| <!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/cbrt.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>cbrt.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_cbrt.c */ |
| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| * |
| * Optimized by Bruce D. Evans. |
| */ |
| /* cbrt(x) |
| * Return cube root of x |
| */ |
| |
| </span><span class="kw">use </span>core::f64; |
| |
| <span class="kw">const </span>B1: u32 = <span class="number">715094163</span>; <span class="comment">/* B1 = (1023-1023/3-0.03306235651)*2**20 */ |
| </span><span class="kw">const </span>B2: u32 = <span class="number">696219795</span>; <span class="comment">/* B2 = (1023-1023/3-54/3-0.03306235651)*2**20 */ |
| |
| /* |1/cbrt(x) - p(x)| < 2**-23.5 (~[-7.93e-8, 7.929e-8]). */ |
| </span><span class="kw">const </span>P0: f64 = <span class="number">1.87595182427177009643</span>; <span class="comment">/* 0x3ffe03e6, 0x0f61e692 */ |
| </span><span class="kw">const </span>P1: f64 = -<span class="number">1.88497979543377169875</span>; <span class="comment">/* 0xbffe28e0, 0x92f02420 */ |
| </span><span class="kw">const </span>P2: f64 = <span class="number">1.621429720105354466140</span>; <span class="comment">/* 0x3ff9f160, 0x4a49d6c2 */ |
| </span><span class="kw">const </span>P3: f64 = -<span class="number">0.758397934778766047437</span>; <span class="comment">/* 0xbfe844cb, 0xbee751d9 */ |
| </span><span class="kw">const </span>P4: f64 = <span class="number">0.145996192886612446982</span>; <span class="comment">/* 0x3fc2b000, 0xd4e4edd7 */ |
| |
| // Cube root (f64) |
| </span><span class="doccomment">/// |
| /// Computes the cube root of the argument. |
| </span><span class="attribute">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
| </span><span class="kw">pub fn </span>cbrt(x: f64) -> f64 { |
| <span class="kw">let </span>x1p54 = f64::from_bits(<span class="number">0x4350000000000000</span>); <span class="comment">// 0x1p54 === 2 ^ 54 |
| |
| </span><span class="kw">let </span><span class="kw-2">mut </span>ui: u64 = x.to_bits(); |
| <span class="kw">let </span><span class="kw-2">mut </span>r: f64; |
| <span class="kw">let </span>s: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>t: f64; |
| <span class="kw">let </span>w: f64; |
| <span class="kw">let </span><span class="kw-2">mut </span>hx: u32 = (ui >> <span class="number">32</span>) <span class="kw">as </span>u32 & <span class="number">0x7fffffff</span>; |
| |
| <span class="kw">if </span>hx >= <span class="number">0x7ff00000 </span>{ |
| <span class="comment">/* cbrt(NaN,INF) is itself */ |
| </span><span class="kw">return </span>x + x; |
| } |
| |
| <span class="comment">/* |
| * Rough cbrt to 5 bits: |
| * cbrt(2**e*(1+m) ~= 2**(e/3)*(1+(e%3+m)/3) |
| * where e is integral and >= 0, m is real and in [0, 1), and "/" and |
| * "%" are integer division and modulus with rounding towards minus |
| * infinity. The RHS is always >= the LHS and has a maximum relative |
| * error of about 1 in 16. Adding a bias of -0.03306235651 to the |
| * (e%3+m)/3 term reduces the error to about 1 in 32. With the IEEE |
| * floating point representation, for finite positive normal values, |
| * ordinary integer divison of the value in bits magically gives |
| * almost exactly the RHS of the above provided we first subtract the |
| * exponent bias (1023 for doubles) and later add it back. We do the |
| * subtraction virtually to keep e >= 0 so that ordinary integer |
| * division rounds towards minus infinity; this is also efficient. |
| */ |
| </span><span class="kw">if </span>hx < <span class="number">0x00100000 </span>{ |
| <span class="comment">/* zero or subnormal? */ |
| </span>ui = (x * x1p54).to_bits(); |
| hx = (ui >> <span class="number">32</span>) <span class="kw">as </span>u32 & <span class="number">0x7fffffff</span>; |
| <span class="kw">if </span>hx == <span class="number">0 </span>{ |
| <span class="kw">return </span>x; <span class="comment">/* cbrt(0) is itself */ |
| </span>} |
| hx = hx / <span class="number">3 </span>+ B2; |
| } <span class="kw">else </span>{ |
| hx = hx / <span class="number">3 </span>+ B1; |
| } |
| ui &= <span class="number">1 </span><< <span class="number">63</span>; |
| ui |= (hx <span class="kw">as </span>u64) << <span class="number">32</span>; |
| t = f64::from_bits(ui); |
| |
| <span class="comment">/* |
| * New cbrt to 23 bits: |
| * cbrt(x) = t*cbrt(x/t**3) ~= t*P(t**3/x) |
| * where P(r) is a polynomial of degree 4 that approximates 1/cbrt(r) |
| * to within 2**-23.5 when |r - 1| < 1/10. The rough approximation |
| * has produced t such than |t/cbrt(x) - 1| ~< 1/32, and cubing this |
| * gives us bounds for r = t**3/x. |
| * |
| * Try to optimize for parallel evaluation as in __tanf.c. |
| */ |
| </span>r = (t * t) * (t / x); |
| t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4)); |
| |
| <span class="comment">/* |
| * Round t away from zero to 23 bits (sloppily except for ensuring that |
| * the result is larger in magnitude than cbrt(x) but not much more than |
| * 2 23-bit ulps larger). With rounding towards zero, the error bound |
| * would be ~5/6 instead of ~4/6. With a maximum error of 2 23-bit ulps |
| * in the rounded t, the infinite-precision error in the Newton |
| * approximation barely affects third digit in the final error |
| * 0.667; the error in the rounded t can be up to about 3 23-bit ulps |
| * before the final error is larger than 0.667 ulps. |
| */ |
| </span>ui = t.to_bits(); |
| ui = (ui + <span class="number">0x80000000</span>) & <span class="number">0xffffffffc0000000</span>; |
| t = f64::from_bits(ui); |
| |
| <span class="comment">/* one step Newton iteration to 53 bits with error < 0.667 ulps */ |
| </span>s = t * t; <span class="comment">/* t*t is exact */ |
| </span>r = x / s; <span class="comment">/* error <= 0.5 ulps; |r| < |t| */ |
| </span>w = t + t; <span class="comment">/* t+t is exact */ |
| </span>r = (r - t) / (w + r); <span class="comment">/* r-t is exact; w+r ~= 3*t */ |
| </span>t = t + t * r; <span class="comment">/* error <= 0.5 + 0.5/3 + epsilon */ |
| </span>t |
| } |
| </code></pre></div> |
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