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155 lines
8.4 KiB
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155 lines
8.4 KiB
HTML
<!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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<head>
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<title>Floating-point Functions (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="Floating-point Functions (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="index.html#Top" rel="up" title="Top">
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<link href="Initializing-Floats.html#Initializing-Floats" rel="next" title="Initializing Floats">
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</head>
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<body lang="en">
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<a name="Floating_002dpoint-Functions"></a>
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<div class="header">
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<p>
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Next: <a href="Low_002dlevel-Functions.html#Low_002dlevel-Functions" accesskey="n" rel="next">Low-level Functions</a>, Previous: <a href="Rational-Number-Functions.html#Rational-Number-Functions" accesskey="p" rel="prev">Rational Number Functions</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</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="Floating_002dpoint-Functions-1"></a>
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<h2 class="chapter">7 Floating-point Functions</h2>
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<a name="index-Floating_002dpoint-functions"></a>
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<a name="index-Float-functions"></a>
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<a name="index-User_002ddefined-precision"></a>
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<a name="index-Precision-of-floats"></a>
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<p>GMP floating point numbers are stored in objects of type <code>mpf_t</code> and
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functions operating on them have an <code>mpf_</code> prefix.
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</p>
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<p>The mantissa of each float has a user-selectable precision, in practice only
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limited by available memory. Each variable has its own precision, and that can
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be increased or decreased at any time. This selectable precision is a minimum
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value, GMP rounds it up to a whole limb.
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</p>
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<p>The accuracy of a calculation is determined by the priorly set precision of the
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destination variable and the numeric values of the input variables. Input
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variables’ set precisions do not affect calculations (except indirectly as
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their values might have been affected when they were assigned).
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</p>
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<p>The exponent of each float has fixed precision, one machine word on most
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systems. In the current implementation the exponent is a count of limbs, so
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for example on a 32-bit system this means a range of roughly
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<em>2^<span class="nolinebreak">-68719476768</span><!-- /@w --></em> to <em>2^68719476736<!-- /@w --></em>, or on a 64-bit system
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this will be much greater. Note however that <code>mpf_get_str</code> can only
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return an exponent which fits an <code>mp_exp_t</code> and currently
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<code>mpf_set_str</code> doesn’t accept exponents bigger than a <code>long</code>.
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</p>
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<p>Each variable keeps track of the mantissa data actually in use. This means
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that if a float is exactly represented in only a few bits then only those bits
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will be used in a calculation, even if the variable’s selected precision is
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high. This is a performance optimization; it does not affect the numeric
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results.
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</p>
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<p>Internally, GMP sometimes calculates with higher precision than that of the
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destination variable in order to limit errors. Final results are always
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truncated to the destination variable’s precision.
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</p>
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<p>The mantissa is stored in binary. One consequence of this is that decimal
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fractions like <em>0.1</em> cannot be represented exactly. The same is true of
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plain IEEE <code>double</code> floats. This makes both highly unsuitable for
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calculations involving money or other values that should be exact decimal
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fractions. (Suitably scaled integers, or perhaps rationals, are better
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choices.)
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</p>
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<p>The <code>mpf</code> functions and variables have no special notion of infinity or
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not-a-number, and applications must take care not to overflow the exponent or
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results will be unpredictable.
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</p>
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<p>Note that the <code>mpf</code> functions are <em>not</em> intended as a smooth
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extension to IEEE P754 arithmetic. In particular results obtained on one
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computer often differ from the results on a computer with a different word
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size.
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</p>
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<p>New projects should consider using the GMP extension library MPFR
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(<a href="http://mpfr.org">http://mpfr.org</a>) instead. MPFR provides well-defined precision and
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accurate rounding, and thereby naturally extends IEEE P754.
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</p>
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<table class="menu" border="0" cellspacing="0">
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<tr><td align="left" valign="top">• <a href="Initializing-Floats.html#Initializing-Floats" accesskey="1">Initializing Floats</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Assigning-Floats.html#Assigning-Floats" accesskey="2">Assigning Floats</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Simultaneous-Float-Init-_0026-Assign.html#Simultaneous-Float-Init-_0026-Assign" accesskey="3">Simultaneous Float Init & Assign</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Converting-Floats.html#Converting-Floats" accesskey="4">Converting Floats</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Float-Arithmetic.html#Float-Arithmetic" accesskey="5">Float Arithmetic</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Float-Comparison.html#Float-Comparison" accesskey="6">Float Comparison</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="I_002fO-of-Floats.html#I_002fO-of-Floats" accesskey="7">I/O of Floats</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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<tr><td align="left" valign="top">• <a href="Miscellaneous-Float-Functions.html#Miscellaneous-Float-Functions" accesskey="8">Miscellaneous Float Functions</a>:</td><td> </td><td align="left" valign="top">
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</td></tr>
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</table>
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<hr>
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<div class="header">
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<p>
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Next: <a href="Low_002dlevel-Functions.html#Low_002dlevel-Functions" accesskey="n" rel="next">Low-level Functions</a>, Previous: <a href="Rational-Number-Functions.html#Rational-Number-Functions" accesskey="p" rel="prev">Rational Number Functions</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</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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