316 lines
10 KiB
C++
Executable File
316 lines
10 KiB
C++
Executable File
// Copyright (c) 2002,2003
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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//
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//
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// Author(s) : Sylvain Pion, Michael Hemmer
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#ifndef CGAL_MPQ_CLASS_H
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#define CGAL_MPQ_CLASS_H
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#include <CGAL/number_type_basic.h>
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#include <CGAL/gmpxx_coercion_traits.h>
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#include <CGAL/mpz_class.h> // for GCD in Type traits
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#include <CGAL/IO/io.h>
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// This file gathers the necessary adaptors so that the following
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// C++ number types that come with GMP can be used by CGAL :
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// - mpq_class
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// Note that GMP++ use the expression template mechanism, which makes things
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// a little bit complicated in order to make square(x+y) work for example.
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// Reading gmpxx.h shows that ::__gmp_expr<T, T> is the mp[zqf]_class proper,
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// while ::__gmp_expr<T, U> is the others "expressions".
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#define CGAL_CHECK_GMP_EXPR \
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CGAL_static_assertion( \
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(::boost::is_same< ::__gmp_expr< T , T >,Type>::value ));
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namespace CGAL {
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// AST for mpq_class
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template<>
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class Algebraic_structure_traits< mpq_class >
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: public Algebraic_structure_traits_base< mpq_class , Field_tag > {
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public:
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typedef mpq_class Type;
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typedef Field_tag Algebraic_category;
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typedef Tag_true Is_exact;
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typedef Tag_false Is_numerical_sensitive;
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struct Is_zero: public CGAL::cpp98::unary_function< mpq_class , bool > {
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template <class T, class U>
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bool operator()( const ::__gmp_expr< T , U >& x) const {
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CGAL_CHECK_GMP_EXPR;
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return ::sgn(x) == 0;
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}
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};
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struct Is_one: public CGAL::cpp98::unary_function< mpq_class , bool > {
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template <typename T, typename U>
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bool operator()( const ::__gmp_expr< T , U >& x) const {
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CGAL_CHECK_GMP_EXPR;
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return x == 1;
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}
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};
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struct Simplify: public CGAL::cpp98::unary_function< mpq_class , void > {
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void operator()( mpq_class& x) const {
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// do nothing because x is already canonical?
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x.canonicalize();
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}
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};
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struct Square: public CGAL::cpp98::unary_function< mpq_class , mpq_class > {
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mpq_class operator()( const mpq_class& x) const {
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return x*x;
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}
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};
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struct Unit_part: public CGAL::cpp98::unary_function< mpq_class , mpq_class > {
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mpq_class operator()( const mpq_class& x) const {
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return( x == 0) ? mpq_class(1) : x;
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}
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};
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struct Integral_division
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: public CGAL::cpp98::binary_function< mpq_class , mpq_class, mpq_class > {
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template <typename T, typename U1, typename U2>
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mpq_class operator()(
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const ::__gmp_expr< T , U1 >& x,
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const ::__gmp_expr< T , U2 > & y) const {
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CGAL_CHECK_GMP_EXPR;
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mpq_class result = x / y;
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CGAL_precondition_msg( result * y == x,
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"'x' must be divisible by 'y' in "
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"Algebraic_structure_traits<mpq_class>::Integral_div()(x,y)" );
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return result;
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}
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CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type )
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};
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class Is_square
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: public CGAL::cpp98::binary_function< mpq_class, mpq_class&, bool > {
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public:
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bool operator()( const mpq_class& x, mpq_class& y ) const {
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y = mpq_class (::sqrt( x.get_num() ), ::sqrt( x.get_den() )) ;
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return y*y == x;
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// for efficiency, only handle den if num is a square
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}
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bool operator()( const mpq_class& x ) const {
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mpq_class y;
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return operator()(x,y);
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}
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};
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};
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// RET for mpq_class
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template < >
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class Real_embeddable_traits< mpq_class >
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: public INTERN_RET::Real_embeddable_traits_base< mpq_class , CGAL::Tag_true > {
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public:
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struct Is_zero: public CGAL::cpp98::unary_function< mpq_class , bool > {
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template <typename T, typename U>
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bool operator()( const ::__gmp_expr< T , U >& x) const {
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CGAL_CHECK_GMP_EXPR;
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return ::sgn(x) == 0;
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}
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};
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struct Is_finite: public CGAL::cpp98::unary_function<mpq_class,bool> {
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template <typename T, typename U>
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bool operator()( const ::__gmp_expr< T , U >&) const {
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CGAL_CHECK_GMP_EXPR;
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return true;
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}
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};
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struct Is_positive: public CGAL::cpp98::unary_function< mpq_class , bool > {
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template <typename T, typename U>
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bool operator()( const ::__gmp_expr< T , U >& x) const {
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CGAL_CHECK_GMP_EXPR;
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return ::sgn(x) > 0;
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}
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};
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struct Is_negative: public CGAL::cpp98::unary_function< mpq_class , bool > {
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template <typename T, typename U>
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bool operator()( const ::__gmp_expr< T , U >& x) const {
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CGAL_CHECK_GMP_EXPR;
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return ::sgn(x) < 0;
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}
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};
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struct Abs: public CGAL::cpp98::unary_function< mpq_class , mpq_class > {
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template <typename T, typename U>
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mpq_class operator()( const ::__gmp_expr< T , U >& x) const {
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CGAL_CHECK_GMP_EXPR;
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return ::abs(x);
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}
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};
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struct Sgn
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: public CGAL::cpp98::unary_function< mpq_class, ::CGAL::Sign > {
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public:
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template <typename T, typename U>
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::CGAL::Sign
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operator()( const ::__gmp_expr< T , U >& x ) const {
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CGAL_CHECK_GMP_EXPR;
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return (::CGAL::Sign) ::sgn( x );
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}
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};
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struct Compare
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: public CGAL::cpp98::binary_function< mpq_class, mpq_class, Comparison_result>
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{
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template <typename T, typename U1, typename U2>
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Comparison_result operator()(
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const ::__gmp_expr< T , U1 >& x,
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const ::__gmp_expr< T , U2 >& y ) const {
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CGAL_CHECK_GMP_EXPR;
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// cmp returns any int value, not just -1/0/1...
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return (Comparison_result) CGAL_NTS sign( ::cmp(x, y) );
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}
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CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT
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( Type, Comparison_result)
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};
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struct To_double
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: public CGAL::cpp98::unary_function< mpq_class, double > {
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double operator()( const mpq_class& x ) const {
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return x.get_d();
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}
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};
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struct To_interval
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: public CGAL::cpp98::unary_function< mpq_class, std::pair< double, double > > {
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std::pair<double, double>
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operator()( const mpq_class& x ) const {
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#if MPFR_VERSION_MAJOR >= 3
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mpfr_exp_t emin = mpfr_get_emin();
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mpfr_set_emin(-1073);
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MPFR_DECL_INIT (y, 53); /* Assume IEEE-754 */
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int r = mpfr_set_q (y, x.get_mpq_t(), MPFR_RNDA);
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r = mpfr_subnormalize (y, r, MPFR_RNDA); /* Round subnormals */
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double i = mpfr_get_d (y, MPFR_RNDA); /* EXACT but can overflow */
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mpfr_set_emin(emin); /* Restore old value, users may care */
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// With mpfr_set_emax(1024) we could drop the is_finite test
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if (r == 0 && is_finite (i))
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return std::pair<double, double>(i, i);
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else
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{
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double s = nextafter (i, 0);
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if (i < 0)
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return std::pair<double, double>(i, s);
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else
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return std::pair<double, double>(s, i);
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}
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#else
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mpfr_t y;
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mpfr_init2 (y, 53); /* Assume IEEE-754 */
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mpfr_set_q (y, x.get_mpq_t(), GMP_RNDD);
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double i = mpfr_get_d (y, GMP_RNDD); /* EXACT but can overflow */
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mpfr_set_q (y, x.get_mpq_t(), GMP_RNDU);
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double s = mpfr_get_d (y, GMP_RNDU); /* EXACT but can overflow */
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mpfr_clear (y);
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return std::pair<double, double>(i, s);
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#endif
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}
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};
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};
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/*! \ingroup NiX_Fraction_traits_spec
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* \brief Specialization of Fraction_traits for mpq_class
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*/
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template <>
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class Fraction_traits< mpq_class > {
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public:
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typedef mpq_class Type;
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typedef ::CGAL::Tag_true Is_fraction;
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typedef mpz_class Numerator_type;
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typedef mpz_class Denominator_type;
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typedef Algebraic_structure_traits< mpz_class >::Gcd Common_factor;
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class Decompose {
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public:
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typedef mpq_class first_argument_type;
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typedef mpz_class& second_argument_type;
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typedef mpz_class& third_argument_type;
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void operator () (
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const mpq_class& rat,
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mpz_class& num,
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mpz_class& den) {
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num = rat.get_num();
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den = rat.get_den();
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}
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};
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class Compose {
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public:
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typedef mpz_class first_argument_type;
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typedef mpz_class second_argument_type;
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typedef mpq_class result_type;
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mpq_class operator ()(
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const mpz_class& num ,
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const mpz_class& den ) {
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mpq_class result(num, den);
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result.canonicalize();
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return result;
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}
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};
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};
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template <>
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class Input_rep<mpq_class> : public IO_rep_is_specialized {
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mpq_class& q;
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public:
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Input_rep( mpq_class& qq) : q(qq) {}
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std::istream& operator()( std::istream& in) const {
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internal::read_float_or_quotient<mpz_class,mpq_class>(in, q);
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return in;
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}
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};
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// Copied from leda_rational.h
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namespace internal {
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// See: Stream_support/include/CGAL/IO/io.h
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template <typename ET>
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void read_float_or_quotient(std::istream & is, ET& et);
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template <>
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inline void read_float_or_quotient(std::istream & is, mpq_class& et)
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{
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internal::read_float_or_quotient<mpz_class,mpq_class>(is, et);
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}
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} // namespace internal
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} //namespace CGAL
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#undef CGAL_CHECK_GMP_EXPR
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#endif // CGAL_MPQ_CLASS_H
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