<!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 to the Rust file `/home/mrh/.cargo/registry/src/github.com-1ecc6299db9ec823/libm-0.1.4/src/math/log1p.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>log1p.rs.html -- source</title><link rel="stylesheet" type="text/css" href="../../../normalize.css"><link rel="stylesheet" type="text/css" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../../dark.css"><link rel="stylesheet" type="text/css" href="../../../light.css" id="themeStyle"><script src="../../../storage.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="shortcut icon" href="../../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../../down-arrow.svg");}</style></head><body class="rustdoc source"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../../libm/index.html'><div class='logo-container'><img src='../../../rust-logo.png' alt='logo'></div></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../../settings.html"><img src="../../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><pre class="line-numbers"><span id="1"> 1</span>
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</pre><div class="example-wrap"><pre class="rust ">
<span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/s_log1p.c */</span>
<span class="comment">/*
* ====================================================
* 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="comment">/* double log1p(double x)
* Return the natural logarithm of 1+x.
*
* Method :
* 1. Argument Reduction: find k and f such that
* 1+x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* Note. If k=0, then f=x is exact. However, if k!=0, then f
* may not be representable exactly. In that case, a correction
* term is need. Let u=1+x rounded. Let c = (1+x)-u, then
* log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u),
* and add back the correction term c/u.
* (Note: when x > 2**53, one can simply return log(x))
*
* 2. Approximation of log(1+f): See log.c
*
* 3. Finally, log1p(x) = k*ln2 + log(1+f) + c/u. See log.c
*
* Special cases:
* log1p(x) is NaN with signal if x < -1 (including -INF) ;
* log1p(+INF) is +INF; log1p(-1) is -INF with signal;
* log1p(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*
* Note: Assuming log() return accurate answer, the following
* algorithm can be used to compute log1p(x) to within a few ULP:
*
* u = 1+x;
* if(u==1.0) return x ; else
* return log(u)*(x/(u-1.0));
*
* See HP-15C Advanced Functions Handbook, p.193.
*/</span>
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">f64</span>;
<span class="kw">const</span> <span class="ident">LN2_HI</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.93147180369123816490e-01</span>; <span class="comment">/* 3fe62e42 fee00000 */</span>
<span class="kw">const</span> <span class="ident">LN2_LO</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.90821492927058770002e-10</span>; <span class="comment">/* 3dea39ef 35793c76 */</span>
<span class="kw">const</span> <span class="ident">LG1</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">6.666666666666735130e-01</span>; <span class="comment">/* 3FE55555 55555593 */</span>
<span class="kw">const</span> <span class="ident">LG2</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">3.999999999940941908e-01</span>; <span class="comment">/* 3FD99999 9997FA04 */</span>
<span class="kw">const</span> <span class="ident">LG3</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.857142874366239149e-01</span>; <span class="comment">/* 3FD24924 94229359 */</span>
<span class="kw">const</span> <span class="ident">LG4</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">2.222219843214978396e-01</span>; <span class="comment">/* 3FCC71C5 1D8E78AF */</span>
<span class="kw">const</span> <span class="ident">LG5</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.818357216161805012e-01</span>; <span class="comment">/* 3FC74664 96CB03DE */</span>
<span class="kw">const</span> <span class="ident">LG6</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.531383769920937332e-01</span>; <span class="comment">/* 3FC39A09 D078C69F */</span>
<span class="kw">const</span> <span class="ident">LG7</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">1.479819860511658591e-01</span>; <span class="comment">/* 3FC2F112 DF3E5244 */</span>
<span class="attribute">#[<span class="ident">inline</span>]</span>
<span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">all</span>(<span class="ident">test</span>, <span class="ident">assert_no_panic</span>), <span class="ident">no_panic</span>::<span class="ident">no_panic</span>)]</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">log1p</span>(<span class="ident">x</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">ui</span>: <span class="ident">u64</span> <span class="op">=</span> <span class="ident">x</span>.<span class="ident">to_bits</span>();
<span class="kw">let</span> <span class="ident">hfsq</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">f</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">0.</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">c</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">0.</span>;
<span class="kw">let</span> <span class="ident">s</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">z</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">r</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">w</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">t1</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">t2</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">dk</span>: <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">hx</span>: <span class="ident">u32</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">hu</span>: <span class="ident">u32</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">k</span>: <span class="ident">i32</span>;
<span class="ident">hx</span> <span class="op">=</span> (<span class="ident">ui</span> <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">u32</span>;
<span class="ident">k</span> <span class="op">=</span> <span class="number">1</span>;
<span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span> <span class="number">0x3fda827a</span> <span class="op">|</span><span class="op">|</span> (<span class="ident">hx</span> <span class="op">></span><span class="op">></span> <span class="number">31</span>) <span class="op">></span> <span class="number">0</span> {
<span class="comment">/* 1+x < sqrt(2)+ */</span>
<span class="kw">if</span> <span class="ident">hx</span> <span class="op">></span><span class="op">=</span> <span class="number">0xbff00000</span> {
<span class="comment">/* x <= -1.0 */</span>
<span class="kw">if</span> <span class="ident">x</span> <span class="op">=</span><span class="op">=</span> <span class="op">-</span><span class="number">1.</span> {
<span class="kw">return</span> <span class="ident">x</span> <span class="op">/</span> <span class="number">0.0</span>; <span class="comment">/* log1p(-1) = -inf */</span>
}
<span class="kw">return</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">x</span>) <span class="op">/</span> <span class="number">0.0</span>; <span class="comment">/* log1p(x<-1) = NaN */</span>
}
<span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span><span class="op"><</span> <span class="number">1</span> <span class="op"><</span> <span class="number">0x3ca00000</span> <span class="op"><</span><span class="op"><</span> <span class="number">1</span> {
<span class="comment">/* |x| < 2**-53 */</span>
<span class="comment">/* underflow if subnormal */</span>
<span class="kw">if</span> (<span class="ident">hx</span> <span class="op">&</span> <span class="number">0x7ff00000</span>) <span class="op">=</span><span class="op">=</span> <span class="number">0</span> {
<span class="macro">force_eval</span><span class="macro">!</span>(<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f32</span>);
}
<span class="kw">return</span> <span class="ident">x</span>;
}
<span class="kw">if</span> <span class="ident">hx</span> <span class="op"><</span><span class="op">=</span> <span class="number">0xbfd2bec4</span> {
<span class="comment">/* sqrt(2)/2- <= 1+x < sqrt(2)+ */</span>
<span class="ident">k</span> <span class="op">=</span> <span class="number">0</span>;
<span class="ident">c</span> <span class="op">=</span> <span class="number">0.</span>;
<span class="ident">f</span> <span class="op">=</span> <span class="ident">x</span>;
}
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">hx</span> <span class="op">></span><span class="op">=</span> <span class="number">0x7ff00000</span> {
<span class="kw">return</span> <span class="ident">x</span>;
}
<span class="kw">if</span> <span class="ident">k</span> <span class="op">></span> <span class="number">0</span> {
<span class="ident">ui</span> <span class="op">=</span> (<span class="number">1.</span> <span class="op">+</span> <span class="ident">x</span>).<span class="ident">to_bits</span>();
<span class="ident">hu</span> <span class="op">=</span> (<span class="ident">ui</span> <span class="op">></span><span class="op">></span> <span class="number">32</span>) <span class="kw">as</span> <span class="ident">u32</span>;
<span class="ident">hu</span> <span class="op">+</span><span class="op">=</span> <span class="number">0x3ff00000</span> <span class="op">-</span> <span class="number">0x3fe6a09e</span>;
<span class="ident">k</span> <span class="op">=</span> (<span class="ident">hu</span> <span class="op">></span><span class="op">></span> <span class="number">20</span>) <span class="kw">as</span> <span class="ident">i32</span> <span class="op">-</span> <span class="number">0x3ff</span>;
<span class="comment">/* correction term ~ log(1+x)-log(u), avoid underflow in c/u */</span>
<span class="kw">if</span> <span class="ident">k</span> <span class="op"><</span> <span class="number">54</span> {
<span class="ident">c</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">k</span> <span class="op">></span><span class="op">=</span> <span class="number">2</span> {
<span class="number">1.</span> <span class="op">-</span> (<span class="ident">f64</span>::<span class="ident">from_bits</span>(<span class="ident">ui</span>) <span class="op">-</span> <span class="ident">x</span>)
} <span class="kw">else</span> {
<span class="ident">x</span> <span class="op">-</span> (<span class="ident">f64</span>::<span class="ident">from_bits</span>(<span class="ident">ui</span>) <span class="op">-</span> <span class="number">1.</span>)
};
<span class="ident">c</span> <span class="op">/</span><span class="op">=</span> <span class="ident">f64</span>::<span class="ident">from_bits</span>(<span class="ident">ui</span>);
} <span class="kw">else</span> {
<span class="ident">c</span> <span class="op">=</span> <span class="number">0.</span>;
}
<span class="comment">/* reduce u into [sqrt(2)/2, sqrt(2)] */</span>
<span class="ident">hu</span> <span class="op">=</span> (<span class="ident">hu</span> <span class="op">&</span> <span class="number">0x000fffff</span>) <span class="op">+</span> <span class="number">0x3fe6a09e</span>;
<span class="ident">ui</span> <span class="op">=</span> (<span class="ident">hu</span> <span class="kw">as</span> <span class="ident">u64</span>) <span class="op"><</span><span class="op"><</span> <span class="number">32</span> <span class="op">|</span> (<span class="ident">ui</span> <span class="op">&</span> <span class="number">0xffffffff</span>);
<span class="ident">f</span> <span class="op">=</span> <span class="ident">f64</span>::<span class="ident">from_bits</span>(<span class="ident">ui</span>) <span class="op">-</span> <span class="number">1.</span>;
}
<span class="ident">hfsq</span> <span class="op">=</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">f</span> <span class="op">*</span> <span class="ident">f</span>;
<span class="ident">s</span> <span class="op">=</span> <span class="ident">f</span> <span class="op">/</span> (<span class="number">2.0</span> <span class="op">+</span> <span class="ident">f</span>);
<span class="ident">z</span> <span class="op">=</span> <span class="ident">s</span> <span class="op">*</span> <span class="ident">s</span>;
<span class="ident">w</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> <span class="ident">z</span>;
<span class="ident">t1</span> <span class="op">=</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG2</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG4</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">LG6</span>));
<span class="ident">t2</span> <span class="op">=</span> <span class="ident">z</span> <span class="op">*</span> (<span class="ident">LG1</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG3</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> (<span class="ident">LG5</span> <span class="op">+</span> <span class="ident">w</span> <span class="op">*</span> <span class="ident">LG7</span>)));
<span class="ident">r</span> <span class="op">=</span> <span class="ident">t2</span> <span class="op">+</span> <span class="ident">t1</span>;
<span class="ident">dk</span> <span class="op">=</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span>;
<span class="ident">s</span> <span class="op">*</span> (<span class="ident">hfsq</span> <span class="op">+</span> <span class="ident">r</span>) <span class="op">+</span> (<span class="ident">dk</span> <span class="op">*</span> <span class="ident">LN2_LO</span> <span class="op">+</span> <span class="ident">c</span>) <span class="op">-</span> <span class="ident">hfsq</span> <span class="op">+</span> <span class="ident">f</span> <span class="op">+</span> <span class="ident">dk</span> <span class="op">*</span> <span class="ident">LN2_HI</span>
}
</pre></div>
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