<!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/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="../../../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_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="attr">#[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>,
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<span class="number">0x3ff40822c367a0bb</span>, <span class="number">0x3d25b80000000000</span>,
<span class="number">0x3ff4160a21f72e95</span>, <span class="number">0x3d1ec00000000000</span>,
<span class="number">0x3ff423fb27094646</span>, <span class="number">0xbd13600000000000</span>,
<span class="number">0x3ff431f5d950a920</span>, <span class="number">0x3d23980000000000</span>,
<span class="number">0x3ff43ffa3f84b9eb</span>, <span class="number">0x3cfa000000000000</span>,
<span class="number">0x3ff44e0860618919</span>, <span class="number">0xbcf6c00000000000</span>,
<span class="number">0x3ff45c2042a7d201</span>, <span class="number">0xbd0bc00000000000</span>,
<span class="number">0x3ff46a41ed1d0016</span>, <span class="number">0xbd12800000000000</span>,
<span class="number">0x3ff4786d668b3326</span>, <span class="number">0x3d30e00000000000</span>,
<span class="number">0x3ff486a2b5c13c00</span>, <span class="number">0xbd2d400000000000</span>,
<span class="number">0x3ff494e1e192af04</span>, <span class="number">0x3d0c200000000000</span>,
<span class="number">0x3ff4a32af0d7d372</span>, <span class="number">0xbd1e500000000000</span>,
<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="attr">#[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="attr">#[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>
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