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90 lines
4.0 KiB
HTML
90 lines
4.0 KiB
HTML
4 years ago
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<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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the terms of the GNU Free Documentation License, Version 1.3 or any later
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version published by the Free Software Foundation; with no Invariant Sections,
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with the Front-Cover Texts being "A GNU Manual", and with the Back-Cover
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Texts being "You have freedom to copy and modify this GNU Manual, like GNU
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software". A copy of the license is included in
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GNU Free Documentation License. -->
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<!-- Created by GNU Texinfo 6.4, http://www.gnu.org/software/texinfo/ -->
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<head>
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<title>Unbalanced Multiplication (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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<meta name="keywords" content="Unbalanced Multiplication (GNU MP 6.1.0)">
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<link href="index.html#Top" rel="start" title="Top">
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<link href="Concept-Index.html#Concept-Index" rel="index" title="Concept Index">
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<link href="Multiplication-Algorithms.html#Multiplication-Algorithms" rel="up" title="Multiplication Algorithms">
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<link href="Division-Algorithms.html#Division-Algorithms" rel="next" title="Division Algorithms">
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<link href="Other-Multiplication.html#Other-Multiplication" rel="prev" title="Other Multiplication">
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</style>
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</head>
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<body lang="en">
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<a name="Unbalanced-Multiplication"></a>
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<div class="header">
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<p>
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Previous: <a href="Other-Multiplication.html#Other-Multiplication" accesskey="p" rel="prev">Other Multiplication</a>, Up: <a href="Multiplication-Algorithms.html#Multiplication-Algorithms" accesskey="u" rel="up">Multiplication 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="Unbalanced-Multiplication-1"></a>
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<h4 class="subsection">15.1.8 Unbalanced Multiplication</h4>
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<a name="index-Unbalanced-multiplication"></a>
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<p>Multiplication of operands with different sizes, both below
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<code>MUL_TOOM22_THRESHOLD</code> are done with plain schoolbook multiplication
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(see <a href="Basecase-Multiplication.html#Basecase-Multiplication">Basecase Multiplication</a>).
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</p>
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<p>For really large operands, we invoke FFT directly.
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</p>
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<p>For operands between these sizes, we use Toom inspired algorithms suggested by
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Alberto Zanoni and Marco Bodrato. The idea is to split the operands into
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polynomials of different degree. GMP currently splits the smaller operand
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onto 2 coefficients, i.e., a polynomial of degree 1, but the larger operand
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can be split into 2, 3, or 4 coefficients, i.e., a polynomial of degree 1 to
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3.
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</p>
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</body>
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</html>
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