<!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/fma.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>fma.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="kw">use </span>core::{f32, f64};
<span class="kw">use </span><span class="kw">super</span>::scalbn;
<span class="kw">const </span>ZEROINFNAN: i32 = <span class="number">0x7ff </span>- <span class="number">0x3ff </span>- <span class="number">52 </span>- <span class="number">1</span>;
<span class="kw">struct </span>Num {
m: u64,
e: i32,
sign: i32,
}
<span class="kw">fn </span>normalize(x: f64) -> Num {
<span class="kw">let </span>x1p63: f64 = f64::from_bits(<span class="number">0x43e0000000000000</span>); <span class="comment">// 0x1p63 === 2 ^ 63
</span><span class="kw">let </span><span class="kw-2">mut </span>ix: u64 = x.to_bits();
<span class="kw">let </span><span class="kw-2">mut </span>e: i32 = (ix >> <span class="number">52</span>) <span class="kw">as </span>i32;
<span class="kw">let </span>sign: i32 = e & <span class="number">0x800</span>;
e &= <span class="number">0x7ff</span>;
<span class="kw">if </span>e == <span class="number">0 </span>{
ix = (x * x1p63).to_bits();
e = (ix >> <span class="number">52</span>) <span class="kw">as </span>i32 & <span class="number">0x7ff</span>;
e = <span class="kw">if </span>e != <span class="number">0 </span>{ e - <span class="number">63 </span>} <span class="kw">else </span>{ <span class="number">0x800 </span>};
}
ix &= (<span class="number">1 </span><< <span class="number">52</span>) - <span class="number">1</span>;
ix |= <span class="number">1 </span><< <span class="number">52</span>;
ix <<= <span class="number">1</span>;
e -= <span class="number">0x3ff </span>+ <span class="number">52 </span>+ <span class="number">1</span>;
Num { m: ix, e, sign }
}
<span class="kw">fn </span>mul(x: u64, y: u64) -> (u64, u64) {
<span class="kw">let </span>t1: u64;
<span class="kw">let </span>t2: u64;
<span class="kw">let </span>t3: u64;
<span class="kw">let </span>xlo: u64 = x <span class="kw">as </span>u32 <span class="kw">as </span>u64;
<span class="kw">let </span>xhi: u64 = x >> <span class="number">32</span>;
<span class="kw">let </span>ylo: u64 = y <span class="kw">as </span>u32 <span class="kw">as </span>u64;
<span class="kw">let </span>yhi: u64 = y >> <span class="number">32</span>;
t1 = xlo * ylo;
t2 = xlo * yhi + xhi * ylo;
t3 = xhi * yhi;
<span class="kw">let </span>lo = t1.wrapping_add(t2 << <span class="number">32</span>);
<span class="kw">let </span>hi = t3 + (t2 >> <span class="number">32</span>) + (t1 > lo) <span class="kw">as </span>u64;
(hi, lo)
}
<span class="doccomment">/// Floating multiply add (f64)
///
/// Computes `(x*y)+z`, rounded as one ternary operation:
/// Computes the value (as if) to infinite precision and rounds once to the result format,
/// according to the rounding mode characterized by the value of FLT_ROUNDS.
</span><span class="attr">#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
</span><span class="kw">pub fn </span>fma(x: f64, y: f64, z: f64) -> f64 {
<span class="kw">let </span>x1p63: f64 = f64::from_bits(<span class="number">0x43e0000000000000</span>); <span class="comment">// 0x1p63 === 2 ^ 63
</span><span class="kw">let </span>x0_ffffff8p_63 = f64::from_bits(<span class="number">0x3bfffffff0000000</span>); <span class="comment">// 0x0.ffffff8p-63
/* normalize so top 10bits and last bit are 0 */
</span><span class="kw">let </span>nx = normalize(x);
<span class="kw">let </span>ny = normalize(y);
<span class="kw">let </span>nz = normalize(z);
<span class="kw">if </span>nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN {
<span class="kw">return </span>x * y + z;
}
<span class="kw">if </span>nz.e >= ZEROINFNAN {
<span class="kw">if </span>nz.e > ZEROINFNAN {
<span class="comment">/* z==0 */
</span><span class="kw">return </span>x * y + z;
}
<span class="kw">return </span>z;
}
<span class="comment">/* mul: r = x*y */
</span><span class="kw">let </span>zhi: u64;
<span class="kw">let </span>zlo: u64;
<span class="kw">let </span>(<span class="kw-2">mut </span>rhi, <span class="kw-2">mut </span>rlo) = mul(nx.m, ny.m);
<span class="comment">/* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
/* align exponents */
</span><span class="kw">let </span><span class="kw-2">mut </span>e: i32 = nx.e + ny.e;
<span class="kw">let </span><span class="kw-2">mut </span>d: i32 = nz.e - e;
<span class="comment">/* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
</span><span class="kw">if </span>d > <span class="number">0 </span>{
<span class="kw">if </span>d < <span class="number">64 </span>{
zlo = nz.m << d;
zhi = nz.m >> (<span class="number">64 </span>- d);
} <span class="kw">else </span>{
zlo = <span class="number">0</span>;
zhi = nz.m;
e = nz.e - <span class="number">64</span>;
d -= <span class="number">64</span>;
<span class="kw">if </span>d == <span class="number">0 </span>{
} <span class="kw">else if </span>d < <span class="number">64 </span>{
rlo = rhi << (<span class="number">64 </span>- d) | rlo >> d | ((rlo << (<span class="number">64 </span>- d)) != <span class="number">0</span>) <span class="kw">as </span>u64;
rhi = rhi >> d;
} <span class="kw">else </span>{
rlo = <span class="number">1</span>;
rhi = <span class="number">0</span>;
}
}
} <span class="kw">else </span>{
zhi = <span class="number">0</span>;
d = -d;
<span class="kw">if </span>d == <span class="number">0 </span>{
zlo = nz.m;
} <span class="kw">else if </span>d < <span class="number">64 </span>{
zlo = nz.m >> d | ((nz.m << (<span class="number">64 </span>- d)) != <span class="number">0</span>) <span class="kw">as </span>u64;
} <span class="kw">else </span>{
zlo = <span class="number">1</span>;
}
}
<span class="comment">/* add */
</span><span class="kw">let </span><span class="kw-2">mut </span>sign: i32 = nx.sign ^ ny.sign;
<span class="kw">let </span>samesign: bool = (sign ^ nz.sign) == <span class="number">0</span>;
<span class="kw">let </span><span class="kw-2">mut </span>nonzero: i32 = <span class="number">1</span>;
<span class="kw">if </span>samesign {
<span class="comment">/* r += z */
</span>rlo = rlo.wrapping_add(zlo);
rhi += zhi + (rlo < zlo) <span class="kw">as </span>u64;
} <span class="kw">else </span>{
<span class="comment">/* r -= z */
</span><span class="kw">let </span>(res, borrow) = rlo.overflowing_sub(zlo);
rlo = res;
rhi = rhi.wrapping_sub(zhi.wrapping_add(borrow <span class="kw">as </span>u64));
<span class="kw">if </span>(rhi >> <span class="number">63</span>) != <span class="number">0 </span>{
rlo = (rlo <span class="kw">as </span>i64).wrapping_neg() <span class="kw">as </span>u64;
rhi = (rhi <span class="kw">as </span>i64).wrapping_neg() <span class="kw">as </span>u64 - (rlo != <span class="number">0</span>) <span class="kw">as </span>u64;
sign = (sign == <span class="number">0</span>) <span class="kw">as </span>i32;
}
nonzero = (rhi != <span class="number">0</span>) <span class="kw">as </span>i32;
}
<span class="comment">/* set rhi to top 63bit of the result (last bit is sticky) */
</span><span class="kw">if </span>nonzero != <span class="number">0 </span>{
e += <span class="number">64</span>;
d = rhi.leading_zeros() <span class="kw">as </span>i32 - <span class="number">1</span>;
<span class="comment">/* note: d > 0 */
</span>rhi = rhi << d | rlo >> (<span class="number">64 </span>- d) | ((rlo << d) != <span class="number">0</span>) <span class="kw">as </span>u64;
} <span class="kw">else if </span>rlo != <span class="number">0 </span>{
d = rlo.leading_zeros() <span class="kw">as </span>i32 - <span class="number">1</span>;
<span class="kw">if </span>d < <span class="number">0 </span>{
rhi = rlo >> <span class="number">1 </span>| (rlo & <span class="number">1</span>);
} <span class="kw">else </span>{
rhi = rlo << d;
}
} <span class="kw">else </span>{
<span class="comment">/* exact +-0 */
</span><span class="kw">return </span>x * y + z;
}
e -= d;
<span class="comment">/* convert to double */
</span><span class="kw">let </span><span class="kw-2">mut </span>i: i64 = rhi <span class="kw">as </span>i64; <span class="comment">/* i is in [1<<62,(1<<63)-1] */
</span><span class="kw">if </span>sign != <span class="number">0 </span>{
i = -i;
}
<span class="kw">let </span><span class="kw-2">mut </span>r: f64 = i <span class="kw">as </span>f64; <span class="comment">/* |r| is in [0x1p62,0x1p63] */
</span><span class="kw">if </span>e < -<span class="number">1022 </span>- <span class="number">62 </span>{
<span class="comment">/* result is subnormal before rounding */
</span><span class="kw">if </span>e == -<span class="number">1022 </span>- <span class="number">63 </span>{
<span class="kw">let </span><span class="kw-2">mut </span>c: f64 = x1p63;
<span class="kw">if </span>sign != <span class="number">0 </span>{
c = -c;
}
<span class="kw">if </span>r == c {
<span class="comment">/* min normal after rounding, underflow depends
on arch behaviour which can be imitated by
a double to float conversion */
</span><span class="kw">let </span>fltmin: f32 = (x0_ffffff8p_63 * f32::MIN_POSITIVE <span class="kw">as </span>f64 * r) <span class="kw">as </span>f32;
<span class="kw">return </span>f64::MIN_POSITIVE / f32::MIN_POSITIVE <span class="kw">as </span>f64 * fltmin <span class="kw">as </span>f64;
}
<span class="comment">/* one bit is lost when scaled, add another top bit to
only round once at conversion if it is inexact */
</span><span class="kw">if </span>(rhi << <span class="number">53</span>) != <span class="number">0 </span>{
i = (rhi >> <span class="number">1 </span>| (rhi & <span class="number">1</span>) | <span class="number">1 </span><< <span class="number">62</span>) <span class="kw">as </span>i64;
<span class="kw">if </span>sign != <span class="number">0 </span>{
i = -i;
}
r = i <span class="kw">as </span>f64;
r = <span class="number">2. </span>* r - c; <span class="comment">/* remove top bit */
/* raise underflow portably, such that it
cannot be optimized away */
</span>{
<span class="kw">let </span>tiny: f64 = f64::MIN_POSITIVE / f32::MIN_POSITIVE <span class="kw">as </span>f64 * r;
r += (tiny * tiny) * (r - r);
}
}
} <span class="kw">else </span>{
<span class="comment">/* only round once when scaled */
</span>d = <span class="number">10</span>;
i = ((rhi >> d | ((rhi << (<span class="number">64 </span>- d)) != <span class="number">0</span>) <span class="kw">as </span>u64) << d) <span class="kw">as </span>i64;
<span class="kw">if </span>sign != <span class="number">0 </span>{
i = -i;
}
r = i <span class="kw">as </span>f64;
}
}
scalbn(r, e)
}
<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="attr">#[test]
</span><span class="kw">fn </span>fma_segfault() {
<span class="comment">// These two inputs cause fma to segfault on release due to overflow:
</span><span class="macro">assert_eq!</span>(
fma(
-<span class="number">0.0000000000000002220446049250313</span>,
-<span class="number">0.0000000000000002220446049250313</span>,
-<span class="number">0.0000000000000002220446049250313
</span>),
-<span class="number">0.00000000000000022204460492503126</span>,
);
<span class="kw">let </span>result = fma(-<span class="number">0.992</span>, -<span class="number">0.992</span>, -<span class="number">0.992</span>);
<span class="comment">//force rounding to storage format on x87 to prevent superious errors.
</span><span class="attr">#[cfg(all(target_arch = <span class="string">"x86"</span>, not(target_feature = <span class="string">"sse2"</span>)))]
</span><span class="kw">let </span>result = <span class="macro">force_eval!</span>(result);
<span class="macro">assert_eq!</span>(result, -<span class="number">0.007936000000000007</span>,);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>fma_sbb() {
<span class="macro">assert_eq!</span>(
fma(-(<span class="number">1.0 </span>- f64::EPSILON), f64::MIN, f64::MIN),
-<span class="number">3991680619069439e277
</span>);
}
<span class="attr">#[test]
</span><span class="kw">fn </span>fma_underflow() {
<span class="macro">assert_eq!</span>(
fma(<span class="number">1.1102230246251565e-16</span>, -<span class="number">9.812526705433188e-305</span>, <span class="number">1.0894e-320</span>),
<span class="number">0.0</span>,
);
}
}
</code></pre></div>
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