/usr/include/CGAL/Interval_nt.h is in libcgal-dev 4.2-5ubuntu1.
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1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 | // Copyright (c) 1998-2005,2007
// 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) : Sylvain Pion, Michael Hemmer
#ifndef CGAL_INTERVAL_NT_H
#define CGAL_INTERVAL_NT_H
// This file contains the description of the following classes:
// - Interval_nt<false> It's a number type that needs the FPU rounding mode
// to be set to +inf. It is also typedef'd to
// Interval_nt_advanced for backward compatibility.
// - Interval_nt<true> Same but it does the rounding mode itself so you
// don't have to worry about it. But it's slower.
//
// Note: When rounding is towards +infinity, to make an operation rounded
// towards -infinity, it's enough to take the opposite of some of the operand,
// and the opposite of the result (see operator+, operator*,...).
// TODO :
// - test whether stopping constant propagation only in functions taking
// double as arguments, improves performance.
#include <utility> // for std::pair
#include <CGAL/number_type_config.h>
#include <CGAL/number_utils.h>
#include <CGAL/utils_classes.h>
#include <CGAL/number_utils.h>
#include <CGAL/Uncertain.h>
#include <CGAL/Interval_traits.h>
#include <CGAL/double.h>
#include <CGAL/FPU.h>
#include <CGAL/IO/io.h>
#include <iostream>
namespace CGAL {
template <bool Protected = true>
class Interval_nt
{
typedef Interval_nt<Protected> IA;
typedef std::pair<double, double> Pair;
public:
typedef double value_type;
typedef Uncertain_conversion_exception unsafe_comparison;
typedef Checked_protect_FPU_rounding<Protected> Internal_protector;
typedef Protect_FPU_rounding<!Protected> Protector;
Interval_nt()
#ifndef CGAL_NO_ASSERTIONS
: _inf(1), _sup(0)
// to early and deterministically detect use of uninitialized
#endif
{}
Interval_nt(int i)
: _inf(i), _sup(i) {}
Interval_nt(unsigned i)
: _inf(i), _sup(i) {}
Interval_nt(long long i)
: _inf((double)i), _sup((double)i)
{
// gcc ignores -frounding-math when converting integers to floats.
#ifdef __GNUC__
long long safe = 1LL << 52; // Use numeric_limits?
bool exact = ((long long)_inf == i) || (i <= safe && i >= -safe);
if (!(__builtin_constant_p(exact) && exact))
#endif
*this += smallest();
}
Interval_nt(unsigned long long i)
: _inf((double)i), _sup((double)i)
{
#ifdef __GNUC__
unsigned long long safe = 1ULL << 52; // Use numeric_limits?
bool exact = ((unsigned long long)_inf == i) || (i <= safe);
if (!(__builtin_constant_p(exact) && exact))
#endif
*this += smallest();
}
Interval_nt(long i)
{
*this = (sizeof(int)==sizeof(long)) ?
Interval_nt((int)i) :
Interval_nt((long long)i);
}
Interval_nt(unsigned long i)
{
*this = (sizeof(int)==sizeof(long)) ?
Interval_nt((unsigned)i) :
Interval_nt((unsigned long long)i);
}
Interval_nt(double d)
: _inf(d), _sup(d) { CGAL_assertion(is_finite(d)); }
// The Intel compiler on Linux is aggressive with constant propagation and
// it seems there is no flag to stop it, so disable this check for it.
#if !defined(CGAL_DISABLE_ROUNDING_MATH_CHECK) && \
defined(__INTEL_COMPILER) && defined(__linux)
# define CGAL_DISABLE_ROUNDING_MATH_CHECK
#endif
Interval_nt(double i, double s)
: _inf(i), _sup(s)
{
// Previously it was:
// CGAL_assertion_msg(!(i>s);
// But MSVC++ 2012 optimizes the test "!(i>s)" to "i<=s", even with
// /fp:strict. If 'i' or 's' is a NaN, that makes a difference.
CGAL_assertion_msg( (!is_valid(i)) || (!is_valid(s)) || (!(i>s)),
" Variable used before being initialized (or CGAL bug)");
#ifndef CGAL_DISABLE_ROUNDING_MATH_CHECK
CGAL_assertion_code((void) tester;) // Necessary to trigger a runtime test of rounding modes.
#endif
}
Interval_nt(const Pair & p)
: _inf(p.first), _sup(p.second) {}
IA operator-() const { return IA (-sup(), -inf()); }
IA & operator+= (const IA &d) { return *this = *this + d; }
IA & operator-= (const IA &d) { return *this = *this - d; }
IA & operator*= (const IA &d) { return *this = *this * d; }
IA & operator/= (const IA &d) { return *this = *this / d; }
bool is_point() const
{
return sup() == inf();
}
bool is_same (const IA & d) const
{
return inf() == d.inf() && sup() == d.sup();
}
bool do_overlap (const IA & d) const
{
return !(d.inf() > sup() || d.sup() < inf());
}
const double & inf() const { return _inf; }
const double & sup() const { return _sup; }
std::pair<double, double> pair() const
{
return std::pair<double, double>(inf(), sup());
}
static IA largest()
{
return IA(-internal::infinity, internal::infinity);
}
static IA smallest()
{
return IA(-CGAL_IA_MIN_DOUBLE, CGAL_IA_MIN_DOUBLE);
}
#if 0 // def CGAL_HISTOGRAM_PROFILER // not yet ready
~Interval_nt()
{
CGAL_HISTOGRAM_PROFILER("[Interval_nt relative precision in log2 scale]",
(unsigned) ( ::log(relative_precision(*this))) / ::log(2.0) ) );
}
#endif
private:
// Pair inf_sup;
double _inf, _sup;
struct Test_runtime_rounding_modes {
Test_runtime_rounding_modes()
{
// We test whether GCC's -frounding-math option has been forgotten.
// The macros CGAL_IA_MUL and CGAL_IA_DIV stop constant propagation only
// on the second argument, so if -fno-rounding-math, the compiler optimizes
// the 2 negations and we get wrong rounding.
typename Interval_nt<>::Internal_protector P;
CGAL_assertion_msg(-CGAL_IA_MUL(-1.1, 10.1) != CGAL_IA_MUL(1.1, 10.1),
"Wrong rounding: did you forget the -frounding-math option if you use GCC (or -fp-model strict for Intel)?");
CGAL_assertion_msg(-CGAL_IA_DIV(-1., 10) != CGAL_IA_DIV(1., 10),
"Wrong rounding: did you forget the -frounding-math option if you use GCC (or -fp-model strict for Intel)?");
}
};
#ifndef CGAL_DISABLE_ROUNDING_MATH_CHECK
static Test_runtime_rounding_modes tester;
#endif
};
#ifndef CGAL_DISABLE_ROUNDING_MATH_CHECK
template <bool Protected>
typename Interval_nt<Protected>::Test_runtime_rounding_modes
Interval_nt<Protected>::tester;
#endif
template <bool Protected>
inline
Uncertain<bool>
operator<(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{
if (a.sup() < b.inf()) return true;
if (a.inf() >= b.sup()) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{ return b < a; }
template <bool Protected>
inline
Uncertain<bool>
operator<=(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{
if (a.sup() <= b.inf()) return true;
if (a.inf() > b.sup()) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>=(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{ return b <= a; }
template <bool Protected>
inline
Uncertain<bool>
operator==(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{
if (b.inf() > a.sup() || b.sup() < a.inf()) return false;
if (b.inf() == a.sup() && b.sup() == a.inf()) return true;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator!=(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{ return ! (a == b); }
// Mixed operators with int.
template <bool Protected>
inline
Uncertain<bool>
operator<(int a, const Interval_nt<Protected> &b)
{
if (a < b.inf()) return true;
if (a >= b.sup()) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>(int a, const Interval_nt<Protected> &b)
{ return b < a; }
template <bool Protected>
inline
Uncertain<bool>
operator<=(int a, const Interval_nt<Protected> &b)
{
if (a <= b.inf()) return true;
if (a > b.sup()) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>=(int a, const Interval_nt<Protected> &b)
{ return b <= a; }
template <bool Protected>
inline
Uncertain<bool>
operator==(int a, const Interval_nt<Protected> &b)
{
if (b.inf() > a || b.sup() < a) return false;
if (b.inf() == a && b.sup() == a) return true;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator!=(int a, const Interval_nt<Protected> &b)
{ return ! (a == b); }
template <bool Protected>
inline
Uncertain<bool>
operator<(const Interval_nt<Protected> &a, int b)
{
if (a.sup() < b) return true;
if (a.inf() >= b) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>(const Interval_nt<Protected> &a, int b)
{ return b < a; }
template <bool Protected>
inline
Uncertain<bool>
operator<=(const Interval_nt<Protected> &a, int b)
{
if (a.sup() <= b) return true;
if (a.inf() > b) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>=(const Interval_nt<Protected> &a, int b)
{ return b <= a; }
template <bool Protected>
inline
Uncertain<bool>
operator==(const Interval_nt<Protected> &a, int b)
{
if (b > a.sup() || b < a.inf()) return false;
if (b == a.sup() && b == a.inf()) return true;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator!=(const Interval_nt<Protected> &a, int b)
{ return ! (a == b); }
// Mixed operators with double.
template <bool Protected>
inline
Uncertain<bool>
operator<(double a, const Interval_nt<Protected> &b)
{
if (a < b.inf()) return true;
if (a >= b.sup()) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>(double a, const Interval_nt<Protected> &b)
{ return b < a; }
template <bool Protected>
inline
Uncertain<bool>
operator<=(double a, const Interval_nt<Protected> &b)
{
if (a <= b.inf()) return true;
if (a > b.sup()) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>=(double a, const Interval_nt<Protected> &b)
{ return b <= a; }
template <bool Protected>
inline
Uncertain<bool>
operator==(double a, const Interval_nt<Protected> &b)
{
if (b.inf() > a || b.sup() < a) return false;
if (b.inf() == a && b.sup() == a) return true;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator!=(double a, const Interval_nt<Protected> &b)
{ return ! (a == b); }
template <bool Protected>
inline
Uncertain<bool>
operator<(const Interval_nt<Protected> &a, double b)
{
if (a.sup() < b) return true;
if (a.inf() >= b) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>(const Interval_nt<Protected> &a, double b)
{ return b < a; }
template <bool Protected>
inline
Uncertain<bool>
operator<=(const Interval_nt<Protected> &a, double b)
{
if (a.sup() <= b) return true;
if (a.inf() > b) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator>=(const Interval_nt<Protected> &a, double b)
{ return b <= a; }
template <bool Protected>
inline
Uncertain<bool>
operator==(const Interval_nt<Protected> &a, double b)
{
if (b > a.sup() || b < a.inf()) return false;
if (b == a.sup() && b == a.inf()) return true;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
operator!=(const Interval_nt<Protected> &a, double b)
{ return ! (a == b); }
// Non-documented
// Returns true if the interval is a unique representable double.
template <bool Protected>
inline
bool
fit_in_double (const Interval_nt<Protected> & d, double &r)
{
bool b = d.is_point();
if (b)
r = d.inf();
return b;
}
// Non-documented
template <bool Protected>
inline
bool
is_singleton (const Interval_nt<Protected> & d)
{
return d.is_point();
}
// Non-documented
template <bool Protected>
inline
double
magnitude (const Interval_nt<Protected> & d)
{
return (std::max)(CGAL::abs(d.inf()), CGAL::abs(d.sup()));
}
// Non-documented
template <bool Protected>
inline
double
width (const Interval_nt<Protected> & d)
{
return d.sup() - d.inf();
}
// Non-documented
template <bool Protected>
inline
double
radius (const Interval_nt<Protected> & d)
{
return width(d)/2; // This could be improved to avoid overflow.
}
// Non-documented
// This is the relative precision of to_double() (the center of the interval),
// hence we use radius() instead of width().
template <bool Protected>
inline
bool
has_smaller_relative_precision(const Interval_nt<Protected> & d, double prec)
{
return magnitude(d) == 0 || radius(d) < prec * magnitude(d);
}
// Non-documented
template <bool Protected>
double
relative_precision(const Interval_nt<Protected> & d)
{
if (magnitude(d) == 0.0)
return 0.0;
return radius(d) / magnitude(d);
}
template< bool Protected >
class Is_valid< Interval_nt<Protected> >
: public std::unary_function< Interval_nt<Protected>, bool > {
public :
bool operator()( const Interval_nt<Protected>& x ) const {
return is_valid(x.inf()) &&
is_valid(x.sup()) &&
x.inf() <= x.sup();
}
};
template <bool Protected>
std::ostream & operator<< (std::ostream &os, const Interval_nt<Protected> & I )
{
return os << "[" << I.inf() << ";" << I.sup() << "]";
}
#define CGAL_SWALLOW(IS,CHAR) \
{ \
char c; \
do c = is.get(); while (isspace(c)); \
if (c != CHAR) { \
is.setstate(std::ios_base::failbit); \
} \
} \
template <bool Protected>
std::istream & operator>> (std::istream &is, Interval_nt<Protected> & I)
{
char c;
do c = is.get(); while (isspace(c));
is.putback(c);
if(c == '['){ // read original output from operator <<
double inf,sup;
CGAL_SWALLOW(is, '[');// read the "["
is >> iformat(inf);
CGAL_SWALLOW(is, ';');// read the ";"
is >> iformat(sup);
CGAL_SWALLOW(is, ']');// read the "]"
I = Interval_nt<Protected>(inf,sup);
}else{ //read double (backward compatibility)
double d;
is >> d;
I = d;
}
return is;
}
#undef CGAL_SWALLOW
typedef Interval_nt<false> Interval_nt_advanced; // for backward-compatibility
template <bool Protected>
inline
Interval_nt<Protected>
operator+ (const Interval_nt<Protected> &a, const Interval_nt<Protected> & b)
{
typename Interval_nt<Protected>::Internal_protector P;
return Interval_nt<Protected> (-CGAL_IA_SUB(-a.inf(), b.inf()),
CGAL_IA_ADD(a.sup(), b.sup()));
}
template <bool Protected>
inline
Interval_nt<Protected>
operator+ (double a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)+b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator+ (const Interval_nt<Protected> & a, double b)
{
return a+Interval_nt<Protected>(b);
}
template <bool Protected>
inline
Interval_nt<Protected>
operator+ (int a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)+b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator+ (const Interval_nt<Protected> & a, int b)
{
return a+Interval_nt<Protected>(b);
}
template< bool Protected >
inline
Interval_nt<Protected>
operator+( const Interval_nt<Protected>& a ) {
return a;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator- (const Interval_nt<Protected> &a, const Interval_nt<Protected> & b)
{
typename Interval_nt<Protected>::Internal_protector P;
return Interval_nt<Protected>(-CGAL_IA_SUB(b.sup(), a.inf()),
CGAL_IA_SUB(a.sup(), b.inf()));
}
template <bool Protected>
inline
Interval_nt<Protected>
operator- (double a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)-b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator- (const Interval_nt<Protected> & a, double b)
{
return a-Interval_nt<Protected>(b);
}
template <bool Protected>
inline
Interval_nt<Protected>
operator- (int a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)-b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator- (const Interval_nt<Protected> & a, int b)
{
return a-Interval_nt<Protected>(b);
}
template <bool Protected>
inline
Interval_nt<Protected>
operator* (const Interval_nt<Protected> &a, const Interval_nt<Protected> & b)
{
typedef Interval_nt<Protected> IA;
typename Interval_nt<Protected>::Internal_protector P;
if (a.inf() >= 0.0) // a>=0
{
// b>=0 [a.inf()*b.inf(); a.sup()*b.sup()]
// b<=0 [a.sup()*b.inf(); a.inf()*b.sup()]
// b~=0 [a.sup()*b.inf(); a.sup()*b.sup()]
double aa = a.inf(), bb = a.sup();
if (b.inf() < 0.0)
{
aa = bb;
if (b.sup() < 0.0)
bb = a.inf();
}
return IA(-CGAL_IA_MUL(aa, -b.inf()), CGAL_IA_MUL(bb, b.sup()));
}
else if (a.sup()<=0.0) // a<=0
{
// b>=0 [a.inf()*b.sup(); a.sup()*b.inf()]
// b<=0 [a.sup()*b.sup(); a.inf()*b.inf()]
// b~=0 [a.inf()*b.sup(); a.inf()*b.inf()]
double aa = a.sup(), bb = a.inf();
if (b.inf() < 0.0)
{
aa=bb;
if (b.sup() < 0.0)
bb=a.sup();
}
return IA(-CGAL_IA_MUL(bb, -b.sup()), CGAL_IA_MUL(aa, b.inf()));
}
else // 0 \in a
{
if (b.inf()>=0.0) // b>=0
return IA(-CGAL_IA_MUL(a.inf(), -b.sup()),
CGAL_IA_MUL(a.sup(), b.sup()));
if (b.sup()<=0.0) // b<=0
return IA(-CGAL_IA_MUL(a.sup(), -b.inf()),
CGAL_IA_MUL(a.inf(), b.inf()));
// 0 \in b
double tmp1 = CGAL_IA_MUL(a.inf(), -b.sup());
double tmp2 = CGAL_IA_MUL(a.sup(), -b.inf());
double tmp3 = CGAL_IA_MUL(a.inf(), b.inf());
double tmp4 = CGAL_IA_MUL(a.sup(), b.sup());
return IA(-(std::max)(tmp1,tmp2), (std::max)(tmp3,tmp4));
}
}
template <bool Protected>
inline
Interval_nt<Protected>
operator* (double a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)*b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator* (const Interval_nt<Protected> & a, double b)
{
return a*Interval_nt<Protected>(b);
}
template <bool Protected>
inline
Interval_nt<Protected>
operator* (int a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)*b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator* (const Interval_nt<Protected> & a, int b)
{
return a*Interval_nt<Protected>(b);
}
template <bool Protected>
inline
Interval_nt<Protected>
operator/ (const Interval_nt<Protected> &a, const Interval_nt<Protected> & b)
{
typedef Interval_nt<Protected> IA;
typename Interval_nt<Protected>::Internal_protector P;
if (b.inf() > 0.0) // b>0
{
// e>=0 [a.inf()/b.sup(); a.sup()/b.inf()]
// e<=0 [a.inf()/b.inf(); a.sup()/b.sup()]
// e~=0 [a.inf()/b.inf(); a.sup()/b.inf()]
double aa = b.sup(), bb = b.inf();
if (a.inf() < 0.0)
{
aa = bb;
if (a.sup() < 0.0)
bb = b.sup();
}
return IA(-CGAL_IA_DIV(a.inf(), -aa), CGAL_IA_DIV(a.sup(), bb));
}
else if (b.sup()<0.0) // b<0
{
// e>=0 [a.sup()/b.sup(); a.inf()/b.inf()]
// e<=0 [a.sup()/b.inf(); a.inf()/b.sup()]
// e~=0 [a.sup()/b.sup(); a.inf()/b.sup()]
double aa = b.sup(), bb = b.inf();
if (a.inf() < 0.0)
{
bb = aa;
if (a.sup() < 0.0)
aa = b.inf();
}
return IA(-CGAL_IA_DIV(a.sup(), -aa), CGAL_IA_DIV(a.inf(), bb));
}
else // b~0
return IA::largest();
// We could do slightly better -> [0;infinity] when b.sup()==0,
// but is this worth ?
}
template <bool Protected>
inline
Interval_nt<Protected>
operator/ (double a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)/b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator/ (const Interval_nt<Protected> & a, double b)
{
return a/Interval_nt<Protected>(b);
}
template <bool Protected>
inline
Interval_nt<Protected>
operator/ (int a, const Interval_nt<Protected> & b)
{
return Interval_nt<Protected>(a)/b;
}
template <bool Protected>
inline
Interval_nt<Protected>
operator/ (const Interval_nt<Protected> & a, int b)
{
return a/Interval_nt<Protected>(b);
}
// TODO: What about these two guys? Where do they belong to?
template <bool Protected>
struct Min <Interval_nt<Protected> >
: public std::binary_function<Interval_nt<Protected>,
Interval_nt<Protected>,
Interval_nt<Protected> >
{
Interval_nt<Protected> operator()( const Interval_nt<Protected>& d,
const Interval_nt<Protected>& e) const
{
return Interval_nt<Protected>(
(std::min)(d.inf(), e.inf()),
(std::min)(d.sup(), e.sup()));
}
};
template <bool Protected>
struct Max <Interval_nt<Protected> >
: public std::binary_function<Interval_nt<Protected>,
Interval_nt<Protected>,
Interval_nt<Protected> >
{
Interval_nt<Protected> operator()( const Interval_nt<Protected>& d,
const Interval_nt<Protected>& e) const
{
return Interval_nt<Protected>(
(std::max)(d.inf(), e.inf()),
(std::max)(d.sup(), e.sup()));
}
};
template<bool Protected> inline
Interval_nt<Protected> min BOOST_PREVENT_MACRO_SUBSTITUTION(
const Interval_nt<Protected> & x,
const Interval_nt<Protected> & y){
return CGAL::Min<Interval_nt<Protected> > ()(x,y);
}
template<bool Protected> inline
Interval_nt<Protected> max BOOST_PREVENT_MACRO_SUBSTITUTION(
const Interval_nt<Protected> & x,
const Interval_nt<Protected> & y){
return CGAL::Max<Interval_nt<Protected> > ()(x,y);
}
// TODO : document, when we are OK with the interface.
// - should it allow other number types for the exponent ?
template < bool b >
Interval_nt<b>
ldexp(const Interval_nt<b> &i, int e)
{
double scale = std::ldexp(1.0, e);
Interval_nt<b> scale_interval (
CGAL_NTS is_finite(scale) ? scale : CGAL_IA_MAX_DOUBLE,
scale == 0 ? CGAL_IA_MIN_DOUBLE : scale);
return i * scale_interval;
}
// We also specialize some corresponding functors returning Uncertain<>.
// TODO: To which concept do these functors belong? Can we remove them??
template < bool b >
struct Equal_to < Interval_nt<b>, Interval_nt<b> >
: public std::binary_function< Interval_nt<b>, Interval_nt<b>, Uncertain<bool> >
{
Uncertain<bool> operator()( const Interval_nt<b>& x,
const Interval_nt<b>& y) const
{ return x == y; }
};
template < bool b >
struct Not_equal_to < Interval_nt<b>, Interval_nt<b> >
: public std::binary_function< Interval_nt<b>, Interval_nt<b>, Uncertain<bool> >
{
Uncertain<bool> operator()( const Interval_nt<b>& x,
const Interval_nt<b>& y) const
{ return x != y; }
};
template < bool b >
struct Greater < Interval_nt<b>, Interval_nt<b> >
: public std::binary_function< Interval_nt<b>, Interval_nt<b>, Uncertain<bool> >
{
Uncertain<bool> operator()( const Interval_nt<b>& x,
const Interval_nt<b>& y) const
{ return x > y; }
};
template < bool b >
struct Less < Interval_nt<b>, Interval_nt<b> >
: public std::binary_function< Interval_nt<b>, Interval_nt<b>, Uncertain<bool> >
{
Uncertain<bool> operator()( const Interval_nt<b>& x,
const Interval_nt<b>& y) const
{ return x < y; }
};
template < bool b >
struct Greater_equal < Interval_nt<b>, Interval_nt<b> >
: public std::binary_function< Interval_nt<b>, Interval_nt<b>, Uncertain<bool> >
{
Uncertain<bool> operator()( const Interval_nt<b>& x,
const Interval_nt<b>& y) const
{ return x >= y; }
};
template < bool b >
struct Less_equal < Interval_nt<b>, Interval_nt<b> >
: public std::binary_function< Interval_nt<b>, Interval_nt<b>, Uncertain<bool> >
{
Uncertain<bool> operator()( const Interval_nt<b>& x,
const Interval_nt<b>& y) const
{ return x <= y; }
};
// As in MP_float.h, the namespace INTERN_INTERVAL_NT contains (now) global
// functions like square or sqrt which would have collided with the new
// global functions from AST/RET
//
// TODO: IMHO, a better solution would be to put the INTERN_MP_FLOAT-functions
// into the MP_Float-class... But there is surely a reason why this is not
// the case..?
namespace INTERN_INTERVAL_NT {
template <bool Protected>
inline
double
to_double (const Interval_nt<Protected> & d)
{
return (d.sup() + d.inf()) * 0.5;
// This may overflow...
}
template <bool Protected>
inline
std::pair<double, double>
to_interval (const Interval_nt<Protected> & d)
{
return d.pair();
}
template <bool Protected>
inline
Interval_nt<Protected>
sqrt (const Interval_nt<Protected> & d)
{
typename Interval_nt<Protected>::Internal_protector P; // not optimal here.
// sqrt([+a,+b]) => [sqrt(+a);sqrt(+b)]
// sqrt([-a,+b]) => [0;sqrt(+b)] => assumes roundoff error.
// sqrt([-a,-b]) => [0;sqrt(-b)] => assumes user bug (unspecified result).
FPU_set_cw(CGAL_FE_DOWNWARD);
double i = (d.inf() > 0.0) ? CGAL_IA_SQRT(d.inf()) : 0.0;
FPU_set_cw(CGAL_FE_UPWARD);
return Interval_nt<Protected>(i, CGAL_IA_SQRT(d.sup()));
}
template <bool Protected>
inline
Interval_nt<Protected>
square (const Interval_nt<Protected> & d)
{
typename Interval_nt<Protected>::Internal_protector P;
if (d.inf()>=0.0)
return Interval_nt<Protected>(-CGAL_IA_MUL(d.inf(), -d.inf()),
CGAL_IA_MUL(d.sup(), d.sup()));
if (d.sup()<=0.0)
return Interval_nt<Protected>(-CGAL_IA_MUL(d.sup(), -d.sup()),
CGAL_IA_MUL(d.inf(), d.inf()));
return Interval_nt<Protected>(0.0, CGAL_IA_SQUARE((std::max)(-d.inf(),
d.sup())));
}
template <bool Protected>
inline
Interval_nt<Protected>
abs (const Interval_nt<Protected> & d)
{
if (d.inf() >= 0.0) return d;
if (d.sup() <= 0.0) return -d;
return Interval_nt<Protected>(0.0, (std::max)(-d.inf(), d.sup()));
}
template <bool Protected>
inline
Uncertain<Sign>
sign (const Interval_nt<Protected> & d)
{
if (d.inf() > 0.0) return POSITIVE;
if (d.sup() < 0.0) return NEGATIVE;
if (d.inf() == d.sup()) return ZERO;
return Uncertain<Sign>::indeterminate();
}
template <bool Protected>
inline
Uncertain<Comparison_result>
compare (const Interval_nt<Protected> & d, const Interval_nt<Protected> & e)
{
if (d.inf() > e.sup()) return LARGER;
if (e.inf() > d.sup()) return SMALLER;
if (e.inf() == d.sup() && d.inf() == e.sup()) return EQUAL;
return Uncertain<Comparison_result>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
is_zero (const Interval_nt<Protected> & d)
{
if (d.inf() > 0.0) return false;
if (d.sup() < 0.0) return false;
if (d.inf() == d.sup()) return true;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
is_one (const Interval_nt<Protected> & d)
{
if (d.inf() > 1) return false;
if (d.sup() < 1) return false;
if (d.inf() == d.sup()) return true;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
is_positive (const Interval_nt<Protected> & d)
{
if (d.inf() > 0.0) return true;
if (d.sup() <= 0.0) return false;
return Uncertain<bool>::indeterminate();
}
template <bool Protected>
inline
Uncertain<bool>
is_negative (const Interval_nt<Protected> & d)
{
if (d.inf() >= 0.0) return false;
if (d.sup() < 0.0) return true;
return Uncertain<bool>::indeterminate();
}
// TODO: Whats this for? Why is this in this file??
inline
std::pair<double, double>
to_interval (const long & l)
{
if (sizeof(double) > sizeof(long)) {
// On 64bit platforms, a long doesn't fit exactly in a double.
// Well, a perfect fix would be to use std::numeric_limits<>, but...
Protect_FPU_rounding<true> P(CGAL_FE_TONEAREST);
Interval_nt<false> approx ((double) l);
FPU_set_cw(CGAL_FE_UPWARD);
approx += Interval_nt<false>::smallest();
return approx.pair();
}
else
return std::pair<double,double>(l,l);
}
} // namespace INTERN_INTERVAL_NT
template< bool B > class Real_embeddable_traits< Interval_nt<B> >
: public INTERN_RET::Real_embeddable_traits_base< Interval_nt<B> , CGAL::Tag_true> {
public:
typedef Interval_nt<B> Type;
typedef Uncertain<CGAL::Sign> Sign;
typedef Uncertain<bool> Boolean;
typedef Uncertain<CGAL::Comparison_result> Comparison_result;
class Abs
: public std::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::abs( x );
}
};
class Sgn
: public std::unary_function< Type, Uncertain< ::CGAL::Sign > > {
public:
Uncertain< ::CGAL::Sign > operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::sign( x );
}
};
class Is_positive
: public std::unary_function< Type, Uncertain<bool> > {
public:
Uncertain<bool> operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::is_positive( x );
}
};
class Is_negative
: public std::unary_function< Type, Uncertain<bool> > {
public:
Uncertain<bool> operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::is_negative( x );
}
};
class Compare
: public std::binary_function< Type, Type, Comparison_result > {
public:
Comparison_result operator()( const Type& x, const Type& y ) const {
return INTERN_INTERVAL_NT::compare( x, y );
}
CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT( Type,
Comparison_result )
};
class To_double
: public std::unary_function< Type, double > {
public:
double operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::to_double( x );
}
};
class To_interval
: public std::unary_function< Type, std::pair< double, double > > {
public:
std::pair<double, double> operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::to_interval( x );
}
};
class Is_finite
: public std::unary_function< Type, Boolean > {
public :
Boolean operator()( const Type& x ) const {
return CGAL_NTS is_finite( x.inf() ) && CGAL_NTS is_finite( x.sup() );
}
};
};
// Algebraic structure traits
template< bool B >
class Algebraic_structure_traits< Interval_nt<B> >
: public Algebraic_structure_traits_base< Interval_nt<B>,
Field_with_sqrt_tag > {
public:
typedef Interval_nt<B> Type;
typedef Tag_false Is_exact;
typedef Tag_true Is_numerical_sensitive;
typedef Uncertain<bool> Boolean;
class Is_zero
: public std::unary_function< Type, Boolean > {
public:
Boolean operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::is_zero( x );
}
};
class Is_one
: public std::unary_function< Type, Boolean > {
public:
Boolean operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::is_one( x );
}
};
class Square
: public std::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::square( x );
}
};
class Sqrt
: public std::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return INTERN_INTERVAL_NT::sqrt( x );
}
};
struct Is_square
:public std::binary_function<Interval_nt<B>,Interval_nt<B>&,Boolean >
{
Boolean operator()(const Interval_nt<B>& x) const {
return INTERN_INTERVAL_NT::is_positive( x );
}
Boolean operator()(
const Interval_nt<B>& x,
Interval_nt<B> & result) const {
Boolean is_positive = INTERN_INTERVAL_NT::is_positive( x );
if ( is_positive.inf() == true ){
typename Algebraic_structure_traits<Interval_nt<B> >::Sqrt sqrt;
result = sqrt(x);
}else{
typename Real_embeddable_traits<Interval_nt<B> >::Abs abs;
typename Algebraic_structure_traits<Interval_nt<B> >::Sqrt sqrt;
result = sqrt(abs(x));
}
return is_positive;
}
};
class Divides
: public std::binary_function< Type, Type, Boolean > {
public:
Boolean operator()( const Type& x, const Type&) const {
return ! Is_zero()(x);
}
// second operator computing q
Boolean operator()( const Type& x, const Type& y, Type& q) const {
if (! Is_zero()(x) )
q = y/x ;
return Boolean(true);
}
};
};
// COERCION_TRAITS BEGIN
template < class A, class B , int > struct Coercion_traits_for_level;
template < class A, class B, class C> struct Coercion_traits_interval_nt;
template<class A ,bool P >
struct Coercion_traits_for_level<A,Interval_nt<P>,CTL_INTERVAL>
:public Coercion_traits_interval_nt<A,Interval_nt<P>,
typename Real_embeddable_traits<A>::Is_real_embeddable>{};
template<class A , bool P>
struct Coercion_traits_for_level<Interval_nt<P>,A,CTL_INTERVAL>
:public Coercion_traits_for_level<A,Interval_nt<P>, CTL_INTERVAL>{};
template<class A , bool P >
struct Coercion_traits_interval_nt<A, Interval_nt<P>,Tag_false>
:public Coercion_traits_for_level<A,Interval_nt<P>,0>{};
template<class A , bool P>
struct Coercion_traits_interval_nt<A, Interval_nt<P>, Tag_true>{
typedef Tag_true Are_explicit_interoperable;
typedef Tag_false Are_implicit_interoperable;
typedef Interval_nt<P> Type;
struct Cast {
typedef Interval_nt<P> result_type;
Interval_nt<P> inline operator()(const Interval_nt<P>& x ) const {
return x;
}
Interval_nt<P> inline operator()(const A& x ) const {
return typename Real_embeddable_traits<A>::To_interval()(x);
}
};
};
// COERCION_TRAITS END
template< bool B >
class Interval_traits< Interval_nt<B> >
: public internal::Interval_traits_base< Interval_nt<B> > {
public:
typedef Interval_traits<Interval_nt<B> > Self;
typedef Interval_nt<B> Interval;
typedef double Bound;
typedef CGAL::Tag_false With_empty_interval;
typedef CGAL::Tag_true Is_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.inf();
}
};
struct Upper :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return a.sup();
}
};
struct Width :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return width(a);
}
};
struct Median :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return (Lower()(a)+Upper()(a))/2.0;
}
};
struct Norm :public std::unary_function<Interval,Bound>{
Bound operator()( const Interval& a ) const {
return magnitude(a);
}
};
struct Singleton :public std::unary_function<Interval,bool>{
bool operator()( const Interval& a ) const {
return Lower()(a) == Upper()(a);
}
};
struct Zero_in :public std::unary_function<Interval,bool>{
bool operator()( const Interval& a ) const {
return Lower()(a) <= 0 && 0 <= Upper()(a);
}
};
struct In :public std::binary_function<Bound,Interval,bool>{
bool operator()( Bound x, const Interval& a ) const {
return Lower()(a) <= x && x <= Upper()(a);
}
};
struct Equal :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return a.is_same(b);
}
};
struct Overlap :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return a.do_overlap(b);
}
};
struct Subset :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return Lower()(b) <= Lower()(a) && Upper()(a) <= Upper()(b) ;
}
};
struct Proper_subset :public std::binary_function<Interval,Interval,bool>{
bool operator()( const Interval& a, const Interval& b ) const {
return Subset()(a,b) && ! Equal()(a,b);
}
};
struct Hull :public std::binary_function<Interval,Interval,Interval>{
Interval operator()( const Interval& a, const Interval& b ) const {
BOOST_USING_STD_MAX();
BOOST_USING_STD_MIN();
return Interval(
std::make_pair(
min BOOST_PREVENT_MACRO_SUBSTITUTION (Lower()(a),b.inf()),
max BOOST_PREVENT_MACRO_SUBSTITUTION (Upper()(a),b.sup())));
}
};
// struct Empty is Null_functor
struct Intersection :public std::binary_function<Interval,Interval,Interval>{
Interval operator()( const Interval& a, const Interval& b ) const {
BOOST_USING_STD_MAX();
BOOST_USING_STD_MIN();
Bound l(max BOOST_PREVENT_MACRO_SUBSTITUTION (Lower()(a),Lower()(b)));
Bound u(min BOOST_PREVENT_MACRO_SUBSTITUTION (Upper()(a),Upper()(b)));
if(u < l ) throw Exception_intersection_is_empty();
return Construct()(l,u);
}
};
};
} //namespace CGAL
namespace Eigen {
template<class> struct NumTraits;
template<bool b> struct NumTraits<CGAL::Interval_nt<b> >
{
typedef CGAL::Interval_nt<b> Real;
typedef CGAL::Interval_nt<b> NonInteger;
typedef CGAL::Interval_nt<b> Nested;
static inline Real epsilon() { return 0; }
// Costs could depend on b.
enum {
IsInteger = 0,
IsSigned = 1,
IsComplex = 0,
RequireInitialization = 0,
ReadCost = 2,
AddCost = 2,
MulCost = 10
};
};
}
#endif // CGAL_INTERVAL_NT_H
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