<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/src/math/k_sin.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>k_sin.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../libm/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
<a href="#2" id="2">2</a>
<a href="#3" id="3">3</a>
<a href="#4" id="4">4</a>
<a href="#5" id="5">5</a>
<a href="#6" id="6">6</a>
<a href="#7" id="7">7</a>
<a href="#8" id="8">8</a>
<a href="#9" id="9">9</a>
<a href="#10" id="10">10</a>
<a href="#11" id="11">11</a>
<a href="#12" id="12">12</a>
<a href="#13" id="13">13</a>
<a href="#14" id="14">14</a>
<a href="#15" id="15">15</a>
<a href="#16" id="16">16</a>
<a href="#17" id="17">17</a>
<a href="#18" id="18">18</a>
<a href="#19" id="19">19</a>
<a href="#20" id="20">20</a>
<a href="#21" id="21">21</a>
<a href="#22" id="22">22</a>
<a href="#23" id="23">23</a>
<a href="#24" id="24">24</a>
<a href="#25" id="25">25</a>
<a href="#26" id="26">26</a>
<a href="#27" id="27">27</a>
<a href="#28" id="28">28</a>
<a href="#29" id="29">29</a>
<a href="#30" id="30">30</a>
<a href="#31" id="31">31</a>
<a href="#32" id="32">32</a>
<a href="#33" id="33">33</a>
<a href="#34" id="34">34</a>
<a href="#35" id="35">35</a>
<a href="#36" id="36">36</a>
<a href="#37" id="37">37</a>
<a href="#38" id="38">38</a>
<a href="#39" id="39">39</a>
<a href="#40" id="40">40</a>
<a href="#41" id="41">41</a>
<a href="#42" id="42">42</a>
<a href="#43" id="43">43</a>
<a href="#44" id="44">44</a>
<a href="#45" id="45">45</a>
<a href="#46" id="46">46</a>
<a href="#47" id="47">47</a>
<a href="#48" id="48">48</a>
<a href="#49" id="49">49</a>
<a href="#50" id="50">50</a>
<a href="#51" id="51">51</a>
<a href="#52" id="52">52</a>
<a href="#53" id="53">53</a>
<a href="#54" id="54">54</a>
<a href="#55" id="55">55</a>
<a href="#56" id="56">56</a>
<a href="#57" id="57">57</a>
</pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/k_sin.c
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunSoft, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
</span><span class="kw">const </span>S1: f64 = -<span class="number">1.66666666666666324348e-01</span>; <span class="comment">/* 0xBFC55555, 0x55555549 */
</span><span class="kw">const </span>S2: f64 = <span class="number">8.33333333332248946124e-03</span>; <span class="comment">/* 0x3F811111, 0x1110F8A6 */
</span><span class="kw">const </span>S3: f64 = -<span class="number">1.98412698298579493134e-04</span>; <span class="comment">/* 0xBF2A01A0, 0x19C161D5 */
</span><span class="kw">const </span>S4: f64 = <span class="number">2.75573137070700676789e-06</span>; <span class="comment">/* 0x3EC71DE3, 0x57B1FE7D */
</span><span class="kw">const </span>S5: f64 = -<span class="number">2.50507602534068634195e-08</span>; <span class="comment">/* 0xBE5AE5E6, 0x8A2B9CEB */
</span><span class="kw">const </span>S6: f64 = <span class="number">1.58969099521155010221e-10</span>; <span class="comment">/* 0x3DE5D93A, 0x5ACFD57C */
// kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
// Input x is assumed to be bounded by ~pi/4 in magnitude.
// Input y is the tail of x.
// Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
//
// Algorithm
// 1. Since sin(-x) = -sin(x), we need only to consider positive x.
// 2. Callers must return sin(-0) = -0 without calling here since our
// odd polynomial is not evaluated in a way that preserves -0.
// Callers may do the optimization sin(x) ~ x for tiny x.
// 3. sin(x) is approximated by a polynomial of degree 13 on
// [0,pi/4]
// 3 13
// sin(x) ~ x + S1*x + ... + S6*x
// where
//
// |sin(x) 2 4 6 8 10 12 | -58
// |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
// | x |
//
// 4. sin(x+y) = sin(x) + sin'(x')*y
// ~ sin(x) + (1-x*x/2)*y
// For better accuracy, let
// 3 2 2 2 2
// r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
// then 3 2
// sin(x) = x + (S1*x + (x *(r-y/2)+y))
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub</span>(<span class="kw">crate</span>) <span class="kw">fn </span>k_sin(x: f64, y: f64, iy: i32) -> f64 {
<span class="kw">let </span>z = x * x;
<span class="kw">let </span>w = z * z;
<span class="kw">let </span>r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
<span class="kw">let </span>v = z * x;
<span class="kw">if </span>iy == <span class="number">0 </span>{
x + v * (S1 + z * r)
} <span class="kw">else </span>{
x - ((z * (<span class="number">0.5 </span>* y - v * r) - y) - v * S1)
}
}
</code></pre></div>
</section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-static-root-path="../../../static.files/" data-current-crate="libm" data-themes="" data-resource-suffix="" data-rustdoc-version="1.67.1 (d5a82bbd2 2023-02-07)" data-search-js="search-444266647c4dba98.js" data-settings-js="settings-bebeae96e00e4617.js" data-settings-css="settings-af96d9e2fc13e081.css" ></div></body></html>