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83 lines
3.7 KiB
HTML
83 lines
3.7 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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<!-- 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>Normal Powering Algorithm (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="Normal Powering Algorithm (GNU MP 6.1.0)">
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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="Powering-Algorithms.html#Powering-Algorithms" rel="up" title="Powering Algorithms">
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<link href="Modular-Powering-Algorithm.html#Modular-Powering-Algorithm" rel="next" title="Modular Powering Algorithm">
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<link href="Powering-Algorithms.html#Powering-Algorithms" rel="prev" title="Powering Algorithms">
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</style>
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</head>
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<body lang="en">
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<a name="Normal-Powering-Algorithm"></a>
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<div class="header">
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<p>
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Next: <a href="Modular-Powering-Algorithm.html#Modular-Powering-Algorithm" accesskey="n" rel="next">Modular Powering Algorithm</a>, Previous: <a href="Powering-Algorithms.html#Powering-Algorithms" accesskey="p" rel="prev">Powering Algorithms</a>, Up: <a href="Powering-Algorithms.html#Powering-Algorithms" accesskey="u" rel="up">Powering 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="Normal-Powering"></a>
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<h4 class="subsection">15.4.1 Normal Powering</h4>
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<p>Normal <code>mpz</code> or <code>mpf</code> powering uses a simple binary algorithm,
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successively squaring and then multiplying by the base when a 1 bit is seen in
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the exponent, as per Knuth section 4.6.3. The “left to right”
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variant described there is used rather than algorithm A, since it’s just as
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easy and can be done with somewhat less temporary memory.
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</p>
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</body>
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</html>
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