| <!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/expm1.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>expm1.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_expm1.c */ |
| /* |
| * ==================================================== |
| * 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 </span>core::f64; |
| |
| <span class="kw">const </span>O_THRESHOLD: f64 = <span class="number">7.09782712893383973096e+02</span>; <span class="comment">/* 0x40862E42, 0xFEFA39EF */ |
| </span><span class="kw">const </span>LN2_HI: f64 = <span class="number">6.93147180369123816490e-01</span>; <span class="comment">/* 0x3fe62e42, 0xfee00000 */ |
| </span><span class="kw">const </span>LN2_LO: f64 = <span class="number">1.90821492927058770002e-10</span>; <span class="comment">/* 0x3dea39ef, 0x35793c76 */ |
| </span><span class="kw">const </span>INVLN2: f64 = <span class="number">1.44269504088896338700e+00</span>; <span class="comment">/* 0x3ff71547, 0x652b82fe */ |
| /* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */ |
| </span><span class="kw">const </span>Q1: f64 = -<span class="number">3.33333333333331316428e-02</span>; <span class="comment">/* BFA11111 111110F4 */ |
| </span><span class="kw">const </span>Q2: f64 = <span class="number">1.58730158725481460165e-03</span>; <span class="comment">/* 3F5A01A0 19FE5585 */ |
| </span><span class="kw">const </span>Q3: f64 = -<span class="number">7.93650757867487942473e-05</span>; <span class="comment">/* BF14CE19 9EAADBB7 */ |
| </span><span class="kw">const </span>Q4: f64 = <span class="number">4.00821782732936239552e-06</span>; <span class="comment">/* 3ED0CFCA 86E65239 */ |
| </span><span class="kw">const </span>Q5: f64 = -<span class="number">2.01099218183624371326e-07</span>; <span class="comment">/* BE8AFDB7 6E09C32D */ |
| |
| </span><span class="doccomment">/// Exponential, base *e*, of x-1 (f64) |
| /// |
| /// Calculates the exponential of `x` and subtract 1, that is, *e* raised |
| /// to the power `x` minus 1 (where *e* is the base of the natural |
| /// system of logarithms, approximately 2.71828). |
| /// The result is accurate even for small values of `x`, |
| /// where using `exp(x)-1` would lose many significant digits. |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>expm1(<span class="kw-2">mut </span>x: f64) -> f64 { |
| <span class="kw">let </span>hi: f64; |
| <span class="kw">let </span>lo: f64; |
| <span class="kw">let </span>k: i32; |
| <span class="kw">let </span>c: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>t: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>y: f64; |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>ui = x.to_bits(); |
| <span class="kw">let </span>hx = ((ui >> <span class="number">32</span>) & <span class="number">0x7fffffff</span>) <span class="kw">as </span>u32; |
| <span class="kw">let </span>sign = (ui >> <span class="number">63</span>) <span class="kw">as </span>i32; |
| |
| <span class="comment">/* filter out huge and non-finite argument */ |
| </span><span class="kw">if </span>hx >= <span class="number">0x4043687A </span>{ |
| <span class="comment">/* if |x|>=56*ln2 */ |
| </span><span class="kw">if </span>x.is_nan() { |
| <span class="kw">return </span>x; |
| } |
| <span class="kw">if </span>sign != <span class="number">0 </span>{ |
| <span class="kw">return </span>-<span class="number">1.0</span>; |
| } |
| <span class="kw">if </span>x > O_THRESHOLD { |
| x <span class="kw-2">*</span>= f64::from_bits(<span class="number">0x7fe0000000000000</span>); |
| <span class="kw">return </span>x; |
| } |
| } |
| |
| <span class="comment">/* argument reduction */ |
| </span><span class="kw">if </span>hx > <span class="number">0x3fd62e42 </span>{ |
| <span class="comment">/* if |x| > 0.5 ln2 */ |
| </span><span class="kw">if </span>hx < <span class="number">0x3FF0A2B2 </span>{ |
| <span class="comment">/* and |x| < 1.5 ln2 */ |
| </span><span class="kw">if </span>sign == <span class="number">0 </span>{ |
| hi = x - LN2_HI; |
| lo = LN2_LO; |
| k = <span class="number">1</span>; |
| } <span class="kw">else </span>{ |
| hi = x + LN2_HI; |
| lo = -LN2_LO; |
| k = -<span class="number">1</span>; |
| } |
| } <span class="kw">else </span>{ |
| k = (INVLN2 * x + <span class="kw">if </span>sign != <span class="number">0 </span>{ -<span class="number">0.5 </span>} <span class="kw">else </span>{ <span class="number">0.5 </span>}) <span class="kw">as </span>i32; |
| t = k <span class="kw">as </span>f64; |
| hi = x - t * LN2_HI; <span class="comment">/* t*ln2_hi is exact here */ |
| </span>lo = t * LN2_LO; |
| } |
| x = hi - lo; |
| c = (hi - x) - lo; |
| } <span class="kw">else if </span>hx < <span class="number">0x3c900000 </span>{ |
| <span class="comment">/* |x| < 2**-54, return x */ |
| </span><span class="kw">if </span>hx < <span class="number">0x00100000 </span>{ |
| <span class="macro">force_eval!</span>(x); |
| } |
| <span class="kw">return </span>x; |
| } <span class="kw">else </span>{ |
| c = <span class="number">0.0</span>; |
| k = <span class="number">0</span>; |
| } |
| |
| <span class="comment">/* x is now in primary range */ |
| </span><span class="kw">let </span>hfx = <span class="number">0.5 </span>* x; |
| <span class="kw">let </span>hxs = x * hfx; |
| <span class="kw">let </span>r1 = <span class="number">1.0 </span>+ hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5)))); |
| t = <span class="number">3.0 </span>- r1 * hfx; |
| <span class="kw">let </span><span class="kw-2">mut </span>e = hxs * ((r1 - t) / (<span class="number">6.0 </span>- x * t)); |
| <span class="kw">if </span>k == <span class="number">0 </span>{ |
| <span class="comment">/* c is 0 */ |
| </span><span class="kw">return </span>x - (x * e - hxs); |
| } |
| e = x * (e - c) - c; |
| e -= hxs; |
| <span class="comment">/* exp(x) ~ 2^k (x_reduced - e + 1) */ |
| </span><span class="kw">if </span>k == -<span class="number">1 </span>{ |
| <span class="kw">return </span><span class="number">0.5 </span>* (x - e) - <span class="number">0.5</span>; |
| } |
| <span class="kw">if </span>k == <span class="number">1 </span>{ |
| <span class="kw">if </span>x < -<span class="number">0.25 </span>{ |
| <span class="kw">return </span>-<span class="number">2.0 </span>* (e - (x + <span class="number">0.5</span>)); |
| } |
| <span class="kw">return </span><span class="number">1.0 </span>+ <span class="number">2.0 </span>* (x - e); |
| } |
| ui = ((<span class="number">0x3ff </span>+ k) <span class="kw">as </span>u64) << <span class="number">52</span>; <span class="comment">/* 2^k */ |
| </span><span class="kw">let </span>twopk = f64::from_bits(ui); |
| <span class="kw">if </span>k < <span class="number">0 </span>|| k > <span class="number">56 </span>{ |
| <span class="comment">/* suffice to return exp(x)-1 */ |
| </span>y = x - e + <span class="number">1.0</span>; |
| <span class="kw">if </span>k == <span class="number">1024 </span>{ |
| y = y * <span class="number">2.0 </span>* f64::from_bits(<span class="number">0x7fe0000000000000</span>); |
| } <span class="kw">else </span>{ |
| y = y * twopk; |
| } |
| <span class="kw">return </span>y - <span class="number">1.0</span>; |
| } |
| ui = ((<span class="number">0x3ff </span>- k) <span class="kw">as </span>u64) << <span class="number">52</span>; <span class="comment">/* 2^-k */ |
| </span><span class="kw">let </span>uf = f64::from_bits(ui); |
| <span class="kw">if </span>k < <span class="number">20 </span>{ |
| y = (x - e + (<span class="number">1.0 </span>- uf)) * twopk; |
| } <span class="kw">else </span>{ |
| y = (x - (e + uf) + <span class="number">1.0</span>) * twopk; |
| } |
| y |
| } |
| |
| <span class="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>sanity_check() { |
| <span class="macro">assert_eq!</span>(<span class="kw">super</span>::expm1(<span class="number">1.1</span>), <span class="number">2.0041660239464334</span>); |
| } |
| } |
| </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> |
