| <!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/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="../../../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/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="attribute">#[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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