/usr/include/CGAL/leda_bigfloat_interval.h is in libcgal-dev 4.2-5ubuntu1.
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// 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) : Michael Hemmer
// TODO: add sign to RET
#ifndef CGAL_LEDA_BIGFLOAT_INTERVAL_H
#define CGAL_LEDA_BIGFLOAT_INTERVAL_H
#include <CGAL/basic.h>
#ifndef CGAL_USE_LEDA
#warning This header file needs LEDA installed in order to work properly.
#else // CGAL_USE_LEDA
#include <CGAL/LEDA_basic.h>
#if CGAL_LEDA_VERSION < 500
#include <LEDA/bigfloat.h>
#else
#include <LEDA/numbers/bigfloat.h>
#endif
#include <boost/numeric/interval.hpp>
#include <CGAL/leda_integer.h>
#include <CGAL/leda_rational.h>
#include <CGAL/leda_real.h>
#include <CGAL/leda_bigfloat.h>
#include <CGAL/Interval_traits.h>
#include <CGAL/Bigfloat_interval_traits.h>
#include <CGAL/ipower.h>
namespace CGAL {
namespace internal {
struct Rounding_for_leda_bigfloat {
private: typedef leda::bigfloat T;
public:
Rounding_for_leda_bigfloat(){};
~Rounding_for_leda_bigfloat(){};
T conv_down(const T& a){
return round(a,leda::bigfloat::get_precision(),leda::TO_N_INF);
};
T conv_up (const T& a){
return round(a,leda::bigfloat::get_precision(),leda::TO_P_INF);
};
// mathematical operations
T add_down(const T& a, const T& b){
return add(a,b,leda::bigfloat::get_precision(),leda::TO_N_INF);
};
T add_up (const T& a, const T& b){
return add(a,b,leda::bigfloat::get_precision(),leda::TO_P_INF);
};
T sub_down(const T& a, const T& b){
return sub(a, b, leda::bigfloat::get_precision(),leda::TO_N_INF);
};
T sub_up (const T& a, const T& b){
return sub(a, b, leda::bigfloat::get_precision(),leda::TO_P_INF);
};
T mul_down(const T& a, const T& b){
return mul(a, b, leda::bigfloat::get_precision(),leda::TO_N_INF);
};
T mul_up (const T& a, const T& b){
return mul(a, b, leda::bigfloat::get_precision(),leda::TO_P_INF);
};
T div_down(const T& a, const T& b){
return div(a, b, leda::bigfloat::get_precision(),leda::TO_N_INF);
};
T div_up (const T& a, const T& b){
return div(a, b, leda::bigfloat::get_precision(),leda::TO_P_INF);
};
T sqrt_down(const T& a){
return sqrt(a, leda::bigfloat::get_precision(),leda::TO_N_INF);
};
T sqrt_up (const T& a){
return sqrt(a, leda::bigfloat::get_precision(),leda::TO_P_INF);
};
T median(const T& a, const T& b){ return (a+b)/2; };
T int_down(const T& a) { return T(floor(a));};
T int_up (const T& a) { return T(ceil(a)); };
};
class Checking_for_leda_bigfloat {
typedef leda::bigfloat T;
public:
static T pos_inf() {
T b = T(5) / T(0);
CGAL_assertion(leda::ispInf(b));
return b;
}
static T neg_inf() {
T b = T(-5) / T(0);
CGAL_assertion(leda::isnInf(b));
return b;
}
static T nan() {
T b = T(0)*pos_inf();
CGAL_assertion(leda::isNaN(b));
return b;
}
static bool is_nan(const T& b) {
return leda::isNaN(b);
}
static T empty_lower() {
return T(1);
}
static T empty_upper() {
return T(0);
}
static bool is_empty(const T& a, const T& b) {
//return a==T(1) && b == T(0);
return a > b;
}
};
} // namespace internal
} //namespace CGAL
namespace boost {
namespace numeric {
inline
std::ostream& operator <<
(std::ostream& os, const boost::numeric::interval<leda::bigfloat>& x)
{
os << "["
<< x.lower().get_significant() << "*2^" << x.lower().get_exponent()
<< " , "
<< x.upper().get_significant() << "*2^" << x.upper().get_exponent()
<< "]";
return os;
}
}//namespace numeric
}//namespace boost
namespace CGAL {
typedef boost::numeric::interval
< leda::bigfloat,
boost::numeric::interval_lib::policies
< internal::Rounding_for_leda_bigfloat,
internal::Checking_for_leda_bigfloat > >
leda_bigfloat_interval;
template <> class Algebraic_structure_traits< leda_bigfloat_interval >
: public Algebraic_structure_traits_base< leda_bigfloat_interval,
Field_with_sqrt_tag > {
public:
typedef Tag_false Is_exact;
typedef Tag_true Is_numerical_sensitive;
class Sqrt
: public std::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return ::boost::numeric::sqrt(x);
}
};
};
template <> class Real_embeddable_traits< leda_bigfloat_interval >
: public INTERN_RET::Real_embeddable_traits_base< leda_bigfloat_interval , CGAL::Tag_true > {
public:
class Abs
: public std::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return ::boost::numeric::abs(x);
}
};
class To_double
: public std::unary_function< Type, double > {
public:
double operator()( const Type& x ) const {
return CGAL::to_double(::boost::numeric::median(x));
}
};
class To_interval
: public std::unary_function< Type, std::pair< double, double > > {
public:
std::pair<double, double> operator()( const Type& x ) const {
std::pair<double, double> lower_I(CGAL::to_interval(x.lower()));
std::pair<double, double> upper_I(CGAL::to_interval(x.upper()));
return std::pair< double, double >(
CGAL::min(lower_I.first , upper_I.first ),
CGAL::max(lower_I.second, upper_I.second));
}
};
};
// Coercion traits:
CGAL_DEFINE_COERCION_TRAITS_FROM_TO(short ,leda_bigfloat_interval)
CGAL_DEFINE_COERCION_TRAITS_FROM_TO(int ,leda_bigfloat_interval)
CGAL_DEFINE_COERCION_TRAITS_FROM_TO(long ,leda_bigfloat_interval)
CGAL_DEFINE_COERCION_TRAITS_FROM_TO(float ,leda_bigfloat_interval)
CGAL_DEFINE_COERCION_TRAITS_FROM_TO(double ,leda_bigfloat_interval)
CGAL_DEFINE_COERCION_TRAITS_FROM_TO(::leda::bigfloat ,leda_bigfloat_interval)
template <>
struct Coercion_traits< leda_bigfloat_interval , ::leda::integer >{
typedef Tag_true Are_explicit_interoperable;
typedef Tag_false Are_implicit_interoperable;
typedef leda_bigfloat_interval Type;
struct Cast{
typedef Type result_type;
Type operator()(const leda_bigfloat_interval& x) const { return x;}
Type operator()(const ::leda::integer& x) const {
leda::bigfloat tmp(x);
leda_bigfloat_interval result(
round(tmp,leda::bigfloat::get_precision(),leda::TO_N_INF),
round(tmp,leda::bigfloat::get_precision(),leda::TO_P_INF));
CGAL_postcondition( result.lower() <= x );
CGAL_postcondition( result.upper() >= x );
return result;
}
};
};
template <>
struct Coercion_traits< leda_bigfloat_interval , ::leda::rational >{
typedef Tag_true Are_explicit_interoperable;
typedef Tag_false Are_implicit_interoperable;
typedef leda_bigfloat_interval Type;
struct Cast{
typedef Type result_type;
Type operator()(const leda_bigfloat_interval& x) const { return x;}
Type operator()(const ::leda::rational& x) const {
long prec = ::leda::bigfloat::get_precision();
leda_bigfloat_interval result (
leda_bigfloat::from_rational(x,prec,leda::TO_N_INF),
leda_bigfloat::from_rational(x,prec,leda::TO_P_INF));
CGAL_postcondition( result.lower() <= x );
CGAL_postcondition( result.upper() >= x );
return result;
}
};
};
template <>
struct Coercion_traits< leda_bigfloat_interval , ::leda::real >{
typedef Tag_true Are_explicit_interoperable;
typedef Tag_false Are_implicit_interoperable;
typedef leda_bigfloat_interval Type;
struct Cast{
typedef Type result_type;
Type operator()(const leda_bigfloat_interval& x) const { return x;}
Type operator()(const ::leda::real& x) const {
long current_prec = ::leda::bigfloat::get_precision();
x.guarantee_relative_error(current_prec);
leda_bigfloat_interval
result(x.get_lower_bound(), x.get_upper_bound());
CGAL_postcondition( result.lower() <= x );
CGAL_postcondition( result.upper() >= x );
return result;
}
};
};
template <> struct Coercion_traits< ::leda::integer, leda_bigfloat_interval >
:public Coercion_traits< leda_bigfloat_interval , ::leda::integer >{};
template <> struct Coercion_traits< ::leda::rational, leda_bigfloat_interval >
:public Coercion_traits< leda_bigfloat_interval , ::leda::rational >{};
template <> struct Coercion_traits< ::leda::real, leda_bigfloat_interval >
:public Coercion_traits< leda_bigfloat_interval , ::leda::real>{};
template<>
class Interval_traits<leda_bigfloat_interval>
:public internal::Interval_traits_base<leda_bigfloat_interval>
{
public:
typedef Interval_traits<leda_bigfloat_interval> Self;
typedef leda_bigfloat_interval Interval;
typedef leda::bigfloat Bound;
typedef CGAL::Tag_true Is_interval;
typedef CGAL::Tag_true With_empty_interval;
struct Construct :public std::binary_function<Bound,Bound,Interval>{
Interval operator()( const Bound& l,const Bound& r) const {
CGAL_precondition( l < r );
return Interval(l,r);
}
};
struct Lower :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return a.lower();
}
};
struct Upper :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return a.upper();
}
};
struct Width :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return ::boost::numeric::width(a);
}
};
struct Median :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return ::boost::numeric::median(a);
}
};
struct Norm :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return ::boost::numeric::norm(a);
}
};
struct Empty :public std::unary_function<Interval,bool>{
bool operator()( const Interval& a ) const {
return ::boost::numeric::empty(a);
}
};
struct Singleton :public std::unary_function<Interval,bool>{
bool operator()( const Interval& a ) const {
return ::boost::numeric::singleton(a);
}
};
struct Zero_in :public std::unary_function<Interval,bool>{
bool operator()( const Interval& a ) const {
return ::boost::numeric::in_zero(a);
}
};
struct In :public std::binary_function<Bound,Interval,bool>{
bool operator()( Bound x, const Interval& a ) const {
return ::boost::numeric::in(x,a);
}
};
struct Equal :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return ::boost::numeric::equal(a,b);
}
};
struct Overlap :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return ::boost::numeric::overlap(a,b);
}
};
struct Subset :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return ::boost::numeric::subset(a,b);
}
};
struct Proper_subset :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return ::boost::numeric::proper_subset(a,b);
}
};
struct Hull :public std::binary_function<Interval,Interval,Interval>{
Interval operator()( const Interval& a, const Interval& b ) const {
return ::boost::numeric::hull(a,b);
}
};
struct Intersection :public std::binary_function<Interval,Interval,Interval>{
Interval operator()( const Interval& a, const Interval& b ) const {
Interval r = ::boost::numeric::intersect(a,b);
return r;
}
};
};
template<>
class Bigfloat_interval_traits<leda_bigfloat_interval>
:public Interval_traits<leda_bigfloat_interval>
{
typedef leda_bigfloat_interval NT;
typedef leda::bigfloat BF;
public:
typedef Bigfloat_interval_traits<leda_bigfloat_interval> Self;
typedef CGAL::Tag_true Is_bigfloat_interval;
// struct Get_significant_bits : public std::unary_function<NT,long>{
// long operator()( NT x) const {
// CGAL_precondition(!Singleton()(x));
// leda::bigfloat lower = x.lower();
// leda::bigfloat upper = x.upper();
// leda::integer lower_m = lower.get_significant();
// leda::integer upper_m = upper.get_significant();
// leda::integer lower_exp = lower.get_exponent();
// leda::integer upper_exp = upper.get_exponent();
// long shift = (upper_exp - lower_exp).to_long();
// if(shift >= 0 ) upper_m = (upper_m << shift);
// else lower_m = (lower_m << -shift);
// //CGAL_postcondition(lower_m.length() == upper_m.length());
// leda::integer err = upper_m - lower_m;
// std::cout <<"LEDA: " << lower_m << " " << err << " " << std::endl;
// return CGAL::abs(lower_m.length()-err.length());
// }
// };
struct Relative_precision: public std::unary_function<NT,long>{
long operator()(const NT& x) const {
CGAL_precondition(!Singleton()(x));
CGAL_precondition(!CGAL::zero_in(x));
leda::bigfloat w = Width()(x);
w = leda::div(w,Lower()(x),Get_precision()(),leda::TO_P_INF);
return -leda::ilog2(w).to_long();
}
};
struct Set_precision : public std::unary_function<long,long> {
long operator()( long prec ) const {
return BF::set_precision(prec);
}
};
struct Get_precision {
// type for the \c AdaptableGenerator concept.
typedef long result_type;
long operator()() const {
return BF::get_precision();
}
};
};
::leda::bigfloat inline relative_error(const leda_bigfloat_interval& x){
if(in_zero(x)){
return CGAL::abs(x).upper();
}else{
return (width(x) / CGAL::abs(x)).upper();
}
}
leda_bigfloat_interval inline ipower(const leda_bigfloat_interval& x, int i ){
return ::boost::numeric::pow(x,i);
}
} //namespace CGAL
#endif // CGAL_USE_LEDA
#endif // CGAL_LEDA_BIGFLOAT_INTERVAL_H
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