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Posted to commits@commons.apache.org by ah...@apache.org on 2022/12/01 16:47:13 UTC
svn commit: r58392 [21/50] - in /dev/commons/statistics/1.0-RC1: ./ binaries/ site/ site/css/ site/images/ site/images/logos/ site/img/ site/js/ site/release-notes/ site/style/ site/userguide/ site/xref-test/ site/xref-test/org/ site/xref-test/org/apac...
Added: dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/ExtendedPrecisionTest.html
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--- dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/ExtendedPrecisionTest.html (added)
+++ dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/ExtendedPrecisionTest.html Thu Dec 1 16:47:12 2022
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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+<head><meta http-equiv="content-type" content="text/html; charset=UTF-8" />
+<title>ExtendedPrecisionTest xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/ExtendedPrecisionTest.html">View Javadoc</a></div><pre>
+<a class="jxr_linenumber" name="L1" href="#L1">1</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L2" href="#L2">2</a> <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em>
+<a class="jxr_linenumber" name="L3" href="#L3">3</a> <em class="jxr_comment"> * contributor license agreements. See the NOTICE file distributed with</em>
+<a class="jxr_linenumber" name="L4" href="#L4">4</a> <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em>
+<a class="jxr_linenumber" name="L5" href="#L5">5</a> <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em>
+<a class="jxr_linenumber" name="L6" href="#L6">6</a> <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em>
+<a class="jxr_linenumber" name="L7" href="#L7">7</a> <em class="jxr_comment"> * the License. You may obtain a copy of the License at</em>
+<a class="jxr_linenumber" name="L8" href="#L8">8</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L9" href="#L9">9</a> <em class="jxr_comment"> * <a href="http://www.apache.org/licenses/LICENSE-2.0" target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.0</a></em>
+<a class="jxr_linenumber" name="L10" href="#L10">10</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L11" href="#L11">11</a> <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em>
+<a class="jxr_linenumber" name="L12" href="#L12">12</a> <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em>
+<a class="jxr_linenumber" name="L13" href="#L13">13</a> <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em>
+<a class="jxr_linenumber" name="L14" href="#L14">14</a> <em class="jxr_comment"> * See the License for the specific language governing permissions and</em>
+<a class="jxr_linenumber" name="L15" href="#L15">15</a> <em class="jxr_comment"> * limitations under the License.</em>
+<a class="jxr_linenumber" name="L16" href="#L16">16</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L17" href="#L17">17</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution;
+<a class="jxr_linenumber" name="L18" href="#L18">18</a>
+<a class="jxr_linenumber" name="L19" href="#L19">19</a> <strong class="jxr_keyword">import</strong> java.math.BigDecimal;
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> java.math.MathContext;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Assertions;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.MethodOrderer;
+<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Order;
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Test;
+<a class="jxr_linenumber" name="L25" href="#L25">25</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.TestMethodOrder;
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.ParameterizedTest;
+<a class="jxr_linenumber" name="L27" href="#L27">27</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.CsvFileSource;
+<a class="jxr_linenumber" name="L28" href="#L28">28</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.ValueSource;
+<a class="jxr_linenumber" name="L29" href="#L29">29</a>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> <em class="jxr_javadoccomment"> * Test for {@link ExtendedPrecision}.</em>
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> @TestMethodOrder(MethodOrderer.OrderAnnotation.<strong class="jxr_keyword">class</strong>)
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <strong class="jxr_keyword">class</strong> <a name="ExtendedPrecisionTest" href="../../../../../org/apache/commons/statistics/distribution/ExtendedPrecisionTest.html#ExtendedPrecisionTest">ExtendedPrecisionTest</a> {
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <em class="jxr_javadoccomment">/** sqrt(2). */</em>
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> ROOT2 = Math.sqrt(2.0);
+<a class="jxr_linenumber" name="L37" href="#L37">37</a> <em class="jxr_javadoccomment">/** sqrt(2 pi) as a String. Computed to 64-digits. */</em>
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> String SQRT_TWO_PI = <span class="jxr_string">"2.506628274631000502415765284811045253006986740609938316629923576"</span>;
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> <em class="jxr_javadoccomment">/** sqrt(2 pi) as a double. Note: This is 1 ULP different from Math.sqrt(2 * Math.PI). */</em>
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> ROOT2PI = Double.parseDouble(SQRT_TWO_PI);
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> <em class="jxr_javadoccomment">/** The sum of the squared ULP error for the first standard computation for sqrt(2 * x * x). */</em>
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> RMS SQRT2XX_RMS1 = <strong class="jxr_keyword">new</strong> RMS();
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> <em class="jxr_javadoccomment">/** The sum of the squared ULP error for the second standard computation for sqrt(2 * x * x). */</em>
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> RMS SQRT2XX_RMS2 = <strong class="jxr_keyword">new</strong> RMS();
+<a class="jxr_linenumber" name="L45" href="#L45">45</a> <em class="jxr_javadoccomment">/** The sum of the squared ULP error for the first computation for x * sqrt(2 pi). */</em>
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> RMS XSQRT2PI_RMS = <strong class="jxr_keyword">new</strong> RMS();
+<a class="jxr_linenumber" name="L47" href="#L47">47</a> <em class="jxr_javadoccomment">/** The sum of the squared ULP error for the first computation for exp(-0.5*x*x). */</em>
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> RMS EXPMHXX_RMS1 = <strong class="jxr_keyword">new</strong> RMS();
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> <em class="jxr_javadoccomment">/** The sum of the squared ULP error for the second computation for exp(-0.5*x*x). */</em>
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">final</strong> RMS EXPMHXX_RMS2 = <strong class="jxr_keyword">new</strong> RMS();
+<a class="jxr_linenumber" name="L51" href="#L51">51</a>
+<a class="jxr_linenumber" name="L52" href="#L52">52</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> <em class="jxr_javadoccomment"> * Class to compute the root mean squared error (RMS).</em>
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> <em class="jxr_javadoccomment"> * @see <a href="<a href="https://en.wikipedia.org/wiki/Root_mean_square" target="alexandria_uri">https://en.wikipedia.org/wiki/Root_mean_square</a>">Wikipedia: RMS</a></em>
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">class</strong> RMS {
+<a class="jxr_linenumber" name="L57" href="#L57">57</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> ss;
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">double</strong> max;
+<a class="jxr_linenumber" name="L59" href="#L59">59</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">int</strong> n;
+<a class="jxr_linenumber" name="L60" href="#L60">60</a>
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> <em class="jxr_javadoccomment"> * @param x Value (assumed to be positive)</em>
+<a class="jxr_linenumber" name="L63" href="#L63">63</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <strong class="jxr_keyword">void</strong> add(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <em class="jxr_comment">// Overflow is not supported.</em>
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> <em class="jxr_comment">// Assume the expected and actual are quite close when measuring the RMS.</em>
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> ss += x * x;
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> n++;
+<a class="jxr_linenumber" name="L69" href="#L69">69</a> <em class="jxr_comment">// Absolute error when detecting the maximum</em>
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> x = Math.abs(x);
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> max = max < x ? x : max;
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> }
+<a class="jxr_linenumber" name="L73" href="#L73">73</a>
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> <em class="jxr_javadoccomment"> * Gets the maximum error.</em>
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L77" href="#L77">77</a> <em class="jxr_javadoccomment"> * <p>This is not used for assertions. It can be used to set maximum ULP thresholds</em>
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> <em class="jxr_javadoccomment"> * for test data if the TestUtils.assertEquals method is used with a large maxUlps</em>
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> <em class="jxr_javadoccomment"> * to measure the ulp (and effectively ignore failures) and the maximum reported</em>
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <em class="jxr_javadoccomment"> * as the end of testing.</em>
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> <em class="jxr_javadoccomment"> * @return maximum error</em>
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> <strong class="jxr_keyword">double</strong> getMax() {
+<a class="jxr_linenumber" name="L85" href="#L85">85</a> <strong class="jxr_keyword">return</strong> max;
+<a class="jxr_linenumber" name="L86" href="#L86">86</a> }
+<a class="jxr_linenumber" name="L87" href="#L87">87</a>
+<a class="jxr_linenumber" name="L88" href="#L88">88</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> <em class="jxr_javadoccomment"> * Gets the root mean squared error (RMS).</em>
+<a class="jxr_linenumber" name="L90" href="#L90">90</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <em class="jxr_javadoccomment"> * <p> Note: If no data has been added this will return 0/0 = nan.</em>
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <em class="jxr_javadoccomment"> * This prevents using in assertions without adding data.</em>
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L94" href="#L94">94</a> <em class="jxr_javadoccomment"> * @return root mean squared error (RMS)</em>
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> <strong class="jxr_keyword">double</strong> getRMS() {
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> <strong class="jxr_keyword">return</strong> Math.sqrt(ss / n);
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> }
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> }
+<a class="jxr_linenumber" name="L100" href="#L100">100</a>
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> @Test
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> <strong class="jxr_keyword">void</strong> testSqrt2PiConstants() {
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> <strong class="jxr_keyword">final</strong> BigDecimal sqrt2pi = <strong class="jxr_keyword">new</strong> BigDecimal(SQRT_TWO_PI);
+<a class="jxr_linenumber" name="L104" href="#L104">104</a>
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <em class="jxr_comment">// Use a 106-bit number as:</em>
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <em class="jxr_comment">// (value, roundOff)</em>
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> value = sqrt2pi.doubleValue();
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> roundOff = sqrt2pi.subtract(<strong class="jxr_keyword">new</strong> BigDecimal(value)).doubleValue();
+<a class="jxr_linenumber" name="L109" href="#L109">109</a> <em class="jxr_comment">// Adding the round-off does not change the value</em>
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> Assertions.assertEquals(ExtendedPrecision.SQRT2PI,
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> ExtendedPrecision.SQRT2PI + ExtendedPrecision.SQRT2PI_R, <span class="jxr_string">"value + round-off"</span>);
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <em class="jxr_comment">// Check constants</em>
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> Assertions.assertEquals(value, ExtendedPrecision.SQRT2PI, <span class="jxr_string">"sqrt(2 pi)"</span>);
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> Assertions.assertEquals(roundOff, ExtendedPrecision.SQRT2PI_R, <span class="jxr_string">"sqrt(2 pi) round-off"</span>);
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> <em class="jxr_comment">// Sanity check against JDK Math</em>
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> Assertions.assertEquals(value, Math.sqrt(2 * Math.PI), Math.ulp(value), <span class="jxr_string">"Math.sqrt(2 pi)"</span>);
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> }
+<a class="jxr_linenumber" name="L118" href="#L118">118</a>
+<a class="jxr_linenumber" name="L119" href="#L119">119</a> @Test
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> <strong class="jxr_keyword">void</strong> testSqrt2xxUnderAndOverflow() {
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x = 1.5;
+<a class="jxr_linenumber" name="L122" href="#L122">122</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> e = 2.12132034355964257320253308631;
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> Assertions.assertEquals(e, ExtendedPrecision.sqrt2xx(x));
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">int</strong> i : <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">int</strong>[] {-1000, -600, -200, 200, 600, 1000}) {
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> scale = Math.scalb(1.0, i);
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x1 = x * scale;
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> e1 = e * scale;
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> Assertions.assertEquals(e1, ExtendedPrecision.sqrt2xx(x1), () -> Double.toString(x1));
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> }
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> }
+<a class="jxr_linenumber" name="L131" href="#L131">131</a>
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> @Test
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> <strong class="jxr_keyword">void</strong> testSqrt2xxExtremes() {
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> <em class="jxr_comment">// Handle big numbers</em>
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, ExtendedPrecision.sqrt2xx(Double.MAX_VALUE));
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> Assertions.assertEquals(Double.POSITIVE_INFINITY, ExtendedPrecision.sqrt2xx(Double.POSITIVE_INFINITY));
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> Assertions.assertEquals(0.0, ExtendedPrecision.sqrt2xx(0));
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> Assertions.assertEquals(ROOT2, ExtendedPrecision.sqrt2xx(1));
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> Assertions.assertEquals(Math.sqrt(8), ExtendedPrecision.sqrt2xx(2));
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> <em class="jxr_comment">// Handle sub-normal numbers</em>
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> <strong class="jxr_keyword">for</strong> (<strong class="jxr_keyword">int</strong> i = 2; i <= 10; i++) {
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> Assertions.assertEquals(i * Double.MIN_VALUE * Math.sqrt(2), ExtendedPrecision.sqrt2xx(i * Double.MIN_VALUE));
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> }
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> <em class="jxr_comment">// Currently the argument is assumed to be positive.</em>
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> Assertions.assertEquals(Double.NaN, ExtendedPrecision.sqrt2xx(Double.NaN));
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> <em class="jxr_comment">// Big negative numbers overflow and the extended precision computation generates NaN.</em>
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> Assertions.assertEquals(Double.NaN, ExtendedPrecision.sqrt2xx(-1e300));
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> }
+<a class="jxr_linenumber" name="L149" href="#L149">149</a>
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> <em class="jxr_javadoccomment"> * Test the extended precision {@code sqrt(2 * x * x)}. The expected result</em>
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> <em class="jxr_javadoccomment"> * is an extended precision computation. For comparison ulp errors are collected for</em>
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> <em class="jxr_javadoccomment"> * two standard precision computations.</em>
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L155" href="#L155">155</a> <em class="jxr_javadoccomment"> * @param x Value x</em>
+<a class="jxr_linenumber" name="L156" href="#L156">156</a> <em class="jxr_javadoccomment"> * @param expected Expected result of {@code sqrt(2 * x * x)}.</em>
+<a class="jxr_linenumber" name="L157" href="#L157">157</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> @Order(1)
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> @CsvFileSource(resources = <span class="jxr_string">"sqrt2xx.csv"</span>)
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> <strong class="jxr_keyword">void</strong> testSqrt2xx(<strong class="jxr_keyword">double</strong> x, BigDecimal expected) {
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> e = expected.doubleValue();
+<a class="jxr_linenumber" name="L163" href="#L163">163</a> Assertions.assertEquals(e, ExtendedPrecision.sqrt2xx(x));
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <em class="jxr_comment">// Compute error for the standard computations</em>
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> addError(Math.sqrt(2 * x * x), expected, e, SQRT2XX_RMS1);
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> addError(x * ROOT2, expected, e, SQRT2XX_RMS2);
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> }
+<a class="jxr_linenumber" name="L168" href="#L168">168</a>
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> @Test
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> <strong class="jxr_keyword">void</strong> testSqrt2xxStandardPrecision1() {
+<a class="jxr_linenumber" name="L171" href="#L171">171</a> <em class="jxr_comment">// Typical result: max 0.7780 rms 0.2144</em>
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> assertPrecision(SQRT2XX_RMS1, 0.9, 0.3);
+<a class="jxr_linenumber" name="L173" href="#L173">173</a> }
+<a class="jxr_linenumber" name="L174" href="#L174">174</a>
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> @Test
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> <strong class="jxr_keyword">void</strong> testSqrt2xxStandardPrecision2() {
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> <em class="jxr_comment">// Typical result: max 1.0598 rms 0.4781</em>
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> assertPrecision(SQRT2XX_RMS2, 1.3, 0.6);
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> }
+<a class="jxr_linenumber" name="L180" href="#L180">180</a>
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> @ValueSource(doubles = {0, 1, Double.MAX_VALUE, Double.POSITIVE_INFINITY, Double.NaN})
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> <strong class="jxr_keyword">void</strong> testXsqrt2piEdgeCases(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> expected = x * ROOT2PI;
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> actual = ExtendedPrecision.xsqrt2pi(x);
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> Assertions.assertEquals(expected, actual, 1e-15);
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> }
+<a class="jxr_linenumber" name="L188" href="#L188">188</a>
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> <em class="jxr_javadoccomment"> * Test the extended precision {@code x * sqrt(2 * pi)}. The expected result</em>
+<a class="jxr_linenumber" name="L191" href="#L191">191</a> <em class="jxr_javadoccomment"> * is an extended precision computation. For comparison ulp errors are collected for</em>
+<a class="jxr_linenumber" name="L192" href="#L192">192</a> <em class="jxr_javadoccomment"> * a standard computation.</em>
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> <em class="jxr_javadoccomment"> * @param x Value x</em>
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> <em class="jxr_javadoccomment"> * @param expected Expected result of {@code x * sqrt(2 * pi)}.</em>
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> @Order(1)
+<a class="jxr_linenumber" name="L199" href="#L199">199</a> @CsvFileSource(resources = <span class="jxr_string">"xsqrt2pi.csv"</span>)
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> <strong class="jxr_keyword">void</strong> testXsqrt2pi(<strong class="jxr_keyword">double</strong> x, BigDecimal expected) {
+<a class="jxr_linenumber" name="L201" href="#L201">201</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> e = expected.doubleValue();
+<a class="jxr_linenumber" name="L202" href="#L202">202</a> Assertions.assertEquals(e, ExtendedPrecision.xsqrt2pi(x));
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> <em class="jxr_comment">// Compute error for the standard computation</em>
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> addError(x * ROOT2PI, expected, e, XSQRT2PI_RMS);
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> }
+<a class="jxr_linenumber" name="L206" href="#L206">206</a>
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> @Test
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> <strong class="jxr_keyword">void</strong> testXsqrt2piPrecision() {
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> <em class="jxr_comment">// Typical result: max 1.1397 rms 0.5368</em>
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> assertPrecision(XSQRT2PI_RMS, 1.2, 0.6);
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> }
+<a class="jxr_linenumber" name="L212" href="#L212">212</a>
+<a class="jxr_linenumber" name="L213" href="#L213">213</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L214" href="#L214">214</a> @ValueSource(doubles = {0, 0.5, 1, 2, 3, 4, 5, 38.5, Double.MAX_VALUE, Double.POSITIVE_INFINITY, Double.NaN})
+<a class="jxr_linenumber" name="L215" href="#L215">215</a> <strong class="jxr_keyword">void</strong> testExpmhxxEdgeCases(<strong class="jxr_keyword">double</strong> x) {
+<a class="jxr_linenumber" name="L216" href="#L216">216</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> expected = Math.exp(-0.5 * x * x);
+<a class="jxr_linenumber" name="L217" href="#L217">217</a> Assertions.assertEquals(expected, ExtendedPrecision.expmhxx(x));
+<a class="jxr_linenumber" name="L218" href="#L218">218</a> Assertions.assertEquals(expected, ExtendedPrecision.expmhxx(-x));
+<a class="jxr_linenumber" name="L219" href="#L219">219</a> }
+<a class="jxr_linenumber" name="L220" href="#L220">220</a>
+<a class="jxr_linenumber" name="L221" href="#L221">221</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L222" href="#L222">222</a> <em class="jxr_javadoccomment"> * Test the extended precision {@code exp(-0.5 * x * x)}. The expected result</em>
+<a class="jxr_linenumber" name="L223" href="#L223">223</a> <em class="jxr_javadoccomment"> * is an extended precision computation. For comparison ulp errors are collected for</em>
+<a class="jxr_linenumber" name="L224" href="#L224">224</a> <em class="jxr_javadoccomment"> * the standard precision computation.</em>
+<a class="jxr_linenumber" name="L225" href="#L225">225</a> <em class="jxr_javadoccomment"> *</em>
+<a class="jxr_linenumber" name="L226" href="#L226">226</a> <em class="jxr_javadoccomment"> * @param x Value x</em>
+<a class="jxr_linenumber" name="L227" href="#L227">227</a> <em class="jxr_javadoccomment"> * @param expected Expected result of {@code exp(-0.5 * x * x)}.</em>
+<a class="jxr_linenumber" name="L228" href="#L228">228</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L229" href="#L229">229</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L230" href="#L230">230</a> @Order(1)
+<a class="jxr_linenumber" name="L231" href="#L231">231</a> @CsvFileSource(resources = <span class="jxr_string">"expmhxx.csv"</span>)
+<a class="jxr_linenumber" name="L232" href="#L232">232</a> <strong class="jxr_keyword">void</strong> testExpmhxx(<strong class="jxr_keyword">double</strong> x, BigDecimal expected) {
+<a class="jxr_linenumber" name="L233" href="#L233">233</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> e = expected.doubleValue();
+<a class="jxr_linenumber" name="L234" href="#L234">234</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> actual = ExtendedPrecision.expmhxx(x);
+<a class="jxr_linenumber" name="L235" href="#L235">235</a> Assertions.assertEquals(e, actual, Math.ulp(e) * 2);
+<a class="jxr_linenumber" name="L236" href="#L236">236</a> <em class="jxr_comment">// Compute errors</em>
+<a class="jxr_linenumber" name="L237" href="#L237">237</a> addError(actual, expected, e, EXPMHXX_RMS1);
+<a class="jxr_linenumber" name="L238" href="#L238">238</a> addError(Math.exp(-0.5 * x * x), expected, e, EXPMHXX_RMS2);
+<a class="jxr_linenumber" name="L239" href="#L239">239</a> }
+<a class="jxr_linenumber" name="L240" href="#L240">240</a>
+<a class="jxr_linenumber" name="L241" href="#L241">241</a> @Test
+<a class="jxr_linenumber" name="L242" href="#L242">242</a> <strong class="jxr_keyword">void</strong> testExpmhxxHighPrecision() {
+<a class="jxr_linenumber" name="L243" href="#L243">243</a> <em class="jxr_comment">// Typical result: max 0.9727 rms 0.3481</em>
+<a class="jxr_linenumber" name="L244" href="#L244">244</a> assertPrecision(EXPMHXX_RMS1, 1.5, 0.5);
+<a class="jxr_linenumber" name="L245" href="#L245">245</a> }
+<a class="jxr_linenumber" name="L246" href="#L246">246</a>
+<a class="jxr_linenumber" name="L247" href="#L247">247</a> @Test
+<a class="jxr_linenumber" name="L248" href="#L248">248</a> <strong class="jxr_keyword">void</strong> testExpmhxxStandardPrecision() {
+<a class="jxr_linenumber" name="L249" href="#L249">249</a> <em class="jxr_comment">// Typical result: max 385.7193 rms 50.7769</em>
+<a class="jxr_linenumber" name="L250" href="#L250">250</a> assertPrecision(EXPMHXX_RMS2, 400, 60);
+<a class="jxr_linenumber" name="L251" href="#L251">251</a> }
+<a class="jxr_linenumber" name="L252" href="#L252">252</a>
+<a class="jxr_linenumber" name="L253" href="#L253">253</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">void</strong> assertPrecision(RMS rms, <strong class="jxr_keyword">double</strong> maxError, <strong class="jxr_keyword">double</strong> rmsError) {
+<a class="jxr_linenumber" name="L254" href="#L254">254</a> Assertions.assertTrue(rms.getMax() < maxError, () -> <span class="jxr_string">"max error: "</span> + rms.getMax());
+<a class="jxr_linenumber" name="L255" href="#L255">255</a> Assertions.assertTrue(rms.getRMS() < rmsError, () -> <span class="jxr_string">"rms error: "</span> + rms.getRMS());
+<a class="jxr_linenumber" name="L256" href="#L256">256</a> }
+<a class="jxr_linenumber" name="L257" href="#L257">257</a>
+<a class="jxr_linenumber" name="L258" href="#L258">258</a> <strong class="jxr_keyword">private</strong> <strong class="jxr_keyword">static</strong> <strong class="jxr_keyword">void</strong> addError(<strong class="jxr_keyword">double</strong> z, BigDecimal expected, <strong class="jxr_keyword">double</strong> e, RMS rms) {
+<a class="jxr_linenumber" name="L259" href="#L259">259</a> <strong class="jxr_keyword">double</strong> error;
+<a class="jxr_linenumber" name="L260" href="#L260">260</a> <strong class="jxr_keyword">if</strong> (z == e) {
+<a class="jxr_linenumber" name="L261" href="#L261">261</a> error = 0;
+<a class="jxr_linenumber" name="L262" href="#L262">262</a> } <strong class="jxr_keyword">else</strong> {
+<a class="jxr_linenumber" name="L263" href="#L263">263</a> <em class="jxr_comment">// Compute ULP error</em>
+<a class="jxr_linenumber" name="L264" href="#L264">264</a> error = expected.subtract(<strong class="jxr_keyword">new</strong> BigDecimal(z))
+<a class="jxr_linenumber" name="L265" href="#L265">265</a> .divide(<strong class="jxr_keyword">new</strong> BigDecimal(Math.ulp(e)), MathContext.DECIMAL64).doubleValue();
+<a class="jxr_linenumber" name="L266" href="#L266">266</a> }
+<a class="jxr_linenumber" name="L267" href="#L267">267</a> rms.add(error);
+<a class="jxr_linenumber" name="L268" href="#L268">268</a> }
+<a class="jxr_linenumber" name="L269" href="#L269">269</a> }
+</pre>
+<hr/>
+<div id="footer">Copyright © 2018–2022 <a href="https://www.apache.org/">The Apache Software Foundation</a>. All rights reserved.</div>
+</body>
+</html>
Added: dev/commons/statistics/1.0-RC1/site/xref-test/org/apache/commons/statistics/distribution/FDistributionTest.html
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@@ -0,0 +1,224 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
+<head><meta http-equiv="content-type" content="text/html; charset=UTF-8" />
+<title>FDistributionTest xref</title>
+<link type="text/css" rel="stylesheet" href="../../../../../stylesheet.css" />
+</head>
+<body>
+<div id="overview"><a href="../../../../../../testapidocs/org/apache/commons/statistics/distribution/FDistributionTest.html">View Javadoc</a></div><pre>
+<a class="jxr_linenumber" name="L1" href="#L1">1</a> <em class="jxr_comment">/*</em>
+<a class="jxr_linenumber" name="L2" href="#L2">2</a> <em class="jxr_comment"> * Licensed to the Apache Software Foundation (ASF) under one or more</em>
+<a class="jxr_linenumber" name="L3" href="#L3">3</a> <em class="jxr_comment"> * contributor license agreements. See the NOTICE file distributed with</em>
+<a class="jxr_linenumber" name="L4" href="#L4">4</a> <em class="jxr_comment"> * this work for additional information regarding copyright ownership.</em>
+<a class="jxr_linenumber" name="L5" href="#L5">5</a> <em class="jxr_comment"> * The ASF licenses this file to You under the Apache License, Version 2.0</em>
+<a class="jxr_linenumber" name="L6" href="#L6">6</a> <em class="jxr_comment"> * (the "License"); you may not use this file except in compliance with</em>
+<a class="jxr_linenumber" name="L7" href="#L7">7</a> <em class="jxr_comment"> * the License. You may obtain a copy of the License at</em>
+<a class="jxr_linenumber" name="L8" href="#L8">8</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L9" href="#L9">9</a> <em class="jxr_comment"> * <a href="http://www.apache.org/licenses/LICENSE-2.0" target="alexandria_uri">http://www.apache.org/licenses/LICENSE-2.0</a></em>
+<a class="jxr_linenumber" name="L10" href="#L10">10</a> <em class="jxr_comment"> *</em>
+<a class="jxr_linenumber" name="L11" href="#L11">11</a> <em class="jxr_comment"> * Unless required by applicable law or agreed to in writing, software</em>
+<a class="jxr_linenumber" name="L12" href="#L12">12</a> <em class="jxr_comment"> * distributed under the License is distributed on an "AS IS" BASIS,</em>
+<a class="jxr_linenumber" name="L13" href="#L13">13</a> <em class="jxr_comment"> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</em>
+<a class="jxr_linenumber" name="L14" href="#L14">14</a> <em class="jxr_comment"> * See the License for the specific language governing permissions and</em>
+<a class="jxr_linenumber" name="L15" href="#L15">15</a> <em class="jxr_comment"> * limitations under the License.</em>
+<a class="jxr_linenumber" name="L16" href="#L16">16</a> <em class="jxr_comment"> */</em>
+<a class="jxr_linenumber" name="L17" href="#L17">17</a> <strong class="jxr_keyword">package</strong> org.apache.commons.statistics.distribution;
+<a class="jxr_linenumber" name="L18" href="#L18">18</a>
+<a class="jxr_linenumber" name="L19" href="#L19">19</a> <strong class="jxr_keyword">import</strong> java.util.stream.Stream;
+<a class="jxr_linenumber" name="L20" href="#L20">20</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Assertions;
+<a class="jxr_linenumber" name="L21" href="#L21">21</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.api.Test;
+<a class="jxr_linenumber" name="L22" href="#L22">22</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.ParameterizedTest;
+<a class="jxr_linenumber" name="L23" href="#L23">23</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.Arguments;
+<a class="jxr_linenumber" name="L24" href="#L24">24</a> <strong class="jxr_keyword">import</strong> org.junit.jupiter.params.provider.MethodSource;
+<a class="jxr_linenumber" name="L25" href="#L25">25</a>
+<a class="jxr_linenumber" name="L26" href="#L26">26</a> <em class="jxr_javadoccomment">/**</em>
+<a class="jxr_linenumber" name="L27" href="#L27">27</a> <em class="jxr_javadoccomment"> * Test cases for {@link FDistribution}.</em>
+<a class="jxr_linenumber" name="L28" href="#L28">28</a> <em class="jxr_javadoccomment"> * Extends {@link BaseContinuousDistributionTest}. See javadoc of that class for details.</em>
+<a class="jxr_linenumber" name="L29" href="#L29">29</a> <em class="jxr_javadoccomment"> */</em>
+<a class="jxr_linenumber" name="L30" href="#L30">30</a> <strong class="jxr_keyword">class</strong> <a name="FDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/FDistributionTest.html#FDistributionTest">FDistributionTest</a> <strong class="jxr_keyword">extends</strong> <a name="BaseContinuousDistributionTest" href="../../../../../org/apache/commons/statistics/distribution/BaseContinuousDistributionTest.html#BaseContinuousDistributionTest">BaseContinuousDistributionTest</a> {
+<a class="jxr_linenumber" name="L31" href="#L31">31</a> @Override
+<a class="jxr_linenumber" name="L32" href="#L32">32</a> ContinuousDistribution makeDistribution(Object... parameters) {
+<a class="jxr_linenumber" name="L33" href="#L33">33</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> df1 = (Double) parameters[0];
+<a class="jxr_linenumber" name="L34" href="#L34">34</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> df2 = (Double) parameters[1];
+<a class="jxr_linenumber" name="L35" href="#L35">35</a> <strong class="jxr_keyword">return</strong> FDistribution.of(df1, df2);
+<a class="jxr_linenumber" name="L36" href="#L36">36</a> }
+<a class="jxr_linenumber" name="L37" href="#L37">37</a>
+<a class="jxr_linenumber" name="L38" href="#L38">38</a> @Override
+<a class="jxr_linenumber" name="L39" href="#L39">39</a> Object[][] makeInvalidParameters() {
+<a class="jxr_linenumber" name="L40" href="#L40">40</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> Object[][] {
+<a class="jxr_linenumber" name="L41" href="#L41">41</a> {0.0, 1.0},
+<a class="jxr_linenumber" name="L42" href="#L42">42</a> {-0.1, 1.0},
+<a class="jxr_linenumber" name="L43" href="#L43">43</a> {1.0, 0.0},
+<a class="jxr_linenumber" name="L44" href="#L44">44</a> {1.0, -0.1},
+<a class="jxr_linenumber" name="L45" href="#L45">45</a> };
+<a class="jxr_linenumber" name="L46" href="#L46">46</a> }
+<a class="jxr_linenumber" name="L47" href="#L47">47</a>
+<a class="jxr_linenumber" name="L48" href="#L48">48</a> @Override
+<a class="jxr_linenumber" name="L49" href="#L49">49</a> String[] getParameterNames() {
+<a class="jxr_linenumber" name="L50" href="#L50">50</a> <strong class="jxr_keyword">return</strong> <strong class="jxr_keyword">new</strong> String[] {<span class="jxr_string">"NumeratorDegreesOfFreedom"</span>, <span class="jxr_string">"DenominatorDegreesOfFreedom"</span>};
+<a class="jxr_linenumber" name="L51" href="#L51">51</a> }
+<a class="jxr_linenumber" name="L52" href="#L52">52</a>
+<a class="jxr_linenumber" name="L53" href="#L53">53</a> @Override
+<a class="jxr_linenumber" name="L54" href="#L54">54</a> <strong class="jxr_keyword">protected</strong> <strong class="jxr_keyword">double</strong> getRelativeTolerance() {
+<a class="jxr_linenumber" name="L55" href="#L55">55</a> <strong class="jxr_keyword">return</strong> 8e-15;
+<a class="jxr_linenumber" name="L56" href="#L56">56</a> }
+<a class="jxr_linenumber" name="L57" href="#L57">57</a>
+<a class="jxr_linenumber" name="L58" href="#L58">58</a> <em class="jxr_comment">//-------------------- Additional test cases -------------------------------</em>
+<a class="jxr_linenumber" name="L59" href="#L59">59</a>
+<a class="jxr_linenumber" name="L60" href="#L60">60</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L61" href="#L61">61</a> @MethodSource
+<a class="jxr_linenumber" name="L62" href="#L62">62</a> <strong class="jxr_keyword">void</strong> testAdditionalMoments(<strong class="jxr_keyword">double</strong> numeratorDegreesOfFreedom,
+<a class="jxr_linenumber" name="L63" href="#L63">63</a> <strong class="jxr_keyword">double</strong> denominatorDegreesOfFreedom,
+<a class="jxr_linenumber" name="L64" href="#L64">64</a> <strong class="jxr_keyword">double</strong> mean,
+<a class="jxr_linenumber" name="L65" href="#L65">65</a> <strong class="jxr_keyword">double</strong> variance) {
+<a class="jxr_linenumber" name="L66" href="#L66">66</a> <strong class="jxr_keyword">final</strong> FDistribution dist = FDistribution.of(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom);
+<a class="jxr_linenumber" name="L67" href="#L67">67</a> testMoments(dist, mean, variance, DoubleTolerances.equals());
+<a class="jxr_linenumber" name="L68" href="#L68">68</a> }
+<a class="jxr_linenumber" name="L69" href="#L69">69</a>
+<a class="jxr_linenumber" name="L70" href="#L70">70</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testAdditionalMoments() {
+<a class="jxr_linenumber" name="L71" href="#L71">71</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L72" href="#L72">72</a> Arguments.of(1, 2, Double.NaN, Double.NaN),
+<a class="jxr_linenumber" name="L73" href="#L73">73</a> Arguments.of(1, 3, 3.0 / (3 - 2), Double.NaN),
+<a class="jxr_linenumber" name="L74" href="#L74">74</a> Arguments.of(1, 5, 5.0 / (5 - 2), (2 * 5 * 5 * 4) / 9.0)
+<a class="jxr_linenumber" name="L75" href="#L75">75</a> );
+<a class="jxr_linenumber" name="L76" href="#L76">76</a> }
+<a class="jxr_linenumber" name="L77" href="#L77">77</a>
+<a class="jxr_linenumber" name="L78" href="#L78">78</a> @Test
+<a class="jxr_linenumber" name="L79" href="#L79">79</a> <strong class="jxr_keyword">void</strong> testLargeDegreesOfFreedom() {
+<a class="jxr_linenumber" name="L80" href="#L80">80</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x0 = 0.999;
+<a class="jxr_linenumber" name="L81" href="#L81">81</a> <strong class="jxr_keyword">final</strong> FDistribution fd = FDistribution.of(100000, 100000);
+<a class="jxr_linenumber" name="L82" href="#L82">82</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> p = fd.cumulativeProbability(x0);
+<a class="jxr_linenumber" name="L83" href="#L83">83</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x = fd.inverseCumulativeProbability(p);
+<a class="jxr_linenumber" name="L84" href="#L84">84</a> Assertions.assertEquals(x0, x, 1.0e-5);
+<a class="jxr_linenumber" name="L85" href="#L85">85</a> }
+<a class="jxr_linenumber" name="L86" href="#L86">86</a>
+<a class="jxr_linenumber" name="L87" href="#L87">87</a> @Test
+<a class="jxr_linenumber" name="L88" href="#L88">88</a> <strong class="jxr_keyword">void</strong> testSmallDegreesOfFreedom() {
+<a class="jxr_linenumber" name="L89" href="#L89">89</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> x0 = 0.975;
+<a class="jxr_linenumber" name="L90" href="#L90">90</a> FDistribution fd = FDistribution.of(1, 1);
+<a class="jxr_linenumber" name="L91" href="#L91">91</a> <strong class="jxr_keyword">double</strong> p = fd.cumulativeProbability(x0);
+<a class="jxr_linenumber" name="L92" href="#L92">92</a> <strong class="jxr_keyword">double</strong> x = fd.inverseCumulativeProbability(p);
+<a class="jxr_linenumber" name="L93" href="#L93">93</a> Assertions.assertEquals(x0, x, 1.0e-5);
+<a class="jxr_linenumber" name="L94" href="#L94">94</a>
+<a class="jxr_linenumber" name="L95" href="#L95">95</a> fd = FDistribution.of(1, 2);
+<a class="jxr_linenumber" name="L96" href="#L96">96</a> p = fd.cumulativeProbability(x0);
+<a class="jxr_linenumber" name="L97" href="#L97">97</a> x = fd.inverseCumulativeProbability(p);
+<a class="jxr_linenumber" name="L98" href="#L98">98</a> Assertions.assertEquals(x0, x, 1.0e-5);
+<a class="jxr_linenumber" name="L99" href="#L99">99</a> }
+<a class="jxr_linenumber" name="L100" href="#L100">100</a>
+<a class="jxr_linenumber" name="L101" href="#L101">101</a> @Test
+<a class="jxr_linenumber" name="L102" href="#L102">102</a> <strong class="jxr_keyword">void</strong> testMath785() {
+<a class="jxr_linenumber" name="L103" href="#L103">103</a> <em class="jxr_comment">// this test was failing due to inaccurate results from ContinuedFraction.</em>
+<a class="jxr_linenumber" name="L104" href="#L104">104</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> prob = 0.01;
+<a class="jxr_linenumber" name="L105" href="#L105">105</a> <strong class="jxr_keyword">final</strong> FDistribution f = FDistribution.of(200000, 200000);
+<a class="jxr_linenumber" name="L106" href="#L106">106</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong> result = f.inverseCumulativeProbability(prob);
+<a class="jxr_linenumber" name="L107" href="#L107">107</a> Assertions.assertTrue(result < 1.0, <span class="jxr_string">"Failing to calculate inverse cumulative probability"</span>);
+<a class="jxr_linenumber" name="L108" href="#L108">108</a> }
+<a class="jxr_linenumber" name="L109" href="#L109">109</a>
+<a class="jxr_linenumber" name="L110" href="#L110">110</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L111" href="#L111">111</a> @MethodSource
+<a class="jxr_linenumber" name="L112" href="#L112">112</a> <strong class="jxr_keyword">void</strong> testAdditionalLogDensity(<strong class="jxr_keyword">double</strong> numeratorDegreesOfFreedom,
+<a class="jxr_linenumber" name="L113" href="#L113">113</a> <strong class="jxr_keyword">double</strong> denominatorDegreesOfFreedom,
+<a class="jxr_linenumber" name="L114" href="#L114">114</a> <strong class="jxr_keyword">double</strong>[] points,
+<a class="jxr_linenumber" name="L115" href="#L115">115</a> <strong class="jxr_keyword">double</strong>[] values) {
+<a class="jxr_linenumber" name="L116" href="#L116">116</a> testLogDensity(FDistribution.of(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom),
+<a class="jxr_linenumber" name="L117" href="#L117">117</a> points, values, createRelTolerance(1e-15));
+<a class="jxr_linenumber" name="L118" href="#L118">118</a> }
+<a class="jxr_linenumber" name="L119" href="#L119">119</a>
+<a class="jxr_linenumber" name="L120" href="#L120">120</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testAdditionalLogDensity() {
+<a class="jxr_linenumber" name="L121" href="#L121">121</a> <em class="jxr_comment">// Computed using Boost multiprecision to 100 digits (output 25 digits).</em>
+<a class="jxr_linenumber" name="L122" href="#L122">122</a>
+<a class="jxr_linenumber" name="L123" href="#L123">123</a> <em class="jxr_comment">// Edge cases when the standard density is sub-normal or zero.</em>
+<a class="jxr_linenumber" name="L124" href="#L124">124</a> <strong class="jxr_keyword">final</strong> <strong class="jxr_keyword">double</strong>[] x = <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9};
+<a class="jxr_linenumber" name="L125" href="#L125">125</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L126" href="#L126">126</a> Arguments.of(100, 100, x,
+<a class="jxr_linenumber" name="L127" href="#L127">127</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {
+<a class="jxr_linenumber" name="L128" href="#L128">128</a> -56.96014024624318913110565,
+<a class="jxr_linenumber" name="L129" href="#L129">129</a> -165.8559950938238412964495,
+<a class="jxr_linenumber" name="L130" href="#L130">130</a> -282.3927517845117162132265,
+<a class="jxr_linenumber" name="L131" href="#L131">131</a> -399.7346409939330236149964,
+<a class="jxr_linenumber" name="L132" href="#L132">132</a> -517.157481231596055999464,
+<a class="jxr_linenumber" name="L133" href="#L133">133</a> -634.5884209792423525846316,
+<a class="jxr_linenumber" name="L134" href="#L134">134</a> -752.0201707219881824362492,
+<a class="jxr_linenumber" name="L135" href="#L135">135</a> -869.4520014646850073211334,
+<a class="jxr_linenumber" name="L136" href="#L136">136</a> -986.883840307381342156051}),
+<a class="jxr_linenumber" name="L137" href="#L137">137</a> Arguments.of(952, 912, x,
+<a class="jxr_linenumber" name="L138" href="#L138">138</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {
+<a class="jxr_linenumber" name="L139" href="#L139">139</a> -509.5128641158461391223255,
+<a class="jxr_linenumber" name="L140" href="#L140">140</a> -1485.417858108384337659572,
+<a class="jxr_linenumber" name="L141" href="#L141">141</a> -2529.705750311339816652123,
+<a class="jxr_linenumber" name="L142" href="#L142">142</a> -3581.184004620825529681231,
+<a class="jxr_linenumber" name="L143" href="#L143">143</a> -4633.385040722443349533971,
+<a class="jxr_linenumber" name="L144" href="#L144">144</a> -5685.658392700035382988623,
+<a class="jxr_linenumber" name="L145" href="#L145">145</a> -6737.938976642435125691553,
+<a class="jxr_linenumber" name="L146" href="#L146">146</a> -7790.220283785087985050541,
+<a class="jxr_linenumber" name="L147" href="#L147">147</a> -8842.501663247803879775318}),
+<a class="jxr_linenumber" name="L148" href="#L148">148</a> <em class="jxr_comment">// This causes intermediate overflow of the density function</em>
+<a class="jxr_linenumber" name="L149" href="#L149">149</a> Arguments.of(1e-100, 1,
+<a class="jxr_linenumber" name="L150" href="#L150">150</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1e-200, 1e-250, 1e-300},
+<a class="jxr_linenumber" name="L151" href="#L151">151</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {
+<a class="jxr_linenumber" name="L152" href="#L152">152</a> 229.5653621188446231302736,
+<a class="jxr_linenumber" name="L153" href="#L153">153</a> 344.6946167685469072592738,
+<a class="jxr_linenumber" name="L154" href="#L154">154</a> 459.8238714182491914891139})
+<a class="jxr_linenumber" name="L155" href="#L155">155</a> );
+<a class="jxr_linenumber" name="L156" href="#L156">156</a> }
+<a class="jxr_linenumber" name="L157" href="#L157">157</a>
+<a class="jxr_linenumber" name="L158" href="#L158">158</a> @ParameterizedTest
+<a class="jxr_linenumber" name="L159" href="#L159">159</a> @MethodSource
+<a class="jxr_linenumber" name="L160" href="#L160">160</a> <strong class="jxr_keyword">void</strong> testAdditionalDensity(<strong class="jxr_keyword">double</strong> numeratorDegreesOfFreedom,
+<a class="jxr_linenumber" name="L161" href="#L161">161</a> <strong class="jxr_keyword">double</strong> denominatorDegreesOfFreedom,
+<a class="jxr_linenumber" name="L162" href="#L162">162</a> <strong class="jxr_keyword">double</strong>[] points,
+<a class="jxr_linenumber" name="L163" href="#L163">163</a> <strong class="jxr_keyword">double</strong>[] values,
+<a class="jxr_linenumber" name="L164" href="#L164">164</a> <strong class="jxr_keyword">double</strong> relativeError) {
+<a class="jxr_linenumber" name="L165" href="#L165">165</a> testDensity(FDistribution.of(numeratorDegreesOfFreedom, denominatorDegreesOfFreedom),
+<a class="jxr_linenumber" name="L166" href="#L166">166</a> points, values, createRelTolerance(relativeError));
+<a class="jxr_linenumber" name="L167" href="#L167">167</a> }
+<a class="jxr_linenumber" name="L168" href="#L168">168</a>
+<a class="jxr_linenumber" name="L169" href="#L169">169</a> <strong class="jxr_keyword">static</strong> Stream<Arguments> testAdditionalDensity() {
+<a class="jxr_linenumber" name="L170" href="#L170">170</a> <em class="jxr_comment">// Computed using Boost multiprecision to 100 digits (output 25 digits).</em>
+<a class="jxr_linenumber" name="L171" href="#L171">171</a>
+<a class="jxr_linenumber" name="L172" href="#L172">172</a> <em class="jxr_comment">// Edge cases when the standard density is sub-normal.</em>
+<a class="jxr_linenumber" name="L173" href="#L173">173</a> <strong class="jxr_keyword">return</strong> Stream.of(
+<a class="jxr_linenumber" name="L174" href="#L174">174</a> Arguments.of(100, 100,
+<a class="jxr_linenumber" name="L175" href="#L175">175</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 3e6, 4e6, 4.5e6, 5e6, 1e7},
+<a class="jxr_linenumber" name="L176" href="#L176">176</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {
+<a class="jxr_linenumber" name="L177" href="#L177">177</a> 1.830313161302986740491046e-25,
+<a class="jxr_linenumber" name="L178" href="#L178">178</a> 9.325165326363852979476269e-73,
+<a class="jxr_linenumber" name="L179" href="#L179">179</a> 2.282370632180103030176872e-123,
+<a class="jxr_linenumber" name="L180" href="#L180">180</a> 2.49718772086196154389661e-174,
+<a class="jxr_linenumber" name="L181" href="#L181">181</a> 2.51976260334572601372639e-225,
+<a class="jxr_linenumber" name="L182" href="#L182">182</a> 2.522031398014840106819471e-276,
+<a class="jxr_linenumber" name="L183" href="#L183">183</a> 1.171103964711921105069224e-300,
+<a class="jxr_linenumber" name="L184" href="#L184">184</a> 4.97420298008526384736197e-307,
+<a class="jxr_linenumber" name="L185" href="#L185">185</a> 1.224464123468993962344698e-309,
+<a class="jxr_linenumber" name="L186" href="#L186">186</a> 5.679564178845752345371413e-312,
+<a class="jxr_linenumber" name="L187" href="#L187">187</a> 0
+<a class="jxr_linenumber" name="L188" href="#L188">188</a> }, 3e-13),
+<a class="jxr_linenumber" name="L189" href="#L189">189</a> Arguments.of(952, 912,
+<a class="jxr_linenumber" name="L190" href="#L190">190</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {10, 11, 12, 13, 14, 15, 16, 17, 18},
+<a class="jxr_linenumber" name="L191" href="#L191">191</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {5.264712450643104177155291e-222,
+<a class="jxr_linenumber" name="L192" href="#L192">192</a> 1.083049754753448067375765e-237,
+<a class="jxr_linenumber" name="L193" href="#L193">193</a> 2.996024821196787172008532e-252,
+<a class="jxr_linenumber" name="L194" href="#L194">194</a> 7.919262482129153149257417e-266,
+<a class="jxr_linenumber" name="L195" href="#L195">195</a> 1.511696585130734458293958e-278,
+<a class="jxr_linenumber" name="L196" href="#L196">196</a> 1.652611434344889324846565e-290,
+<a class="jxr_linenumber" name="L197" href="#L197">197</a> 8.522337060963566999523664e-302,
+<a class="jxr_linenumber" name="L198" href="#L198">198</a> 1.760000675560273604454495e-312,
+<a class="jxr_linenumber" name="L199" href="#L199">199</a> 1.266172656954210816606837e-322
+<a class="jxr_linenumber" name="L200" href="#L200">200</a> }, 2e-13),
+<a class="jxr_linenumber" name="L201" href="#L201">201</a> <em class="jxr_comment">// This causes intermediate overflow of the density function</em>
+<a class="jxr_linenumber" name="L202" href="#L202">202</a> Arguments.of(1e-100, 1,
+<a class="jxr_linenumber" name="L203" href="#L203">203</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {1e-200, 1e-250, 1e-300},
+<a class="jxr_linenumber" name="L204" href="#L204">204</a> <strong class="jxr_keyword">new</strong> <strong class="jxr_keyword">double</strong>[] {
+<a class="jxr_linenumber" name="L205" href="#L205">205</a> 5.000000000000000189458187e+99,
+<a class="jxr_linenumber" name="L206" href="#L206">206</a> 4.999999999999999829961813e+149,
+<a class="jxr_linenumber" name="L207" href="#L207">207</a> 4.99999999999999997466404e+199
+<a class="jxr_linenumber" name="L208" href="#L208">208</a> }, 5e-14)
+<a class="jxr_linenumber" name="L209" href="#L209">209</a> );
+<a class="jxr_linenumber" name="L210" href="#L210">210</a> }
+<a class="jxr_linenumber" name="L211" href="#L211">211</a> }
+</pre>
+<hr/>
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