| <!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/log.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>log.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_log.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. |
| * ==================================================== |
| */ |
| /* log(x) |
| * Return the logarithm of x |
| * |
| * Method : |
| * 1. Argument Reduction: find k and f such that |
| * x = 2^k * (1+f), |
| * where sqrt(2)/2 < 1+f < sqrt(2) . |
| * |
| * 2. Approximation of log(1+f). |
| * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) |
| * = 2s + 2/3 s**3 + 2/5 s**5 + ....., |
| * = 2s + s*R |
| * We use a special Remez algorithm on [0,0.1716] to generate |
| * a polynomial of degree 14 to approximate R The maximum error |
| * of this polynomial approximation is bounded by 2**-58.45. In |
| * other words, |
| * 2 4 6 8 10 12 14 |
| * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s |
| * (the values of Lg1 to Lg7 are listed in the program) |
| * and |
| * | 2 14 | -58.45 |
| * | Lg1*s +...+Lg7*s - R(z) | <= 2 |
| * | | |
| * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. |
| * In order to guarantee error in log below 1ulp, we compute log |
| * by |
| * log(1+f) = f - s*(f - R) (if f is not too large) |
| * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) |
| * |
| * 3. Finally, log(x) = k*ln2 + log(1+f). |
| * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) |
| * Here ln2 is split into two floating point number: |
| * ln2_hi + ln2_lo, |
| * where n*ln2_hi is always exact for |n| < 2000. |
| * |
| * Special cases: |
| * log(x) is NaN with signal if x < 0 (including -INF) ; |
| * log(+INF) is +INF; log(0) is -INF with signal; |
| * log(NaN) is that NaN with no signal. |
| * |
| * Accuracy: |
| * according to an error analysis, the error is always less than |
| * 1 ulp (unit in the last place). |
| * |
| * Constants: |
| * The hexadecimal values are the intended ones for the following |
| * constants. The decimal values may be used, provided that the |
| * compiler will convert from decimal to binary accurately enough |
| * to produce the hexadecimal values shown. |
| */ |
| |
| </span><span class="kw">const </span>LN2_HI: f64 = <span class="number">6.93147180369123816490e-01</span>; <span class="comment">/* 3fe62e42 fee00000 */ |
| </span><span class="kw">const </span>LN2_LO: f64 = <span class="number">1.90821492927058770002e-10</span>; <span class="comment">/* 3dea39ef 35793c76 */ |
| </span><span class="kw">const </span>LG1: f64 = <span class="number">6.666666666666735130e-01</span>; <span class="comment">/* 3FE55555 55555593 */ |
| </span><span class="kw">const </span>LG2: f64 = <span class="number">3.999999999940941908e-01</span>; <span class="comment">/* 3FD99999 9997FA04 */ |
| </span><span class="kw">const </span>LG3: f64 = <span class="number">2.857142874366239149e-01</span>; <span class="comment">/* 3FD24924 94229359 */ |
| </span><span class="kw">const </span>LG4: f64 = <span class="number">2.222219843214978396e-01</span>; <span class="comment">/* 3FCC71C5 1D8E78AF */ |
| </span><span class="kw">const </span>LG5: f64 = <span class="number">1.818357216161805012e-01</span>; <span class="comment">/* 3FC74664 96CB03DE */ |
| </span><span class="kw">const </span>LG6: f64 = <span class="number">1.531383769920937332e-01</span>; <span class="comment">/* 3FC39A09 D078C69F */ |
| </span><span class="kw">const </span>LG7: f64 = <span class="number">1.479819860511658591e-01</span>; <span class="comment">/* 3FC2F112 DF3E5244 */ |
| |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>log(<span class="kw-2">mut </span>x: f64) -> f64 { |
| <span class="kw">let </span>x1p54 = f64::from_bits(<span class="number">0x4350000000000000</span>); <span class="comment">// 0x1p54 === 2 ^ 54 |
| |
| </span><span class="kw">let </span><span class="kw-2">mut </span>ui = x.to_bits(); |
| <span class="kw">let </span><span class="kw-2">mut </span>hx: u32 = (ui >> <span class="number">32</span>) <span class="kw">as </span>u32; |
| <span class="kw">let </span><span class="kw-2">mut </span>k: i32 = <span class="number">0</span>; |
| |
| <span class="kw">if </span>(hx < <span class="number">0x00100000</span>) || ((hx >> <span class="number">31</span>) != <span class="number">0</span>) { |
| <span class="comment">/* x < 2**-126 */ |
| </span><span class="kw">if </span>ui << <span class="number">1 </span>== <span class="number">0 </span>{ |
| <span class="kw">return </span>-<span class="number">1. </span>/ (x * x); <span class="comment">/* log(+-0)=-inf */ |
| </span>} |
| <span class="kw">if </span>hx >> <span class="number">31 </span>!= <span class="number">0 </span>{ |
| <span class="kw">return </span>(x - x) / <span class="number">0.0</span>; <span class="comment">/* log(-#) = NaN */ |
| </span>} |
| <span class="comment">/* subnormal number, scale x up */ |
| </span>k -= <span class="number">54</span>; |
| x <span class="kw-2">*</span>= x1p54; |
| ui = x.to_bits(); |
| hx = (ui >> <span class="number">32</span>) <span class="kw">as </span>u32; |
| } <span class="kw">else if </span>hx >= <span class="number">0x7ff00000 </span>{ |
| <span class="kw">return </span>x; |
| } <span class="kw">else if </span>hx == <span class="number">0x3ff00000 </span>&& ui << <span class="number">32 </span>== <span class="number">0 </span>{ |
| <span class="kw">return </span><span class="number">0.</span>; |
| } |
| |
| <span class="comment">/* reduce x into [sqrt(2)/2, sqrt(2)] */ |
| </span>hx += <span class="number">0x3ff00000 </span>- <span class="number">0x3fe6a09e</span>; |
| k += ((hx >> <span class="number">20</span>) <span class="kw">as </span>i32) - <span class="number">0x3ff</span>; |
| hx = (hx & <span class="number">0x000fffff</span>) + <span class="number">0x3fe6a09e</span>; |
| ui = ((hx <span class="kw">as </span>u64) << <span class="number">32</span>) | (ui & <span class="number">0xffffffff</span>); |
| x = f64::from_bits(ui); |
| |
| <span class="kw">let </span>f: f64 = x - <span class="number">1.0</span>; |
| <span class="kw">let </span>hfsq: f64 = <span class="number">0.5 </span>* f * f; |
| <span class="kw">let </span>s: f64 = f / (<span class="number">2.0 </span>+ f); |
| <span class="kw">let </span>z: f64 = s * s; |
| <span class="kw">let </span>w: f64 = z * z; |
| <span class="kw">let </span>t1: f64 = w * (LG2 + w * (LG4 + w * LG6)); |
| <span class="kw">let </span>t2: f64 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7))); |
| <span class="kw">let </span>r: f64 = t2 + t1; |
| <span class="kw">let </span>dk: f64 = k <span class="kw">as </span>f64; |
| s * (hfsq + r) + dk * LN2_LO - hfsq + f + dk * LN2_HI |
| } |
| </code></pre></div> |
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