| <!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/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="../../../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> |
| <span id="2">2</span> |
| <span id="3">3</span> |
| <span id="4">4</span> |
| <span id="5">5</span> |
| <span id="6">6</span> |
| <span id="7">7</span> |
| <span id="8">8</span> |
| <span id="9">9</span> |
| <span id="10">10</span> |
| <span id="11">11</span> |
| <span id="12">12</span> |
| <span id="13">13</span> |
| <span id="14">14</span> |
| <span id="15">15</span> |
| <span id="16">16</span> |
| <span id="17">17</span> |
| <span id="18">18</span> |
| <span id="19">19</span> |
| <span id="20">20</span> |
| <span id="21">21</span> |
| <span id="22">22</span> |
| <span id="23">23</span> |
| <span id="24">24</span> |
| <span id="25">25</span> |
| <span id="26">26</span> |
| <span id="27">27</span> |
| <span id="28">28</span> |
| <span id="29">29</span> |
| <span id="30">30</span> |
| <span id="31">31</span> |
| <span id="32">32</span> |
| <span id="33">33</span> |
| <span id="34">34</span> |
| <span id="35">35</span> |
| <span id="36">36</span> |
| <span id="37">37</span> |
| <span id="38">38</span> |
| <span id="39">39</span> |
| <span id="40">40</span> |
| <span id="41">41</span> |
| <span id="42">42</span> |
| <span id="43">43</span> |
| <span id="44">44</span> |
| <span id="45">45</span> |
| <span id="46">46</span> |
| <span id="47">47</span> |
| <span id="48">48</span> |
| <span id="49">49</span> |
| <span id="50">50</span> |
| <span id="51">51</span> |
| <span id="52">52</span> |
| <span id="53">53</span> |
| <span id="54">54</span> |
| <span id="55">55</span> |
| <span id="56">56</span> |
| <span id="57">57</span> |
| <span id="58">58</span> |
| <span id="59">59</span> |
| <span id="60">60</span> |
| <span id="61">61</span> |
| <span id="62">62</span> |
| <span id="63">63</span> |
| <span id="64">64</span> |
| <span id="65">65</span> |
| <span id="66">66</span> |
| <span id="67">67</span> |
| <span id="68">68</span> |
| <span id="69">69</span> |
| <span id="70">70</span> |
| <span id="71">71</span> |
| <span id="72">72</span> |
| <span id="73">73</span> |
| <span id="74">74</span> |
| <span id="75">75</span> |
| <span id="76">76</span> |
| <span id="77">77</span> |
| <span id="78">78</span> |
| <span id="79">79</span> |
| <span id="80">80</span> |
| <span id="81">81</span> |
| <span id="82">82</span> |
| <span id="83">83</span> |
| <span id="84">84</span> |
| <span id="85">85</span> |
| <span id="86">86</span> |
| <span id="87">87</span> |
| <span id="88">88</span> |
| <span id="89">89</span> |
| <span id="90">90</span> |
| <span id="91">91</span> |
| <span id="92">92</span> |
| <span id="93">93</span> |
| <span id="94">94</span> |
| <span id="95">95</span> |
| <span id="96">96</span> |
| <span id="97">97</span> |
| <span id="98">98</span> |
| <span id="99">99</span> |
| <span id="100">100</span> |
| <span id="101">101</span> |
| <span id="102">102</span> |
| <span id="103">103</span> |
| <span id="104">104</span> |
| <span id="105">105</span> |
| <span id="106">106</span> |
| <span id="107">107</span> |
| <span id="108">108</span> |
| <span id="109">109</span> |
| <span id="110">110</span> |
| <span id="111">111</span> |
| <span id="112">112</span> |
| <span id="113">113</span> |
| <span id="114">114</span> |
| <span id="115">115</span> |
| <span id="116">116</span> |
| <span id="117">117</span> |
| <span id="118">118</span> |
| <span id="119">119</span> |
| <span id="120">120</span> |
| <span id="121">121</span> |
| <span id="122">122</span> |
| <span id="123">123</span> |
| <span id="124">124</span> |
| <span id="125">125</span> |
| <span id="126">126</span> |
| <span id="127">127</span> |
| <span id="128">128</span> |
| <span id="129">129</span> |
| <span id="130">130</span> |
| <span id="131">131</span> |
| <span id="132">132</span> |
| <span id="133">133</span> |
| <span id="134">134</span> |
| <span id="135">135</span> |
| <span id="136">136</span> |
| <span id="137">137</span> |
| <span id="138">138</span> |
| <span id="139">139</span> |
| <span id="140">140</span> |
| <span id="141">141</span> |
| <span id="142">142</span> |
| <span id="143">143</span> |
| <span id="144">144</span> |
| <span id="145">145</span> |
| <span id="146">146</span> |
| <span id="147">147</span> |
| <span id="148">148</span> |
| <span id="149">149</span> |
| <span id="150">150</span> |
| <span id="151">151</span> |
| <span id="152">152</span> |
| <span id="153">153</span> |
| <span id="154">154</span> |
| <span id="155">155</span> |
| <span id="156">156</span> |
| <span id="157">157</span> |
| <span id="158">158</span> |
| <span id="159">159</span> |
| <span id="160">160</span> |
| <span id="161">161</span> |
| <span id="162">162</span> |
| <span id="163">163</span> |
| <span id="164">164</span> |
| <span id="165">165</span> |
| <span id="166">166</span> |
| <span id="167">167</span> |
| <span id="168">168</span> |
| <span id="169">169</span> |
| <span id="170">170</span> |
| <span id="171">171</span> |
| <span id="172">172</span> |
| <span id="173">173</span> |
| <span id="174">174</span> |
| <span id="175">175</span> |
| <span id="176">176</span> |
| <span id="177">177</span> |
| <span id="178">178</span> |
| <span id="179">179</span> |
| <span id="180">180</span> |
| <span id="181">181</span> |
| <span id="182">182</span> |
| <span id="183">183</span> |
| <span id="184">184</span> |
| <span id="185">185</span> |
| <span id="186">186</span> |
| <span id="187">187</span> |
| <span id="188">188</span> |
| <span id="189">189</span> |
| <span id="190">190</span> |
| <span id="191">191</span> |
| <span id="192">192</span> |
| <span id="193">193</span> |
| <span id="194">194</span> |
| <span id="195">195</span> |
| <span id="196">196</span> |
| <span id="197">197</span> |
| <span id="198">198</span> |
| <span id="199">199</span> |
| <span id="200">200</span> |
| <span id="201">201</span> |
| <span id="202">202</span> |
| <span id="203">203</span> |
| <span id="204">204</span> |
| <span id="205">205</span> |
| <span id="206">206</span> |
| <span id="207">207</span> |
| <span id="208">208</span> |
| <span id="209">209</span> |
| <span id="210">210</span> |
| <span id="211">211</span> |
| <span id="212">212</span> |
| <span id="213">213</span> |
| <span id="214">214</span> |
| <span id="215">215</span> |
| <span id="216">216</span> |
| <span id="217">217</span> |
| <span id="218">218</span> |
| <span id="219">219</span> |
| <span id="220">220</span> |
| <span id="221">221</span> |
| <span id="222">222</span> |
| <span id="223">223</span> |
| <span id="224">224</span> |
| <span id="225">225</span> |
| <span id="226">226</span> |
| <span id="227">227</span> |
| <span id="228">228</span> |
| <span id="229">229</span> |
| <span id="230">230</span> |
| <span id="231">231</span> |
| <span id="232">232</span> |
| </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="attribute">#[inline] |
| </span><span class="kw">fn </span>mul(x: u64, y: u64) -> (u64, u64) { |
| <span class="kw">let </span>t = (x <span class="kw">as </span>u128).wrapping_mul(y <span class="kw">as </span>u128); |
| ((t >> <span class="number">64</span>) <span class="kw">as </span>u64, t <span class="kw">as </span>u64) |
| } |
| |
| <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="attribute">#[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="attribute">#[cfg(test)] |
| </span><span class="kw">mod </span>tests { |
| <span class="kw">use super</span>::<span class="kw-2">*</span>; |
| <span class="attribute">#[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="attribute">#[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="attribute">#[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="attribute">#[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> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="libm" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
