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131 lines
6.0 KiB
HTML
131 lines
6.0 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>Integer Internals (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="Integer Internals (GNU MP 6.1.0)">
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<meta name="resource-type" content="document">
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<meta name="distribution" content="global">
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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="Internals.html#Internals" rel="up" title="Internals">
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<link href="Rational-Internals.html#Rational-Internals" rel="next" title="Rational Internals">
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<link href="Internals.html#Internals" rel="prev" title="Internals">
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-->
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</style>
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</head>
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<body lang="en">
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<a name="Integer-Internals"></a>
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<div class="header">
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<p>
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Next: <a href="Rational-Internals.html#Rational-Internals" accesskey="n" rel="next">Rational Internals</a>, Previous: <a href="Internals.html#Internals" accesskey="p" rel="prev">Internals</a>, Up: <a href="Internals.html#Internals" accesskey="u" rel="up">Internals</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="Integer-Internals-1"></a>
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<h3 class="section">16.1 Integer Internals</h3>
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<a name="index-Integer-internals"></a>
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<p><code>mpz_t</code> variables represent integers using sign and magnitude, in space
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dynamically allocated and reallocated. The fields are as follows.
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</p>
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<dl compact="compact">
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<dt><code>_mp_size</code></dt>
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<dd><p>The number of limbs, or the negative of that when representing a negative
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integer. Zero is represented by <code>_mp_size</code> set to zero, in which case
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the <code>_mp_d</code> data is unused.
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</p>
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</dd>
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<dt><code>_mp_d</code></dt>
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<dd><p>A pointer to an array of limbs which is the magnitude. These are stored
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“little endian” as per the <code>mpn</code> functions, so <code>_mp_d[0]</code> is the
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least significant limb and <code>_mp_d[ABS(_mp_size)-1]</code> is the most
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significant. Whenever <code>_mp_size</code> is non-zero, the most significant limb
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is non-zero.
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</p>
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<p>Currently there’s always at least one limb allocated, so for instance
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<code>mpz_set_ui</code> never needs to reallocate, and <code>mpz_get_ui</code> can fetch
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<code>_mp_d[0]</code> unconditionally (though its value is then only wanted if
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<code>_mp_size</code> is non-zero).
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</p>
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</dd>
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<dt><code>_mp_alloc</code></dt>
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<dd><p><code>_mp_alloc</code> is the number of limbs currently allocated at <code>_mp_d</code>,
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and naturally <code>_mp_alloc >= ABS(_mp_size)</code>. When an <code>mpz</code> routine
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is about to (or might be about to) increase <code>_mp_size</code>, it checks
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<code>_mp_alloc</code> to see whether there’s enough space, and reallocates if not.
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<code>MPZ_REALLOC</code> is generally used for this.
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</p></dd>
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</dl>
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<p>The various bitwise logical functions like <code>mpz_and</code> behave as if
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negative values were twos complement. But sign and magnitude is always used
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internally, and necessary adjustments are made during the calculations.
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Sometimes this isn’t pretty, but sign and magnitude are best for other
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routines.
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</p>
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<p>Some internal temporary variables are setup with <code>MPZ_TMP_INIT</code> and these
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have <code>_mp_d</code> space obtained from <code>TMP_ALLOC</code> rather than the memory
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allocation functions. Care is taken to ensure that these are big enough that
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no reallocation is necessary (since it would have unpredictable consequences).
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</p>
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<p><code>_mp_size</code> and <code>_mp_alloc</code> are <code>int</code>, although <code>mp_size_t</code>
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is usually a <code>long</code>. This is done to make the fields just 32 bits on
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some 64 bits systems, thereby saving a few bytes of data space but still
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providing plenty of range.
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</p>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Rational-Internals.html#Rational-Internals" accesskey="n" rel="next">Rational Internals</a>, Previous: <a href="Internals.html#Internals" accesskey="p" rel="prev">Internals</a>, Up: <a href="Internals.html#Internals" accesskey="u" rel="up">Internals</a> [<a href="Concept-Index.html#Concept-Index" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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