| <!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/exp.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>exp.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_exp.c */ |
| /* |
| * ==================================================== |
| * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| /* exp(x) |
| * Returns the exponential of x. |
| * |
| * Method |
| * 1. Argument reduction: |
| * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. |
| * Given x, find r and integer k such that |
| * |
| * x = k*ln2 + r, |r| <= 0.5*ln2. |
| * |
| * Here r will be represented as r = hi-lo for better |
| * accuracy. |
| * |
| * 2. Approximation of exp(r) by a special rational function on |
| * the interval [0,0.34658]: |
| * Write |
| * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... |
| * We use a special Remez algorithm on [0,0.34658] to generate |
| * a polynomial of degree 5 to approximate R. The maximum error |
| * of this polynomial approximation is bounded by 2**-59. In |
| * other words, |
| * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 |
| * (where z=r*r, and the values of P1 to P5 are listed below) |
| * and |
| * | 5 | -59 |
| * | 2.0+P1*z+...+P5*z - R(z) | <= 2 |
| * | | |
| * The computation of exp(r) thus becomes |
| * 2*r |
| * exp(r) = 1 + ---------- |
| * R(r) - r |
| * r*c(r) |
| * = 1 + r + ----------- (for better accuracy) |
| * 2 - c(r) |
| * where |
| * 2 4 10 |
| * c(r) = r - (P1*r + P2*r + ... + P5*r ). |
| * |
| * 3. Scale back to obtain exp(x): |
| * From step 1, we have |
| * exp(x) = 2^k * exp(r) |
| * |
| * Special cases: |
| * exp(INF) is INF, exp(NaN) is NaN; |
| * exp(-INF) is 0, and |
| * for finite argument, only exp(0)=1 is exact. |
| * |
| * Accuracy: |
| * according to an error analysis, the error is always less than |
| * 1 ulp (unit in the last place). |
| * |
| * Misc. info. |
| * For IEEE double |
| * if x > 709.782712893383973096 then exp(x) overflows |
| * if x < -745.133219101941108420 then exp(x) underflows |
| */ |
| |
| </span><span class="kw">use </span><span class="kw">super</span>::scalbn; |
| |
| <span class="kw">const </span>HALF: [f64; <span class="number">2</span>] = [<span class="number">0.5</span>, -<span class="number">0.5</span>]; |
| <span class="kw">const </span>LN2HI: f64 = <span class="number">6.93147180369123816490e-01</span>; <span class="comment">/* 0x3fe62e42, 0xfee00000 */ |
| </span><span class="kw">const </span>LN2LO: 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 */ |
| </span><span class="kw">const </span>P1: f64 = <span class="number">1.66666666666666019037e-01</span>; <span class="comment">/* 0x3FC55555, 0x5555553E */ |
| </span><span class="kw">const </span>P2: f64 = -<span class="number">2.77777777770155933842e-03</span>; <span class="comment">/* 0xBF66C16C, 0x16BEBD93 */ |
| </span><span class="kw">const </span>P3: f64 = <span class="number">6.61375632143793436117e-05</span>; <span class="comment">/* 0x3F11566A, 0xAF25DE2C */ |
| </span><span class="kw">const </span>P4: f64 = -<span class="number">1.65339022054652515390e-06</span>; <span class="comment">/* 0xBEBBBD41, 0xC5D26BF1 */ |
| </span><span class="kw">const </span>P5: f64 = <span class="number">4.13813679705723846039e-08</span>; <span class="comment">/* 0x3E663769, 0x72BEA4D0 */ |
| |
| </span><span class="doccomment">/// Exponential, base *e* (f64) |
| /// |
| /// Calculate the exponential of `x`, that is, *e* raised to the power `x` |
| /// (where *e* is the base of the natural system of logarithms, approximately 2.71828). |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>exp(<span class="kw-2">mut </span>x: f64) -> f64 { |
| <span class="kw">let </span>x1p1023 = f64::from_bits(<span class="number">0x7fe0000000000000</span>); <span class="comment">// 0x1p1023 === 2 ^ 1023 |
| </span><span class="kw">let </span>x1p_149 = f64::from_bits(<span class="number">0x36a0000000000000</span>); <span class="comment">// 0x1p-149 === 2 ^ -149 |
| |
| </span><span class="kw">let </span>hi: f64; |
| <span class="kw">let </span>lo: f64; |
| <span class="kw">let </span>c: f64; |
| <span class="kw">let </span>xx: f64; |
| <span class="kw">let </span>y: f64; |
| <span class="kw">let </span>k: i32; |
| <span class="kw">let </span>sign: i32; |
| <span class="kw">let </span><span class="kw-2">mut </span>hx: u32; |
| |
| hx = (x.to_bits() >> <span class="number">32</span>) <span class="kw">as </span>u32; |
| sign = (hx >> <span class="number">31</span>) <span class="kw">as </span>i32; |
| hx &= <span class="number">0x7fffffff</span>; <span class="comment">/* high word of |x| */ |
| |
| /* special cases */ |
| </span><span class="kw">if </span>hx >= <span class="number">0x4086232b </span>{ |
| <span class="comment">/* if |x| >= 708.39... */ |
| </span><span class="kw">if </span>x.is_nan() { |
| <span class="kw">return </span>x; |
| } |
| <span class="kw">if </span>x > <span class="number">709.782712893383973096 </span>{ |
| <span class="comment">/* overflow if x!=inf */ |
| </span>x <span class="kw-2">*</span>= x1p1023; |
| <span class="kw">return </span>x; |
| } |
| <span class="kw">if </span>x < -<span class="number">708.39641853226410622 </span>{ |
| <span class="comment">/* underflow if x!=-inf */ |
| </span><span class="macro">force_eval!</span>((-x1p_149 / x) <span class="kw">as </span>f32); |
| <span class="kw">if </span>x < -<span class="number">745.13321910194110842 </span>{ |
| <span class="kw">return </span><span class="number">0.</span>; |
| } |
| } |
| } |
| |
| <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">/* if |x| >= 1.5 ln2 */ |
| </span>k = (INVLN2 * x + <span class="macro">i!</span>(HALF, sign <span class="kw">as </span>usize)) <span class="kw">as </span>i32; |
| } <span class="kw">else </span>{ |
| k = <span class="number">1 </span>- sign - sign; |
| } |
| hi = x - k <span class="kw">as </span>f64 * LN2HI; <span class="comment">/* k*ln2hi is exact here */ |
| </span>lo = k <span class="kw">as </span>f64 * LN2LO; |
| x = hi - lo; |
| } <span class="kw">else if </span>hx > <span class="number">0x3e300000 </span>{ |
| <span class="comment">/* if |x| > 2**-28 */ |
| </span>k = <span class="number">0</span>; |
| hi = x; |
| lo = <span class="number">0.</span>; |
| } <span class="kw">else </span>{ |
| <span class="comment">/* inexact if x!=0 */ |
| </span><span class="macro">force_eval!</span>(x1p1023 + x); |
| <span class="kw">return </span><span class="number">1. </span>+ x; |
| } |
| |
| <span class="comment">/* x is now in primary range */ |
| </span>xx = x * x; |
| c = x - xx * (P1 + xx * (P2 + xx * (P3 + xx * (P4 + xx * P5)))); |
| y = <span class="number">1. </span>+ (x * c / (<span class="number">2. </span>- c) - lo + hi); |
| <span class="kw">if </span>k == <span class="number">0 </span>{ |
| y |
| } <span class="kw">else </span>{ |
| scalbn(y, k) |
| } |
| } |
| </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> |
