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cgal/Packages/Interval_arithmetic/include/CGAL/Interval_arithmetic.h

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// ============================================================================
//
// Copyright (c) 1998,1999,2000,2001,2002 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------------
//
// release :
// release_date :
//
// file : include/CGAL/Interval_arithmetic.h
// revision : $Revision$
// revision_date : $Date$
// package : Interval Arithmetic
// author(s) : Sylvain Pion
// coordinator : INRIA Sophia-Antipolis (<Mariette.Yvinec@sophia.inria.fr>)
//
// ============================================================================
#ifndef CGAL_INTERVAL_ARITHMETIC_H
#define CGAL_INTERVAL_ARITHMETIC_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*,...).
#include <CGAL/basic.h>
#include <iostream>
#include <CGAL/FPU.h>
CGAL_BEGIN_NAMESPACE
namespace CGALi {
struct Unsafe_comparison {}; // Exception class.
const double Huge_val = HUGE_VAL; // Workaround for G++ 2.95 on Linux.
}
template <bool Protected = true>
class Interval_nt
{
typedef Interval_nt<Protected> IA;
typedef std::pair<double, double> Pair;
public:
typedef Tag_false Has_gcd;
typedef Tag_true Has_division;
typedef Tag_true Has_sqrt;
typedef CGALi::Unsafe_comparison unsafe_comparison;
static unsigned number_of_failures; // Number of filter failures.
Interval_nt() {}
Interval_nt(double d)
: inf_sup(d, d) {}
Interval_nt(double i, double s)
: inf_sup(i, s)
{
// VC++ should use instead : (i<=s) || !is_valid(i) || !is_valid(s)
// Or should I use is_valid() ? or is_valid_or_nan() ?
CGAL_assertion_msg(!(i>s),
" Variable used before being initialized (or CGAL bug)");
}
// This copy ctor, normally equivalent to the one created by the compiler,
// appears to fix a code generation problem with GCC 3.0.4...
// (see test/IA/gcc_3.0.bug.C).
Interval_nt(const Interval_nt & i)
: inf_sup(i.pair()) {}
Interval_nt(const Pair & p)
: inf_sup(p) {}
// The advantage of non-member operators is that (double * IA) just works...
// But is it really useful and wishable in CGAL ?
// Probably YES => TODO.
IA operator+ (const IA &d) const
{
Protect_FPU_rounding<Protected> P;
return IA(-CGAL_IA_SUB(-inf(), d.inf()), CGAL_IA_ADD(sup(), d.sup()));
}
IA operator- (const IA &d) const
{
Protect_FPU_rounding<Protected> P;
return IA(-CGAL_IA_SUB(d.sup(), inf()), CGAL_IA_SUB(sup(), d.inf()));
}
IA operator* (const IA &) const;
IA operator/ (const IA &) const;
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; }
static void overlap_action() // throw (unsafe_comparison)
{
number_of_failures++;
throw unsafe_comparison();
}
// TODO : Maybe I should suppress these : they are useless and risky.
// The (join, union, ||) operator.
IA operator|| (const IA & d) const
{
return IA(std::min(inf(), d.inf()), std::max(sup(), d.sup()));
}
// The (meet, intersection, &&) operator. Valid if intervals overlap.
IA operator&& (const IA & d) const
{
return IA(std::max(inf(), d.inf()), std::min(sup(), d.sup()));
}
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());
}
double inf() const { return inf_sup.first; }
double sup() const { return inf_sup.second; }
const std::pair<double,double>& pair() const
{
return inf_sup;
}
static IA largest()
{
// G++ 2.95 on Linux has problems with HUGE_VAL in template context.
// (it's a macro defined by "__extension__ ..." and it gets lost.
return IA(-CGALi::Huge_val, CGALi::Huge_val);
}
static IA smallest()
{
return IA(-CGAL_IA_MIN_DOUBLE, CGAL_IA_MIN_DOUBLE);
}
private:
Pair inf_sup;
};
template <bool Protected>
unsigned Interval_nt<Protected>::number_of_failures;
template <bool Protected>
inline
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;
a.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator>(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{ return b < a; }
template <bool Protected>
inline
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;
a.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator>=(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{ return b <= a; }
template <bool Protected>
inline
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;
a.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator!=(const Interval_nt<Protected> &a, const Interval_nt<Protected> &b)
{ return ! (a == b); }
// Mixed operators.
template <bool Protected>
inline
bool
operator<(int a, const Interval_nt<Protected> &b)
{
if (a < b.inf()) return true;
if (a >= b.sup()) return false;
b.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator>(int a, const Interval_nt<Protected> &b)
{ return b < a; }
template <bool Protected>
inline
bool
operator<=(int a, const Interval_nt<Protected> &b)
{
if (a <= b.inf()) return true;
if (a > b.sup()) return false;
b.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator>=(int a, const Interval_nt<Protected> &b)
{ return b <= a; }
template <bool Protected>
inline
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;
b.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator!=(int a, const Interval_nt<Protected> &b)
{ return ! (a == b); }
template <bool Protected>
inline
bool
operator<(const Interval_nt<Protected> &a, int b)
{
if (a.sup() < b) return true;
if (a.inf() >= b) return false;
a.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator>(const Interval_nt<Protected> &a, int b)
{ return b < a; }
template <bool Protected>
inline
bool
operator<=(const Interval_nt<Protected> &a, int b)
{
if (a.sup() <= b) return true;
if (a.inf() > b) return false;
a.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator>=(const Interval_nt<Protected> &a, int b)
{ return b <= a; }
template <bool Protected>
inline
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;
a.overlap_action();
return false;
}
template <bool Protected>
inline
bool
operator!=(const Interval_nt<Protected> &a, int b)
{ return ! (a == b); }
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
const std::pair<double,double> &
to_interval (const Interval_nt<Protected> & d)
{
return d.pair();
}
template <bool Protected>
inline
bool
is_valid (const Interval_nt<Protected> & d)
{
#if defined _MSC_VER || defined __sgi || defined __BORLANDC__
return CGAL::is_valid(d.inf()) &&
CGAL::is_valid(d.sup()) &&
d.inf() <= d.sup();
#else
// The 2 first is_valid() are implicitely done by the 3rd test ;-)
return d.inf() <= d.sup();
#endif
}
template <bool Protected>
inline
bool
is_finite (const Interval_nt<Protected> & d)
{
return CGAL::is_finite(d.inf()) && CGAL::is_finite(d.sup());
}
template <bool Protected>
inline
io_Operator
io_tag (const Interval_nt<Protected> &)
{
return io_Operator();
}
template <bool Protected>
std::ostream & operator<< (std::ostream &os, const Interval_nt<Protected> & I )
{
return os << "[" << I.inf() << ";" << I.sup() << "]";
}
template <bool Protected>
std::istream & operator>> (std::istream &is, Interval_nt<Protected> & I)
{
double d;
is >> d;
I = d;
return is;
}
typedef Interval_nt<false> Interval_nt_advanced; // for back-compatibility
template <bool Protected>
#ifndef CGAL_IA_NO_INLINE
inline
#endif
Interval_nt<Protected>
Interval_nt<Protected>::operator* (const Interval_nt<Protected> & d) const
{
Protect_FPU_rounding<Protected> P;
if (inf()>=0.0) // e>=0
{
// d>=0 [inf()*d.inf(); sup()*d.sup()]
// d<=0 [sup()*d.inf(); inf()*d.sup()]
// d~=0 [sup()*d.inf(); sup()*d.sup()]
double a = inf(), b = sup();
if (d.inf() < 0.0)
{
a=b;
if (d.sup() < 0.0)
b=inf();
}
return IA(-CGAL_IA_MUL(a, -d.inf()), CGAL_IA_MUL(b, d.sup()));
}
else if (sup()<=0.0) // e<=0
{
// d>=0 [inf()*d.sup(); sup()*d.inf()]
// d<=0 [sup()*d.sup(); inf()*d.inf()]
// d~=0 [inf()*d.sup(); inf()*d.inf()]
double a = sup(), b = inf();
if (d.inf() < 0.0)
{
a=b;
if (d.sup() < 0.0)
b=sup();
}
return IA(-CGAL_IA_MUL(b, -d.sup()), CGAL_IA_MUL(a, d.inf()));
}
else // 0 \in [inf();sup()]
{
if (d.inf()>=0.0) // d>=0
return IA(-CGAL_IA_MUL(-inf(), d.sup()), CGAL_IA_MUL(sup(), d.sup()));
if (d.sup()<=0.0) // d<=0
return IA(-CGAL_IA_MUL(sup(), -d.inf()), CGAL_IA_MUL(inf(), d.inf()));
// 0 \in d
double tmp1 = CGAL_IA_MUL(-inf(), d.sup());
double tmp2 = CGAL_IA_MUL(sup(), -d.inf());
double tmp3 = CGAL_IA_MUL(inf(), d.inf());
double tmp4 = CGAL_IA_MUL(sup(), d.sup());
return IA(-std::max(tmp1,tmp2), std::max(tmp3,tmp4));
};
}
template <bool Protected>
#ifndef CGAL_IA_NO_INLINE
inline
#endif
Interval_nt<Protected>
Interval_nt<Protected>::operator/ (const Interval_nt<Protected> & d) const
{
Protect_FPU_rounding<Protected> P;
if (d.inf()>0.0) // d>0
{
// e>=0 [inf()/d.sup(); sup()/d.inf()]
// e<=0 [inf()/d.inf(); sup()/d.sup()]
// e~=0 [inf()/d.inf(); sup()/d.inf()]
double a = d.sup(), b = d.inf();
if (inf()<0.0)
{
a=b;
if (sup()<0.0)
b=d.sup();
};
return IA(-CGAL_IA_DIV(-inf(), a), CGAL_IA_DIV(sup(), b));
}
else if (d.sup()<0.0) // d<0
{
// e>=0 [sup()/d.sup(); inf()/d.inf()]
// e<=0 [sup()/d.inf(); inf()/d.sup()]
// e~=0 [sup()/d.sup(); inf()/d.sup()]
double a = d.sup(), b = d.inf();
if (inf()<0.0)
{
b=a;
if (sup()<0.0)
a=d.inf();
};
return IA(-CGAL_IA_DIV(-sup(), a), CGAL_IA_DIV(inf(), b));
}
else // d~0
return IA::largest();
// We could do slightly better -> [0;HUGE_VAL] when d.sup()==0,
// but is this worth ?
}
template <bool Protected>
inline
Interval_nt<Protected>
sqrt (const Interval_nt<Protected> & d)
{
Protect_FPU_rounding<Protected> 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()));
}
#ifndef CGAL_CFG_MATCHING_BUG_2
template <bool Protected>
inline
Interval_nt<Protected>
min (const Interval_nt<Protected> & d, const Interval_nt<Protected> & e)
{
return Interval_nt<Protected>(std::min(d.inf(), e.inf()),
std::min(d.sup(), e.sup()));
}
template <bool Protected>
inline
Interval_nt<Protected>
max (const Interval_nt<Protected> & d, const Interval_nt<Protected> & e)
{
return Interval_nt<Protected>(std::max(d.inf(), e.inf()),
std::max(d.sup(), e.sup()));
}
#else
inline
Interval_nt<false>
min (const Interval_nt<false> & d, const Interval_nt<false> & e)
{
return Interval_nt<false>(min(d.inf(), e.inf()),min(d.sup(), e.sup()));
}
inline
Interval_nt<false>
max (const Interval_nt<false> & d, const Interval_nt<false> & e)
{
return Interval_nt<false>(max(d.inf(), e.inf()),max(d.sup(), e.sup()));
}
inline
Interval_nt<true>
min (const Interval_nt<true> & d, const Interval_nt<true> & e)
{
return Interval_nt<true>(min(d.inf(), e.inf()),min(d.sup(), e.sup()));
}
inline
Interval_nt<true>
max (const Interval_nt<true> & d, const Interval_nt<true> & e)
{
return Interval_nt<true>(max(d.inf(), e.inf()),max(d.sup(), e.sup()));
}
#endif // CGAL_CFG_MATCHING_BUG_2
#ifndef CGAL_CFG_MATCHING_BUG_2
template <bool Protected>
inline
Interval_nt<Protected>
square (const Interval_nt<Protected> & d)
{
Protect_FPU_rounding<Protected> 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
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;
Interval_nt<Protected>::overlap_action();
return ZERO;
}
template <bool Protected>
inline
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;
Interval_nt<Protected>::overlap_action();
return EQUAL;
}
#else // CGAL_CFG_MATCHING_BUG_2
// For crappy "compilers", we have to define complete overloaded functions.
// First we overload for true.
inline
Interval_nt<true>
square (const Interval_nt<true> & d)
{
Protect_FPU_rounding<true> P;
if (d.inf()>=0.0)
return Interval_nt<true>(-CGAL_IA_MUL(d.inf(), -d.inf()),
CGAL_IA_MUL(d.sup(), d.sup()));
if (d.sup()<=0.0)
return Interval_nt<true>(-CGAL_IA_MUL(d.sup(), -d.sup()),
CGAL_IA_MUL(d.inf(), d.inf()));
return Interval_nt<true>(0.0, CGAL_IA_SQUARE(std::max(-d.inf(), d.sup())));
}
inline
Interval_nt<true>
abs (const Interval_nt<true> & d)
{
if (d.inf() >= 0.0) return d;
if (d.sup() <= 0.0) return -d;
return Interval_nt<true>(0.0, std::max(-d.inf(), d.sup()));
}
inline
Sign
sign (const Interval_nt<true> & d)
{
if (d.inf() > 0.0) return POSITIVE;
if (d.sup() < 0.0) return NEGATIVE;
if (d.inf() == d.sup()) return ZERO;
Interval_nt<true>::overlap_action();
return ZERO;
}
inline
Comparison_result
compare (const Interval_nt<true> & d, const Interval_nt<true> & 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;
Interval_nt<true>::overlap_action();
return EQUAL;
}
// Then we overload for false.
inline
Interval_nt<false>
square (const Interval_nt<false> & d)
{
Protect_FPU_rounding<false> P;
if (d.inf()>=0.0)
return Interval_nt<false>(-CGAL_IA_MUL(d.inf(), -d.inf()),
CGAL_IA_MUL(d.sup(), d.sup()));
if (d.sup()<=0.0)
return Interval_nt<false>(-CGAL_IA_MUL(d.sup(), -d.sup()),
CGAL_IA_MUL(d.inf(), d.inf()));
return Interval_nt<false>(0.0, CGAL_IA_SQUARE(std::max(-d.inf(), d.sup())));
}
inline
Interval_nt<false>
abs (const Interval_nt<false> & d)
{
if (d.inf() >= 0.0) return d;
if (d.sup() <= 0.0) return -d;
return Interval_nt<false>(0.0, std::max(-d.inf(), d.sup()));
}
inline
Sign
sign (const Interval_nt<false> & d)
{
if (d.inf() > 0.0) return POSITIVE;
if (d.sup() < 0.0) return NEGATIVE;
if (d.inf() == d.sup()) return ZERO;
Interval_nt<false>::overlap_action();
return ZERO;
}
inline
Comparison_result
compare (const Interval_nt<false> & d, const Interval_nt<false> & 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;
Interval_nt<false>::overlap_action();
return EQUAL;
}
#endif // CGAL_CFG_MATCHING_BUG_2
inline
std::pair<double,double>
to_interval (const long & l)
{
#ifndef __BORLANDC__ // The stupid Borland compiler generates warnings...
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
#endif
return std::pair<double,double>(l,l);
}
CGAL_END_NAMESPACE
#endif // CGAL_INTERVAL_ARITHMETIC_H
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