| <!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 `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.7/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="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.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"><a class="sidebar-logo" href="../../../libm/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../libm/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" 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="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </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="attribute">#[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> |
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