250 lines
18 KiB
HTML
250 lines
18 KiB
HTML
<!DOCTYPE html>
|
|
<html lang="zh" dir="ltr" class="client-nojs" xmlns="http://www.w3.org/1999/xhtml" xml:lang="zh">
|
|
<head><meta http-equiv="x-ua-compatible" content="ie=edge">
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
|
<title>fma, fmaf, fmal</title>
|
|
<link rel="stylesheet" href="ext.css" />
|
|
<link rel="stylesheet" href="site_modules.css" />
|
|
</head>
|
|
<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-c_numeric_math_fma skin-cppreference2 action-view cpp-navbar">
|
|
<div id="cpp-content-base">
|
|
<div id="content"><a id="top"></a>
|
|
<h1 id="firstHeading" class="firstHeading">fma, fmaf, fmal</h1>
|
|
<div id="bodyContent">
|
|
<div id="contentSub"><span class="subpages">< <a href="c.html">c</a>‎ | <a href="c-numeric.html">numeric</a>‎ | <a href="c-numeric-math.html">math</a></span></div>
|
|
<div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr" xml:lang="zh">
|
|
<table class="t-dcl-begin">
|
|
<tbody>
|
|
<tr class="t-dsc-header">
|
|
<td>
|
|
<div>定义于头文件 <code><math.h></code></div>
|
|
</td>
|
|
<td></td>
|
|
<td></td>
|
|
</tr>
|
|
<tr class="t-dcl t-since-c99">
|
|
<td>
|
|
<div><span class="mw-geshi c source-c"><span class="kw4">float</span> fmaf<span class="br0">(</span> <span class="kw4">float</span> x, <span class="kw4">float</span> y, <span class="kw4">float</span> z <span class="br0">)</span><span class="sy4">;</span></span></div>
|
|
</td>
|
|
<td>(1)</td>
|
|
<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
|
|
</tr>
|
|
<tr class="t-dcl t-since-c99">
|
|
<td>
|
|
<div><span class="mw-geshi c source-c"><span class="kw4">double</span> fma<span class="br0">(</span> <span class="kw4">double</span> x, <span class="kw4">double</span> y, <span class="kw4">double</span> z <span class="br0">)</span><span class="sy4">;</span></span></div>
|
|
</td>
|
|
<td>(2)</td>
|
|
<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
|
|
</tr>
|
|
<tr class="t-dcl t-since-c99">
|
|
<td>
|
|
<div><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> fmal<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> x, <span class="kw4">long</span> <span class="kw4">double</span> y, <span class="kw4">long</span> <span class="kw4">double</span> z <span class="br0">)</span><span class="sy4">;</span></span></div>
|
|
</td>
|
|
<td>(3)</td>
|
|
<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
|
|
</tr>
|
|
<tr class="t-dcl t-since-c99">
|
|
<td>
|
|
<div><span class="mw-geshi c source-c"><span class="co2">#define FP_FAST_FMA /* implementation-defined */</span></span></div>
|
|
</td>
|
|
<td>(4)</td>
|
|
<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
|
|
</tr>
|
|
<tr class="t-dcl t-since-c99">
|
|
<td>
|
|
<div><span class="mw-geshi c source-c"><span class="co2">#define FP_FAST_FMAF /* implementation-defined */</span></span></div>
|
|
</td>
|
|
<td>(5)</td>
|
|
<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
|
|
</tr>
|
|
<tr class="t-dcl t-since-c99">
|
|
<td>
|
|
<div><span class="mw-geshi c source-c"><span class="co2">#define FP_FAST_FMAL /* implementation-defined */</span></span></div>
|
|
</td>
|
|
<td>(6)</td>
|
|
<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc-header">
|
|
<td>
|
|
<div>定义于头文件 <code><tgmath.h></code></div>
|
|
</td>
|
|
<td></td>
|
|
<td></td>
|
|
</tr>
|
|
<tr class="t-dcl t-since-c99">
|
|
<td>
|
|
<div><span class="mw-geshi c source-c"><span class="co2">#define fma( x, y, z )</span></span></div>
|
|
</td>
|
|
<td>(7)</td>
|
|
<td><span class="t-mark-rev t-since-c99">(C99 起)</span></td>
|
|
</tr>
|
|
<tr class="t-dcl-sep">
|
|
<td></td>
|
|
<td></td>
|
|
<td></td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
<div class="t-li1"><span class="t-li">1-3)</span> 计算 <span class="t-c"><span class="mw-geshi c source-c"><span class="br0">(</span>x<span class="sy2">*</span>y<span class="br0">)</span> <span class="sy2">+</span> z</span></span> ，如同用无限精度，而仅舍入一次到结果类型。</div>
|
|
<div class="t-li1"><span class="t-li">4-6)</span> 若定义宏常量 <code>FP_FAST_FMAF</code> 、 <code>FP_FAST_FMA</code> 或 <code>FP_FAST_FMAL</code> ，则对应函数 <code>fmaf</code> 、 <code>fma</code> 或 <code>fmal</code> 分别求值快于（并且精度高于） <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 和 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 参数的表达式 <span class="t-c"><span class="mw-geshi c source-c">x<span class="sy2">*</span>y<span class="sy2">+</span>z</span></span> 。若定义，则这些宏求值为整数 <span class="t-c"><span class="mw-geshi c source-c"><span class="nu0">1</span></span></span> 。</div>
|
|
<div class="t-li1"><span class="t-li">7)</span> 泛型宏：若任何参数拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span></span></span> 类型，则调用 <code>fmal</code> 。否则若任何参数拥有整数类型或 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span></span></span> 类型，则调用 <code>fma</code> 。否则调用<code>fmaf</code>。</div>
|
|
<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
|
|
<table class="t-par-begin">
|
|
<tr class="t-par">
|
|
<td>x, y, z</td>
|
|
<td>-</td>
|
|
<td>浮点值</td>
|
|
</tr>
|
|
</table>
|
|
<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
|
|
<p>若成功，则返回 <span class="t-c"><span class="mw-geshi c source-c"><span class="br0">(</span>x<span class="sy2">*</span>y<span class="br0">)</span> <span class="sy2">+</span> z</span></span> 的值，如同计算为无限精度再舍入一次以适合目标类型（或者说是作为单次三元浮点运算计算）。</p>
|
|
<p>若出现上溢所致的值域错误，则返回 <code>±HUGE_VAL</code> 、 <code>±HUGE_VALF</code> 或 <code>±HUGE_VALL</code> 。</p>
|
|
<p>若出现下溢所致的值域错误，则返回（舍入后的）正确结果。</p>
|
|
<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86">错误处理</span></h3>
|
|
<p>报告 <a href="c-numeric-math-math_errhandling.html">math_errhandling</a> 中指定的错误</p>
|
|
<p>若实现支持 IEEE 浮点算术（ IEC 60559 ），则</p>
|
|
<ul>
|
|
<li>若 x 为零而 y 为无穷大或 x 为无穷大而 y 为零，且 z 非 NaN ，则返回 NaN 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
|
|
<li>若 x 为零而 y 为无穷大或 x 为无穷大而 y 为零，且 z 为 NaN ，则返回 NaN 并可能引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
|
|
<li>若 x*y 为准确的无穷大且 z 为带相反符号的无穷大，则返回 NaN 并引发 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span></li>
|
|
<li>若 x 或 y 为 NaN ，则返回 NaN</li>
|
|
<li>若 z 为 NaN ，且 x*y 不是 0*Inf 或 Inf*0 ，则返回 NaN （而无 FE_INVALID ）</li>
|
|
</ul>
|
|
<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
|
|
<p>此运算经常在硬件中实现为<a href="https://en.wikipedia.org/wiki/Multiply%E2%80%93accumulate_operation" class="extiw" title="enwiki:Multiply–accumulate operation">融合乘加</a> CPU 指令。若硬件支持，则期待定义相应的 <code>FP_FAST_FMA*</code> 宏，但多数实现即使在不定义这些宏时也利用该 CPU 指令。</p>
|
|
<p><a rel="nofollow" class="external text" href="http://pubs.opengroup.org/onlinepubs/9699919799/functions/fma.html">POSIX 另外指定</a>被指定为返回 <span class="t-lc"><a href="c-numeric-fenv-FE_exceptions.html">FE_INVALID</a></span> 的情形是定义域错误。</p>
|
|
<p>由于其无限的中间精度， <code>fma</code> 是其他正确舍入数学运算，如 <span class="t-lc"><a href="c-numeric-math-sqrt.html">sqrt</a></span> 或甚至除法（在 CPU 不支持的平台上，例如 Itanium ）的常用构建块。</p>
|
|
<p>同所有浮点表达式，表达式 <span class="t-c"><span class="mw-geshi c source-c"><span class="br0">(</span>x<span class="sy2">*</span>y<span class="br0">)</span> <span class="sy2">+</span> z</span></span> 可编译为融合乘加，除非 <a href="cpp-preprocessor-impl.html">#pragma</a> <span class="t-c"><span class="mw-geshi c source-c">STDC FP_CONTRACT</span></span> 为关闭。</p>
|
|
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
|
|
<div class="t-example">
|
|
<div class="t-example-live-link"></div>
|
|
<div dir="ltr" class="mw-geshi" style="text-align: left;">
|
|
<div class="c source-c">
|
|
<pre class="de1"><span class="co2">#include <stdio.h></span>
|
|
<span class="co2">#include <math.h></span>
|
|
<span class="co2">#include <float.h></span>
|
|
<span class="co2">#include <fenv.h></span>
|
|
<span class="co2">#pragma STDC FENV_ACCESS ON</span>
|
|
<span class="kw4">int</span> main<span class="br0">(</span><span class="kw4">void</span><span class="br0">)</span>
|
|
<span class="br0">{</span>
|
|
<span class="co1">// 演示 fma 和内建运算符间的区别</span>
|
|
<span class="kw4">double</span> in <span class="sy1">=</span> <span class="nu16">0.1</span><span class="sy4">;</span>
|
|
<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"0.1 double is %.23f (%a)<span class="es1">\n</span>"</span>, in, in<span class="br0">)</span><span class="sy4">;</span>
|
|
<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p-3),"</span>
|
|
<span class="st0">" or 1.0 if rounded to double<span class="es1">\n</span>"</span><span class="br0">)</span><span class="sy4">;</span>
|
|
<span class="kw4">double</span> expr_result <span class="sy1">=</span> <span class="nu16">0.1</span> <span class="sy2">*</span> <span class="nu0">10</span> <span class="sy2">-</span> <span class="nu0">1</span><span class="sy4">;</span>
|
|
<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"0.1 * 10 - 1 = %g : 1 subtracted after "</span>
|
|
<span class="st0">"intermediate rounding to 1.0<span class="es1">\n</span>"</span>, expr_result<span class="br0">)</span><span class="sy4">;</span>
|
|
<span class="kw4">double</span> fma_result <span class="sy1">=</span> fma<span class="br0">(</span><span class="nu16">0.1</span>, <span class="nu0">10</span>, <span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
|
|
<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"fma(0.1, 10, -1) = %g (%a)<span class="es1">\n</span>"</span>, fma_result, fma_result<span class="br0">)</span><span class="sy4">;</span>
|
|
|
|
<span class="co1">// fma 用于 double-double</span>
|
|
<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"<span class="es1">\n</span>in double-double arithmetic, 0.1 * 10 is representable as "</span><span class="br0">)</span><span class="sy4">;</span>
|
|
<span class="kw4">double</span> high <span class="sy1">=</span> <span class="nu16">0.1</span> <span class="sy2">*</span> <span class="nu0">10</span><span class="sy4">;</span>
|
|
<span class="kw4">double</span> low <span class="sy1">=</span> fma<span class="br0">(</span><span class="nu16">0.1</span>, <span class="nu0">10</span>, <span class="sy2">-</span>high<span class="br0">)</span><span class="sy4">;</span>
|
|
<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"%g + %g<span class="es1">\n</span><span class="es1">\n</span>"</span>, high, low<span class="br0">)</span><span class="sy4">;</span>
|
|
|
|
<span class="co1">// 错误处理</span>
|
|
<a href="c-numeric-fenv-feclearexcept.html"><span class="kw717">feclearexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw728">FE_ALL_EXCEPT</span></a><span class="br0">)</span><span class="sy4">;</span>
|
|
<a href="c-io-fprintf.html"><span class="kw850">printf</span></a><span class="br0">(</span><span class="st0">"fma(+Inf, 10, -Inf) = %f<span class="es1">\n</span>"</span>, fma<span class="br0">(</span>INFINITY, <span class="nu0">10</span>, <span class="sy2">-</span>INFINITY<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
|
|
<span class="kw1">if</span><span class="br0">(</span><a href="c-numeric-fenv-fetestexcept.html"><span class="kw718">fetestexcept</span></a><span class="br0">(</span><a href="c-numeric-fenv-FE_exceptions.html"><span class="kw731">FE_INVALID</span></a><span class="br0">)</span><span class="br0">)</span> <a href="c-io-puts.html"><span class="kw835">puts</span></a><span class="br0">(</span><span class="st0">" FE_INVALID raised"</span><span class="br0">)</span><span class="sy4">;</span>
|
|
<span class="br0">}</span></pre></div>
|
|
</div>
|
|
<p>可能的输出：</p>
|
|
<div dir="ltr" class="mw-geshi" style="text-align: left;">
|
|
<div class="text source-text">
|
|
<pre class="de1">0.1 double is 0.10000000000000000555112 (0x1.999999999999ap-4)
|
|
0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p-3), or 1.0 if rounded to double
|
|
0.1 * 10 - 1 = 0 : 1 subtracted after intermediate rounding to 1.0
|
|
fma(0.1, 10, -1) = 5.55112e-17 (0x1p-54)
|
|
|
|
in double-double arithmetic, 0.1 * 10 is representable as 1 + 5.55112e-17
|
|
|
|
fma(+Inf, 10, -Inf) = -nan
|
|
FE_INVALID raised</pre></div>
|
|
</div>
|
|
</div>
|
|
<h3><span class="mw-headline" id=".E5.BC.95.E7.94.A8">引用</span></h3>
|
|
<div class="t-ref-std-11">
|
|
<ul>
|
|
<li>C11 标准（ISO/IEC 9899:2011）：</li>
|
|
</ul>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.12.13.1 The fma functions (p: 258)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.25 Type-generic math <tgmath.h> (p: 373-375)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>F.10.10.1 The fma functions (p: 530)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<div class="t-ref-std-c99">
|
|
<ul>
|
|
<li>C99 标准（ISO/IEC 9899:1999）：</li>
|
|
</ul>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.12.13.1 The fma functions (p: 239)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>7.22 Type-generic math <tgmath.h> (p: 335-337)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
<dl>
|
|
<dd>
|
|
<ul>
|
|
<li>F.9.10.1 The fma functions (p: 466)</li>
|
|
</ul>
|
|
</dd>
|
|
</dl>
|
|
</div>
|
|
<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
|
|
<table class="t-dsc-begin">
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-math-remainder.html"><span class="t-lines"><span>remainder</span><span>remainderf</span><span>remainderl</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算浮点除法运算的带符号余数<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
<tr class="t-dsc">
|
|
<td>
|
|
<div class="t-dsc-member-div">
|
|
<div><a href="c-numeric-math-remquo.html"><span class="t-lines"><span>remquo</span><span>remquof</span><span>remquol</span></span></a></div>
|
|
<div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div>
|
|
</div>
|
|
</td>
|
|
<td>计算除法运算的带符号余数，以及商的后三位<br />
|
|
<span class="t-mark">(函数)</span></td>
|
|
</tr>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
<div class="visualClear"></div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</body>
|
|
</html>
|