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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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<a name="Multiplication"></a>
<h3 class="section">15.1 Multiplication</h3>
<a name="index-Multiplication-algorithms"></a>
<p>NxN limb multiplications and squares are done using one of seven
algorithms, as the size N increases.
</p>
<blockquote>
<table>
<tr><td>Algorithm</td><td>Threshold</td></tr>
<tr><td>Basecase</td><td>(none)</td></tr>
<tr><td>Karatsuba</td><td><code>MUL_TOOM22_THRESHOLD</code></td></tr>
<tr><td>Toom-3</td><td><code>MUL_TOOM33_THRESHOLD</code></td></tr>
<tr><td>Toom-4</td><td><code>MUL_TOOM44_THRESHOLD</code></td></tr>
<tr><td>Toom-6.5</td><td><code>MUL_TOOM6H_THRESHOLD</code></td></tr>
<tr><td>Toom-8.5</td><td><code>MUL_TOOM8H_THRESHOLD</code></td></tr>
<tr><td>FFT</td><td><code>MUL_FFT_THRESHOLD</code></td></tr>
</table>
</blockquote>
<p>Similarly for squaring, with the <code>SQR</code> thresholds.
</p>
<p>NxM multiplications of operands with different sizes above
<code>MUL_TOOM22_THRESHOLD</code> are currently done by special Toom-inspired
algorithms or directly with FFT, depending on operand size (see <a href="Unbalanced-Multiplication.html#Unbalanced-Multiplication">Unbalanced Multiplication</a>).
</p>
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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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<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">
</td></tr>
<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">
</td></tr>
<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">
</td></tr>
<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">
</td></tr>
<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">
</td></tr>
<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">
</td></tr>
<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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