| <!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/log10.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>log10.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_log10.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. |
| * ==================================================== |
| */ |
| /* |
| * Return the base 10 logarithm of x. See log.c for most comments. |
| * |
| * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2 |
| * as in log.c, then combine and scale in extra precision: |
| * log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2) |
| */ |
| |
| </span><span class="kw">use </span>core::f64; |
| |
| <span class="kw">const </span>IVLN10HI: f64 = <span class="number">4.34294481878168880939e-01</span>; <span class="comment">/* 0x3fdbcb7b, 0x15200000 */ |
| </span><span class="kw">const </span>IVLN10LO: f64 = <span class="number">2.50829467116452752298e-11</span>; <span class="comment">/* 0x3dbb9438, 0xca9aadd5 */ |
| </span><span class="kw">const </span>LOG10_2HI: f64 = <span class="number">3.01029995663611771306e-01</span>; <span class="comment">/* 0x3FD34413, 0x509F6000 */ |
| </span><span class="kw">const </span>LOG10_2LO: f64 = <span class="number">3.69423907715893078616e-13</span>; <span class="comment">/* 0x3D59FEF3, 0x11F12B36 */ |
| </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>log10(<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: u64 = x.to_bits(); |
| <span class="kw">let </span>hfsq: f64; |
| <span class="kw">let </span>f: f64; |
| <span class="kw">let </span>s: f64; |
| <span class="kw">let </span>z: f64; |
| <span class="kw">let </span>r: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>w: f64; |
| <span class="kw">let </span>t1: f64; |
| <span class="kw">let </span>t2: f64; |
| <span class="kw">let </span>dk: f64; |
| <span class="kw">let </span>y: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>hi: f64; |
| <span class="kw">let </span>lo: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>val_hi: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>val_lo: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>hx: u32; |
| <span class="kw">let </span><span class="kw-2">mut </span>k: i32; |
| |
| hx = (ui >> <span class="number">32</span>) <span class="kw">as </span>u32; |
| k = <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="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); |
| |
| f = x - <span class="number">1.0</span>; |
| hfsq = <span class="number">0.5 </span>* f * f; |
| s = f / (<span class="number">2.0 </span>+ f); |
| z = s * s; |
| w = z * z; |
| t1 = w * (LG2 + w * (LG4 + w * LG6)); |
| t2 = z * (LG1 + w * (LG3 + w * (LG5 + w * LG7))); |
| r = t2 + t1; |
| |
| <span class="comment">/* See log2.c for details. */ |
| /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */ |
| </span>hi = f - hfsq; |
| ui = hi.to_bits(); |
| ui &= (-<span class="number">1i64 </span><span class="kw">as </span>u64) << <span class="number">32</span>; |
| hi = f64::from_bits(ui); |
| lo = f - hi - hfsq + s * (hfsq + r); |
| |
| <span class="comment">/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */ |
| </span>val_hi = hi * IVLN10HI; |
| dk = k <span class="kw">as </span>f64; |
| y = dk * LOG10_2HI; |
| val_lo = dk * LOG10_2LO + (lo + hi) * IVLN10LO + lo * IVLN10HI; |
| |
| <span class="comment">/* |
| * Extra precision in for adding y is not strictly needed |
| * since there is no very large cancellation near x = sqrt(2) or |
| * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs |
| * with some parallelism and it reduces the error for many args. |
| */ |
| </span>w = y + val_hi; |
| val_lo += (y - w) + val_hi; |
| val_hi = w; |
| |
| val_lo + val_hi |
| } |
| </code></pre></div> |
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