<!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 `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.2.6/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="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../../static.files/favicon-2c020d218678b618.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"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../libm/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" 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="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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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="attr">#[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="attr">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="attr">#[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>
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