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182 lines
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182 lines
7.1 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>C++ Interface 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="C++ Interface 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="Contributors.html#Contributors" rel="next" title="Contributors">
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<link href="Raw-Output-Internals.html#Raw-Output-Internals" rel="prev" title="Raw Output Internals">
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</head>
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<body lang="en">
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<a name="C_002b_002b-Interface-Internals"></a>
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<div class="header">
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<p>
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Previous: <a href="Raw-Output-Internals.html#Raw-Output-Internals" accesskey="p" rel="prev">Raw Output 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="C_002b_002b-Interface-Internals-1"></a>
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<h3 class="section">16.5 C++ Interface Internals</h3>
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<a name="index-C_002b_002b-interface-internals"></a>
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<p>A system of expression templates is used to ensure something like <code>a=b+c</code>
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turns into a simple call to <code>mpz_add</code> etc. For <code>mpf_class</code>
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the scheme also ensures the precision of the final
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destination is used for any temporaries within a statement like
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<code>f=w*x+y*z</code>. These are important features which a naive implementation
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cannot provide.
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</p>
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<p>A simplified description of the scheme follows. The true scheme is
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complicated by the fact that expressions have different return types. For
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detailed information, refer to the source code.
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</p>
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<p>To perform an operation, say, addition, we first define a “function object”
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evaluating it,
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</p>
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<div class="example">
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<pre class="example">struct __gmp_binary_plus
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{
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static void eval(mpf_t f, const mpf_t g, const mpf_t h)
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{
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mpf_add(f, g, h);
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}
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};
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</pre></div>
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<p>And an “additive expression” object,
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</p>
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<div class="example">
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<pre class="example">__gmp_expr<__gmp_binary_expr<mpf_class, mpf_class, __gmp_binary_plus> >
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operator+(const mpf_class &f, const mpf_class &g)
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{
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return __gmp_expr
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<__gmp_binary_expr<mpf_class, mpf_class, __gmp_binary_plus> >(f, g);
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}
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</pre></div>
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<p>The seemingly redundant <code>__gmp_expr<__gmp_binary_expr<…>></code> is used to
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encapsulate any possible kind of expression into a single template type. In
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fact even <code>mpf_class</code> etc are <code>typedef</code> specializations of
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<code>__gmp_expr</code>.
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</p>
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<p>Next we define assignment of <code>__gmp_expr</code> to <code>mpf_class</code>.
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</p>
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<div class="example">
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<pre class="example">template <class T>
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mpf_class & mpf_class::operator=(const __gmp_expr<T> &expr)
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{
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expr.eval(this->get_mpf_t(), this->precision());
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return *this;
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}
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template <class Op>
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void __gmp_expr<__gmp_binary_expr<mpf_class, mpf_class, Op> >::eval
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(mpf_t f, mp_bitcnt_t precision)
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{
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Op::eval(f, expr.val1.get_mpf_t(), expr.val2.get_mpf_t());
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}
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</pre></div>
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<p>where <code>expr.val1</code> and <code>expr.val2</code> are references to the expression’s
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operands (here <code>expr</code> is the <code>__gmp_binary_expr</code> stored within the
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<code>__gmp_expr</code>).
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</p>
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<p>This way, the expression is actually evaluated only at the time of assignment,
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when the required precision (that of <code>f</code>) is known. Furthermore the
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target <code>mpf_t</code> is now available, thus we can call <code>mpf_add</code> directly
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with <code>f</code> as the output argument.
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</p>
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<p>Compound expressions are handled by defining operators taking subexpressions
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as their arguments, like this:
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</p>
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<div class="example">
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<pre class="example">template <class T, class U>
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__gmp_expr
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<__gmp_binary_expr<__gmp_expr<T>, __gmp_expr<U>, __gmp_binary_plus> >
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operator+(const __gmp_expr<T> &expr1, const __gmp_expr<U> &expr2)
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{
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return __gmp_expr
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<__gmp_binary_expr<__gmp_expr<T>, __gmp_expr<U>, __gmp_binary_plus> >
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(expr1, expr2);
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}
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</pre></div>
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<p>And the corresponding specializations of <code>__gmp_expr::eval</code>:
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</p>
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<div class="example">
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<pre class="example">template <class T, class U, class Op>
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void __gmp_expr
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<__gmp_binary_expr<__gmp_expr<T>, __gmp_expr<U>, Op> >::eval
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(mpf_t f, mp_bitcnt_t precision)
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{
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// declare two temporaries
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mpf_class temp1(expr.val1, precision), temp2(expr.val2, precision);
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Op::eval(f, temp1.get_mpf_t(), temp2.get_mpf_t());
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}
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</pre></div>
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<p>The expression is thus recursively evaluated to any level of complexity and
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all subexpressions are evaluated to the precision of <code>f</code>.
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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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Previous: <a href="Raw-Output-Internals.html#Raw-Output-Internals" accesskey="p" rel="prev">Raw Output 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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