| <!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/erff.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>erff.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/s_erff.c */ |
| /* |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| */ |
| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */ |
| |
| </span><span class="kw">use super</span>::{expf, fabsf}; |
| |
| <span class="kw">const </span>ERX: f32 = <span class="number">8.4506291151e-01</span>; <span class="comment">/* 0x3f58560b */ |
| /* |
| * Coefficients for approximation to erf on [0,0.84375] |
| */ |
| </span><span class="kw">const </span>EFX8: f32 = <span class="number">1.0270333290e+00</span>; <span class="comment">/* 0x3f8375d4 */ |
| </span><span class="kw">const </span>PP0: f32 = <span class="number">1.2837916613e-01</span>; <span class="comment">/* 0x3e0375d4 */ |
| </span><span class="kw">const </span>PP1: f32 = -<span class="number">3.2504209876e-01</span>; <span class="comment">/* 0xbea66beb */ |
| </span><span class="kw">const </span>PP2: f32 = -<span class="number">2.8481749818e-02</span>; <span class="comment">/* 0xbce9528f */ |
| </span><span class="kw">const </span>PP3: f32 = -<span class="number">5.7702702470e-03</span>; <span class="comment">/* 0xbbbd1489 */ |
| </span><span class="kw">const </span>PP4: f32 = -<span class="number">2.3763017452e-05</span>; <span class="comment">/* 0xb7c756b1 */ |
| </span><span class="kw">const </span>QQ1: f32 = <span class="number">3.9791721106e-01</span>; <span class="comment">/* 0x3ecbbbce */ |
| </span><span class="kw">const </span>QQ2: f32 = <span class="number">6.5022252500e-02</span>; <span class="comment">/* 0x3d852a63 */ |
| </span><span class="kw">const </span>QQ3: f32 = <span class="number">5.0813062117e-03</span>; <span class="comment">/* 0x3ba68116 */ |
| </span><span class="kw">const </span>QQ4: f32 = <span class="number">1.3249473704e-04</span>; <span class="comment">/* 0x390aee49 */ |
| </span><span class="kw">const </span>QQ5: f32 = -<span class="number">3.9602282413e-06</span>; <span class="comment">/* 0xb684e21a */ |
| /* |
| * Coefficients for approximation to erf in [0.84375,1.25] |
| */ |
| </span><span class="kw">const </span>PA0: f32 = -<span class="number">2.3621185683e-03</span>; <span class="comment">/* 0xbb1acdc6 */ |
| </span><span class="kw">const </span>PA1: f32 = <span class="number">4.1485610604e-01</span>; <span class="comment">/* 0x3ed46805 */ |
| </span><span class="kw">const </span>PA2: f32 = -<span class="number">3.7220788002e-01</span>; <span class="comment">/* 0xbebe9208 */ |
| </span><span class="kw">const </span>PA3: f32 = <span class="number">3.1834661961e-01</span>; <span class="comment">/* 0x3ea2fe54 */ |
| </span><span class="kw">const </span>PA4: f32 = -<span class="number">1.1089469492e-01</span>; <span class="comment">/* 0xbde31cc2 */ |
| </span><span class="kw">const </span>PA5: f32 = <span class="number">3.5478305072e-02</span>; <span class="comment">/* 0x3d1151b3 */ |
| </span><span class="kw">const </span>PA6: f32 = -<span class="number">2.1663755178e-03</span>; <span class="comment">/* 0xbb0df9c0 */ |
| </span><span class="kw">const </span>QA1: f32 = <span class="number">1.0642088205e-01</span>; <span class="comment">/* 0x3dd9f331 */ |
| </span><span class="kw">const </span>QA2: f32 = <span class="number">5.4039794207e-01</span>; <span class="comment">/* 0x3f0a5785 */ |
| </span><span class="kw">const </span>QA3: f32 = <span class="number">7.1828655899e-02</span>; <span class="comment">/* 0x3d931ae7 */ |
| </span><span class="kw">const </span>QA4: f32 = <span class="number">1.2617121637e-01</span>; <span class="comment">/* 0x3e013307 */ |
| </span><span class="kw">const </span>QA5: f32 = <span class="number">1.3637083583e-02</span>; <span class="comment">/* 0x3c5f6e13 */ |
| </span><span class="kw">const </span>QA6: f32 = <span class="number">1.1984500103e-02</span>; <span class="comment">/* 0x3c445aa3 */ |
| /* |
| * Coefficients for approximation to erfc in [1.25,1/0.35] |
| */ |
| </span><span class="kw">const </span>RA0: f32 = -<span class="number">9.8649440333e-03</span>; <span class="comment">/* 0xbc21a093 */ |
| </span><span class="kw">const </span>RA1: f32 = -<span class="number">6.9385856390e-01</span>; <span class="comment">/* 0xbf31a0b7 */ |
| </span><span class="kw">const </span>RA2: f32 = -<span class="number">1.0558626175e+01</span>; <span class="comment">/* 0xc128f022 */ |
| </span><span class="kw">const </span>RA3: f32 = -<span class="number">6.2375331879e+01</span>; <span class="comment">/* 0xc2798057 */ |
| </span><span class="kw">const </span>RA4: f32 = -<span class="number">1.6239666748e+02</span>; <span class="comment">/* 0xc322658c */ |
| </span><span class="kw">const </span>RA5: f32 = -<span class="number">1.8460508728e+02</span>; <span class="comment">/* 0xc3389ae7 */ |
| </span><span class="kw">const </span>RA6: f32 = -<span class="number">8.1287437439e+01</span>; <span class="comment">/* 0xc2a2932b */ |
| </span><span class="kw">const </span>RA7: f32 = -<span class="number">9.8143291473e+00</span>; <span class="comment">/* 0xc11d077e */ |
| </span><span class="kw">const </span>SA1: f32 = <span class="number">1.9651271820e+01</span>; <span class="comment">/* 0x419d35ce */ |
| </span><span class="kw">const </span>SA2: f32 = <span class="number">1.3765776062e+02</span>; <span class="comment">/* 0x4309a863 */ |
| </span><span class="kw">const </span>SA3: f32 = <span class="number">4.3456588745e+02</span>; <span class="comment">/* 0x43d9486f */ |
| </span><span class="kw">const </span>SA4: f32 = <span class="number">6.4538726807e+02</span>; <span class="comment">/* 0x442158c9 */ |
| </span><span class="kw">const </span>SA5: f32 = <span class="number">4.2900814819e+02</span>; <span class="comment">/* 0x43d6810b */ |
| </span><span class="kw">const </span>SA6: f32 = <span class="number">1.0863500214e+02</span>; <span class="comment">/* 0x42d9451f */ |
| </span><span class="kw">const </span>SA7: f32 = <span class="number">6.5702495575e+00</span>; <span class="comment">/* 0x40d23f7c */ |
| </span><span class="kw">const </span>SA8: f32 = -<span class="number">6.0424413532e-02</span>; <span class="comment">/* 0xbd777f97 */ |
| /* |
| * Coefficients for approximation to erfc in [1/.35,28] |
| */ |
| </span><span class="kw">const </span>RB0: f32 = -<span class="number">9.8649431020e-03</span>; <span class="comment">/* 0xbc21a092 */ |
| </span><span class="kw">const </span>RB1: f32 = -<span class="number">7.9928326607e-01</span>; <span class="comment">/* 0xbf4c9dd4 */ |
| </span><span class="kw">const </span>RB2: f32 = -<span class="number">1.7757955551e+01</span>; <span class="comment">/* 0xc18e104b */ |
| </span><span class="kw">const </span>RB3: f32 = -<span class="number">1.6063638306e+02</span>; <span class="comment">/* 0xc320a2ea */ |
| </span><span class="kw">const </span>RB4: f32 = -<span class="number">6.3756646729e+02</span>; <span class="comment">/* 0xc41f6441 */ |
| </span><span class="kw">const </span>RB5: f32 = -<span class="number">1.0250950928e+03</span>; <span class="comment">/* 0xc480230b */ |
| </span><span class="kw">const </span>RB6: f32 = -<span class="number">4.8351919556e+02</span>; <span class="comment">/* 0xc3f1c275 */ |
| </span><span class="kw">const </span>SB1: f32 = <span class="number">3.0338060379e+01</span>; <span class="comment">/* 0x41f2b459 */ |
| </span><span class="kw">const </span>SB2: f32 = <span class="number">3.2579251099e+02</span>; <span class="comment">/* 0x43a2e571 */ |
| </span><span class="kw">const </span>SB3: f32 = <span class="number">1.5367296143e+03</span>; <span class="comment">/* 0x44c01759 */ |
| </span><span class="kw">const </span>SB4: f32 = <span class="number">3.1998581543e+03</span>; <span class="comment">/* 0x4547fdbb */ |
| </span><span class="kw">const </span>SB5: f32 = <span class="number">2.5530502930e+03</span>; <span class="comment">/* 0x451f90ce */ |
| </span><span class="kw">const </span>SB6: f32 = <span class="number">4.7452853394e+02</span>; <span class="comment">/* 0x43ed43a7 */ |
| </span><span class="kw">const </span>SB7: f32 = -<span class="number">2.2440952301e+01</span>; <span class="comment">/* 0xc1b38712 */ |
| |
| </span><span class="kw">fn </span>erfc1(x: f32) -> f32 { |
| <span class="kw">let </span>s: f32; |
| <span class="kw">let </span>p: f32; |
| <span class="kw">let </span>q: f32; |
| |
| s = fabsf(x) - <span class="number">1.0</span>; |
| p = PA0 + s * (PA1 + s * (PA2 + s * (PA3 + s * (PA4 + s * (PA5 + s * PA6))))); |
| q = <span class="number">1.0 </span>+ s * (QA1 + s * (QA2 + s * (QA3 + s * (QA4 + s * (QA5 + s * QA6))))); |
| <span class="kw">return </span><span class="number">1.0 </span>- ERX - p / q; |
| } |
| |
| <span class="kw">fn </span>erfc2(<span class="kw-2">mut </span>ix: u32, <span class="kw-2">mut </span>x: f32) -> f32 { |
| <span class="kw">let </span>s: f32; |
| <span class="kw">let </span>r: f32; |
| <span class="kw">let </span>big_s: f32; |
| <span class="kw">let </span>z: f32; |
| |
| <span class="kw">if </span>ix < <span class="number">0x3fa00000 </span>{ |
| <span class="comment">/* |x| < 1.25 */ |
| </span><span class="kw">return </span>erfc1(x); |
| } |
| |
| x = fabsf(x); |
| s = <span class="number">1.0 </span>/ (x * x); |
| <span class="kw">if </span>ix < <span class="number">0x4036db6d </span>{ |
| <span class="comment">/* |x| < 1/0.35 */ |
| </span>r = RA0 + s * (RA1 + s * (RA2 + s * (RA3 + s * (RA4 + s * (RA5 + s * (RA6 + s * RA7)))))); |
| big_s = <span class="number">1.0 |
| </span>+ s * (SA1 |
| + s * (SA2 + s * (SA3 + s * (SA4 + s * (SA5 + s * (SA6 + s * (SA7 + s * SA8))))))); |
| } <span class="kw">else </span>{ |
| <span class="comment">/* |x| >= 1/0.35 */ |
| </span>r = RB0 + s * (RB1 + s * (RB2 + s * (RB3 + s * (RB4 + s * (RB5 + s * RB6))))); |
| big_s = |
| <span class="number">1.0 </span>+ s * (SB1 + s * (SB2 + s * (SB3 + s * (SB4 + s * (SB5 + s * (SB6 + s * SB7)))))); |
| } |
| ix = x.to_bits(); |
| z = f32::from_bits(ix & <span class="number">0xffffe000</span>); |
| |
| expf(-z * z - <span class="number">0.5625</span>) * expf((z - x) * (z + x) + r / big_s) / x |
| } |
| |
| <span class="doccomment">/// Error function (f32) |
| /// |
| /// Calculates an approximation to the “error function”, which estimates |
| /// the probability that an observation will fall within x standard |
| /// deviations of the mean (assuming a normal distribution). |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>erff(x: f32) -> f32 { |
| <span class="kw">let </span>r: f32; |
| <span class="kw">let </span>s: f32; |
| <span class="kw">let </span>z: f32; |
| <span class="kw">let </span>y: f32; |
| <span class="kw">let </span><span class="kw-2">mut </span>ix: u32; |
| <span class="kw">let </span>sign: usize; |
| |
| ix = x.to_bits(); |
| sign = (ix >> <span class="number">31</span>) <span class="kw">as </span>usize; |
| ix &= <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x7f800000 </span>{ |
| <span class="comment">/* erf(nan)=nan, erf(+-inf)=+-1 */ |
| </span><span class="kw">return </span><span class="number">1.0 </span>- <span class="number">2.0 </span>* (sign <span class="kw">as </span>f32) + <span class="number">1.0 </span>/ x; |
| } |
| <span class="kw">if </span>ix < <span class="number">0x3f580000 </span>{ |
| <span class="comment">/* |x| < 0.84375 */ |
| </span><span class="kw">if </span>ix < <span class="number">0x31800000 </span>{ |
| <span class="comment">/* |x| < 2**-28 */ |
| /*avoid underflow */ |
| </span><span class="kw">return </span><span class="number">0.125 </span>* (<span class="number">8.0 </span>* x + EFX8 * x); |
| } |
| z = x * x; |
| r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4))); |
| s = <span class="number">1.0 </span>+ z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5)))); |
| y = r / s; |
| <span class="kw">return </span>x + x * y; |
| } |
| <span class="kw">if </span>ix < <span class="number">0x40c00000 </span>{ |
| <span class="comment">/* |x| < 6 */ |
| </span>y = <span class="number">1.0 </span>- erfc2(ix, x); |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>x1p_120 = f32::from_bits(<span class="number">0x03800000</span>); |
| y = <span class="number">1.0 </span>- x1p_120; |
| } |
| |
| <span class="kw">if </span>sign != <span class="number">0 </span>{ |
| -y |
| } <span class="kw">else </span>{ |
| y |
| } |
| } |
| |
| <span class="doccomment">/// Complementary error function (f32) |
| /// |
| /// Calculates the complementary probability. |
| /// Is `1 - erf(x)`. Is computed directly, so that you can use it to avoid |
| /// the loss of precision that would result from subtracting |
| /// large probabilities (on large `x`) from 1. |
| </span><span class="kw">pub fn </span>erfcf(x: f32) -> f32 { |
| <span class="kw">let </span>r: f32; |
| <span class="kw">let </span>s: f32; |
| <span class="kw">let </span>z: f32; |
| <span class="kw">let </span>y: f32; |
| <span class="kw">let </span><span class="kw-2">mut </span>ix: u32; |
| <span class="kw">let </span>sign: usize; |
| |
| ix = x.to_bits(); |
| sign = (ix >> <span class="number">31</span>) <span class="kw">as </span>usize; |
| ix &= <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x7f800000 </span>{ |
| <span class="comment">/* erfc(nan)=nan, erfc(+-inf)=0,2 */ |
| </span><span class="kw">return </span><span class="number">2.0 </span>* (sign <span class="kw">as </span>f32) + <span class="number">1.0 </span>/ x; |
| } |
| |
| <span class="kw">if </span>ix < <span class="number">0x3f580000 </span>{ |
| <span class="comment">/* |x| < 0.84375 */ |
| </span><span class="kw">if </span>ix < <span class="number">0x23800000 </span>{ |
| <span class="comment">/* |x| < 2**-56 */ |
| </span><span class="kw">return </span><span class="number">1.0 </span>- x; |
| } |
| z = x * x; |
| r = PP0 + z * (PP1 + z * (PP2 + z * (PP3 + z * PP4))); |
| s = <span class="number">1.0 </span>+ z * (QQ1 + z * (QQ2 + z * (QQ3 + z * (QQ4 + z * QQ5)))); |
| y = r / s; |
| <span class="kw">if </span>sign != <span class="number">0 </span>|| ix < <span class="number">0x3e800000 </span>{ |
| <span class="comment">/* x < 1/4 */ |
| </span><span class="kw">return </span><span class="number">1.0 </span>- (x + x * y); |
| } |
| <span class="kw">return </span><span class="number">0.5 </span>- (x - <span class="number">0.5 </span>+ x * y); |
| } |
| <span class="kw">if </span>ix < <span class="number">0x41e00000 </span>{ |
| <span class="comment">/* |x| < 28 */ |
| </span><span class="kw">if </span>sign != <span class="number">0 </span>{ |
| <span class="kw">return </span><span class="number">2.0 </span>- erfc2(ix, x); |
| } <span class="kw">else </span>{ |
| <span class="kw">return </span>erfc2(ix, x); |
| } |
| } |
| |
| <span class="kw">let </span>x1p_120 = f32::from_bits(<span class="number">0x03800000</span>); |
| <span class="kw">if </span>sign != <span class="number">0 </span>{ |
| <span class="number">2.0 </span>- x1p_120 |
| } <span class="kw">else </span>{ |
| x1p_120 * x1p_120 |
| } |
| } |
| </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> |
