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119 lines
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119 lines
6.0 KiB
HTML
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<!-- This manual describes how to install and use the GNU multiple precision
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arithmetic library, version 6.1.0.
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Copyright 1991, 1993-2015 Free Software Foundation, Inc.
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Permission is granted to copy, distribute and/or modify this document under
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<title>Multiplication Algorithms (GNU MP 6.1.0)</title>
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<meta name="description" content="How to install and use the GNU multiple precision arithmetic library, version 6.1.0.">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="Algorithms.html#Algorithms" rel="up" title="Algorithms">
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<link href="Basecase-Multiplication.html#Basecase-Multiplication" rel="next" title="Basecase Multiplication">
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<a name="Multiplication-Algorithms"></a>
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<div class="header">
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<p>
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Next: <a href="Division-Algorithms.html#Division-Algorithms" accesskey="n" rel="next">Division Algorithms</a>, Previous: <a href="Algorithms.html#Algorithms" accesskey="p" rel="prev">Algorithms</a>, Up: <a href="Algorithms.html#Algorithms" accesskey="u" rel="up">Algorithms</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<a name="Multiplication"></a>
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<h3 class="section">15.1 Multiplication</h3>
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<a name="index-Multiplication-algorithms"></a>
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<p>NxN limb multiplications and squares are done using one of seven
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algorithms, as the size N increases.
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</p>
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<blockquote>
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<table>
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<tr><td>Algorithm</td><td>Threshold</td></tr>
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<tr><td>Basecase</td><td>(none)</td></tr>
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<tr><td>Karatsuba</td><td><code>MUL_TOOM22_THRESHOLD</code></td></tr>
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<tr><td>Toom-3</td><td><code>MUL_TOOM33_THRESHOLD</code></td></tr>
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<tr><td>Toom-4</td><td><code>MUL_TOOM44_THRESHOLD</code></td></tr>
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<tr><td>Toom-6.5</td><td><code>MUL_TOOM6H_THRESHOLD</code></td></tr>
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<tr><td>Toom-8.5</td><td><code>MUL_TOOM8H_THRESHOLD</code></td></tr>
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<tr><td>FFT</td><td><code>MUL_FFT_THRESHOLD</code></td></tr>
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</table>
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</blockquote>
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<p>Similarly for squaring, with the <code>SQR</code> thresholds.
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</p>
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<p>NxM multiplications of operands with different sizes above
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<code>MUL_TOOM22_THRESHOLD</code> are currently done by special Toom-inspired
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algorithms or directly with FFT, depending on operand size (see <a href="Unbalanced-Multiplication.html#Unbalanced-Multiplication">Unbalanced Multiplication</a>).
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</p>
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<table class="menu" border="0" cellspacing="0">
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<tr><td align="left" valign="top">• <a href="Basecase-Multiplication.html#Basecase-Multiplication" accesskey="1">Basecase Multiplication</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Karatsuba-Multiplication.html#Karatsuba-Multiplication" accesskey="2">Karatsuba Multiplication</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Toom-3_002dWay-Multiplication.html#Toom-3_002dWay-Multiplication" accesskey="3">Toom 3-Way Multiplication</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Toom-4_002dWay-Multiplication.html#Toom-4_002dWay-Multiplication" accesskey="4">Toom 4-Way Multiplication</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Higher-degree-Toom_0027n_0027half.html#Higher-degree-Toom_0027n_0027half" accesskey="5">Higher degree Toom'n'half</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="FFT-Multiplication.html#FFT-Multiplication" accesskey="6">FFT Multiplication</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Other-Multiplication.html#Other-Multiplication" accesskey="7">Other Multiplication</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Unbalanced-Multiplication.html#Unbalanced-Multiplication" accesskey="8">Unbalanced Multiplication</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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</table>
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</body>
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