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| 58 | <span id="Fused-Multiply_002dAdd"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="Error-Recovery.html" accesskey="n" rel="next">Error Recovery</a>, Previous: <a href="Significance-Loss.html" accesskey="p" rel="prev">Significance Loss</a>, Up: <a href="Floating-Point-in-Depth.html" accesskey="u" rel="up">Floating Point in Depth</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 61 | </div>
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| 62 | <hr>
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| 63 | <span id="Fused-Multiply_002dAdd-1"></span><h3 class="section">28.10 Fused Multiply-Add</h3>
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| 64 | <span id="index-fused-multiply_002dadd-in-floating_002dpoint-computations"></span>
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| 65 | <span id="index-floating_002dpoint-fused-multiply_002dadd"></span>
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| 66 |
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| 67 | <p>In 1990, when IBM introduced the POWER architecture, the CPU
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| 68 | provided a previously unknown instruction, the <em>fused
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| 69 | multiply-add</em> (FMA). It computes the value <code>x * y + z</code> with
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| 70 | an <strong>exact</strong> double-length product, followed by an addition with a
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| 71 | <em>single</em> rounding. Numerical computation often needs pairs of
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| 72 | multiply and add operations, for which the FMA is well-suited.
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| 73 | </p>
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| 74 | <p>On the POWER architecture, there are two dedicated registers that
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| 75 | hold permanent values of <code>0.0</code> and <code>1.0</code>, and the
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| 76 | normal <em>multiply</em> and <em>add</em> instructions are just
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| 77 | wrappers around the FMA that compute <code>x * y + 0.0</code> and
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| 78 | <code>x * 1.0 + z</code>, respectively.
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| 79 | </p>
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| 80 | <p>In the early days, it appeared that the main benefit of the FMA
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| 81 | was getting two floating-point operations for the price of one,
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| 82 | almost doubling the performance of some algorithms. However,
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| 83 | numerical analysts have since shown numerous uses of the FMA for
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| 84 | significantly enhancing accuracy. We discuss one of the most
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| 85 | important ones in the next section.
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| 86 | </p>
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| 87 | <p>A few other architectures have since included the FMA, and most
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| 88 | provide variants for the related operations <code>x * y - z</code>
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| 89 | (FMS), <code>-x * y + z</code> (FNMA), and <code>-x * y - z</code> (FNMS).
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| 90 | </p>
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| 91 | <p>The functions <code>fmaf</code>, <code>fma</code>, and <code>fmal</code> implement fused
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| 92 | multiply-add for the <code>float</code>, <code>double</code>, and <code>long
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| 93 | double</code> data types. Correct implementation of the FMA in software is
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| 94 | difficult, and some systems that appear to provide those functions do
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| 95 | not satisfy the single-rounding requirement. That situation should
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| 96 | change as more programmers use the FMA operation, and more CPUs
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| 97 | provide FMA in hardware.
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| 98 | </p>
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| 99 | <p>Use the <samp>-ffp-contract=fast</samp> option to allow generation of FMA
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| 100 | instructions, or <samp>-ffp-contract=off</samp> to disallow it.
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| 101 | </p>
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| 102 |
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| 103 | <hr>
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| 104 | <div class="header">
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| 105 | <p>
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| 106 | Next: <a href="Error-Recovery.html" accesskey="n" rel="next">Error Recovery</a>, Previous: <a href="Significance-Loss.html" accesskey="p" rel="prev">Significance Loss</a>, Up: <a href="Floating-Point-in-Depth.html" accesskey="u" rel="up">Floating Point in Depth</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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