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110 lines
4.5 KiB
HTML
110 lines
4.5 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 documents how to install and use the Multiple Precision
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Floating-Point Reliable Library, version 3.1.4.
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Copyright 1991, 1993-2016 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 1.2 or any later
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version published by the Free Software Foundation; with no Invariant Sections,
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with no Front-Cover Texts, and with no Back-Cover Texts. A copy of the
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license is included in 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>Internals (GNU MPFR 3.1.4)</title>
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<meta name="description" content="How to install and use GNU MPFR, a library for reliable multiple precision
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floating-point arithmetic, version 3.1.4.">
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<meta name="keywords" content="Internals (GNU MPFR 3.1.4)">
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<meta name="resource-type" content="document">
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<meta name="distribution" content="global">
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<meta name="Generator" content="makeinfo">
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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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="MPFR-Interface.html#MPFR-Interface" rel="up" title="MPFR Interface">
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<link href="API-Compatibility.html#API-Compatibility" rel="next" title="API Compatibility">
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<link href="Custom-Interface.html#Custom-Interface" rel="prev" title="Custom Interface">
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<style type="text/css">
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span.roman {font-family: initial; font-weight: normal}
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span.sansserif {font-family: sans-serif; font-weight: normal}
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ul.no-bullet {list-style: none}
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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="Internals"></a>
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<div class="header">
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<p>
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Previous: <a href="Custom-Interface.html#Custom-Interface" accesskey="p" rel="prev">Custom Interface</a>, Up: <a href="MPFR-Interface.html#MPFR-Interface" accesskey="u" rel="up">MPFR Interface</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="index-Internals"></a>
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<a name="Internals-1"></a>
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<h3 class="section">5.16 Internals</h3>
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<a name="index-Limb"></a>
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<p>A <em>limb</em> means the part of a multi-precision number that fits in a single
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word. Usually a limb contains
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32 or 64 bits. The C data type for a limb is <code>mp_limb_t</code>.
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</p>
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<p>The <code>mpfr_t</code> type is internally defined as a one-element
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array of a structure, and <code>mpfr_ptr</code> is the C data type representing
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a pointer to this structure.
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The <code>mpfr_t</code> type consists of four fields:
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</p>
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<ul>
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<li> The <code>_mpfr_prec</code> field is used to store the precision of
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the variable (in bits); this is not less than <code>MPFR_PREC_MIN</code>.
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</li><li> The <code>_mpfr_sign</code> field is used to store the sign of the variable.
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</li><li> The <code>_mpfr_exp</code> field stores the exponent.
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An exponent of 0 means a radix point just above the most significant
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limb. Non-zero values <em>n</em> are a multiplier <em>2^n</em> relative to that
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point.
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A NaN, an infinity and a zero are indicated by special values of the exponent
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field.
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</li><li> Finally, the <code>_mpfr_d</code> field is a pointer to the limbs, least
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significant limbs stored first.
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The number of limbs in use is controlled by <code>_mpfr_prec</code>, namely
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ceil(<code>_mpfr_prec</code>/<code>mp_bits_per_limb</code>).
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Non-singular (i.e., different from NaN, Infinity or zero)
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values always have the most significant bit of the most
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significant limb set to 1. When the precision does not correspond to a
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whole number of limbs, the excess bits at the low end of the data are zeros.
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</li></ul>
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</body>
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</html>
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