<!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/sqrt.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>sqrt.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/e_sqrt.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* sqrt(x)
* Return correctly rounded sqrt.
* ------------------------------------------
* | Use the hardware sqrt if you have one |
* ------------------------------------------
* Method:
* Bit by bit method using integer arithmetic. (Slow, but portable)
* 1. Normalization
* Scale x to y in [1,4) with even powers of 2:
* find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
* sqrt(x) = 2^k * sqrt(y)
* 2. Bit by bit computation
* Let q = sqrt(y) truncated to i bit after binary point (q = 1),
* i 0
* i+1 2
* s = 2*q , and y = 2 * ( y - q ). (1)
* i i i i
*
* To compute q from q , one checks whether
* i+1 i
*
* -(i+1) 2
* (q + 2 ) <= y. (2)
* i
* -(i+1)
* If (2) is false, then q = q ; otherwise q = q + 2 .
* i+1 i i+1 i
*
* With some algebraic manipulation, it is not difficult to see
* that (2) is equivalent to
* -(i+1)
* s + 2 <= y (3)
* i i
*
* The advantage of (3) is that s and y can be computed by
* i i
* the following recurrence formula:
* if (3) is false
*
* s = s , y = y ; (4)
* i+1 i i+1 i
*
* otherwise,
* -i -(i+1)
* s = s + 2 , y = y - s - 2 (5)
* i+1 i i+1 i i
*
* One may easily use induction to prove (4) and (5).
* Note. Since the left hand side of (3) contain only i+2 bits,
* it does not necessary to do a full (53-bit) comparison
* in (3).
* 3. Final rounding
* After generating the 53 bits result, we compute one more bit.
* Together with the remainder, we can decide whether the
* result is exact, bigger than 1/2ulp, or less than 1/2ulp
* (it will never equal to 1/2ulp).
* The rounding mode can be detected by checking whether
* huge + tiny is equal to huge, and whether huge - tiny is
* equal to huge for some floating point number "huge" and "tiny".
*
* Special cases:
* sqrt(+-0) = +-0 ... exact
* sqrt(inf) = inf
* sqrt(-ve) = NaN ... with invalid signal
* sqrt(NaN) = NaN ... with invalid signal for signaling NaN
*/
</span><span class="kw">use </span>core::f64;
<span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>sqrt(x: f64) -> f64 {
<span class="comment">// On wasm32 we know that LLVM's intrinsic will compile to an optimized
// `f64.sqrt` native instruction, so we can leverage this for both code size
// and speed.
</span><span class="macro">llvm_intrinsically_optimized! </span>{
<span class="attr">#[cfg(target_arch = <span class="string">"wasm32"</span>)] </span>{
<span class="kw">return if </span>x < <span class="number">0.0 </span>{
f64::NAN
} <span class="kw">else </span>{
<span class="kw">unsafe </span>{ ::core::intrinsics::sqrtf64(x) }
}
}
}
<span class="attr">#[cfg(target_feature = <span class="string">"sse2"</span>)]
</span>{
<span class="comment">// Note: This path is unlikely since LLVM will usually have already
// optimized sqrt calls into hardware instructions if sse2 is available,
// but if someone does end up here they'll apprected the speed increase.
</span><span class="attr">#[cfg(target_arch = <span class="string">"x86"</span>)]
</span><span class="kw">use </span>core::arch::x86::<span class="kw-2">*</span>;
<span class="attr">#[cfg(target_arch = <span class="string">"x86_64"</span>)]
</span><span class="kw">use </span>core::arch::x86_64::<span class="kw-2">*</span>;
<span class="kw">unsafe </span>{
<span class="kw">let </span>m = _mm_set_sd(x);
<span class="kw">let </span>m_sqrt = _mm_sqrt_pd(m);
_mm_cvtsd_f64(m_sqrt)
}
}
<span class="attr">#[cfg(not(target_feature = <span class="string">"sse2"</span>))]
</span>{
<span class="kw">use </span>core::num::Wrapping;
<span class="kw">const </span>TINY: f64 = <span class="number">1.0e-300</span>;
<span class="kw">let </span><span class="kw-2">mut </span>z: f64;
<span class="kw">let </span>sign: Wrapping<u32> = Wrapping(<span class="number">0x80000000</span>);
<span class="kw">let </span><span class="kw-2">mut </span>ix0: i32;
<span class="kw">let </span><span class="kw-2">mut </span>s0: i32;
<span class="kw">let </span><span class="kw-2">mut </span>q: i32;
<span class="kw">let </span><span class="kw-2">mut </span>m: i32;
<span class="kw">let </span><span class="kw-2">mut </span>t: i32;
<span class="kw">let </span><span class="kw-2">mut </span>i: i32;
<span class="kw">let </span><span class="kw-2">mut </span>r: Wrapping<u32>;
<span class="kw">let </span><span class="kw-2">mut </span>t1: Wrapping<u32>;
<span class="kw">let </span><span class="kw-2">mut </span>s1: Wrapping<u32>;
<span class="kw">let </span><span class="kw-2">mut </span>ix1: Wrapping<u32>;
<span class="kw">let </span><span class="kw-2">mut </span>q1: Wrapping<u32>;
ix0 = (x.to_bits() >> <span class="number">32</span>) <span class="kw">as </span>i32;
ix1 = Wrapping(x.to_bits() <span class="kw">as </span>u32);
<span class="comment">/* take care of Inf and NaN */
</span><span class="kw">if </span>(ix0 & <span class="number">0x7ff00000</span>) == <span class="number">0x7ff00000 </span>{
<span class="kw">return </span>x * x + x; <span class="comment">/* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
</span>}
<span class="comment">/* take care of zero */
</span><span class="kw">if </span>ix0 <= <span class="number">0 </span>{
<span class="kw">if </span>((ix0 & !(sign.<span class="number">0 </span><span class="kw">as </span>i32)) | ix1.<span class="number">0 </span><span class="kw">as </span>i32) == <span class="number">0 </span>{
<span class="kw">return </span>x; <span class="comment">/* sqrt(+-0) = +-0 */
</span>}
<span class="kw">if </span>ix0 < <span class="number">0 </span>{
<span class="kw">return </span>(x - x) / (x - x); <span class="comment">/* sqrt(-ve) = sNaN */
</span>}
}
<span class="comment">/* normalize x */
</span>m = ix0 >> <span class="number">20</span>;
<span class="kw">if </span>m == <span class="number">0 </span>{
<span class="comment">/* subnormal x */
</span><span class="kw">while </span>ix0 == <span class="number">0 </span>{
m -= <span class="number">21</span>;
ix0 |= (ix1 >> <span class="number">11</span>).<span class="number">0 </span><span class="kw">as </span>i32;
ix1 <<= <span class="number">21</span>;
}
i = <span class="number">0</span>;
<span class="kw">while </span>(ix0 & <span class="number">0x00100000</span>) == <span class="number">0 </span>{
i += <span class="number">1</span>;
ix0 <<= <span class="number">1</span>;
}
m -= i - <span class="number">1</span>;
ix0 |= (ix1 >> (<span class="number">32 </span>- i) <span class="kw">as </span>usize).<span class="number">0 </span><span class="kw">as </span>i32;
ix1 = ix1 << i <span class="kw">as </span>usize;
}
m -= <span class="number">1023</span>; <span class="comment">/* unbias exponent */
</span>ix0 = (ix0 & <span class="number">0x000fffff</span>) | <span class="number">0x00100000</span>;
<span class="kw">if </span>(m & <span class="number">1</span>) == <span class="number">1 </span>{
<span class="comment">/* odd m, double x to make it even */
</span>ix0 += ix0 + ((ix1 & sign) >> <span class="number">31</span>).<span class="number">0 </span><span class="kw">as </span>i32;
ix1 += ix1;
}
m >>= <span class="number">1</span>; <span class="comment">/* m = [m/2] */
/* generate sqrt(x) bit by bit */
</span>ix0 += ix0 + ((ix1 & sign) >> <span class="number">31</span>).<span class="number">0 </span><span class="kw">as </span>i32;
ix1 += ix1;
q = <span class="number">0</span>; <span class="comment">/* [q,q1] = sqrt(x) */
</span>q1 = Wrapping(<span class="number">0</span>);
s0 = <span class="number">0</span>;
s1 = Wrapping(<span class="number">0</span>);
r = Wrapping(<span class="number">0x00200000</span>); <span class="comment">/* r = moving bit from right to left */
</span><span class="kw">while </span>r != Wrapping(<span class="number">0</span>) {
t = s0 + r.<span class="number">0 </span><span class="kw">as </span>i32;
<span class="kw">if </span>t <= ix0 {
s0 = t + r.<span class="number">0 </span><span class="kw">as </span>i32;
ix0 -= t;
q += r.<span class="number">0 </span><span class="kw">as </span>i32;
}
ix0 += ix0 + ((ix1 & sign) >> <span class="number">31</span>).<span class="number">0 </span><span class="kw">as </span>i32;
ix1 += ix1;
r >>= <span class="number">1</span>;
}
r = sign;
<span class="kw">while </span>r != Wrapping(<span class="number">0</span>) {
t1 = s1 + r;
t = s0;
<span class="kw">if </span>t < ix0 || (t == ix0 && t1 <= ix1) {
s1 = t1 + r;
<span class="kw">if </span>(t1 & sign) == sign && (s1 & sign) == Wrapping(<span class="number">0</span>) {
s0 += <span class="number">1</span>;
}
ix0 -= t;
<span class="kw">if </span>ix1 < t1 {
ix0 -= <span class="number">1</span>;
}
ix1 -= t1;
q1 += r;
}
ix0 += ix0 + ((ix1 & sign) >> <span class="number">31</span>).<span class="number">0 </span><span class="kw">as </span>i32;
ix1 += ix1;
r >>= <span class="number">1</span>;
}
<span class="comment">/* use floating add to find out rounding direction */
</span><span class="kw">if </span>(ix0 <span class="kw">as </span>u32 | ix1.<span class="number">0</span>) != <span class="number">0 </span>{
z = <span class="number">1.0 </span>- TINY; <span class="comment">/* raise inexact flag */
</span><span class="kw">if </span>z >= <span class="number">1.0 </span>{
z = <span class="number">1.0 </span>+ TINY;
<span class="kw">if </span>q1.<span class="number">0 </span>== <span class="number">0xffffffff </span>{
q1 = Wrapping(<span class="number">0</span>);
q += <span class="number">1</span>;
} <span class="kw">else if </span>z > <span class="number">1.0 </span>{
<span class="kw">if </span>q1.<span class="number">0 </span>== <span class="number">0xfffffffe </span>{
q += <span class="number">1</span>;
}
q1 += Wrapping(<span class="number">2</span>);
} <span class="kw">else </span>{
q1 += q1 & Wrapping(<span class="number">1</span>);
}
}
}
ix0 = (q >> <span class="number">1</span>) + <span class="number">0x3fe00000</span>;
ix1 = q1 >> <span class="number">1</span>;
<span class="kw">if </span>(q & <span class="number">1</span>) == <span class="number">1 </span>{
ix1 |= sign;
}
ix0 += m << <span class="number">20</span>;
f64::from_bits((ix0 <span class="kw">as </span>u64) << <span class="number">32 </span>| ix1.<span class="number">0 </span><span class="kw">as </span>u64)
}
}
<span class="attr">#[cfg(test)]
</span><span class="kw">mod </span>tests {
<span class="kw">use super</span>::<span class="kw-2">*</span>;
<span class="kw">use </span>core::f64::<span class="kw-2">*</span>;
<span class="attr">#[test]
</span><span class="kw">fn </span>sanity_check() {
<span class="macro">assert_eq!</span>(sqrt(<span class="number">100.0</span>), <span class="number">10.0</span>);
<span class="macro">assert_eq!</span>(sqrt(<span class="number">4.0</span>), <span class="number">2.0</span>);
}
<span class="doccomment">/// The spec: https://en.cppreference.com/w/cpp/numeric/math/sqrt
</span><span class="attr">#[test]
</span><span class="kw">fn </span>spec_tests() {
<span class="comment">// Not Asserted: FE_INVALID exception is raised if argument is negative.
</span><span class="macro">assert!</span>(sqrt(-<span class="number">1.0</span>).is_nan());
<span class="macro">assert!</span>(sqrt(NAN).is_nan());
<span class="kw">for </span>f <span class="kw">in </span>[<span class="number">0.0</span>, -<span class="number">0.0</span>, INFINITY].iter().copied() {
<span class="macro">assert_eq!</span>(sqrt(f), f);
}
}
}
</code></pre></div>
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