><td><a id="l45"></a><a href="#l45">45</a><td><tr><td><a id="l46"></a><a href="#l46">46</a><td><tr><td><a id="l47"></a><a href="#l47">47</a><td>/**<tr><td><a id="l48"></a><a href="#l48">48</a><td> * Takes a number and clamps it to within the provided bounds.<tr><td><a id="l49"></a><a href="#l49">49</a><td> * @param {number} value The input number.<tr><td><a id="l50"></a><a href="#l50">50</a><td> * @param {number} min The minimum value to return.<tr><td><a id="l51"></a><a href="#l51">51</a><td> * @param {number} max The maximum value to return.<tr><td><a id="l52"></a><a href="#l52">52</a><td> * @return {number} The input number if it is within bounds, or the nearest<tr><td><a id="l53"></a><a href="#l53">53</a><td> * number within the bounds.<tr><td><a id="l54"></a><a href="#l54">54</a><td> */<tr><td><a id="l55"></a><a href="#l55">55</a><td>goog.math.clamp = function(value, min, max) {<tr><td><a id="l56"></a><a href="#l56">56</a><td> return Math.min(Math.max(value, min), max);<tr><td><a id="l57"></a><a href="#l57">57</a><td>};<tr><td><a id="l58"></a><a href="#l58">58</a><td><tr><td><a id="l59"></a><a href="#l59">59</a><td><tr><td><a id="l60"></a><a href="#l60">60</a><td>/**<tr><td><a id="l61"></a><a href="#l61">61</a><td> * The % operator in JavaScript returns the remainder of a / b, but differs from<tr><td><a id="l62"></a><a href="#l62">62</a><td> * some other languages in that the result will have the same sign as the<tr><td><a id="l63"></a><a href="#l63">63</a><td> * dividend. For example, -1 % 8 == -1, whereas in some other languages<tr><td><a id="l64"></a><a href="#l64">64</a><td> * (such as Python) the result would be 7. This function emulates the more<tr><td><a id="l65"></a><a href="#l65">65</a><td> * correct modulo behavior, which is useful for certain applications such as<tr><td><a id="l66"></a><a href="#l66">66</a><td> * calculating an offset index in a circular list.<tr><td><a id="l67"></a><a href="#l67">67</a><td> *<tr><td><a id="l68"></a><a href="#l68">68</a><td> * @param {number} a The dividend.<tr><td><a id="l69"></a><a href="#l69">69</a><td> * @param {number} b The divisor.<tr><td><a id="l70"></a><a href="#l70">70</a><td> * @return {number} a % b where the result is between 0 and b (either 0 <= x < b<tr><td><a id="l71"></a><a href="#l71">71</a><td> * or b < x <= 0, depending on the sign of b).<tr><td><a id="l72"></a><a href="#l72">72</a><td> */<tr><td><a id="l73"></a><a href="#l73">73</a><td>goog.math.modulo = function(a, b) {<tr><td><a id="l74"></a><a href="#l74">74</a><td> var r = a % b;<tr><td><a id="l75"></a><a 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 id="l76"></a><a href="#l76">76</a><td> return (r * b < 0) ? r + b : r;<tr><td><a id="l77"></a><a href="#l77">77</a><td>};<tr><td><a id="l78"></a><a href="#l78">78</a><td><tr><td><a id="l79"></a><a href="#l79">79</a><td><tr><td><a id="l80"></a><a href="#l80">80</a><td>/**<tr><td><a id="l81"></a><a href="#l81">81</a><td> * Performs linear interpolation between values a and b. Returns the value<tr><td><a id="l82"></a><a 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 id="l83"></a><a href="#l83">83</a><td> * outside this range, the return value is a linear extrapolation).<tr><td><a id="l84"></a><a href="#l84">84</a><td> * @param {number} a A number.<tr><td><a id="l85"></a><a href="#l85">85</a><td> * @param {number} b A number.<tr><td><a id="l86"></a><a href="#l86">86</a><td> * @param {number} x The proportion between a and b.<tr><td><a id="l87"></a><a href="#l87">87</a><td> * @return {number} The interpolated value between a and b.<tr><td><a id="l88"></a><a href="#l88">88</a><td> */<tr><td><a id="l89"></a><a href="#l89">89</a><td>goog.math.lerp = function(a, b, x) {<tr><td><a id="l90"></a><a href="#l90">90</a><td> return a + x * (b - a);<tr><td><a id="l91"></a><a href="#l91">91</a><td>};<tr><td><a id="l92"></a><a href="#l92">92</a><td><tr><td><a id="l93"></a><a href="#l93">93</a><td><tr><td><a id="l94"></a><a href="#l94">94</a><td>/**<tr><td><a id="l95"></a><a href="#l95">95</a><td> * Tests whether the two values are equal to each other, within a certain<tr><td><a id="l96"></a><a href="#l96">96</a><td> * tolerance to adjust for floating point errors.<tr><td><a id="l97"></a><a href="#l97">97</a><td> * @param {number} a A number.<tr><td><a id="l98"></a><a href="#l98">98</a><td> * @param {number} b A number.<tr><td><a id="l99"></a><a href="#l99">99</a><td> * @param {number=} opt_tolerance Optional tolerance range. Defaults<tr><td><a id="l100"></a><a href="#l100">100</a><td> * to 0.000001. If specified, should be greater than 0.<tr><td><a id="l101"></a><a href="#l101">101</a><td> * @return {boolean} Whether {@code a} and {@code b} are nearly equal.<tr><td><a id="l102"></a><a href="#l102">102</a><td> */<tr><td><a id="l103"></a><a href="#l103">103</a><td>goog.math.nearlyEquals = function(a, b, opt_tolerance) {<tr><td><a id="l104"></a><a href="#l104">104</a><td> return Math.abs(a - b) <= (opt_tolerance || 0.000001);<tr><td><a id="l105"></a><a href="#l105">105</a><td>};<tr><td><a id="l106"></a><a href="#l106">106</a><td><tr><td><a id="l107"></a><a href="#l107">107</a><td><tr><td><a id="l108"></a><a href="#l108">108</a><td>// TODO(user): Rename to normalizeAngle, retaining old name as deprecated<tr><td><a id="l109"></a><a href="#l109">109</a><td>// alias.<tr><td><a id="l110"></a><a href="#l110">110</a><td>/**<tr><td><a id="l111"></a><a href="#l111">111</a><td> * Normalizes an angle to be in range [0-360). Angles outside this range will<tr><td><a id="l112"></a><a href="#l112">112</a><td> * be normalized to be the equivalent angle with that range.<tr><td><a id="l113"></a><a href="#l113">113</a><td> * @param {number} angle Angle in degrees.<tr><td><a id="l114"></a><a href="#l114">114</a><td> * @return {number} Standardized angle.<tr><td><a id="l115"></a><a href="#l115">115</a><td> */<tr><td><a id="l116"></a><a href="#l116">116</a><td>goog.math.standardAngle = function(angle) {<tr><td><a id="l117"></a><a href="#l117">117</a><td> return goog.math.modulo(angle, 360);<tr><td><a id="l118"></a><a href="#l118">118</a><td>};<tr><td><a id="l119"></a><a href="#l119">119</a><td><tr><td><a id="l120"></a><a href="#l120">120</a><td><tr><td><a id="l121"></a><a href="#l121">121</a><td>/**<tr><td><a id="l122"></a><a href="#l122">122</a><td> * Normalizes an angle to be in range [0-2*PI). Angles outside this range will<tr><td><a id="l123"></a><a href="#l123">123</a><td> * be normalized to be the equivalent angle with that range.<tr><td><a id="l124"></a><a href="#l124">124</a><td> * @param {number} angle Angle in radians.<tr><td><a id="l125"></a><a href="#l125">125</a><td> * @return {number} Standardized angle.<tr><td><a id="l126"></a><a href="#l126">126</a><td> */<tr><td><a id="l127"></a><a href="#l127">127</a><td>goog.math.standardAngleInRadians = function(angle) {<tr><td><a id="l128"></a><a href="#l128">128</a><td> return goog.math.modulo(angle, 2 * Math.PI);<tr><td><a id="l129"></a><a href="#l129">129</a><td>};<tr><td><a id="l130"></a><a href="#l130">130</a><td><tr><td><a id="l131"></a><a href="#l131">131</a><td><tr><td><a id="l132"></a><a href="#l132">132</a><td>/**<tr><td><a id="l133"></a><a href="#l133">133</a><td> * Converts degrees to radians.<tr><td><a id="l134"></a><a href="#l134">134</a><td> * @param {number} angleDegrees Angle in degrees.<tr><td><a id="l135"></a><a href="#l135">135</a><td> * @return {number} Angle in radians.<tr><td><a id="l136"></a><a href="#l136">136</a><td> */<tr><td><a id="l137"></a><a href="#l137">137</a><td>goog.math.toRadians = function(angleDegrees) {<tr><td><a id="l138"></a><a href="#l138">138</a><td> return angleDegrees * Math.PI / 180;<tr><td><a id="l139"></a><a href="#l139">139</a><td>};<tr><td><a id="l140"></a><a href="#l140">140</a><td><tr><td><a id="l141"></a><a href="#l141">141</a><td><tr><td><a id="l142"></a><a href="#l142">142</a><td>/**<tr><td><a id="l143"></a><a href="#l143">143</a><td> * Converts radians to degrees.<tr><td><a id="l144"></a><a href="#l144">144</a><td> * @param {number} angleRadians Angle in radians.<tr><td><a id="l145"></a><a href="#l145">145</a><td> * @return {number} Angle in degrees.<tr><td><a id="l146"></a><a href="#l146">146</a><td> */<tr><td><a id="l147"></a><a href="#l147">147</a><td>goog.math.toDegrees = function(angleRadians) {<tr><td><a id="l148"></a><a href="#l148">148</a><td> return angleRadians * 180 / Math.PI;<tr><td><a id="l149"></a><a href="#l149">149</a><td>};<tr><td><a id="l150"></a><a href="#l150">150</a><td><tr><td><a id="l151"></a><a href="#l151">151</a><td><tr><td><a id="l152"></a><a href="#l152">152</a><td>/**<tr><td><a id="l153"></a><a href="#l153">153</a><td> * For a given angle and radius, finds the X portion of the offset.<tr><td><a id="l154"></a><a href="#l154">154</a><td> * @param {number} degrees Angle in degrees (zero points in +X direction).<tr><td><a id="l155"></a><a href="#l155">155</a><td> * @param {number} radius Radius.<tr><td><a id="l156"></a><a href="#l156">156</a><td> * @return {number} The x-distance for the angle and radius.<tr><td><a id="l157"></a><a href="#l157">157</a><td> */<tr><td><a id="l158"></a><a href="#l158">158</a><td>goog.math.angleDx = function(degrees, radius) {<tr><td><a id="l159"></a><a href="#l159">159</a><td> return radius * Math.cos(goog.math.toRadians(degrees));<tr><td><a id="l160"></a><a href="#l160">160</a><td>};<tr><td><a id="l161"></a><a href="#l161">161</a><td><tr><td><a id="l162"></a><a href="#l162">162</a><td><tr><td><a id="l163"></a><a href="#l163">163</a><td>/**<tr><td><a id="l164"></a><a href="#l164">164</a><td> * For a given angle and radius, finds the Y portion of the offset.<tr><td><a id="l165"></a><a href="#l165">165</a><td> * @param {number} degrees Angle in degrees (zero points in +X direction).<tr><td><a id="l166"></a><a href="#l166">166</a><td> * @param {number} radius Radius.<tr><td><a id="l167"></a><a href="#l167">167</a><td> * @return {number} The y-distance for the angle and radius.<tr><td><a id="l168"></a><a href="#l168">168</a><td> */<tr><td><a id="l169"></a><a href="#l169">169</a><td>goog.math.angleDy = function(degrees, radius) {<tr><td><a id="l170"></a><a href="#l170">170</a><td> return radius * Math.sin(goog.math.toRadians(degrees));<tr><td><a id="l171"></a><a href="#l171">171</a><td>};<tr><td><a id="l172"></a><a href="#l172">172</a><td><tr><td><a id="l173"></a><a href="#l173">173</a><td><tr><td><a id="l174"></a><a href="#l174">174</a><td>/**<tr><td><a id="l175"></a><a href="#l175">175</a><td> * Computes the angle between two points (x1,y1) and (x2,y2).<tr><td><a id="l176"></a><a href="#l176">176</a><td> * Angle zero points in the +X direction, 90 degrees points in the +Y<tr><td><a id="l177"></a><a href="#l177">177</a><td> * direction (down) and from there we grow clockwise towards 360 degrees.<tr><td><a id="l178"></a><a href="#l178">178</a><td> * @param {number} x1 x of first point.<tr><td><a id="l179"></a><a href="#l179">179</a><td> * @param {number} y1 y of first point.<tr><td><a id="l180"></a><a href="#l180">180</a><td> * @param {number} x2 x of second point.<tr><td><a id="l181"></a><a href="#l181">181</a><td> * @param {number} y2 y of second point.<tr><td><a id="l182"></a><a href="#l182">182</a><td> * @return {number} Standardized angle in degrees of the vector from<tr><td><a id="l183"></a><a href="#l183">183</a><td> * x1,y1 to x2,y2.<tr><td><a id="l184"></a><a href="#l184">184</a><td> */<tr><td><a id="l185"></a><a href="#l185">185</a><td>goog.math.angle = function(x1, y1, x2, y2) {<tr><td><a id="l186"></a><a href="#l186">186</a><td> return goog.math.standardAngle(goog.math.toDegrees(Math.atan2(y2 - y1,<tr><td><a id="l187"></a><a href="#l187">187</a><td> x2 - x1)));<tr><td><a id="l188"></a><a href="#l188">188</a><td>};<tr><td><a id="l189"></a><a href="#l189">189</a><td><tr><td><a id="l190"></a><a href="#l190">190</a><td><tr><td><a id="l191"></a><a href="#l191">191</a><td>/**<tr><td><a id="l192"></a><a href="#l192">192</a><td> * Computes the difference between startAngle and endAngle (angles in degrees).<tr><td><a id="l193"></a><a href="#l193">193</a><td> * @param {number} startAngle Start angle in degrees.<tr><td><a id="l194"></a><a href="#l194">194</a><td> * @param {number} endAngle End angle in degrees.<tr><td><a id="l195"></a><a href="#l195">195</a><td> * @return {number} The number of degrees that when added to<tr><td><a id="l196"></a><a href="#l196">196</a><td> * startAngle will result in endAngle. Positive numbers mean that the<tr><td><a id="l197"></a><a href="#l197">197</a><td> * direction is clockwise. Negative numbers indicate a counter-clockwise<tr><td><a id="l198"></a><a href="#l198">198</a><td> * direction.<tr><td><a id="l199"></a><a href="#l199">199</a><td> * The shortest route (clockwise vs counter-clockwise) between the angles<tr><td><a id="l200"></a><a href="#l200">200</a><td> * is used.<tr><td><a id="l201"></a><a href="#l201">201</a><td> * When the difference is 180 degrees, the function returns 180 (not -180)<tr><td><a id="l202"></a><a href="#l202">202</a><td> * angleDifference(30, 40) is 10, and angleDifference(40, 30) is -10.<tr><td><a id="l203"></a><a href="#l203">203</a><td> * angleDifference(350, 10) is 20, and angleDifference(10, 350) is -20.<tr><td><a id="l204"></a><a href="#l204">204</a><td> */<tr><td><a id="l205"></a><a href="#l205">205</a><td>goog.math.angleDifference = function(startAngle, endAngle) {<tr><td><a id="l206"></a><a href="#l206">206</a><td> var d = goog.math.standardAngle(endAngle) -<tr><td><a id="l207"></a><a href="#l207">207</a><td> goog.math.standardAngle(startAngle);<tr><td><a id="l208"></a><a href="#l208">208</a><td> if (d > 180) {<tr><td><a id="l209"></a><a href="#l209">209</a><td> d = d - 360;<tr><td><a id="l210"></a><a href="#l210">210</a><td> } else if (d <= -180) {<tr><td><a id="l211"></a><a href="#l211">211</a><td> d = 360 + d;<tr><td><a id="l212"></a><a href="#l212">212</a><td> }<tr><td><a id="l213"></a><a href="#l213">213</a><td> return d;<tr><td><a id="l214"></a><a href="#l214">214</a><td>};<tr><td><a id="l215"></a><a href="#l215">215</a><td><tr><td><a id="l216"></a><a href="#l216">216</a><td><tr><td><a id="l217"></a><a href="#l217">217</a><td>/**<tr><td><a id="l218"></a><a href="#l218">218</a><td> * Returns the sign of a number as per the "sign" or "signum" function.<tr><td><a id="l219"></a><a href="#l219">219</a><td> * @param {number} x The number to take the sign of.<tr><td><a id="l220"></a><a href="#l220">220</a><td> * @return {number} -1 when negative, 1 when positive, 0 when 0. Preserves<tr><td><a id="l221"></a><a href="#l221">221</a><td> * signed zeros and NaN.<tr><td><a id="l222"></a><a href="#l222">222</a><td> */<tr><td><a id="l223"></a><a href="#l223">223</a><td>goog.math.sign = Math.sign || function(x) {<tr><td><a id="l224"></a><a href="#l224">224</a><td> if (x > 0) {<tr><td><a id="l225"></a><a href="#l225">225</a><td> return 1;<tr><td><a id="l226"></a><a href="#l226">226</a><td> }<tr><td><a id="l227"></a><a href="#l227">227</a><td> if (x < 0) {<tr><td><a id="l228"></a><a href="#l228">228</a><td> return -1;<tr><td><a id="l229"></a><a href="#l229">229</a><td> }<tr><td><a id="l230"></a><a href="#l230">230</a><td> return x; // Preserves signed zeros and NaN.<tr><td><a id="l231"></a><a href="#l231">231</a><td>};<tr><td><a id="l232"></a><a href="#l232">232</a><td><tr><td><a id="l233"></a><a href="#l233">233</a><td><tr><td><a id="l234"></a><a href="#l234">234</a><td>/**<tr><td><a id="l235"></a><a href="#l235">235</a><td> * JavaScript implementation of Longest Common Subsequence problem.<tr><td><a id="l236"></a><a href="#l236">236</a><td> * http://en.wikipedia.org/wiki/Longest_common_subsequence<tr><td><a id="l237"></a><a href="#l237">237</a><td> *<tr><td><a id="l238"></a><a href="#l238">238</a><td> * Returns the longest possible array that is subarray of both of given arrays.<tr><td><a id="l239"></a><a href="#l239">239</a><td> *<tr><td><a id="l240"></a><a href="#l240">240</a><td> * @param {Array<Object>} array1 First array of objects.<tr><td><a id="l241"></a><a href="#l241">241</a><td> * @param {Array<Object>} array2 Second array of objects.<tr><td><a id="l242"></a><a href="#l242">242</a><td> * @param {Function=} opt_compareFn Function that acts as a custom comparator<tr><td><a id="l243"></a><a href="#l243">243</a><td> * for the array ojects. Function should return true if objects are equal,<tr><td><a id="l244"></a><a href="#l244">244</a><td> * otherwise false.<tr><td><a id="l245"></a><a href="#l245">245</a><td> * @param {Function=} opt_collectorFn Function used to decide what to return<tr><td><a id="l246"></a><a href="#l246">246</a><td> * as a result subsequence. It accepts 2 arguments: index of common element<tr><td><a id="l247"></a><a href="#l247">247</a><td> * in the first array and index in the second. The default function returns<tr><td><a id="l248"></a><a href="#l248">248</a><td> * element from the first array.<tr><td><a id="l249"></a><a href="#l249">249</a><td> * @return {!Array<Object>} A list of objects that are common to both arrays<tr><td><a id="l250"></a><a href="#l250">250</a><td> * such that there is no common subsequence with size greater than the<tr><td><a id="l251"></a><a href="#l251">251</a><td> * length of the list.<tr><td><a id="l252"></a><a href="#l252">252</a><td> */<tr><td><a id="l253"></a><a href="#l253">253</a><td>goog.math.longestCommonSubsequence = function(<tr><td><a id="l254"></a><a href="#l254">254</a><td> array1, array2, opt_compareFn, opt_collectorFn) {<tr><td><a id="l255"></a><a href="#l255">255</a><td><tr><td><a id="l256"></a><a href="#l256">256</a><td> var compare = opt_compareFn || function(a, b) {<tr><td><a id="l257"></a><a href="#l257">257</a><td> return a == b;<tr><td><a id="l258"></a><a href="#l258">258</a><td> };<tr><td><a id="l259"></a><a href="#l259">259</a><td><tr><td><a id="l260"></a><a href="#l260">260</a><td> var collect = opt_collectorFn || function(i1, i2) {<tr><td><a id="l261"></a><a href="#l261">261</a><td> return array1[i1];<tr><td><a id="l262"></a><a href="#l262">262</a><td> };<tr><td><a id="l263"></a><a href="#l263">263</a><td><tr><td><a id="l264"></a><a href="#l264">264</a><td> var length1 = array1.length;<tr><td><a id="l265"></a><a href="#l265">265</a><td> var length2 = array2.length;<tr><td><a id="l266"></a><a href="#l266">266</a><td><tr><td><a id="l267"></a><a href="#l267">267</a><td> var arr = [];<tr><td><a id="l268"></a><a href="#l268">268</a><td> for (var i = 0; i < length1 + 1; i++) {<tr><td><a id="l269"></a><a href="#l269">269</a><td> arr[i] = [];<tr><td><a id="l270"></a><a href="#l270">270</a><td> arr[i][0] = 0;<tr><td><a id="l271"></a><a href="#l271">271</a><td> }<tr><td><a id="l272"></a><a href="#l272">272</a><td><tr><td><a id="l273"></a><a href="#l273">273</a><td> for (var j = 0; j < length2 + 1; j++) {<tr><td><a id="l274"></a><a href="#l274">274</a><td> arr[0][j] = 0;<tr><td><a id="l275"></a><a href="#l275">275</a><td> }<tr><td><a id="l276"></a><a href="#l276">276</a><td><tr><td><a id="l277"></a><a href="#l277">277</a><td> for (i = 1; i <= length1; i++) {<tr><td><a id="l278"></a><a href="#l278">278</a><td> for (j = 1; j <= length2; j++) {<tr><td><a id="l279"></a><a href="#l279">279</a><td> if (compare(array1[i - 1], array2[j - 1])) {<tr><td><a id="l280"></a><a href="#l280">280</a><td> arr[i][j] = arr[i - 1][j - 1] + 1;<tr><td><a id="l281"></a><a href="#l281">281</a><td> } else {<tr><td><a id="l282"></a><a href="#l282">282</a><td> arr[i][j] = Math.max(arr[i - 1][j], arr[i][j - 1]);<tr><td><a id="l283"></a><a href="#l283">283</a><td> }<tr><td><a id="l284"></a><a href="#l284">284</a><td> }<tr><td><a id="l285"></a><a href="#l285">285</a><td> }<tr><td><a id="l286"></a><a href="#l286">286</a><td><tr><td><a id="l287"></a><a href="#l287">287</a><td> // Backtracking<tr><td><a id="l288"></a><a href="#l288">288</a><td> var result = [];<tr><td><a id="l289"></a><a href="#l289">289</a><td> var i = length1, j = length2;<tr><td><a id="l290"></a><a href="#l290">290</a><td> while (i > 0 && j > 0) {<tr><td><a id="l291"></a><a href="#l291">291</a><td> if (compare(array1[i - 1], array2[j - 1])) {<tr><td><a id="l292"></a><a href="#l292">292</a><td> result.unshift(collect(i - 1, j - 1));<tr><td><a id="l293"></a><a href="#l293">293</a><td> i--;<tr><td><a id="l294"></a><a href="#l294">294</a><td> j--;<tr><td><a id="l295"></a><a href="#l295">295</a><td> } else {<tr><td><a id="l296"></a><a href="#l296">296</a><td> if (arr[i - 1][j] > arr[i][j - 1]) {<tr><td><a id="l297"></a><a href="#l297">297</a><td> i--;<tr><td><a id="l298"></a><a href="#l298">298</a><td> } else {<tr><td><a id="l299"></a><a href="#l299">299</a><td> j--;<tr><td><a id="l300"></a><a href="#l300">300</a><td> }<tr><td><a id="l301"></a><a href="#l301">301</a><td> }<tr><td><a id="l302"></a><a href="#l302">302</a><td> }<tr><td><a id="l303"></a><a href="#l303">303</a><td><tr><td><a id="l304"></a><a href="#l304">304</a><td> return result;<tr><td><a id="l305"></a><a href="#l305">305</a><td>};<tr><td><a id="l306"></a><a href="#l306">306</a><td><tr><td><a id="l307"></a><a href="#l307">307</a><td><tr><td><a id="l308"></a><a href="#l308">308</a><td>/**<tr><td><a id="l309"></a><a href="#l309">309</a><td> * Returns the sum of the arguments.<tr><td><a id="l310"></a><a href="#l310">310</a><td> * @param {...number} var_args Numbers to add.<tr><td><a id="l311"></a><a href="#l311">311</a><td> * @return {number} The sum of the arguments (0 if no arguments were provided,<tr><td><a id="l312"></a><a href="#l312">312</a><td> * {@code NaN} if any of the arguments is not a valid number).<tr><td><a id="l313"></a><a href="#l313">313</a><td> */<tr><td><a id="l314"></a><a href="#l314">314</a><td>goog.math.sum = function(var_args) {<tr><td><a id="l315"></a><a href="#l315">315</a><td> return /** @type {number} */ (goog.array.reduce(arguments,<tr><td><a id="l316"></a><a href="#l316">316</a><td> function(sum, value) {<tr><td><a id="l317"></a><a href="#l317">317</a><td> return sum + value;<tr><td><a id="l318"></a><a href="#l318">318</a><td> }, 0));<tr><td><a id="l319"></a><a href="#l319">319</a><td>};<tr><td><a id="l320"></a><a href="#l320">320</a><td><tr><td><a id="l321"></a><a href="#l321">321</a><td><tr><td><a id="l322"></a><a href="#l322">322</a><td>/**<tr><td><a id="l323"></a><a href="#l323">323</a><td> * Returns the arithmetic mean of the arguments.<tr><td><a id="l324"></a><a href="#l324">324</a><td> * @param {...number} var_args Numbers to average.<tr><td><a id="l325"></a><a href="#l325">325</a><td> * @return {number} The average of the arguments ({@code NaN} if no arguments<tr><td><a id="l326"></a><a href="#l326">326</a><td> * were provided or any of the arguments is not a valid number).<tr><td><a id="l327"></a><a href="#l327">327</a><td> */<tr><td><a id="l328"></a><a href="#l328">328</a><td>goog.math.average = function(var_args) {<tr><td><a id="l329"></a><a href="#l329">329</a><td> return goog.math.sum.apply(null, arguments) / arguments.length;<tr><td><a id="l330"></a><a href="#l330">330</a><td>};<tr><td><a id="l331"></a><a href="#l331">331</a><td><tr><td><a id="l332"></a><a href="#l332">332</a><td><tr><td><a id="l333"></a><a href="#l333">333</a><td>/**<tr><td><a id="l334"></a><a href="#l334">334</a><td> * Returns the unbiased sample variance of the arguments. For a definition,<tr><td><a id="l335"></a><a href="#l335">335</a><td> * see e.g. http://en.wikipedia.org/wiki/Variance<tr><td><a id="l336"></a><a href="#l336">336</a><td> * @param {...number} var_args Number samples to analyze.<tr><td><a id="l337"></a><a href="#l337">337</a><td> * @return {number} The unbiased sample variance of the arguments (0 if fewer<tr><td><a id="l338"></a><a href="#l338">338</a><td> * than two samples were provided, or {@code NaN} if any of the samples is<tr><td><a id="l339"></a><a href="#l339">339</a><td> * not a valid number).<tr><td><a id="l340"></a><a href="#l340">340</a><td> */<tr><td><a id="l341"></a><a href="#l341">341</a><td>goog.math.sampleVariance = function(var_args) {<tr><td><a id="l342"></a><a href="#l342">342</a><td> var sampleSize = arguments.length;<tr><td><a id="l343"></a><a href="#l343">343</a><td> if (sampleSize < 2) {<tr><td><a id="l344"></a><a href="#l344">344</a><td> return 0;<tr><td><a id="l345"></a><a href="#l345">345</a><td> }<tr><td><a id="l346"></a><a href="#l346">346</a><td><tr><td><a id="l347"></a><a href="#l347">347</a><td> var mean = goog.math.average.apply(null, arguments);<tr><td><a id="l348"></a><a href="#l348">348</a><td> var variance = goog.math.sum.apply(null, goog.array.map(arguments,<tr><td><a id="l349"></a><a href="#l349">349</a><td> function(val) {<tr><td><a id="l350"></a><a href="#l350">350</a><td> return Math.pow(val - mean, 2);<tr><td><a id="l351"></a><a href="#l351">351</a><td> })) / (sampleSize - 1);<tr><td><a id="l352"></a><a href="#l352">352</a><td><tr><td><a id="l353"></a><a href="#l353">353</a><td> return variance;<tr><td><a id="l354"></a><a href="#l354">354</a><td>};<tr><td><a id="l355"></a><a href="#l355">355</a><td><tr><td><a id="l356"></a><a href="#l356">356</a><td><tr><td><a id="l357"></a><a href="#l357">357</a><td>/**<tr><td><a id="l358"></a><a href="#l358">358</a><td> * Returns the sample standard deviation of the arguments. For a definition of<tr><td><a id="l359"></a><a href="#l359">359</a><td> * sample standard deviation, see e.g.<tr><td><a id="l360"></a><a href="#l360">360</a><td> * http://en.wikipedia.org/wiki/Standard_deviation<tr><td><a id="l361"></a><a href="#l361">361</a><td> * @param {...number} var_args Number samples to analyze.<tr><td><a id="l362"></a><a href="#l362">362</a><td> * @return {number} The sample standard deviation of the arguments (0 if fewer<tr><td><a id="l363"></a><a href="#l363">363</a><td> * than two samples were provided, or {@code NaN} if any of the samples is<tr><td><a id="l364"></a><a href="#l364">364</a><td> * not a valid number).<tr><td><a id="l365"></a><a href="#l365">365</a><td> */<tr><td><a id="l366"></a><a href="#l366">366</a><td>goog.math.standardDeviation = function(var_args) {<tr><td><a id="l367"></a><a href="#l367">367</a><td> return Math.sqrt(goog.math.sampleVariance.apply(null, arguments));<tr><td><a id="l368"></a><a href="#l368">368</a><td>};<tr><td><a id="l369"></a><a href="#l369">369</a><td><tr><td><a id="l370"></a><a href="#l370">370</a><td><tr><td><a id="l371"></a><a href="#l371">371</a><td>/**<tr><td><a id="l372"></a><a href="#l372">372</a><td> * Returns whether the supplied number represents an integer, i.e. that is has<tr><td><a id="l373"></a><a href="#l373">373</a><td> * no fractional component. No range-checking is performed on the number.<tr><td><a id="l374"></a><a href="#l374">374</a><td> * @param {number} num The number to test.<tr><td><a id="l375"></a><a href="#l375">375</a><td> * @return {boolean} Whether {@code num} is an integer.<tr><td><a id="l376"></a><a href="#l376">376</a><td> */<tr><td><a id="l377"></a><a href="#l377">377</a><td>goog.math.isInt = function(num) {<tr><td><a id="l378"></a><a href="#l378">378</a><td> return isFinite(num) && num % 1 == 0;<tr><td><a id="l379"></a><a href="#l379">379</a><td>};<tr><td><a id="l380"></a><a href="#l380">380</a><td><tr><td><a id="l381"></a><a href="#l381">381</a><td><tr><td><a id="l382"></a><a href="#l382">382</a><td>/**<tr><td><a id="l383"></a><a href="#l383">383</a><td> * Returns whether the supplied number is finite and not NaN.<tr><td><a id="l384"></a><a href="#l384">384</a><td> * @param {number} num The number to test.<tr><td><a id="l385"></a><a href="#l385">385</a><td> * @return {boolean} Whether {@code num} is a finite number.<tr><td><a id="l386"></a><a href="#l386">386</a><td> */<tr><td><a id="l387"></a><a href="#l387">387</a><td>goog.math.isFiniteNumber = function(num) {<tr><td><a id="l388"></a><a href="#l388">388</a><td> return isFinite(num) && !isNaN(num);<tr><td><a id="l389"></a><a href="#l389">389</a><td>};<tr><td><a id="l390"></a><a href="#l390">390</a><td><tr><td><a id="l391"></a><a href="#l391">391</a><td><tr><td><a id="l392"></a><a href="#l392">392</a><td>/**<tr><td><a id="l393"></a><a href="#l393">393</a><td> * @param {number} num The number to test.<tr><td><a id="l394"></a><a href="#l394">394</a><td> * @return {boolean} Whether it is negative zero.<tr><td><a id="l395"></a><a href="#l395">395</a><td> */<tr><td><a id="l396"></a><a href="#l396">396</a><td>goog.math.isNegativeZero = function(num) {<tr><td><a id="l397"></a><a href="#l397">397</a><td> return num == 0 && 1 / num < 0;<tr><td><a id="l398"></a><a href="#l398">398</a><td>};<tr><td><a id="l399"></a><a href="#l399">399</a><td><tr><td><a id="l400"></a><a href="#l400">400</a><td><tr><td><a id="l401"></a><a href="#l401">401</a><td>/**<tr><td><a id="l402"></a><a href="#l402">402</a><td> * Returns the precise value of floor(log10(num)).<tr><td><a id="l403"></a><a href="#l403">403</a><td> * Simpler implementations didn't work because of floating point rounding<tr><td><a id="l404"></a><a href="#l404">404</a><td> * errors. For example<tr><td><a id="l405"></a><a href="#l405">405</a><td> * <ul><tr><td><a id="l406"></a><a href="#l406">406</a><td> * <li>Math.floor(Math.log(num) / Math.LN10) is off by one for num == 1e+3.<tr><td><a id="l407"></a><a href="#l407">407</a><td> * <li>Math.floor(Math.log(num) * Math.LOG10E) is off by one for num == 1e+15.<tr><td><a id="l408"></a><a href="#l408">408</a><td> * <li>Math.floor(Math.log10(num)) is off by one for num == 1e+15 - 1.<tr><td><a id="l409"></a><a href="#l409">409</a><td> * </ul><tr><td><a id="l410"></a><a href="#l410">410</a><td> * @param {number} num A floating point number.<tr><td><a id="l411"></a><a href="#l411">411</a><td> * @return {number} Its logarithm to base 10 rounded down to the nearest<tr><td><a id="l412"></a><a href="#l412">412</a><td> * integer if num > 0. -Infinity if num == 0. NaN if num < 0.<tr><td><a id="l413"></a><a href="#l413">413</a><td> */<tr><td><a id="l414"></a><a href="#l414">414</a><td>goog.math.log10Floor = function(num) {<tr><td><a id="l415"></a><a href="#l415">415</a><td> if (num > 0) {<tr><td><a id="l416"></a><a href="#l416">416</a><td> var x = Math.round(Math.log(num) * Math.LOG10E);<tr><td><a id="l417"></a><a href="#l417">417</a><td> return x - (parseFloat('1e' + x) > num ? 1 : 0);<tr><td><a id="l418"></a><a href="#l418">418</a><td> }<tr><td><a id="l419"></a><a href="#l419">419</a><td> return num == 0 ? -Infinity : NaN;<tr><td><a id="l420"></a><a href="#l420">420</a><td>};<tr><td><a id="l421"></a><a href="#l421">421</a><td><tr><td><a id="l422"></a><a href="#l422">422</a><td><tr><td><a id="l423"></a><a href="#l423">423</a><td>/**<tr><td><a id="l424"></a><a href="#l424">424</a><td> * A tweaked variant of {@code Math.floor} which tolerates if the passed number<tr><td><a id="l425"></a><a href="#l425">425</a><td> * is infinitesimally smaller than the closest integer. It often happens with<tr><td><a id="l426"></a><a href="#l426">426</a><td> * the results of floating point calculations because of the finite precision<tr><td><a id="l427"></a><a href="#l427">427</a><td> * of the intermediate results. For example {@code Math.floor(Math.log(1000) /<tr><td><a id="l428"></a><a href="#l428">428</a><td> * Math.LN10) == 2}, not 3 as one would expect.<tr><td><a id="l429"></a><a href="#l429">429</a><td> * @param {number} num A number.<tr><td><a id="l430"></a><a href="#l430">430</a><td> * @param {number=} opt_epsilon An infinitesimally small positive number, the<tr><td><a id="l431"></a><a href="#l431">431</a><td> * rounding error to tolerate.<tr><td><a id="l432"></a><a href="#l432">432</a><td> * @return {number} The largest integer less than or equal to {@code num}.<tr><td><a id="l433"></a><a href="#l433">433</a><td> */<tr><td><a id="l434"></a><a href="#l434">434</a><td>goog.math.safeFloor = function(num, opt_epsilon) {<tr><td><a id="l435"></a><a href="#l435">435</a><td> goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);<tr><td><a id="l436"></a><a href="#l436">436</a><td> return Math.floor(num + (opt_epsilon || 2e-15));<tr><td><a id="l437"></a><a href="#l437">437</a><td>};<tr><td><a id="l438"></a><a href="#l438">438</a><td><tr><td><a id="l439"></a><a href="#l439">439</a><td><tr><td><a id="l440"></a><a href="#l440">440</a><td>/**<tr><td><a id="l441"></a><a href="#l441">441</a><td> * A tweaked variant of {@code Math.ceil}. See {@code goog.math.safeFloor} for<tr><td><a id="l442"></a><a href="#l442">442</a><td> * details.<tr><td><a id="l443"></a><a href="#l443">443</a><td> * @param {number} num A number.<tr><td><a id="l444"></a><a href="#l444">444</a><td> * @param {number=} opt_epsilon An infinitesimally small positive number, the<tr><td><a id="l445"></a><a href="#l445">445</a><td> * rounding error to tolerate.<tr><td><a id="l446"></a><a href="#l446">446</a><td> * @return {number} The smallest integer greater than or equal to {@code num}.<tr><td><a id="l447"></a><a href="#l447">447</a><td> */<tr><td><a id="l448"></a><a href="#l448">448</a><td>goog.math.safeCeil = function(num, opt_epsilon) {<tr><td><a id="l449"></a><a href="#l449">449</a><td> goog.asserts.assert(!goog.isDef(opt_epsilon) || opt_epsilon > 0);<tr><td><a id="l450"></a><a href="#l450">450</a><td> return Math.ceil(num - (opt_epsilon || 2e-15));<tr><td><a id="l451"></a><a href="#l451">451</a><td>};</table></div></article><nav><h3><a href="../../../../index.html" tabindex="2">Overview</a></h3><div><input type="checkbox" id="nav-modules" checked/><label for="nav-modules"><h3><span class="selectable" tabindex="2">Modules</span></h3></label><div id="nav-modules-view"></div></div><div><input type="checkbox" id="nav-types" checked/><label for="nav-types"><h3><span class="selectable" tabindex="2">Types</span></h3></label><div id="nav-types-view"></div></div><h3><a href="../../../../Changes.html" tabindex="2">Changes</a></h3></nav></main><footer><div><a href="https://github.com/jleyba/js-dossier">Generated by dossier</a></div></footer><script src="../../../../types.js"></script><script src="../../../../dossier.js"></script>