<!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/acos.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>acos.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/e_acos.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.
* ====================================================
*/
/* acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
</span><span class="kw">use </span><span class="kw">super</span>::sqrt;
<span class="kw">const </span>PIO2_HI: f64 = <span class="number">1.57079632679489655800e+00</span>; <span class="comment">/* 0x3FF921FB, 0x54442D18 */
</span><span class="kw">const </span>PIO2_LO: f64 = <span class="number">6.12323399573676603587e-17</span>; <span class="comment">/* 0x3C91A626, 0x33145C07 */
</span><span class="kw">const </span>PS0: f64 = <span class="number">1.66666666666666657415e-01</span>; <span class="comment">/* 0x3FC55555, 0x55555555 */
</span><span class="kw">const </span>PS1: f64 = -<span class="number">3.25565818622400915405e-01</span>; <span class="comment">/* 0xBFD4D612, 0x03EB6F7D */
</span><span class="kw">const </span>PS2: f64 = <span class="number">2.01212532134862925881e-01</span>; <span class="comment">/* 0x3FC9C155, 0x0E884455 */
</span><span class="kw">const </span>PS3: f64 = -<span class="number">4.00555345006794114027e-02</span>; <span class="comment">/* 0xBFA48228, 0xB5688F3B */
</span><span class="kw">const </span>PS4: f64 = <span class="number">7.91534994289814532176e-04</span>; <span class="comment">/* 0x3F49EFE0, 0x7501B288 */
</span><span class="kw">const </span>PS5: f64 = <span class="number">3.47933107596021167570e-05</span>; <span class="comment">/* 0x3F023DE1, 0x0DFDF709 */
</span><span class="kw">const </span>QS1: f64 = -<span class="number">2.40339491173441421878e+00</span>; <span class="comment">/* 0xC0033A27, 0x1C8A2D4B */
</span><span class="kw">const </span>QS2: f64 = <span class="number">2.02094576023350569471e+00</span>; <span class="comment">/* 0x40002AE5, 0x9C598AC8 */
</span><span class="kw">const </span>QS3: f64 = -<span class="number">6.88283971605453293030e-01</span>; <span class="comment">/* 0xBFE6066C, 0x1B8D0159 */
</span><span class="kw">const </span>QS4: f64 = <span class="number">7.70381505559019352791e-02</span>; <span class="comment">/* 0x3FB3B8C5, 0xB12E9282 */
</span><span class="kw">fn </span>r(z: f64) -> f64 {
<span class="kw">let </span>p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
<span class="kw">let </span>q: f64 = <span class="number">1.0 </span>+ z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
p / q
}
<span class="doccomment">/// Arccosine (f64)
///
/// Computes the inverse cosine (arc cosine) of the input value.
/// Arguments must be in the range -1 to 1.
/// Returns values in radians, in the range of 0 to pi.
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>acos(x: f64) -> f64 {
<span class="kw">let </span>x1p_120f = f64::from_bits(<span class="number">0x3870000000000000</span>); <span class="comment">// 0x1p-120 === 2 ^ -120
</span><span class="kw">let </span>z: f64;
<span class="kw">let </span>w: f64;
<span class="kw">let </span>s: f64;
<span class="kw">let </span>c: f64;
<span class="kw">let </span>df: f64;
<span class="kw">let </span>hx: u32;
<span class="kw">let </span>ix: u32;
hx = (x.to_bits() >> <span class="number">32</span>) <span class="kw">as </span>u32;
ix = hx & <span class="number">0x7fffffff</span>;
<span class="comment">/* |x| >= 1 or nan */
</span><span class="kw">if </span>ix >= <span class="number">0x3ff00000 </span>{
<span class="kw">let </span>lx: u32 = x.to_bits() <span class="kw">as </span>u32;
<span class="kw">if </span>((ix - <span class="number">0x3ff00000</span>) | lx) == <span class="number">0 </span>{
<span class="comment">/* acos(1)=0, acos(-1)=pi */
</span><span class="kw">if </span>(hx >> <span class="number">31</span>) != <span class="number">0 </span>{
<span class="kw">return </span><span class="number">2. </span>* PIO2_HI + x1p_120f;
}
<span class="kw">return </span><span class="number">0.</span>;
}
<span class="kw">return </span><span class="number">0. </span>/ (x - x);
}
<span class="comment">/* |x| < 0.5 */
</span><span class="kw">if </span>ix < <span class="number">0x3fe00000 </span>{
<span class="kw">if </span>ix <= <span class="number">0x3c600000 </span>{
<span class="comment">/* |x| < 2**-57 */
</span><span class="kw">return </span>PIO2_HI + x1p_120f;
}
<span class="kw">return </span>PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
}
<span class="comment">/* x < -0.5 */
</span><span class="kw">if </span>(hx >> <span class="number">31</span>) != <span class="number">0 </span>{
z = (<span class="number">1.0 </span>+ x) * <span class="number">0.5</span>;
s = sqrt(z);
w = r(z) * s - PIO2_LO;
<span class="kw">return </span><span class="number">2. </span>* (PIO2_HI - (s + w));
}
<span class="comment">/* x > 0.5 */
</span>z = (<span class="number">1.0 </span>- x) * <span class="number">0.5</span>;
s = sqrt(z);
<span class="comment">// Set the low 4 bytes to zero
</span>df = f64::from_bits(s.to_bits() & <span class="number">0xff_ff_ff_ff_00_00_00_00</span>);
c = (z - df * df) / (s + df);
w = r(z) * s + c;
<span class="number">2. </span>* (df + w)
}
</code></pre></div>
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