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| </pre><pre class="rust"><code><span class="comment">/* origin: FreeBSD /usr/src/lib/msun/src/s_fmaf.c */</span> |
| <span class="comment">/*- |
| * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG> |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| */</span> |
| |
| <span class="kw">use</span> <span class="ident">core::f32</span>; |
| <span class="kw">use</span> <span class="ident">core::ptr::read_volatile</span>; |
| |
| <span class="kw">use</span> <span class="ident"><span class="kw">super</span>::fenv</span>::{ |
| <span class="ident">feclearexcept</span>, <span class="ident">fegetround</span>, <span class="ident">feraiseexcept</span>, <span class="ident">fesetround</span>, <span class="ident">fetestexcept</span>, <span class="ident">FE_INEXACT</span>, <span class="ident">FE_TONEAREST</span>, |
| <span class="ident">FE_TOWARDZERO</span>, <span class="ident">FE_UNDERFLOW</span>, |
| }; |
| |
| <span class="comment">/* |
| * Fused multiply-add: Compute x * y + z with a single rounding error. |
| * |
| * A double has more than twice as much precision than a float, so |
| * direct double-precision arithmetic suffices, except where double |
| * rounding occurs. |
| */</span> |
| |
| <span class="doccomment">/// Floating multiply add (f32)</span> |
| <span class="doccomment">///</span> |
| <span class="doccomment">/// Computes `(x*y)+z`, rounded as one ternary operation:</span> |
| <span class="doccomment">/// Computes the value (as if) to infinite precision and rounds once to the result format,</span> |
| <span class="doccomment">/// according to the rounding mode characterized by the value of FLT_ROUNDS.</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::no_panic</span>)]</span> |
| <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">fmaf</span>(<span class="ident">x</span>: <span class="ident">f32</span>, <span class="ident">y</span>: <span class="ident">f32</span>, <span class="kw-2">mut</span> <span class="ident">z</span>: <span class="ident">f32</span>) -> <span class="ident">f32</span> { |
| <span class="kw">let</span> <span class="ident">xy</span>: <span class="ident">f64</span>; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">result</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="kw">let</span> <span class="ident">e</span>: <span class="ident">i32</span>; |
| |
| <span class="ident">xy</span> <span class="op">=</span> <span class="ident">x</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">y</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">result</span> <span class="op">=</span> <span class="ident">xy</span> <span class="op">+</span> <span class="ident">z</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">ui</span> <span class="op">=</span> <span class="ident">result</span>.<span class="ident">to_bits</span>(); |
| <span class="ident">e</span> <span class="op">=</span> (<span class="ident">ui</span> <span class="op">></span><span class="op">></span> <span class="number">52</span>) <span class="kw">as</span> <span class="ident">i32</span> <span class="op">&</span> <span class="number">0x7ff</span>; |
| <span class="comment">/* Common case: The double precision result is fine. */</span> |
| <span class="kw">if</span> ( |
| <span class="comment">/* not a halfway case */</span> |
| <span class="ident">ui</span> <span class="op">&</span> <span class="number">0x1fffffff</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0x10000000</span> <span class="op">|</span><span class="op">|</span> |
| <span class="comment">/* NaN */</span> |
| <span class="ident">e</span> <span class="op">==</span> <span class="number">0x7ff</span> <span class="op">|</span><span class="op">|</span> |
| <span class="comment">/* exact */</span> |
| (<span class="ident">result</span> <span class="op">-</span> <span class="ident">xy</span> <span class="op">==</span> <span class="ident">z</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">&&</span> <span class="ident">result</span> <span class="op">-</span> <span class="ident">z</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">==</span> <span class="ident">xy</span>) <span class="op">|</span><span class="op">|</span> |
| <span class="comment">/* not round-to-nearest */</span> |
| <span class="ident">fegetround</span>() <span class="op">!</span><span class="op">=</span> <span class="ident">FE_TONEAREST</span> |
| { |
| <span class="comment">/* |
| underflow may not be raised correctly, example: |
| fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f) |
| */</span> |
| <span class="kw">if</span> <span class="ident">e</span> <span class="op"><</span> <span class="number">0x3ff</span> <span class="op">-</span> <span class="number">126</span> <span class="op">&&</span> <span class="ident">e</span> <span class="op">></span><span class="op">=</span> <span class="number">0x3ff</span> <span class="op">-</span> <span class="number">149</span> <span class="op">&&</span> <span class="ident">fetestexcept</span>(<span class="ident">FE_INEXACT</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="ident">feclearexcept</span>(<span class="ident">FE_INEXACT</span>); |
| <span class="comment">// prevent `xy + vz` from being CSE'd with `xy + z` above</span> |
| <span class="kw">let</span> <span class="ident">vz</span>: <span class="ident">f32</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">read_volatile</span>(<span class="kw-2">&</span><span class="ident">z</span>) }; |
| <span class="ident">result</span> <span class="op">=</span> <span class="ident">xy</span> <span class="op">+</span> <span class="ident">vz</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="kw">if</span> <span class="ident">fetestexcept</span>(<span class="ident">FE_INEXACT</span>) <span class="op">!</span><span class="op">=</span> <span class="number">0</span> { |
| <span class="ident">feraiseexcept</span>(<span class="ident">FE_UNDERFLOW</span>); |
| } <span class="kw">else</span> { |
| <span class="ident">feraiseexcept</span>(<span class="ident">FE_INEXACT</span>); |
| } |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">result</span> <span class="kw">as</span> <span class="ident">f32</span>; |
| <span class="kw">return</span> <span class="ident">z</span>; |
| } |
| |
| <span class="comment">/* |
| * If result is inexact, and exactly halfway between two float values, |
| * we need to adjust the low-order bit in the direction of the error. |
| */</span> |
| <span class="ident">fesetround</span>(<span class="ident">FE_TOWARDZERO</span>); |
| <span class="comment">// prevent `vxy + z` from being CSE'd with `xy + z` above</span> |
| <span class="kw">let</span> <span class="ident">vxy</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="kw">unsafe</span> { <span class="ident">read_volatile</span>(<span class="kw-2">&</span><span class="ident">xy</span>) }; |
| <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">adjusted_result</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">vxy</span> <span class="op">+</span> <span class="ident">z</span> <span class="kw">as</span> <span class="ident">f64</span>; |
| <span class="ident">fesetround</span>(<span class="ident">FE_TONEAREST</span>); |
| <span class="kw">if</span> <span class="ident">result</span> <span class="op">==</span> <span class="ident">adjusted_result</span> { |
| <span class="ident">ui</span> <span class="op">=</span> <span class="ident">adjusted_result</span>.<span class="ident">to_bits</span>(); |
| <span class="ident">ui</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>; |
| <span class="ident">adjusted_result</span> <span class="op">=</span> <span class="ident">f64::from_bits</span>(<span class="ident">ui</span>); |
| } |
| <span class="ident">z</span> <span class="op">=</span> <span class="ident">adjusted_result</span> <span class="kw">as</span> <span class="ident">f32</span>; |
| <span class="ident">z</span> |
| } |
| </code></pre></div> |
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