/usr/include/CGAL/Quotient.h is in libcgal-dev 4.2-5ubuntu1.
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// 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.
//
// $URL$
// $Id$
//
//
// Author(s) : Stefan Schirra, Sylvain Pion, Michael Hemmer
// The template class Quotient<NT> is based on the LEDA class
// leda_rational written by Stefan Naeher and Christian Uhrig.
// It is basically a templated version with restricted functionality
// of the version of rational in LEDA release 3.3.
// The modification was done by Stefan.Schirra@mpi-sb.mpg.de
// The include is done before the protect macro on purpose, because
// of a cyclic dependency.
#include <CGAL/number_type_basic.h>
#ifndef CGAL_QUOTIENT_H
#define CGAL_QUOTIENT_H
#include <utility>
#include <istream>
#include <CGAL/Interval_nt.h>
#include <CGAL/Kernel/mpl.h>
#include <boost/operators.hpp>
namespace CGAL {
#define CGAL_int(T) typename First_if_different<int, T>::Type
#define CGAL_double(T) typename First_if_different<double, T>::Type
// Simplify the quotient numerator/denominator.
// Currently the default template doesn't do anything.
// This function is not documented as a number type requirement for now.
template < typename NT >
inline void
simplify_quotient(NT &, NT &) {}
// This one should be replaced by some functor or tag.
// Meanwhile, the class is specialized for Gmpz, mpz_class, leda_integer.
template < typename NT >
struct Split_double
{
void operator()(double d, NT &num, NT &den) const
{
num = NT(d);
den = 1;
}
};
template <class NT_>
class Quotient
: boost::ordered_field_operators1< Quotient<NT_>
, boost::ordered_field_operators2< Quotient<NT_>, NT_
, boost::ordered_field_operators2< Quotient<NT_>, CGAL_int(NT_)
, boost::ordered_field_operators2< Quotient<NT_>, CGAL_double(NT_)
> > > >
{
public:
typedef NT_ NT;
Quotient()
: num(0), den(1) {}
Quotient(const NT& n)
: num(n), den(1) {}
Quotient(const CGAL_double(NT) & n)
{ Split_double<NT>()(n, num, den); }
Quotient(const CGAL_int(NT) & n)
: num(n), den(1) {}
template <class T>
explicit Quotient(const T& n) : num(n), den(1) {}
template <class T>
Quotient(const Quotient<T>& n) : num(n.numerator()), den(n.denominator()) {}
Quotient& operator=(const NT & n)
{
num = n;
den = 1;
return *this;
}
Quotient& operator=(const CGAL_double(NT) & n)
{
num = n;
den = 1;
return *this;
}
Quotient& operator=(const CGAL_int(NT) & n)
{
num = n;
den = 1;
return *this;
}
#ifdef CGAL_CFG_NO_CPP0X_RVALUE_REFERENCE
template <class T1, class T2>
Quotient(const T1& n, const T2& d) : num(n), den(d)
{ CGAL_precondition( d != 0 ); }
#else
template <class T1, class T2>
Quotient(T1 && n, T2 && d)
: num(std::forward<T1>(n)), den(std::forward<T2>(d))
{ CGAL_postcondition( den != 0 ); }
Quotient(NT && n)
: num(std::move(n)), den(1) {}
Quotient& operator=(NT && n)
{
num = std::move(n);
den = 1;
return *this;
}
#endif
Quotient<NT>& operator+= (const Quotient<NT>& r);
Quotient<NT>& operator-= (const Quotient<NT>& r);
Quotient<NT>& operator*= (const Quotient<NT>& r);
Quotient<NT>& operator/= (const Quotient<NT>& r);
Quotient<NT>& operator+= (const NT& r);
Quotient<NT>& operator-= (const NT& r);
Quotient<NT>& operator*= (const NT& r);
Quotient<NT>& operator/= (const NT& r);
Quotient<NT>& operator+= (const CGAL_int(NT)& r);
Quotient<NT>& operator-= (const CGAL_int(NT)& r);
Quotient<NT>& operator*= (const CGAL_int(NT)& r);
Quotient<NT>& operator/= (const CGAL_int(NT)& r);
Quotient<NT>& operator+= (const CGAL_double(NT)& r);
Quotient<NT>& operator-= (const CGAL_double(NT)& r);
Quotient<NT>& operator*= (const CGAL_double(NT)& r);
Quotient<NT>& operator/= (const CGAL_double(NT)& r);
Quotient<NT>& normalize();
const NT& numerator() const { return num; }
const NT& denominator() const { return den; }
void swap(Quotient &q)
{
using std::swap;
swap(num, q.num);
swap(den, q.den);
}
#ifdef CGAL_ROOT_OF_2_ENABLE_HISTOGRAM_OF_NUMBER_OF_DIGIT_ON_THE_COMPLEX_CONSTRUCTOR
int tam() const { return std::max(num.tam(), den.tam()); }
#endif
public:
NT num;
NT den;
};
template <class NT>
inline
void swap(Quotient<NT> &p, Quotient<NT> &q)
{
p.swap(q);
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::normalize()
{
if (num == den)
{
num = den = 1;
return *this;
}
if (-num == den)
{
num = -1;
den = 1;
return *this;
}
NT ggt = CGAL_NTS gcd(num, den);
if (ggt != 1 )
{
num = CGAL::integral_division(num, ggt);
den = CGAL::integral_division(den, ggt);
}
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator+= (const Quotient<NT>& r)
{
num = num * r.den + r.num * den;
den *= r.den;
simplify_quotient(num, den);
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator-= (const Quotient<NT>& r)
{
num = num * r.den - r.num * den;
den *= r.den;
simplify_quotient(num, den);
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator*= (const Quotient<NT>& r)
{
num *= r.num;
den *= r.den;
simplify_quotient(num, den);
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator/= (const Quotient<NT>& r)
{
CGAL_precondition( r.num != 0 );
num *= r.den;
den *= r.num;
simplify_quotient(num, den);
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator+= (const NT& r)
{
num += r * den;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator-= (const NT& r)
{
num -= r * den;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator*= (const NT& r)
{
num *= r;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator/= (const NT& r)
{
CGAL_precondition( r != 0 );
den *= r;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator+= (const CGAL_int(NT)& r)
{
num += r * den;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator-= (const CGAL_int(NT)& r)
{
num -= r * den;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator*= (const CGAL_int(NT)& r)
{
num *= r;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator/= (const CGAL_int(NT)& r)
{
CGAL_precondition( r != 0 );
den *= r;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator+= (const CGAL_double(NT)& r)
{
//num += r * den;
NT r_num, r_den;
Split_double<NT>()(r,r_num,r_den);
num = num*r_den + r_num*den;
den *=r_den;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator-= (const CGAL_double(NT)& r)
{
//num -= r * den;
NT r_num, r_den;
Split_double<NT>()(r,r_num,r_den);
num = num*r_den - r_num*den;
den *= r_den;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator*= (const CGAL_double(NT)& r)
{
// num *= r;
NT r_num, r_den;
Split_double<NT>()(r,r_num,r_den);
num *= r_num;
den *= r_den;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Quotient<NT>&
Quotient<NT>::operator/= (const CGAL_double(NT)& r)
{
CGAL_precondition( r != 0 );
NT r_num, r_den;
Split_double<NT>()(r,r_num,r_den);
num *= r_den;
den *= r_num;
return *this;
}
template <class NT>
CGAL_MEDIUM_INLINE
Comparison_result
quotient_cmp(const Quotient<NT>& x, const Quotient<NT>& y)
{
// No assumptions on the sign of den are made
// code assumes that SMALLER == - 1;
CGAL_precondition( SMALLER == static_cast<Comparison_result>(-1) );
int xsign = CGAL_NTS sign(x.num) * CGAL_NTS sign(x.den) ;
int ysign = CGAL_NTS sign(y.num) * CGAL_NTS sign(y.den) ;
if (xsign == 0) return static_cast<Comparison_result>(-ysign);
if (ysign == 0) return static_cast<Comparison_result>(xsign);
// now (x != 0) && (y != 0)
int diff = xsign - ysign;
if (diff == 0)
{
int msign = CGAL_NTS sign(x.den) * CGAL_NTS sign(y.den);
NT leftop = x.num * y.den * msign;
NT rightop = y.num * x.den * msign;
return CGAL_NTS compare(leftop, rightop);
}
else
{
return (xsign < ysign) ? SMALLER : LARGER;
}
}
template <class NT>
std::ostream&
operator<<(std::ostream& s, const Quotient<NT>& r)
{
return s << r.numerator() << '/' << r.denominator();
}
template <class NT>
std::istream&
operator>>(std::istream& in, Quotient<NT>& r)
{
/* format num/den or simply num */
NT num,den=1;
in >> num;
if(!in) return in;
std::istream::sentry s(in); // skip whitespace
if(in.peek()!='/'){
if(!in.good()){
in.clear(std::ios_base::eofbit);
// unlikely to be some other reason?
}
} else {
char c;
in.get(c); // remove the '/'
in >> den;
if(!in) return in;
}
r=Quotient<NT>(num,den);
return in;
}
template< class NT >
inline
Quotient<NT>
operator+( const Quotient<NT>& x ) {
return Quotient<NT>(x);
}
template <class NT>
inline
Quotient<NT>
operator-(const Quotient<NT>& x)
{ return Quotient<NT>(-x.num,x.den); }
template <class NT>
CGAL_MEDIUM_INLINE
NT
quotient_truncation(const Quotient<NT>& r)
{ return (r.num / r.den); }
template <class NT>
CGAL_MEDIUM_INLINE
bool
operator==(const Quotient<NT>& x, const Quotient<NT>& y)
{ return x.num * y.den == x.den * y.num; }
template <class NT>
CGAL_MEDIUM_INLINE
bool
operator==(const Quotient<NT>& x, const NT& y)
{ return x.den * y == x.num; }
template <class NT>
inline
bool
operator==(const Quotient<NT>& x, const CGAL_int(NT) & y)
{ return x.den * y == x.num; }
template <class NT>
inline
bool
operator==(const Quotient<NT>& x, const CGAL_double(NT) & y)
{ return x.den * y == x.num; }
template <class NT>
CGAL_MEDIUM_INLINE
bool
operator<(const Quotient<NT>& x, const Quotient<NT>& y)
{
return quotient_cmp(x,y) == SMALLER;
}
template <class NT>
CGAL_MEDIUM_INLINE
bool
operator<(const Quotient<NT>& x, const NT& y)
{
return quotient_cmp(x,Quotient<NT>(y)) == SMALLER;
}
template <class NT>
CGAL_MEDIUM_INLINE
bool
operator<(const Quotient<NT>& x, const CGAL_int(NT)& y)
{
return quotient_cmp(x,Quotient<NT>(y)) == SMALLER;
}
template <class NT>
CGAL_MEDIUM_INLINE
bool
operator<(const Quotient<NT>& x, const CGAL_double(NT)& y)
{
return quotient_cmp(x,Quotient<NT>(y)) == SMALLER;
}
template <class NT>
inline
bool
operator>(const Quotient<NT>& x, const NT& y)
{ return quotient_cmp(x,Quotient<NT>(y)) == LARGER; }
template <class NT>
inline
bool
operator>(const Quotient<NT>& x, const CGAL_int(NT)& y)
{ return quotient_cmp(x, Quotient<NT>(y)) == LARGER; }
template <class NT>
inline
bool
operator>(const Quotient<NT>& x, const CGAL_double(NT)& y)
{ return quotient_cmp(x, Quotient<NT>(y)) == LARGER; }
template< class NT >
class Is_valid< Quotient<NT> >
: public std::unary_function< Quotient<NT>, bool > {
public :
bool operator()( const Quotient<NT>& x ) const {
return is_valid(x.num) && is_valid(x.den);
}
};
template <class NT>
inline
const NT&
denominator(const Quotient<NT>& q)
{ return q.den ; }
template <class NT>
inline
const NT&
numerator(const Quotient<NT>& q)
{ return q.num ; }
// The min/max are functions are needed since LEDA defines template
// min/max functions which clash with std::min/max with ADL.
template <class NT>
inline
const Quotient<NT>&
min
BOOST_PREVENT_MACRO_SUBSTITUTION
(const Quotient<NT>& p, const Quotient<NT>& q)
{
return (std::min)(p, q);
}
template <class NT>
inline
const Quotient<NT>&
max
BOOST_PREVENT_MACRO_SUBSTITUTION
(const Quotient<NT>& p, const Quotient<NT>& q)
{
return (std::max)(p, q);
}
/*
template <class NT>
NT
gcd(const NT&, const NT&)
{ return NT(1); }
*/
#undef CGAL_double
#undef CGAL_int
//
// Algebraic structure traits
//
namespace INTERN_QUOTIENT {
template< class NT, class Sqrt_functor >
class Sqrt_selector {
public:
class Sqrt
: public std::unary_function< NT, NT > {
public:
NT operator()( const NT& x ) const {
CGAL_precondition(x > 0);
return NT(CGAL_NTS sqrt(x.numerator()*x.denominator()),
x.denominator());
}
};
};
template< class NT >
class Sqrt_selector< NT, Null_functor > {
public:
typedef Null_functor Sqrt;
};
// TODO: Algebraic_category could be Field_with_sqrt_tag, if NT
// is INEXACT (because Sqrt can be inexact) and has a Sqrt-functor.
template<class NT> class Algebraic_structure_traits_quotient_base;
template< class NT > class Algebraic_structure_traits_quotient_base< Quotient<NT> >
: public Algebraic_structure_traits_base< Quotient<NT>, Field_tag > {
public:
typedef Quotient<NT> Type;
typedef typename Algebraic_structure_traits<NT>::Is_exact Is_exact;
typedef Tag_false Is_numerical_sensitive;
class Is_square
: public std::binary_function< Quotient<NT>, Quotient<NT>&, bool > {
public:
bool operator()( Quotient<NT> x, Quotient<NT>& y ) const {
NT x_num, x_den, y_num, y_den;
x.normalize();
x_num = x.numerator();
x_den = x.denominator();
typename Algebraic_structure_traits<NT>::Is_square is_square;
bool num_is_square = is_square(x_num,y_num);
bool den_is_square = is_square(x_den,y_den);
y= Quotient<NT>(y_num,y_den);
return num_is_square && den_is_square;
}
bool operator()(Quotient<NT> x) const {
x.normalize();
typename Algebraic_structure_traits<NT>::Is_square is_square;
return is_square(x.numerator())&&is_square(x.denominator());
}
};
typedef typename boost::mpl::if_c<
!boost::is_same< typename Algebraic_structure_traits<NT>::Sqrt,
Null_functor >::value,
typename INTERN_QUOTIENT::Sqrt_selector< Type,
Is_exact >::Sqrt,
Null_functor
>::type Sqrt;
class Simplify
: public std::unary_function< Type&, void > {
public:
void operator()( Type& x) const {
x.normalize();
}
};
};
template<class NT> class Real_embeddable_traits_quotient_base;
// Real embeddable traits
template < class NT > class Real_embeddable_traits_quotient_base< Quotient<NT> >
: public INTERN_RET::Real_embeddable_traits_base< Quotient<NT>,
typename Real_embeddable_traits< NT >::Is_real_embeddable > {
public:
typedef Quotient<NT> Type;
class Compare
: public std::binary_function< Type, Type,
Comparison_result > {
public:
Comparison_result operator()( const Type& x,
const Type& y ) const {
return quotient_cmp(x, y);
}
};
class To_double
: public std::unary_function< Type, double > {
public:
double operator()( const Type& x ) const {
// Original global function was marked with an TODO!!
if (x.num == 0 )
return 0;
double nd = CGAL_NTS to_double( x.num );
if (x.den == 1 )
return nd;
double dd = CGAL_NTS to_double( x.den );
if ( CGAL_NTS is_finite( x.den ) && CGAL_NTS is_finite( x.num ) )
return nd/dd;
if ( CGAL_NTS abs(x.num) > CGAL_NTS abs(x.den) )
{
NT nt_div = x.num / x.den;
double divd = CGAL_NTS to_double(nt_div);
if ( divd >= std::ldexp(1.0,53) )
{ return divd; }
}
if ( CGAL_NTS abs(x.num) < CGAL_NTS abs(x.den) )
{ return 1.0 / CGAL_NTS to_double( NT(1) / x ); }
return nd/dd;
}
};
class To_interval
: public std::unary_function< Type, std::pair< double, double > > {
public:
std::pair<double, double> operator()( const Type& x ) const {
Interval_nt<> quot =
Interval_nt<>(CGAL_NTS to_interval(x.numerator())) /
Interval_nt<>(CGAL_NTS to_interval(x.denominator()));
return std::make_pair(quot.inf(), quot.sup());
}
};
class Is_finite
: public std::unary_function< Type, bool > {
public:
bool operator()( const Type& x ) const {
return CGAL_NTS is_finite(x.num) && CGAL_NTS is_finite(x.den);
}
};
};
} // namespace INTERN_QUOTIENT
template< class NT > class Algebraic_structure_traits< Quotient<NT> >
: public INTERN_QUOTIENT::Algebraic_structure_traits_quotient_base<
Quotient<NT> >{};
template< class NT > class Real_embeddable_traits< Quotient<NT> >
: public INTERN_QUOTIENT::Real_embeddable_traits_quotient_base<
Quotient<NT> >{};
// self coercion
CGAL_DEFINE_COERCION_TRAITS_FOR_SELF_TEM( Quotient<NT>, class NT)
// from int to Quotient
template <class NT>
struct Coercion_traits<typename First_if_different<int, NT>::Type,Quotient<NT> >
{
typedef Tag_true Are_explicit_interoperable;
typedef Tag_true Are_implicit_interoperable;
typedef Quotient<NT> Type;
struct Cast{
typedef Type result_type;
Type operator()(const Quotient<NT>& x) const { return x;}
Type operator()(
const typename First_if_different<int, NT>::Type& x) const {
return Type(x);}
};
};
template <class NT>
struct Coercion_traits<Quotient<NT>,typename First_if_different<int, NT>::Type>
:public Coercion_traits<typename First_if_different<int, NT>::Type,
Quotient<NT> >{};
// from double to Quotient
template <class NT>
struct Coercion_traits<typename First_if_different<double, NT>::Type,
Quotient<NT> >{
typedef Tag_true Are_explicit_interoperable;
typedef Tag_true Are_implicit_interoperable;
typedef Quotient<NT> Type;
struct Cast{
typedef Type result_type;
Type operator()(const Quotient<NT>& x) const { return x;}
Type operator()(
const typename First_if_different<double, NT>::Type& x) const {
return Type(x);}
};
};
template <class NT>
struct Coercion_traits<Quotient<NT>,
typename First_if_different<double, NT>::Type>
:public Coercion_traits<typename First_if_different<double, NT>::Type,
Quotient<NT> >
{};
// from NT to Quotient
CGAL_DEFINE_COERCION_TRAITS_FROM_TO_TEM ( NT, Quotient<NT>, class NT)
/*! \ingroup NiX_Fraction_traits_spec
* \brief Specialization of Fraction_traits for Quotient<NT>
*/
template <class NT>
class Fraction_traits< Quotient<NT> > {
public:
typedef Quotient<NT> Type;
typedef ::CGAL::Tag_true Is_fraction;
typedef NT Numerator_type;
typedef Numerator_type Denominator_type;
//TODO: check whether Numerator_type has a GCD.
//will use Scalar_factor from Scalar_factor_traits (not implemented yet)
//for more details see EXACUS:NumeriX/include/NiX/Scalar_factor_traits.h
typedef typename Algebraic_structure_traits< Numerator_type >::Gcd Common_factor;
class Decompose {
public:
typedef Type first_argument_type;
typedef Numerator_type& second_argument_type;
typedef Numerator_type& third_argument_type;
void operator () (
const Type& rat,
Numerator_type& num,
Numerator_type& den) {
num = rat.numerator();
den = rat.denominator();
}
};
class Compose {
public:
typedef Numerator_type first_argument_type;
typedef Numerator_type second_argument_type;
typedef Type result_type;
Type operator ()(
const Numerator_type& num ,
const Numerator_type& den ) {
Type result(num, den);
return result;
}
};
};
} //namespace CGAL
namespace Eigen {
template<class> struct NumTraits;
template<class NT> struct NumTraits<CGAL::Quotient<NT> >
{
typedef CGAL::Quotient<NT> Real;
typedef CGAL::Quotient<NT> NonInteger;
typedef CGAL::Quotient<NT> Nested;
static inline Real epsilon() { return NumTraits<NT>::epsilon(); }
enum {
IsInteger = 0,
IsSigned = 1,
IsComplex = 0,
RequireInitialization = NumTraits<NT>::RequireInitialization,
ReadCost = 2*NumTraits<NT>::ReadCost,
AddCost = 150,
MulCost = 100
};
};
}
#endif // CGAL_QUOTIENT_H
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