| <!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/lgamma_r.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>lgamma_r.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_lgamma_r.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. |
| * ==================================================== |
| * |
| */ |
| /* lgamma_r(x, signgamp) |
| * Reentrant version of the logarithm of the Gamma function |
| * with user provide pointer for the sign of Gamma(x). |
| * |
| * Method: |
| * 1. Argument Reduction for 0 < x <= 8 |
| * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may |
| * reduce x to a number in [1.5,2.5] by |
| * lgamma(1+s) = log(s) + lgamma(s) |
| * for example, |
| * lgamma(7.3) = log(6.3) + lgamma(6.3) |
| * = log(6.3*5.3) + lgamma(5.3) |
| * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) |
| * 2. Polynomial approximation of lgamma around its |
| * minimun ymin=1.461632144968362245 to maintain monotonicity. |
| * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use |
| * Let z = x-ymin; |
| * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) |
| * where |
| * poly(z) is a 14 degree polynomial. |
| * 2. Rational approximation in the primary interval [2,3] |
| * We use the following approximation: |
| * s = x-2.0; |
| * lgamma(x) = 0.5*s + s*P(s)/Q(s) |
| * with accuracy |
| * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 |
| * Our algorithms are based on the following observation |
| * |
| * zeta(2)-1 2 zeta(3)-1 3 |
| * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... |
| * 2 3 |
| * |
| * where Euler = 0.5771... is the Euler constant, which is very |
| * close to 0.5. |
| * |
| * 3. For x>=8, we have |
| * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... |
| * (better formula: |
| * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) |
| * Let z = 1/x, then we approximation |
| * f(z) = lgamma(x) - (x-0.5)(log(x)-1) |
| * by |
| * 3 5 11 |
| * w = w0 + w1*z + w2*z + w3*z + ... + w6*z |
| * where |
| * |w - f(z)| < 2**-58.74 |
| * |
| * 4. For negative x, since (G is gamma function) |
| * -x*G(-x)*G(x) = PI/sin(PI*x), |
| * we have |
| * G(x) = PI/(sin(PI*x)*(-x)*G(-x)) |
| * since G(-x) is positive, sign(G(x)) = sign(sin(PI*x)) for x<0 |
| * Hence, for x<0, signgam = sign(sin(PI*x)) and |
| * lgamma(x) = log(|Gamma(x)|) |
| * = log(PI/(|x*sin(PI*x)|)) - lgamma(-x); |
| * Note: one should avoid compute PI*(-x) directly in the |
| * computation of sin(PI*(-x)). |
| * |
| * 5. Special Cases |
| * lgamma(2+s) ~ s*(1-Euler) for tiny s |
| * lgamma(1) = lgamma(2) = 0 |
| * lgamma(x) ~ -log(|x|) for tiny x |
| * lgamma(0) = lgamma(neg.integer) = inf and raise divide-by-zero |
| * lgamma(inf) = inf |
| * lgamma(-inf) = inf (bug for bug compatible with C99!?) |
| * |
| */ |
| |
| </span><span class="kw">use super</span>::{floor, k_cos, k_sin, log}; |
| |
| <span class="kw">const </span>PI: f64 = <span class="number">3.14159265358979311600e+00</span>; <span class="comment">/* 0x400921FB, 0x54442D18 */ |
| </span><span class="kw">const </span>A0: f64 = <span class="number">7.72156649015328655494e-02</span>; <span class="comment">/* 0x3FB3C467, 0xE37DB0C8 */ |
| </span><span class="kw">const </span>A1: f64 = <span class="number">3.22467033424113591611e-01</span>; <span class="comment">/* 0x3FD4A34C, 0xC4A60FAD */ |
| </span><span class="kw">const </span>A2: f64 = <span class="number">6.73523010531292681824e-02</span>; <span class="comment">/* 0x3FB13E00, 0x1A5562A7 */ |
| </span><span class="kw">const </span>A3: f64 = <span class="number">2.05808084325167332806e-02</span>; <span class="comment">/* 0x3F951322, 0xAC92547B */ |
| </span><span class="kw">const </span>A4: f64 = <span class="number">7.38555086081402883957e-03</span>; <span class="comment">/* 0x3F7E404F, 0xB68FEFE8 */ |
| </span><span class="kw">const </span>A5: f64 = <span class="number">2.89051383673415629091e-03</span>; <span class="comment">/* 0x3F67ADD8, 0xCCB7926B */ |
| </span><span class="kw">const </span>A6: f64 = <span class="number">1.19270763183362067845e-03</span>; <span class="comment">/* 0x3F538A94, 0x116F3F5D */ |
| </span><span class="kw">const </span>A7: f64 = <span class="number">5.10069792153511336608e-04</span>; <span class="comment">/* 0x3F40B6C6, 0x89B99C00 */ |
| </span><span class="kw">const </span>A8: f64 = <span class="number">2.20862790713908385557e-04</span>; <span class="comment">/* 0x3F2CF2EC, 0xED10E54D */ |
| </span><span class="kw">const </span>A9: f64 = <span class="number">1.08011567247583939954e-04</span>; <span class="comment">/* 0x3F1C5088, 0x987DFB07 */ |
| </span><span class="kw">const </span>A10: f64 = <span class="number">2.52144565451257326939e-05</span>; <span class="comment">/* 0x3EFA7074, 0x428CFA52 */ |
| </span><span class="kw">const </span>A11: f64 = <span class="number">4.48640949618915160150e-05</span>; <span class="comment">/* 0x3F07858E, 0x90A45837 */ |
| </span><span class="kw">const </span>TC: f64 = <span class="number">1.46163214496836224576e+00</span>; <span class="comment">/* 0x3FF762D8, 0x6356BE3F */ |
| </span><span class="kw">const </span>TF: f64 = -<span class="number">1.21486290535849611461e-01</span>; <span class="comment">/* 0xBFBF19B9, 0xBCC38A42 */ |
| /* tt = -(tail of TF) */ |
| </span><span class="kw">const </span>TT: f64 = -<span class="number">3.63867699703950536541e-18</span>; <span class="comment">/* 0xBC50C7CA, 0xA48A971F */ |
| </span><span class="kw">const </span>T0: f64 = <span class="number">4.83836122723810047042e-01</span>; <span class="comment">/* 0x3FDEF72B, 0xC8EE38A2 */ |
| </span><span class="kw">const </span>T1: f64 = -<span class="number">1.47587722994593911752e-01</span>; <span class="comment">/* 0xBFC2E427, 0x8DC6C509 */ |
| </span><span class="kw">const </span>T2: f64 = <span class="number">6.46249402391333854778e-02</span>; <span class="comment">/* 0x3FB08B42, 0x94D5419B */ |
| </span><span class="kw">const </span>T3: f64 = -<span class="number">3.27885410759859649565e-02</span>; <span class="comment">/* 0xBFA0C9A8, 0xDF35B713 */ |
| </span><span class="kw">const </span>T4: f64 = <span class="number">1.79706750811820387126e-02</span>; <span class="comment">/* 0x3F9266E7, 0x970AF9EC */ |
| </span><span class="kw">const </span>T5: f64 = -<span class="number">1.03142241298341437450e-02</span>; <span class="comment">/* 0xBF851F9F, 0xBA91EC6A */ |
| </span><span class="kw">const </span>T6: f64 = <span class="number">6.10053870246291332635e-03</span>; <span class="comment">/* 0x3F78FCE0, 0xE370E344 */ |
| </span><span class="kw">const </span>T7: f64 = -<span class="number">3.68452016781138256760e-03</span>; <span class="comment">/* 0xBF6E2EFF, 0xB3E914D7 */ |
| </span><span class="kw">const </span>T8: f64 = <span class="number">2.25964780900612472250e-03</span>; <span class="comment">/* 0x3F6282D3, 0x2E15C915 */ |
| </span><span class="kw">const </span>T9: f64 = -<span class="number">1.40346469989232843813e-03</span>; <span class="comment">/* 0xBF56FE8E, 0xBF2D1AF1 */ |
| </span><span class="kw">const </span>T10: f64 = <span class="number">8.81081882437654011382e-04</span>; <span class="comment">/* 0x3F4CDF0C, 0xEF61A8E9 */ |
| </span><span class="kw">const </span>T11: f64 = -<span class="number">5.38595305356740546715e-04</span>; <span class="comment">/* 0xBF41A610, 0x9C73E0EC */ |
| </span><span class="kw">const </span>T12: f64 = <span class="number">3.15632070903625950361e-04</span>; <span class="comment">/* 0x3F34AF6D, 0x6C0EBBF7 */ |
| </span><span class="kw">const </span>T13: f64 = -<span class="number">3.12754168375120860518e-04</span>; <span class="comment">/* 0xBF347F24, 0xECC38C38 */ |
| </span><span class="kw">const </span>T14: f64 = <span class="number">3.35529192635519073543e-04</span>; <span class="comment">/* 0x3F35FD3E, 0xE8C2D3F4 */ |
| </span><span class="kw">const </span>U0: f64 = -<span class="number">7.72156649015328655494e-02</span>; <span class="comment">/* 0xBFB3C467, 0xE37DB0C8 */ |
| </span><span class="kw">const </span>U1: f64 = <span class="number">6.32827064025093366517e-01</span>; <span class="comment">/* 0x3FE4401E, 0x8B005DFF */ |
| </span><span class="kw">const </span>U2: f64 = <span class="number">1.45492250137234768737e+00</span>; <span class="comment">/* 0x3FF7475C, 0xD119BD6F */ |
| </span><span class="kw">const </span>U3: f64 = <span class="number">9.77717527963372745603e-01</span>; <span class="comment">/* 0x3FEF4976, 0x44EA8450 */ |
| </span><span class="kw">const </span>U4: f64 = <span class="number">2.28963728064692451092e-01</span>; <span class="comment">/* 0x3FCD4EAE, 0xF6010924 */ |
| </span><span class="kw">const </span>U5: f64 = <span class="number">1.33810918536787660377e-02</span>; <span class="comment">/* 0x3F8B678B, 0xBF2BAB09 */ |
| </span><span class="kw">const </span>V1: f64 = <span class="number">2.45597793713041134822e+00</span>; <span class="comment">/* 0x4003A5D7, 0xC2BD619C */ |
| </span><span class="kw">const </span>V2: f64 = <span class="number">2.12848976379893395361e+00</span>; <span class="comment">/* 0x40010725, 0xA42B18F5 */ |
| </span><span class="kw">const </span>V3: f64 = <span class="number">7.69285150456672783825e-01</span>; <span class="comment">/* 0x3FE89DFB, 0xE45050AF */ |
| </span><span class="kw">const </span>V4: f64 = <span class="number">1.04222645593369134254e-01</span>; <span class="comment">/* 0x3FBAAE55, 0xD6537C88 */ |
| </span><span class="kw">const </span>V5: f64 = <span class="number">3.21709242282423911810e-03</span>; <span class="comment">/* 0x3F6A5ABB, 0x57D0CF61 */ |
| </span><span class="kw">const </span>S0: f64 = -<span class="number">7.72156649015328655494e-02</span>; <span class="comment">/* 0xBFB3C467, 0xE37DB0C8 */ |
| </span><span class="kw">const </span>S1: f64 = <span class="number">2.14982415960608852501e-01</span>; <span class="comment">/* 0x3FCB848B, 0x36E20878 */ |
| </span><span class="kw">const </span>S2: f64 = <span class="number">3.25778796408930981787e-01</span>; <span class="comment">/* 0x3FD4D98F, 0x4F139F59 */ |
| </span><span class="kw">const </span>S3: f64 = <span class="number">1.46350472652464452805e-01</span>; <span class="comment">/* 0x3FC2BB9C, 0xBEE5F2F7 */ |
| </span><span class="kw">const </span>S4: f64 = <span class="number">2.66422703033638609560e-02</span>; <span class="comment">/* 0x3F9B481C, 0x7E939961 */ |
| </span><span class="kw">const </span>S5: f64 = <span class="number">1.84028451407337715652e-03</span>; <span class="comment">/* 0x3F5E26B6, 0x7368F239 */ |
| </span><span class="kw">const </span>S6: f64 = <span class="number">3.19475326584100867617e-05</span>; <span class="comment">/* 0x3F00BFEC, 0xDD17E945 */ |
| </span><span class="kw">const </span>R1: f64 = <span class="number">1.39200533467621045958e+00</span>; <span class="comment">/* 0x3FF645A7, 0x62C4AB74 */ |
| </span><span class="kw">const </span>R2: f64 = <span class="number">7.21935547567138069525e-01</span>; <span class="comment">/* 0x3FE71A18, 0x93D3DCDC */ |
| </span><span class="kw">const </span>R3: f64 = <span class="number">1.71933865632803078993e-01</span>; <span class="comment">/* 0x3FC601ED, 0xCCFBDF27 */ |
| </span><span class="kw">const </span>R4: f64 = <span class="number">1.86459191715652901344e-02</span>; <span class="comment">/* 0x3F9317EA, 0x742ED475 */ |
| </span><span class="kw">const </span>R5: f64 = <span class="number">7.77942496381893596434e-04</span>; <span class="comment">/* 0x3F497DDA, 0xCA41A95B */ |
| </span><span class="kw">const </span>R6: f64 = <span class="number">7.32668430744625636189e-06</span>; <span class="comment">/* 0x3EDEBAF7, 0xA5B38140 */ |
| </span><span class="kw">const </span>W0: f64 = <span class="number">4.18938533204672725052e-01</span>; <span class="comment">/* 0x3FDACFE3, 0x90C97D69 */ |
| </span><span class="kw">const </span>W1: f64 = <span class="number">8.33333333333329678849e-02</span>; <span class="comment">/* 0x3FB55555, 0x5555553B */ |
| </span><span class="kw">const </span>W2: f64 = -<span class="number">2.77777777728775536470e-03</span>; <span class="comment">/* 0xBF66C16C, 0x16B02E5C */ |
| </span><span class="kw">const </span>W3: f64 = <span class="number">7.93650558643019558500e-04</span>; <span class="comment">/* 0x3F4A019F, 0x98CF38B6 */ |
| </span><span class="kw">const </span>W4: f64 = -<span class="number">5.95187557450339963135e-04</span>; <span class="comment">/* 0xBF4380CB, 0x8C0FE741 */ |
| </span><span class="kw">const </span>W5: f64 = <span class="number">8.36339918996282139126e-04</span>; <span class="comment">/* 0x3F4B67BA, 0x4CDAD5D1 */ |
| </span><span class="kw">const </span>W6: f64 = -<span class="number">1.63092934096575273989e-03</span>; <span class="comment">/* 0xBF5AB89D, 0x0B9E43E4 */ |
| |
| /* sin(PI*x) assuming x > 2^-100, if sin(PI*x)==0 the sign is arbitrary */ |
| </span><span class="kw">fn </span>sin_pi(<span class="kw-2">mut </span>x: f64) -> f64 { |
| <span class="kw">let </span><span class="kw-2">mut </span>n: i32; |
| |
| <span class="comment">/* spurious inexact if odd int */ |
| </span>x = <span class="number">2.0 </span>* (x * <span class="number">0.5 </span>- floor(x * <span class="number">0.5</span>)); <span class="comment">/* x mod 2.0 */ |
| |
| </span>n = (x * <span class="number">4.0</span>) <span class="kw">as </span>i32; |
| n = <span class="macro">div!</span>(n + <span class="number">1</span>, <span class="number">2</span>); |
| x -= (n <span class="kw">as </span>f64) * <span class="number">0.5</span>; |
| x <span class="kw-2">*</span>= PI; |
| |
| <span class="kw">match </span>n { |
| <span class="number">1 </span>=> k_cos(x, <span class="number">0.0</span>), |
| <span class="number">2 </span>=> k_sin(-x, <span class="number">0.0</span>, <span class="number">0</span>), |
| <span class="number">3 </span>=> -k_cos(x, <span class="number">0.0</span>), |
| <span class="number">0 </span>| <span class="kw">_ </span>=> k_sin(x, <span class="number">0.0</span>, <span class="number">0</span>), |
| } |
| } |
| |
| <span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>lgamma_r(<span class="kw-2">mut </span>x: f64) -> (f64, i32) { |
| <span class="kw">let </span>u: u64 = x.to_bits(); |
| <span class="kw">let </span><span class="kw-2">mut </span>t: f64; |
| <span class="kw">let </span>y: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>z: f64; |
| <span class="kw">let </span>nadj: f64; |
| <span class="kw">let </span>p: f64; |
| <span class="kw">let </span>p1: f64; |
| <span class="kw">let </span>p2: f64; |
| <span class="kw">let </span>p3: f64; |
| <span class="kw">let </span>q: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>r: f64; |
| <span class="kw">let </span>w: f64; |
| <span class="kw">let </span>ix: u32; |
| <span class="kw">let </span>sign: bool; |
| <span class="kw">let </span>i: i32; |
| <span class="kw">let </span><span class="kw-2">mut </span>signgam: i32; |
| |
| <span class="comment">/* purge off +-inf, NaN, +-0, tiny and negative arguments */ |
| </span>signgam = <span class="number">1</span>; |
| sign = (u >> <span class="number">63</span>) != <span class="number">0</span>; |
| ix = ((u >> <span class="number">32</span>) <span class="kw">as </span>u32) & <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x7ff00000 </span>{ |
| <span class="kw">return </span>(x * x, signgam); |
| } |
| <span class="kw">if </span>ix < (<span class="number">0x3ff </span>- <span class="number">70</span>) << <span class="number">20 </span>{ |
| <span class="comment">/* |x|<2**-70, return -log(|x|) */ |
| </span><span class="kw">if </span>sign { |
| x = -x; |
| signgam = -<span class="number">1</span>; |
| } |
| <span class="kw">return </span>(-log(x), signgam); |
| } |
| <span class="kw">if </span>sign { |
| x = -x; |
| t = sin_pi(x); |
| <span class="kw">if </span>t == <span class="number">0.0 </span>{ |
| <span class="comment">/* -integer */ |
| </span><span class="kw">return </span>(<span class="number">1.0 </span>/ (x - x), signgam); |
| } |
| <span class="kw">if </span>t > <span class="number">0.0 </span>{ |
| signgam = -<span class="number">1</span>; |
| } <span class="kw">else </span>{ |
| t = -t; |
| } |
| nadj = log(PI / (t * x)); |
| } <span class="kw">else </span>{ |
| nadj = <span class="number">0.0</span>; |
| } |
| |
| <span class="comment">/* purge off 1 and 2 */ |
| </span><span class="kw">if </span>(ix == <span class="number">0x3ff00000 </span>|| ix == <span class="number">0x40000000</span>) && (u & <span class="number">0xffffffff</span>) == <span class="number">0 </span>{ |
| r = <span class="number">0.0</span>; |
| } |
| <span class="comment">/* for x < 2.0 */ |
| </span><span class="kw">else if </span>ix < <span class="number">0x40000000 </span>{ |
| <span class="kw">if </span>ix <= <span class="number">0x3feccccc </span>{ |
| <span class="comment">/* lgamma(x) = lgamma(x+1)-log(x) */ |
| </span>r = -log(x); |
| <span class="kw">if </span>ix >= <span class="number">0x3FE76944 </span>{ |
| y = <span class="number">1.0 </span>- x; |
| i = <span class="number">0</span>; |
| } <span class="kw">else if </span>ix >= <span class="number">0x3FCDA661 </span>{ |
| y = x - (TC - <span class="number">1.0</span>); |
| i = <span class="number">1</span>; |
| } <span class="kw">else </span>{ |
| y = x; |
| i = <span class="number">2</span>; |
| } |
| } <span class="kw">else </span>{ |
| r = <span class="number">0.0</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x3FFBB4C3 </span>{ |
| <span class="comment">/* [1.7316,2] */ |
| </span>y = <span class="number">2.0 </span>- x; |
| i = <span class="number">0</span>; |
| } <span class="kw">else if </span>ix >= <span class="number">0x3FF3B4C4 </span>{ |
| <span class="comment">/* [1.23,1.73] */ |
| </span>y = x - TC; |
| i = <span class="number">1</span>; |
| } <span class="kw">else </span>{ |
| y = x - <span class="number">1.0</span>; |
| i = <span class="number">2</span>; |
| } |
| } |
| <span class="kw">match </span>i { |
| <span class="number">0 </span>=> { |
| z = y * y; |
| p1 = A0 + z * (A2 + z * (A4 + z * (A6 + z * (A8 + z * A10)))); |
| p2 = z * (A1 + z * (A3 + z * (A5 + z * (A7 + z * (A9 + z * A11))))); |
| p = y * p1 + p2; |
| r += p - <span class="number">0.5 </span>* y; |
| } |
| <span class="number">1 </span>=> { |
| z = y * y; |
| w = z * y; |
| p1 = T0 + w * (T3 + w * (T6 + w * (T9 + w * T12))); <span class="comment">/* parallel comp */ |
| </span>p2 = T1 + w * (T4 + w * (T7 + w * (T10 + w * T13))); |
| p3 = T2 + w * (T5 + w * (T8 + w * (T11 + w * T14))); |
| p = z * p1 - (TT - w * (p2 + y * p3)); |
| r += TF + p; |
| } |
| <span class="number">2 </span>=> { |
| p1 = y * (U0 + y * (U1 + y * (U2 + y * (U3 + y * (U4 + y * U5))))); |
| p2 = <span class="number">1.0 </span>+ y * (V1 + y * (V2 + y * (V3 + y * (V4 + y * V5)))); |
| r += -<span class="number">0.5 </span>* y + p1 / p2; |
| } |
| <span class="attribute">#[cfg(debug_assertions)] |
| </span><span class="kw">_ </span>=> <span class="macro">unreachable!</span>(), |
| <span class="attribute">#[cfg(not(debug_assertions))] |
| </span><span class="kw">_ </span>=> {} |
| } |
| } <span class="kw">else if </span>ix < <span class="number">0x40200000 </span>{ |
| <span class="comment">/* x < 8.0 */ |
| </span>i = x <span class="kw">as </span>i32; |
| y = x - (i <span class="kw">as </span>f64); |
| p = y * (S0 + y * (S1 + y * (S2 + y * (S3 + y * (S4 + y * (S5 + y * S6)))))); |
| q = <span class="number">1.0 </span>+ y * (R1 + y * (R2 + y * (R3 + y * (R4 + y * (R5 + y * R6))))); |
| r = <span class="number">0.5 </span>* y + p / q; |
| z = <span class="number">1.0</span>; <span class="comment">/* lgamma(1+s) = log(s) + lgamma(s) */ |
| // TODO: In C, this was implemented using switch jumps with fallthrough. |
| // Does this implementation have performance problems? |
| </span><span class="kw">if </span>i >= <span class="number">7 </span>{ |
| z <span class="kw-2">*</span>= y + <span class="number">6.0</span>; |
| } |
| <span class="kw">if </span>i >= <span class="number">6 </span>{ |
| z <span class="kw-2">*</span>= y + <span class="number">5.0</span>; |
| } |
| <span class="kw">if </span>i >= <span class="number">5 </span>{ |
| z <span class="kw-2">*</span>= y + <span class="number">4.0</span>; |
| } |
| <span class="kw">if </span>i >= <span class="number">4 </span>{ |
| z <span class="kw-2">*</span>= y + <span class="number">3.0</span>; |
| } |
| <span class="kw">if </span>i >= <span class="number">3 </span>{ |
| z <span class="kw-2">*</span>= y + <span class="number">2.0</span>; |
| r += log(z); |
| } |
| } <span class="kw">else if </span>ix < <span class="number">0x43900000 </span>{ |
| <span class="comment">/* 8.0 <= x < 2**58 */ |
| </span>t = log(x); |
| z = <span class="number">1.0 </span>/ x; |
| y = z * z; |
| w = W0 + z * (W1 + y * (W2 + y * (W3 + y * (W4 + y * (W5 + y * W6))))); |
| r = (x - <span class="number">0.5</span>) * (t - <span class="number">1.0</span>) + w; |
| } <span class="kw">else </span>{ |
| <span class="comment">/* 2**58 <= x <= inf */ |
| </span>r = x * (log(x) - <span class="number">1.0</span>); |
| } |
| <span class="kw">if </span>sign { |
| r = nadj - r; |
| } |
| <span class="kw">return </span>(r, signgam); |
| } |
| </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> |
