<!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/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="../../../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/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="attr">#[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="attr">#[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="attr">#[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="attr">#[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="attr">#[test]
</span><span class="kw">fn </span>infinity() {
<span class="macro">assert_eq!</span>(atan(f64::INFINITY), f64::consts::FRAC_PI_2);
}
<span class="attr">#[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="attr">#[test]
</span><span class="kw">fn </span>nan() {
<span class="macro">assert!</span>(atan(f64::NAN).is_nan());
}
}
</code></pre></div>
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