| <!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/exp2f.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>exp2f.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_exp2f.c |
| //- |
| // Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> |
| // All rights reserved. |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions |
| // are met: |
| // 1. Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // 2. Redistributions in binary form must reproduce the above copyright |
| // notice, this list of conditions and the following disclaimer in the |
| // documentation and/or other materials provided with the distribution. |
| // |
| // THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
| // ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| // ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| // OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| // HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| // LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| // OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| // SUCH DAMAGE. |
| |
| </span><span class="kw">const </span>TBLSIZE: usize = <span class="number">16</span>; |
| |
| <span class="kw">static </span>EXP2FT: [u64; TBLSIZE] = [ |
| <span class="number">0x3fe6a09e667f3bcd</span>, |
| <span class="number">0x3fe7a11473eb0187</span>, |
| <span class="number">0x3fe8ace5422aa0db</span>, |
| <span class="number">0x3fe9c49182a3f090</span>, |
| <span class="number">0x3feae89f995ad3ad</span>, |
| <span class="number">0x3fec199bdd85529c</span>, |
| <span class="number">0x3fed5818dcfba487</span>, |
| <span class="number">0x3feea4afa2a490da</span>, |
| <span class="number">0x3ff0000000000000</span>, |
| <span class="number">0x3ff0b5586cf9890f</span>, |
| <span class="number">0x3ff172b83c7d517b</span>, |
| <span class="number">0x3ff2387a6e756238</span>, |
| <span class="number">0x3ff306fe0a31b715</span>, |
| <span class="number">0x3ff3dea64c123422</span>, |
| <span class="number">0x3ff4bfdad5362a27</span>, |
| <span class="number">0x3ff5ab07dd485429</span>, |
| ]; |
| |
| <span class="comment">// exp2f(x): compute the base 2 exponential of x |
| // |
| // Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927. |
| // |
| // Method: (equally-spaced tables) |
| // |
| // Reduce x: |
| // x = k + y, for integer k and |y| <= 1/2. |
| // Thus we have exp2f(x) = 2**k * exp2(y). |
| // |
| // Reduce y: |
| // y = i/TBLSIZE + z for integer i near y * TBLSIZE. |
| // Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), |
| // with |z| <= 2**-(TBLSIZE+1). |
| // |
| // We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a |
| // degree-4 minimax polynomial with maximum error under 1.4 * 2**-33. |
| // Using double precision for everything except the reduction makes |
| // roundoff error insignificant and simplifies the scaling step. |
| // |
| // This method is due to Tang, but I do not use his suggested parameters: |
| // |
| // Tang, P. Table-driven Implementation of the Exponential Function |
| // in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989). |
| |
| </span><span class="doccomment">/// Exponential, base 2 (f32) |
| /// |
| /// Calculate `2^x`, that is, 2 raised to the power `x`. |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>exp2f(<span class="kw-2">mut </span>x: f32) -> f32 { |
| <span class="kw">let </span>redux = f32::from_bits(<span class="number">0x4b400000</span>) / TBLSIZE <span class="kw">as </span>f32; |
| <span class="kw">let </span>p1 = f32::from_bits(<span class="number">0x3f317218</span>); |
| <span class="kw">let </span>p2 = f32::from_bits(<span class="number">0x3e75fdf0</span>); |
| <span class="kw">let </span>p3 = f32::from_bits(<span class="number">0x3d6359a4</span>); |
| <span class="kw">let </span>p4 = f32::from_bits(<span class="number">0x3c1d964e</span>); |
| |
| <span class="comment">// double_t t, r, z; |
| // uint32_t ix, i0, k; |
| |
| </span><span class="kw">let </span>x1p127 = f32::from_bits(<span class="number">0x7f000000</span>); |
| |
| <span class="comment">/* Filter out exceptional cases. */ |
| </span><span class="kw">let </span>ui = f32::to_bits(x); |
| <span class="kw">let </span>ix = ui & <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>ix > <span class="number">0x42fc0000 </span>{ |
| <span class="comment">/* |x| > 126 */ |
| </span><span class="kw">if </span>ix > <span class="number">0x7f800000 </span>{ |
| <span class="comment">/* NaN */ |
| </span><span class="kw">return </span>x; |
| } |
| <span class="kw">if </span>ui >= <span class="number">0x43000000 </span>&& ui < <span class="number">0x80000000 </span>{ |
| <span class="comment">/* x >= 128 */ |
| </span>x <span class="kw-2">*</span>= x1p127; |
| <span class="kw">return </span>x; |
| } |
| <span class="kw">if </span>ui >= <span class="number">0x80000000 </span>{ |
| <span class="comment">/* x < -126 */ |
| </span><span class="kw">if </span>ui >= <span class="number">0xc3160000 </span>|| (ui & <span class="number">0x0000ffff </span>!= <span class="number">0</span>) { |
| <span class="macro">force_eval!</span>(f32::from_bits(<span class="number">0x80000001</span>) / x); |
| } |
| <span class="kw">if </span>ui >= <span class="number">0xc3160000 </span>{ |
| <span class="comment">/* x <= -150 */ |
| </span><span class="kw">return </span><span class="number">0.0</span>; |
| } |
| } |
| } <span class="kw">else if </span>ix <= <span class="number">0x33000000 </span>{ |
| <span class="comment">/* |x| <= 0x1p-25 */ |
| </span><span class="kw">return </span><span class="number">1.0 </span>+ x; |
| } |
| |
| <span class="comment">/* Reduce x, computing z, i0, and k. */ |
| </span><span class="kw">let </span>ui = f32::to_bits(x + redux); |
| <span class="kw">let </span><span class="kw-2">mut </span>i0 = ui; |
| i0 += TBLSIZE <span class="kw">as </span>u32 / <span class="number">2</span>; |
| <span class="kw">let </span>k = i0 / TBLSIZE <span class="kw">as </span>u32; |
| <span class="kw">let </span>ukf = f64::from_bits(((<span class="number">0x3ff </span>+ k) <span class="kw">as </span>u64) << <span class="number">52</span>); |
| i0 &= TBLSIZE <span class="kw">as </span>u32 - <span class="number">1</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>uf = f32::from_bits(ui); |
| uf -= redux; |
| <span class="kw">let </span>z: f64 = (x - uf) <span class="kw">as </span>f64; |
| <span class="comment">/* Compute r = exp2(y) = exp2ft[i0] * p(z). */ |
| </span><span class="kw">let </span>r: f64 = f64::from_bits(<span class="macro">i!</span>(EXP2FT, i0 <span class="kw">as </span>usize)); |
| <span class="kw">let </span>t: f64 = r <span class="kw">as </span>f64 * z; |
| <span class="kw">let </span>r: f64 = r + t * (p1 <span class="kw">as </span>f64 + z * p2 <span class="kw">as </span>f64) + t * (z * z) * (p3 <span class="kw">as </span>f64 + z * p4 <span class="kw">as </span>f64); |
| |
| <span class="comment">/* Scale by 2**k */ |
| </span>(r * ukf) <span class="kw">as </span>f32 |
| } |
| </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> |
