<!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_cos.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>k_cos.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>
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</pre><pre class="rust"><code><span class="comment">// origin: FreeBSD /usr/src/lib/msun/src/k_cos.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>C1: f64 = <span class="number">4.16666666666666019037e-02</span>; <span class="comment">/* 0x3FA55555, 0x5555554C */
</span><span class="kw">const </span>C2: f64 = -<span class="number">1.38888888888741095749e-03</span>; <span class="comment">/* 0xBF56C16C, 0x16C15177 */
</span><span class="kw">const </span>C3: f64 = <span class="number">2.48015872894767294178e-05</span>; <span class="comment">/* 0x3EFA01A0, 0x19CB1590 */
</span><span class="kw">const </span>C4: f64 = -<span class="number">2.75573143513906633035e-07</span>; <span class="comment">/* 0xBE927E4F, 0x809C52AD */
</span><span class="kw">const </span>C5: f64 = <span class="number">2.08757232129817482790e-09</span>; <span class="comment">/* 0x3E21EE9E, 0xBDB4B1C4 */
</span><span class="kw">const </span>C6: f64 = -<span class="number">1.13596475577881948265e-11</span>; <span class="comment">/* 0xBDA8FAE9, 0xBE8838D4 */
// kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
// Input x is assumed to be bounded by ~pi/4 in magnitude.
// Input y is the tail of x.
//
// Algorithm
// 1. Since cos(-x) = cos(x), we need only to consider positive x.
// 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
// 3. cos(x) is approximated by a polynomial of degree 14 on
// [0,pi/4]
// 4 14
// cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
// where the remez error is
//
// | 2 4 6 8 10 12 14 | -58
// |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
// | |
//
// 4 6 8 10 12 14
// 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
// cos(x) ~ 1 - x*x/2 + r
// since cos(x+y) ~ cos(x) - sin(x)*y
// ~ cos(x) - x*y,
// a correction term is necessary in cos(x) and hence
// cos(x+y) = 1 - (x*x/2 - (r - x*y))
// For better accuracy, rearrange to
// cos(x+y) ~ w + (tmp + (r-x*y))
// where w = 1 - x*x/2 and tmp is a tiny correction term
// (1 - x*x/2 == w + tmp exactly in infinite precision).
// The exactness of w + tmp in infinite precision depends on w
// and tmp having the same precision as x. If they have extra
// precision due to compiler bugs, then the extra precision is
// only good provided it is retained in all terms of the final
// expression for cos(). Retention happens in all cases tested
// under FreeBSD, so don't pessimize things by forcibly clipping
// any extra precision in w.
</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_cos(x: f64, y: f64) -> f64 {
<span class="kw">let </span>z = x * x;
<span class="kw">let </span>w = z * z;
<span class="kw">let </span>r = z * (C1 + z * (C2 + z * C3)) + w * w * (C4 + z * (C5 + z * C6));
<span class="kw">let </span>hz = <span class="number">0.5 </span>* z;
<span class="kw">let </span>w = <span class="number">1.0 </span>- hz;
w + (((<span class="number">1.0 </span>- w) - hz) + (z * r - x * y))
}
</code></pre></div>
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