| <!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/exp2.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>exp2.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_exp2.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">use </span><span class="kw">super</span>::scalbn; |
| |
| <span class="kw">const </span>TBLSIZE: usize = <span class="number">256</span>; |
| |
| <span class="attribute">#[cfg_attr(rustfmt, rustfmt_skip)] |
| </span><span class="kw">static </span>TBL: [u64; TBLSIZE * <span class="number">2</span>] = [ |
| <span class="comment">// exp2(z + eps) eps |
| </span><span class="number">0x3fe6a09e667f3d5d</span>, <span class="number">0x3d39880000000000</span>, |
| <span class="number">0x3fe6b052fa751744</span>, <span class="number">0x3cd8000000000000</span>, |
| <span class="number">0x3fe6c012750bd9fe</span>, <span class="number">0xbd28780000000000</span>, |
| <span class="number">0x3fe6cfdcddd476bf</span>, <span class="number">0x3d1ec00000000000</span>, |
| <span class="number">0x3fe6dfb23c651a29</span>, <span class="number">0xbcd8000000000000</span>, |
| <span class="number">0x3fe6ef9298593ae3</span>, <span class="number">0xbcbc000000000000</span>, |
| <span class="number">0x3fe6ff7df9519386</span>, <span class="number">0xbd2fd80000000000</span>, |
| <span class="number">0x3fe70f7466f42da3</span>, <span class="number">0xbd2c880000000000</span>, |
| <span class="number">0x3fe71f75e8ec5fc3</span>, <span class="number">0x3d13c00000000000</span>, |
| <span class="number">0x3fe72f8286eacf05</span>, <span class="number">0xbd38300000000000</span>, |
| <span class="number">0x3fe73f9a48a58152</span>, <span class="number">0xbd00c00000000000</span>, |
| <span class="number">0x3fe74fbd35d7ccfc</span>, <span class="number">0x3d2f880000000000</span>, |
| <span class="number">0x3fe75feb564267f1</span>, <span class="number">0x3d03e00000000000</span>, |
| <span class="number">0x3fe77024b1ab6d48</span>, <span class="number">0xbd27d00000000000</span>, |
| <span class="number">0x3fe780694fde5d38</span>, <span class="number">0xbcdd000000000000</span>, |
| <span class="number">0x3fe790b938ac1d00</span>, <span class="number">0x3ce3000000000000</span>, |
| <span class="number">0x3fe7a11473eb0178</span>, <span class="number">0xbced000000000000</span>, |
| <span class="number">0x3fe7b17b0976d060</span>, <span class="number">0x3d20400000000000</span>, |
| <span class="number">0x3fe7c1ed0130c133</span>, <span class="number">0x3ca0000000000000</span>, |
| <span class="number">0x3fe7d26a62ff8636</span>, <span class="number">0xbd26900000000000</span>, |
| <span class="number">0x3fe7e2f336cf4e3b</span>, <span class="number">0xbd02e00000000000</span>, |
| <span class="number">0x3fe7f3878491c3e8</span>, <span class="number">0xbd24580000000000</span>, |
| <span class="number">0x3fe80427543e1b4e</span>, <span class="number">0x3d33000000000000</span>, |
| <span class="number">0x3fe814d2add1071a</span>, <span class="number">0x3d0f000000000000</span>, |
| <span class="number">0x3fe82589994ccd7e</span>, <span class="number">0xbd21c00000000000</span>, |
| <span class="number">0x3fe8364c1eb942d0</span>, <span class="number">0x3d29d00000000000</span>, |
| <span class="number">0x3fe8471a4623cab5</span>, <span class="number">0x3d47100000000000</span>, |
| <span class="number">0x3fe857f4179f5bbc</span>, <span class="number">0x3d22600000000000</span>, |
| <span class="number">0x3fe868d99b4491af</span>, <span class="number">0xbd32c40000000000</span>, |
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| <span class="number">0x3ff4b17dea6db801</span>, <span class="number">0x3d07800000000000</span>, |
| <span class="number">0x3ff4bfdad53629e1</span>, <span class="number">0xbd13800000000000</span>, |
| <span class="number">0x3ff4ce41b817c132</span>, <span class="number">0x3d00800000000000</span>, |
| <span class="number">0x3ff4dcb299fddddb</span>, <span class="number">0x3d2c700000000000</span>, |
| <span class="number">0x3ff4eb2d81d8ab96</span>, <span class="number">0xbd1ce00000000000</span>, |
| <span class="number">0x3ff4f9b2769d2d02</span>, <span class="number">0x3d19200000000000</span>, |
| <span class="number">0x3ff508417f4531c1</span>, <span class="number">0xbd08c00000000000</span>, |
| <span class="number">0x3ff516daa2cf662a</span>, <span class="number">0xbcfa000000000000</span>, |
| <span class="number">0x3ff5257de83f51ea</span>, <span class="number">0x3d4a080000000000</span>, |
| <span class="number">0x3ff5342b569d4eda</span>, <span class="number">0xbd26d80000000000</span>, |
| <span class="number">0x3ff542e2f4f6ac1a</span>, <span class="number">0xbd32440000000000</span>, |
| <span class="number">0x3ff551a4ca5d94db</span>, <span class="number">0x3d483c0000000000</span>, |
| <span class="number">0x3ff56070dde9116b</span>, <span class="number">0x3d24b00000000000</span>, |
| <span class="number">0x3ff56f4736b529de</span>, <span class="number">0x3d415a0000000000</span>, |
| <span class="number">0x3ff57e27dbe2c40e</span>, <span class="number">0xbd29e00000000000</span>, |
| <span class="number">0x3ff58d12d497c76f</span>, <span class="number">0xbd23080000000000</span>, |
| <span class="number">0x3ff59c0827ff0b4c</span>, <span class="number">0x3d4dec0000000000</span>, |
| <span class="number">0x3ff5ab07dd485427</span>, <span class="number">0xbcc4000000000000</span>, |
| <span class="number">0x3ff5ba11fba87af4</span>, <span class="number">0x3d30080000000000</span>, |
| <span class="number">0x3ff5c9268a59460b</span>, <span class="number">0xbd26c80000000000</span>, |
| <span class="number">0x3ff5d84590998e3f</span>, <span class="number">0x3d469a0000000000</span>, |
| <span class="number">0x3ff5e76f15ad20e1</span>, <span class="number">0xbd1b400000000000</span>, |
| <span class="number">0x3ff5f6a320dcebca</span>, <span class="number">0x3d17700000000000</span>, |
| <span class="number">0x3ff605e1b976dcb8</span>, <span class="number">0x3d26f80000000000</span>, |
| <span class="number">0x3ff6152ae6cdf715</span>, <span class="number">0x3d01000000000000</span>, |
| <span class="number">0x3ff6247eb03a5531</span>, <span class="number">0xbd15d00000000000</span>, |
| <span class="number">0x3ff633dd1d1929b5</span>, <span class="number">0xbd12d00000000000</span>, |
| <span class="number">0x3ff6434634ccc313</span>, <span class="number">0xbcea800000000000</span>, |
| <span class="number">0x3ff652b9febc8efa</span>, <span class="number">0xbd28600000000000</span>, |
| <span class="number">0x3ff6623882553397</span>, <span class="number">0x3d71fe0000000000</span>, |
| <span class="number">0x3ff671c1c708328e</span>, <span class="number">0xbd37200000000000</span>, |
| <span class="number">0x3ff68155d44ca97e</span>, <span class="number">0x3ce6800000000000</span>, |
| <span class="number">0x3ff690f4b19e9471</span>, <span class="number">0xbd29780000000000</span>, |
| ]; |
| |
| <span class="comment">// exp2(x): compute the base 2 exponential of x |
| // |
| // Accuracy: Peak error < 0.503 ulp for normalized results. |
| // |
| // Method: (accurate tables) |
| // |
| // Reduce x: |
| // x = k + y, for integer k and |y| <= 1/2. |
| // Thus we have exp2(x) = 2**k * exp2(y). |
| // |
| // Reduce y: |
| // y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. |
| // Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), |
| // with |z - eps[i]| <= 2**-9 + 2**-39 for the table used. |
| // |
| // We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via |
| // a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61. |
| // The values in exp2t[] and eps[] are chosen such that |
| // exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such |
| // that exp2t[i] is accurate to 2**-64. |
| // |
| // Note that the range of i is +-TBLSIZE/2, so we actually index the tables |
| // by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are |
| // virtual tables, interleaved in the real table tbl[]. |
| // |
| // This method is due to Gal, with many details due to Gal and Bachelis: |
| // |
| // Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library |
| // for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). |
| |
| </span><span class="doccomment">/// Exponential, base 2 (f64) |
| /// |
| /// 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>exp2(<span class="kw-2">mut </span>x: f64) -> f64 { |
| <span class="kw">let </span>redux = f64::from_bits(<span class="number">0x4338000000000000</span>) / TBLSIZE <span class="kw">as </span>f64; |
| <span class="kw">let </span>p1 = f64::from_bits(<span class="number">0x3fe62e42fefa39ef</span>); |
| <span class="kw">let </span>p2 = f64::from_bits(<span class="number">0x3fcebfbdff82c575</span>); |
| <span class="kw">let </span>p3 = f64::from_bits(<span class="number">0x3fac6b08d704a0a6</span>); |
| <span class="kw">let </span>p4 = f64::from_bits(<span class="number">0x3f83b2ab88f70400</span>); |
| <span class="kw">let </span>p5 = f64::from_bits(<span class="number">0x3f55d88003875c74</span>); |
| |
| <span class="comment">// double_t r, t, z; |
| // uint32_t ix, i0; |
| // union {double f; uint64_t i;} u = {x}; |
| // union {uint32_t u; int32_t i;} k; |
| </span><span class="kw">let </span>x1p1023 = f64::from_bits(<span class="number">0x7fe0000000000000</span>); |
| <span class="kw">let </span>x1p52 = f64::from_bits(<span class="number">0x4330000000000000</span>); |
| <span class="kw">let </span>_0x1p_149 = f64::from_bits(<span class="number">0xb6a0000000000000</span>); |
| |
| <span class="comment">/* Filter out exceptional cases. */ |
| </span><span class="kw">let </span>ui = f64::to_bits(x); |
| <span class="kw">let </span>ix = ui >> <span class="number">32 </span>& <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>ix >= <span class="number">0x408ff000 </span>{ |
| <span class="comment">/* |x| >= 1022 or nan */ |
| </span><span class="kw">if </span>ix >= <span class="number">0x40900000 </span>&& ui >> <span class="number">63 </span>== <span class="number">0 </span>{ |
| <span class="comment">/* x >= 1024 or nan */ |
| /* overflow */ |
| </span>x <span class="kw-2">*</span>= x1p1023; |
| <span class="kw">return </span>x; |
| } |
| <span class="kw">if </span>ix >= <span class="number">0x7ff00000 </span>{ |
| <span class="comment">/* -inf or -nan */ |
| </span><span class="kw">return </span>-<span class="number">1.0 </span>/ x; |
| } |
| <span class="kw">if </span>ui >> <span class="number">63 </span>!= <span class="number">0 </span>{ |
| <span class="comment">/* x <= -1022 */ |
| /* underflow */ |
| </span><span class="kw">if </span>x <= -<span class="number">1075.0 </span>|| x - x1p52 + x1p52 != x { |
| <span class="macro">force_eval!</span>((_0x1p_149 / x) <span class="kw">as </span>f32); |
| } |
| <span class="kw">if </span>x <= -<span class="number">1075.0 </span>{ |
| <span class="kw">return </span><span class="number">0.0</span>; |
| } |
| } |
| } <span class="kw">else if </span>ix < <span class="number">0x3c900000 </span>{ |
| <span class="comment">/* |x| < 0x1p-54 */ |
| </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 = f64::to_bits(x + redux); |
| <span class="kw">let </span><span class="kw-2">mut </span>i0 = ui <span class="kw">as </span>u32; |
| i0 = i0.wrapping_add(TBLSIZE <span class="kw">as </span>u32 / <span class="number">2</span>); |
| <span class="kw">let </span>ku = i0 / TBLSIZE <span class="kw">as </span>u32 * TBLSIZE <span class="kw">as </span>u32; |
| <span class="kw">let </span>ki = <span class="macro">div!</span>(ku <span class="kw">as </span>i32, TBLSIZE <span class="kw">as </span>i32); |
| i0 %= TBLSIZE <span class="kw">as </span>u32; |
| <span class="kw">let </span>uf = f64::from_bits(ui) - redux; |
| <span class="kw">let </span><span class="kw-2">mut </span>z = x - uf; |
| |
| <span class="comment">/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ |
| </span><span class="kw">let </span>t = f64::from_bits(<span class="macro">i!</span>(TBL, <span class="number">2 </span>* i0 <span class="kw">as </span>usize)); <span class="comment">/* exp2t[i0] */ |
| </span>z -= f64::from_bits(<span class="macro">i!</span>(TBL, <span class="number">2 </span>* i0 <span class="kw">as </span>usize + <span class="number">1</span>)); <span class="comment">/* eps[i0] */ |
| </span><span class="kw">let </span>r = t + t * z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * p5)))); |
| |
| scalbn(r, ki) |
| } |
| |
| <span class="attribute">#[test] |
| </span><span class="kw">fn </span>i0_wrap_test() { |
| <span class="kw">let </span>x = -<span class="number">3.0 </span>/ <span class="number">256.0</span>; |
| <span class="macro">assert_eq!</span>(exp2(x), f64::from_bits(<span class="number">0x3fefbdba3692d514</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> |