| <!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/atan.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>atan.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/s_atan.c */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| /* atan(x) |
| * Method |
| * 1. Reduce x to positive by atan(x) = -atan(-x). |
| * 2. According to the integer k=4t+0.25 chopped, t=x, the argument |
| * is further reduced to one of the following intervals and the |
| * arctangent of t is evaluated by the corresponding formula: |
| * |
| * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) |
| * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) |
| * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) |
| * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) |
| * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) |
| * |
| * Constants: |
| * The hexadecimal values are the intended ones for the following |
| * constants. The decimal values may be used, provided that the |
| * compiler will convert from decimal to binary accurately enough |
| * to produce the hexadecimal values shown. |
| */ |
| |
| </span><span class="kw">use </span><span class="kw">super</span>::fabs; |
| <span class="kw">use </span>core::f64; |
| |
| <span class="kw">const </span>ATANHI: [f64; <span class="number">4</span>] = [ |
| <span class="number">4.63647609000806093515e-01</span>, <span class="comment">/* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ |
| </span><span class="number">7.85398163397448278999e-01</span>, <span class="comment">/* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ |
| </span><span class="number">9.82793723247329054082e-01</span>, <span class="comment">/* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ |
| </span><span class="number">1.57079632679489655800e+00</span>, <span class="comment">/* atan(inf)hi 0x3FF921FB, 0x54442D18 */ |
| </span>]; |
| |
| <span class="kw">const </span>ATANLO: [f64; <span class="number">4</span>] = [ |
| <span class="number">2.26987774529616870924e-17</span>, <span class="comment">/* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ |
| </span><span class="number">3.06161699786838301793e-17</span>, <span class="comment">/* atan(1.0)lo 0x3C81A626, 0x33145C07 */ |
| </span><span class="number">1.39033110312309984516e-17</span>, <span class="comment">/* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ |
| </span><span class="number">6.12323399573676603587e-17</span>, <span class="comment">/* atan(inf)lo 0x3C91A626, 0x33145C07 */ |
| </span>]; |
| |
| <span class="kw">const </span>AT: [f64; <span class="number">11</span>] = [ |
| <span class="number">3.33333333333329318027e-01</span>, <span class="comment">/* 0x3FD55555, 0x5555550D */ |
| </span>-<span class="number">1.99999999998764832476e-01</span>, <span class="comment">/* 0xBFC99999, 0x9998EBC4 */ |
| </span><span class="number">1.42857142725034663711e-01</span>, <span class="comment">/* 0x3FC24924, 0x920083FF */ |
| </span>-<span class="number">1.11111104054623557880e-01</span>, <span class="comment">/* 0xBFBC71C6, 0xFE231671 */ |
| </span><span class="number">9.09088713343650656196e-02</span>, <span class="comment">/* 0x3FB745CD, 0xC54C206E */ |
| </span>-<span class="number">7.69187620504482999495e-02</span>, <span class="comment">/* 0xBFB3B0F2, 0xAF749A6D */ |
| </span><span class="number">6.66107313738753120669e-02</span>, <span class="comment">/* 0x3FB10D66, 0xA0D03D51 */ |
| </span>-<span class="number">5.83357013379057348645e-02</span>, <span class="comment">/* 0xBFADDE2D, 0x52DEFD9A */ |
| </span><span class="number">4.97687799461593236017e-02</span>, <span class="comment">/* 0x3FA97B4B, 0x24760DEB */ |
| </span>-<span class="number">3.65315727442169155270e-02</span>, <span class="comment">/* 0xBFA2B444, 0x2C6A6C2F */ |
| </span><span class="number">1.62858201153657823623e-02</span>, <span class="comment">/* 0x3F90AD3A, 0xE322DA11 */ |
| </span>]; |
| |
| <span class="doccomment">/// Arctangent (f64) |
| /// |
| /// Computes the inverse tangent (arc tangent) of the input value. |
| /// Returns a value in radians, in the range of -pi/2 to pi/2. |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>atan(x: f64) -> f64 { |
| <span class="kw">let </span><span class="kw-2">mut </span>x = x; |
| <span class="kw">let </span><span class="kw-2">mut </span>ix = (x.to_bits() >> <span class="number">32</span>) <span class="kw">as </span>u32; |
| <span class="kw">let </span>sign = ix >> <span class="number">31</span>; |
| ix &= <span class="number">0x7fff_ffff</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x4410_0000 </span>{ |
| <span class="kw">if </span>x.is_nan() { |
| <span class="kw">return </span>x; |
| } |
| |
| <span class="kw">let </span>z = ATANHI[<span class="number">3</span>] + f64::from_bits(<span class="number">0x0380_0000</span>); <span class="comment">// 0x1p-120f |
| </span><span class="kw">return if </span>sign != <span class="number">0 </span>{ -z } <span class="kw">else </span>{ z }; |
| } |
| |
| <span class="kw">let </span>id = <span class="kw">if </span>ix < <span class="number">0x3fdc_0000 </span>{ |
| <span class="comment">/* |x| < 0.4375 */ |
| </span><span class="kw">if </span>ix < <span class="number">0x3e40_0000 </span>{ |
| <span class="comment">/* |x| < 2^-27 */ |
| </span><span class="kw">if </span>ix < <span class="number">0x0010_0000 </span>{ |
| <span class="comment">/* raise underflow for subnormal x */ |
| </span><span class="macro">force_eval!</span>(x <span class="kw">as </span>f32); |
| } |
| |
| <span class="kw">return </span>x; |
| } |
| |
| -<span class="number">1 |
| </span>} <span class="kw">else </span>{ |
| x = fabs(x); |
| <span class="kw">if </span>ix < <span class="number">0x3ff30000 </span>{ |
| <span class="comment">/* |x| < 1.1875 */ |
| </span><span class="kw">if </span>ix < <span class="number">0x3fe60000 </span>{ |
| <span class="comment">/* 7/16 <= |x| < 11/16 */ |
| </span>x = (<span class="number">2. </span>* x - <span class="number">1.</span>) / (<span class="number">2. </span>+ x); |
| <span class="number">0 |
| </span>} <span class="kw">else </span>{ |
| <span class="comment">/* 11/16 <= |x| < 19/16 */ |
| </span>x = (x - <span class="number">1.</span>) / (x + <span class="number">1.</span>); |
| <span class="number">1 |
| </span>} |
| } <span class="kw">else if </span>ix < <span class="number">0x40038000 </span>{ |
| <span class="comment">/* |x| < 2.4375 */ |
| </span>x = (x - <span class="number">1.5</span>) / (<span class="number">1. </span>+ <span class="number">1.5 </span>* x); |
| <span class="number">2 |
| </span>} <span class="kw">else </span>{ |
| <span class="comment">/* 2.4375 <= |x| < 2^66 */ |
| </span>x = -<span class="number">1. </span>/ x; |
| <span class="number">3 |
| </span>} |
| }; |
| |
| <span class="kw">let </span>z = x * x; |
| <span class="kw">let </span>w = z * z; |
| <span class="comment">/* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */ |
| </span><span class="kw">let </span>s1 = z * (AT[<span class="number">0</span>] + w * (AT[<span class="number">2</span>] + w * (AT[<span class="number">4</span>] + w * (AT[<span class="number">6</span>] + w * (AT[<span class="number">8</span>] + w * AT[<span class="number">10</span>]))))); |
| <span class="kw">let </span>s2 = w * (AT[<span class="number">1</span>] + w * (AT[<span class="number">3</span>] + w * (AT[<span class="number">5</span>] + w * (AT[<span class="number">7</span>] + w * AT[<span class="number">9</span>])))); |
| |
| <span class="kw">if </span>id < <span class="number">0 </span>{ |
| <span class="kw">return </span>x - x * (s1 + s2); |
| } |
| |
| <span class="kw">let </span>z = <span class="macro">i!</span>(ATANHI, id <span class="kw">as </span>usize) - (x * (s1 + s2) - <span class="macro">i!</span>(ATANLO, id <span class="kw">as </span>usize) - x); |
| |
| <span class="kw">if </span>sign != <span class="number">0 </span>{ |
| -z |
| } <span class="kw">else </span>{ |
| z |
| } |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use </span><span class="kw">super</span>::atan; |
| <span class="kw">use </span>core::f64; |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>sanity_check() { |
| <span class="kw">for </span>(input, answer) <span class="kw">in </span>[ |
| (<span class="number">3.0_f64</span>.sqrt() / <span class="number">3.0</span>, f64::consts::FRAC_PI_6), |
| (<span class="number">1.0</span>, f64::consts::FRAC_PI_4), |
| (<span class="number">3.0_f64</span>.sqrt(), f64::consts::FRAC_PI_3), |
| (-<span class="number">3.0_f64</span>.sqrt() / <span class="number">3.0</span>, -f64::consts::FRAC_PI_6), |
| (-<span class="number">1.0</span>, -f64::consts::FRAC_PI_4), |
| (-<span class="number">3.0_f64</span>.sqrt(), -f64::consts::FRAC_PI_3), |
| ] |
| .iter() |
| { |
| <span class="macro">assert!</span>( |
| (atan(<span class="kw-2">*</span>input) - answer) / answer < <span class="number">1e-5</span>, |
| <span class="string">"\natan({:.4}/16) = {:.4}, actual: {}"</span>, |
| input * <span class="number">16.0</span>, |
| answer, |
| atan(<span class="kw-2">*</span>input) |
| ); |
| } |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>zero() { |
| <span class="macro">assert_eq!</span>(atan(<span class="number">0.0</span>), <span class="number">0.0</span>); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>infinity() { |
| <span class="macro">assert_eq!</span>(atan(f64::INFINITY), f64::consts::FRAC_PI_2); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>minus_infinity() { |
| <span class="macro">assert_eq!</span>(atan(f64::NEG_INFINITY), -f64::consts::FRAC_PI_2); |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>nan() { |
| <span class="macro">assert!</span>(atan(f64::NAN).is_nan()); |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="libm" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
