| <!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/asin.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>asin.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_asin.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. |
| * ==================================================== |
| */ |
| /* asin(x) |
| * Method : |
| * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... |
| * we approximate asin(x) on [0,0.5] by |
| * asin(x) = x + x*x^2*R(x^2) |
| * where |
| * R(x^2) is a rational approximation of (asin(x)-x)/x^3 |
| * and its remez error is bounded by |
| * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) |
| * |
| * For x in [0.5,1] |
| * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) |
| * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; |
| * then for x>0.98 |
| * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
| * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) |
| * For x<=0.98, let pio4_hi = pio2_hi/2, then |
| * f = hi part of s; |
| * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) |
| * and |
| * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
| * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) |
| * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) |
| * |
| * Special cases: |
| * if x is NaN, return x itself; |
| * if |x|>1, return NaN with invalid signal. |
| * |
| */ |
| |
| </span><span class="kw">use super</span>::{fabs, get_high_word, get_low_word, sqrt, with_set_low_word}; |
| |
| <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 */ |
| /* coefficients for R(x^2) */ |
| </span><span class="kw">const </span>P_S0: f64 = <span class="number">1.66666666666666657415e-01</span>; <span class="comment">/* 0x3FC55555, 0x55555555 */ |
| </span><span class="kw">const </span>P_S1: f64 = -<span class="number">3.25565818622400915405e-01</span>; <span class="comment">/* 0xBFD4D612, 0x03EB6F7D */ |
| </span><span class="kw">const </span>P_S2: f64 = <span class="number">2.01212532134862925881e-01</span>; <span class="comment">/* 0x3FC9C155, 0x0E884455 */ |
| </span><span class="kw">const </span>P_S3: f64 = -<span class="number">4.00555345006794114027e-02</span>; <span class="comment">/* 0xBFA48228, 0xB5688F3B */ |
| </span><span class="kw">const </span>P_S4: f64 = <span class="number">7.91534994289814532176e-04</span>; <span class="comment">/* 0x3F49EFE0, 0x7501B288 */ |
| </span><span class="kw">const </span>P_S5: f64 = <span class="number">3.47933107596021167570e-05</span>; <span class="comment">/* 0x3F023DE1, 0x0DFDF709 */ |
| </span><span class="kw">const </span>Q_S1: f64 = -<span class="number">2.40339491173441421878e+00</span>; <span class="comment">/* 0xC0033A27, 0x1C8A2D4B */ |
| </span><span class="kw">const </span>Q_S2: f64 = <span class="number">2.02094576023350569471e+00</span>; <span class="comment">/* 0x40002AE5, 0x9C598AC8 */ |
| </span><span class="kw">const </span>Q_S3: f64 = -<span class="number">6.88283971605453293030e-01</span>; <span class="comment">/* 0xBFE6066C, 0x1B8D0159 */ |
| </span><span class="kw">const </span>Q_S4: f64 = <span class="number">7.70381505559019352791e-02</span>; <span class="comment">/* 0x3FB3B8C5, 0xB12E9282 */ |
| |
| </span><span class="kw">fn </span>comp_r(z: f64) -> f64 { |
| <span class="kw">let </span>p = z * (P_S0 + z * (P_S1 + z * (P_S2 + z * (P_S3 + z * (P_S4 + z * P_S5))))); |
| <span class="kw">let </span>q = <span class="number">1.0 </span>+ z * (Q_S1 + z * (Q_S2 + z * (Q_S3 + z * Q_S4))); |
| p / q |
| } |
| |
| <span class="doccomment">/// Arcsine (f64) |
| /// |
| /// Computes the inverse sine (arc sine) of the argument `x`. |
| /// Arguments to asin must be in the range -1 to 1. |
| /// Returns values 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>asin(<span class="kw-2">mut </span>x: f64) -> f64 { |
| <span class="kw">let </span>z: f64; |
| <span class="kw">let </span>r: f64; |
| <span class="kw">let </span>s: f64; |
| <span class="kw">let </span>hx: u32; |
| <span class="kw">let </span>ix: u32; |
| |
| hx = get_high_word(x); |
| 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; |
| lx = get_low_word(x); |
| <span class="kw">if </span>((ix - <span class="number">0x3ff00000</span>) | lx) == <span class="number">0 </span>{ |
| <span class="comment">/* asin(1) = +-pi/2 with inexact */ |
| </span><span class="kw">return </span>x * PIO2_HI + f64::from_bits(<span class="number">0x3870000000000000</span>); |
| } <span class="kw">else </span>{ |
| <span class="kw">return </span><span class="number">0.0 </span>/ (x - x); |
| } |
| } |
| <span class="comment">/* |x| < 0.5 */ |
| </span><span class="kw">if </span>ix < <span class="number">0x3fe00000 </span>{ |
| <span class="comment">/* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */ |
| </span><span class="kw">if </span>ix < <span class="number">0x3e500000 </span>&& ix >= <span class="number">0x00100000 </span>{ |
| <span class="kw">return </span>x; |
| } <span class="kw">else </span>{ |
| <span class="kw">return </span>x + x * comp_r(x * x); |
| } |
| } |
| <span class="comment">/* 1 > |x| >= 0.5 */ |
| </span>z = (<span class="number">1.0 </span>- fabs(x)) * <span class="number">0.5</span>; |
| s = sqrt(z); |
| r = comp_r(z); |
| <span class="kw">if </span>ix >= <span class="number">0x3fef3333 </span>{ |
| <span class="comment">/* if |x| > 0.975 */ |
| </span>x = PIO2_HI - (<span class="number">2. </span>* (s + s * r) - PIO2_LO); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>f: f64; |
| <span class="kw">let </span>c: f64; |
| <span class="comment">/* f+c = sqrt(z) */ |
| </span>f = with_set_low_word(s, <span class="number">0</span>); |
| c = (z - f * f) / (s + f); |
| x = <span class="number">0.5 </span>* PIO2_HI - (<span class="number">2.0 </span>* s * r - (PIO2_LO - <span class="number">2.0 </span>* c) - (<span class="number">0.5 </span>* PIO2_HI - <span class="number">2.0 </span>* f)); |
| } |
| <span class="kw">if </span>hx >> <span class="number">31 </span>!= <span class="number">0 </span>{ |
| -x |
| } <span class="kw">else </span>{ |
| x |
| } |
| } |
| </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> |
