337 lines
9.7 KiB
C
337 lines
9.7 KiB
C
|
// Copyright (c) 1999
|
||
|
|
// Utrecht University (The Netherlands),
|
||
|
|
// ETH Zurich (Switzerland),
|
||
|
|
// INRIA Sophia-Antipolis (France),
|
||
|
|
// Max-Planck-Institute Saarbruecken (Germany),
|
||
|
|
// and Tel-Aviv University (Israel). All rights reserved.
|
||
|
|
//
|
||
|
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||
|
|
// modify it under the terms of the GNU Lesser General Public License as
|
||
|
|
// published by the Free Software Foundation; either version 3 of the License,
|
||
|
|
// or (at your option) any later version.
|
||
|
|
//
|
||
|
|
// Licensees holding a valid commercial license may use this file in
|
||
|
|
// accordance with the commercial license agreement provided with the software.
|
||
|
|
//
|
||
|
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||
|
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||
|
|
//
|
||
|
|
// $URL$
|
||
|
|
// $Id$
|
||
|
|
// SPDX-License-Identifier: LGPL-3.0+
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// Author(s) : Stefan Schirra
|
||
|
|
|
||
|
|
#ifndef CGAL_NUMBER_UTILS_H
|
||
|
|
#define CGAL_NUMBER_UTILS_H
|
||
|
|
|
||
|
|
#include <CGAL/number_type_config.h>
|
||
|
|
#include <CGAL/Algebraic_structure_traits.h>
|
||
|
|
#include <CGAL/Real_embeddable_traits.h>
|
||
|
|
|
||
|
|
namespace CGAL {
|
||
|
|
CGAL_NTS_BEGIN_NAMESPACE
|
||
|
|
|
||
|
|
|
||
|
|
// AST-Functor adapting functions UNARY
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
void
|
||
|
|
simplify( AS& x ) {
|
||
|
|
typename Algebraic_structure_traits< AS >::Simplify simplify;
|
||
|
|
simplify( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< AS >::Unit_part::result_type
|
||
|
|
unit_part( const AS& x ) {
|
||
|
|
typename Algebraic_structure_traits< AS >::Unit_part unit_part;
|
||
|
|
return unit_part( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< AS >::Is_square::result_type
|
||
|
|
is_square( const AS& x,
|
||
|
|
typename Algebraic_structure_traits< AS >::Is_square::second_argument_type y )
|
||
|
|
{
|
||
|
|
typename Algebraic_structure_traits< AS >::Is_square is_square;
|
||
|
|
return is_square( x, y );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< AS >::Is_square::result_type
|
||
|
|
is_square( const AS& x){
|
||
|
|
typename Algebraic_structure_traits< AS >::Is_square is_square;
|
||
|
|
return is_square( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< AS >::Square::result_type
|
||
|
|
square( const AS& x ) {
|
||
|
|
typename Algebraic_structure_traits< AS >::Square square;
|
||
|
|
return square( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< AS >::Inverse::result_type
|
||
|
|
inverse( const AS& x ) {
|
||
|
|
typename Algebraic_structure_traits< AS >::Inverse inverse;
|
||
|
|
return inverse( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits<AS>::Is_one::result_type
|
||
|
|
is_one( const AS& x ) {
|
||
|
|
typename Algebraic_structure_traits< AS >::Is_one is_one;
|
||
|
|
return is_one( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< AS >::Sqrt::result_type
|
||
|
|
sqrt( const AS& x ) {
|
||
|
|
typename Algebraic_structure_traits< AS >::Sqrt sqrt;
|
||
|
|
return sqrt( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
// AST-Functor adapting functions BINARY
|
||
|
|
|
||
|
|
template< class A, class B >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< typename Coercion_traits<A,B>::Type>
|
||
|
|
::Integral_division::result_type
|
||
|
|
integral_division( const A& x, const B& y ) {
|
||
|
|
typedef typename Coercion_traits<A,B>::Type Type;
|
||
|
|
typename Algebraic_structure_traits< Type >::Integral_division
|
||
|
|
integral_division;
|
||
|
|
return integral_division( x, y );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class A, class B >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< typename Coercion_traits<A,B>::Type>
|
||
|
|
::Divides::result_type
|
||
|
|
divides( const A& x, const B& y ) {
|
||
|
|
typedef typename Coercion_traits<A,B>::Type Type;
|
||
|
|
typename Algebraic_structure_traits< Type >::Divides divides;
|
||
|
|
return divides( x, y );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class Type >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits<Type>::Divides::result_type
|
||
|
|
divides( const Type& x, const Type& y, Type& q ) {
|
||
|
|
typename Algebraic_structure_traits< Type >::Divides divides;
|
||
|
|
return divides( x, y, q);
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class A, class B >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< typename Coercion_traits<A,B>::Type >
|
||
|
|
::Gcd::result_type
|
||
|
|
gcd( const A& x, const B& y ) {
|
||
|
|
typedef typename Coercion_traits<A,B>::Type Type;
|
||
|
|
typename Algebraic_structure_traits< Type >::Gcd gcd;
|
||
|
|
return gcd( x, y );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template< class A, class B >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< typename Coercion_traits<A,B>::Type >
|
||
|
|
::Mod::result_type
|
||
|
|
mod( const A& x, const B& y ) {
|
||
|
|
typedef typename Coercion_traits<A,B>::Type Type;
|
||
|
|
typename Algebraic_structure_traits<Type >::Mod mod;
|
||
|
|
return mod( x, y );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class A, class B >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< typename Coercion_traits<A,B>::Type>::Div::result_type
|
||
|
|
div( const A& x, const B& y ) {
|
||
|
|
typedef typename Coercion_traits<A,B>::Type Type;
|
||
|
|
typename Algebraic_structure_traits<Type >::Div div;
|
||
|
|
return div( x, y );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class A, class B >
|
||
|
|
inline
|
||
|
|
void
|
||
|
|
div_mod(
|
||
|
|
const A& x,
|
||
|
|
const B& y,
|
||
|
|
typename Coercion_traits<A,B>::Type& q,
|
||
|
|
typename Coercion_traits<A,B>::Type& r ) {
|
||
|
|
typedef typename Coercion_traits<A,B>::Type Type;
|
||
|
|
typename Algebraic_structure_traits< Type >::Div_mod div_mod;
|
||
|
|
div_mod( x, y, q, r );
|
||
|
|
}
|
||
|
|
|
||
|
|
// others
|
||
|
|
template< class AS >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< AS >::Kth_root::result_type
|
||
|
|
kth_root( int k, const AS& x ) {
|
||
|
|
typename Algebraic_structure_traits< AS >::Kth_root
|
||
|
|
kth_root;
|
||
|
|
return kth_root( k, x );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template< class Input_iterator >
|
||
|
|
inline
|
||
|
|
typename Algebraic_structure_traits< typename std::iterator_traits<Input_iterator>::value_type >
|
||
|
|
::Root_of::result_type
|
||
|
|
root_of( int k, Input_iterator begin, Input_iterator end ) {
|
||
|
|
typedef typename std::iterator_traits<Input_iterator>::value_type AS;
|
||
|
|
return typename Algebraic_structure_traits<AS>::Root_of()( k, begin, end );
|
||
|
|
}
|
||
|
|
|
||
|
|
// AST- and RET-functor adapting function
|
||
|
|
template< class Number_type >
|
||
|
|
inline
|
||
|
|
// select a Is_zero functor
|
||
|
|
typename boost::mpl::if_c<
|
||
|
|
::boost::is_same< typename Algebraic_structure_traits< Number_type >::Is_zero,
|
||
|
|
Null_functor >::value ,
|
||
|
|
typename Real_embeddable_traits< Number_type >::Is_zero,
|
||
|
|
typename Algebraic_structure_traits< Number_type >::Is_zero
|
||
|
|
>::type::result_type
|
||
|
|
is_zero( const Number_type& x ) {
|
||
|
|
// We take the Algebraic_structure_traits<>::Is_zero functor by default. If it
|
||
|
|
// is not available, we take the Real_embeddable_traits functor
|
||
|
|
typename ::boost::mpl::if_c<
|
||
|
|
::boost::is_same<
|
||
|
|
typename Algebraic_structure_traits< Number_type >::Is_zero,
|
||
|
|
Null_functor >::value ,
|
||
|
|
typename Real_embeddable_traits< Number_type >::Is_zero,
|
||
|
|
typename Algebraic_structure_traits< Number_type >::Is_zero >::type
|
||
|
|
is_zero;
|
||
|
|
return is_zero( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class A, class B>
|
||
|
|
inline
|
||
|
|
typename Real_embeddable_traits< typename Coercion_traits<A,B>::Type >
|
||
|
|
::Compare::result_type
|
||
|
|
compare(const A& a, const B& b)
|
||
|
|
{
|
||
|
|
typedef typename Coercion_traits<A,B>::Type Type;
|
||
|
|
typename Real_embeddable_traits<Type>::Compare compare;
|
||
|
|
return compare (a,b);
|
||
|
|
// return (a < b) ? SMALLER : (b < a) ? LARGER : EQUAL;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
// RET-Functor adapting functions
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
//Real_embeddable
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Abs::result_type
|
||
|
|
abs( const Real_embeddable& x ) {
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Abs abs;
|
||
|
|
return abs( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
//::Sign
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Sgn::result_type
|
||
|
|
sign( const Real_embeddable& x ) {
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Sgn sgn;
|
||
|
|
return sgn( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
//bool
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Is_finite::result_type
|
||
|
|
is_finite( const Real_embeddable& x ) {
|
||
|
|
return typename Real_embeddable_traits< Real_embeddable >::Is_finite()( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Is_positive::result_type
|
||
|
|
is_positive( const Real_embeddable& x ) {
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Is_positive
|
||
|
|
is_positive;
|
||
|
|
return is_positive( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Is_negative::result_type
|
||
|
|
is_negative( const Real_embeddable& x ) {
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Is_negative
|
||
|
|
is_negative;
|
||
|
|
return is_negative( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Compare::result_type
|
||
|
|
//Comparison_result
|
||
|
|
compare( const Real_embeddable& x, const Real_embeddable& y ) {
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::Compare compare;
|
||
|
|
return compare( x, y );
|
||
|
|
}
|
||
|
|
*/
|
||
|
|
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::To_double::result_type
|
||
|
|
//double
|
||
|
|
to_double( const Real_embeddable& x ) {
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::To_double to_double;
|
||
|
|
return to_double( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template< class Real_embeddable >
|
||
|
|
inline
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::To_interval::result_type
|
||
|
|
//std::pair< double, double >
|
||
|
|
to_interval( const Real_embeddable& x) {
|
||
|
|
typename Real_embeddable_traits< Real_embeddable >::To_interval
|
||
|
|
to_interval;
|
||
|
|
return to_interval( x );
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename NT>
|
||
|
|
NT approximate_sqrt(const NT& nt, CGAL::Field_tag)
|
||
|
|
{
|
||
|
|
return NT(sqrt(CGAL::to_double(nt)));
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename NT>
|
||
|
|
NT approximate_sqrt(const NT& nt, CGAL::Field_with_sqrt_tag)
|
||
|
|
{
|
||
|
|
return sqrt(nt);
|
||
|
|
}
|
||
|
|
|
||
|
|
template <typename NT>
|
||
|
|
NT approximate_sqrt(const NT& nt)
|
||
|
|
{
|
||
|
|
typedef CGAL::Algebraic_structure_traits<NT> AST;
|
||
|
|
typedef typename AST::Algebraic_category Algebraic_category;
|
||
|
|
return approximate_sqrt(nt, Algebraic_category());
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL_NTS_END_NAMESPACE
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_NUMBER_UTILS_H
|