| <!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_tan.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>k_tan.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_tan.c */ |
| // |
| // ==================================================== |
| // Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. |
| // |
| // Permission to use, copy, modify, and distribute this |
| // software is freely granted, provided that this notice |
| // is preserved. |
| // ==================================================== |
| |
| // kernel tan 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 odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned. |
| // |
| // Algorithm |
| // 1. Since tan(-x) = -tan(x), we need only to consider positive x. |
| // 2. Callers must return tan(-0) = -0 without calling here since our |
| // odd polynomial is not evaluated in a way that preserves -0. |
| // Callers may do the optimization tan(x) ~ x for tiny x. |
| // 3. tan(x) is approximated by a odd polynomial of degree 27 on |
| // [0,0.67434] |
| // 3 27 |
| // tan(x) ~ x + T1*x + ... + T13*x |
| // where |
| // |
| // |tan(x) 2 4 26 | -59.2 |
| // |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 |
| // | x | |
| // |
| // Note: tan(x+y) = tan(x) + tan'(x)*y |
| // ~ tan(x) + (1+x*x)*y |
| // Therefore, for better accuracy in computing tan(x+y), let |
| // 3 2 2 2 2 |
| // r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) |
| // then |
| // 3 2 |
| // tan(x+y) = x + (T1*x + (x *(r+y)+y)) |
| // |
| // 4. For x in [0.67434,pi/4], let y = pi/4 - x, then |
| // tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) |
| // = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) |
| </span><span class="kw">static </span>T: [f64; <span class="number">13</span>] = [ |
| <span class="number">3.33333333333334091986e-01</span>, <span class="comment">/* 3FD55555, 55555563 */ |
| </span><span class="number">1.33333333333201242699e-01</span>, <span class="comment">/* 3FC11111, 1110FE7A */ |
| </span><span class="number">5.39682539762260521377e-02</span>, <span class="comment">/* 3FABA1BA, 1BB341FE */ |
| </span><span class="number">2.18694882948595424599e-02</span>, <span class="comment">/* 3F9664F4, 8406D637 */ |
| </span><span class="number">8.86323982359930005737e-03</span>, <span class="comment">/* 3F8226E3, E96E8493 */ |
| </span><span class="number">3.59207910759131235356e-03</span>, <span class="comment">/* 3F6D6D22, C9560328 */ |
| </span><span class="number">1.45620945432529025516e-03</span>, <span class="comment">/* 3F57DBC8, FEE08315 */ |
| </span><span class="number">5.88041240820264096874e-04</span>, <span class="comment">/* 3F4344D8, F2F26501 */ |
| </span><span class="number">2.46463134818469906812e-04</span>, <span class="comment">/* 3F3026F7, 1A8D1068 */ |
| </span><span class="number">7.81794442939557092300e-05</span>, <span class="comment">/* 3F147E88, A03792A6 */ |
| </span><span class="number">7.14072491382608190305e-05</span>, <span class="comment">/* 3F12B80F, 32F0A7E9 */ |
| </span>-<span class="number">1.85586374855275456654e-05</span>, <span class="comment">/* BEF375CB, DB605373 */ |
| </span><span class="number">2.59073051863633712884e-05</span>, <span class="comment">/* 3EFB2A70, 74BF7AD4 */ |
| </span>]; |
| <span class="kw">const </span>PIO4: f64 = <span class="number">7.85398163397448278999e-01</span>; <span class="comment">/* 3FE921FB, 54442D18 */ |
| </span><span class="kw">const </span>PIO4_LO: f64 = <span class="number">3.06161699786838301793e-17</span>; <span class="comment">/* 3C81A626, 33145C07 */ |
| |
| </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_tan(<span class="kw-2">mut </span>x: f64, <span class="kw-2">mut </span>y: f64, odd: i32) -> f64 { |
| <span class="kw">let </span>hx = (f64::to_bits(x) >> <span class="number">32</span>) <span class="kw">as </span>u32; |
| <span class="kw">let </span>big = (hx & <span class="number">0x7fffffff</span>) >= <span class="number">0x3FE59428</span>; <span class="comment">/* |x| >= 0.6744 */ |
| </span><span class="kw">if </span>big { |
| <span class="kw">let </span>sign = hx >> <span class="number">31</span>; |
| <span class="kw">if </span>sign != <span class="number">0 </span>{ |
| x = -x; |
| y = -y; |
| } |
| x = (PIO4 - x) + (PIO4_LO - y); |
| y = <span class="number">0.0</span>; |
| } |
| <span class="kw">let </span>z = x * x; |
| <span class="kw">let </span>w = z * z; |
| <span class="comment">/* |
| * Break x^5*(T[1]+x^2*T[2]+...) into |
| * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + |
| * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) |
| */ |
| </span><span class="kw">let </span>r = T[<span class="number">1</span>] + w * (T[<span class="number">3</span>] + w * (T[<span class="number">5</span>] + w * (T[<span class="number">7</span>] + w * (T[<span class="number">9</span>] + w * T[<span class="number">11</span>])))); |
| <span class="kw">let </span>v = z * (T[<span class="number">2</span>] + w * (T[<span class="number">4</span>] + w * (T[<span class="number">6</span>] + w * (T[<span class="number">8</span>] + w * (T[<span class="number">10</span>] + w * T[<span class="number">12</span>]))))); |
| <span class="kw">let </span>s = z * x; |
| <span class="kw">let </span>r = y + z * (s * (r + v) + y) + s * T[<span class="number">0</span>]; |
| <span class="kw">let </span>w = x + r; |
| <span class="kw">if </span>big { |
| <span class="kw">let </span>sign = hx >> <span class="number">31</span>; |
| <span class="kw">let </span>s = <span class="number">1.0 </span>- <span class="number">2.0 </span>* odd <span class="kw">as </span>f64; |
| <span class="kw">let </span>v = s - <span class="number">2.0 </span>* (x + (r - w * w / (w + s))); |
| <span class="kw">return if </span>sign != <span class="number">0 </span>{ -v } <span class="kw">else </span>{ v }; |
| } |
| <span class="kw">if </span>odd == <span class="number">0 </span>{ |
| <span class="kw">return </span>w; |
| } |
| <span class="comment">/* -1.0/(x+r) has up to 2ulp error, so compute it accurately */ |
| </span><span class="kw">let </span>w0 = zero_low_word(w); |
| <span class="kw">let </span>v = r - (w0 - x); <span class="comment">/* w0+v = r+x */ |
| </span><span class="kw">let </span>a = -<span class="number">1.0 </span>/ w; |
| <span class="kw">let </span>a0 = zero_low_word(a); |
| a0 + a * (<span class="number">1.0 </span>+ a0 * w0 + a0 * v) |
| } |
| |
| <span class="kw">fn </span>zero_low_word(x: f64) -> f64 { |
| f64::from_bits(f64::to_bits(x) & <span class="number">0xFFFF_FFFF_0000_0000</span>) |
| } |
| </code></pre></div> |
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