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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 <CGAL/FPU.h>
#include <CGAL/Interval_base.h>
CGAL_BEGIN_NAMESPACE
template <bool Protected = true>
struct Interval_nt : public Interval_base
{
typedef Tag_false Has_gcd;
typedef Tag_true Has_division;
typedef Tag_true Has_sqrt;
typedef Interval_nt<Protected> IA;
Interval_nt() {}
Interval_nt(const double d)
: Interval_base(d) {}
Interval_nt(const double i, const double s)
: Interval_base(i,s) {}
Interval_nt(const Interval_base & d)
: Interval_base(d) {}
// 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();
}
bool operator< (const IA &d) const
{
if (sup_ < d.inf_) return true;
if (inf_ >= d.sup_) return false;
overlap_action();
return false;
}
bool operator> (const IA &d) const
{
return d < *this;
}
bool operator<= (const IA &d) const
{
if (sup_ <= d.inf_) return true;
if (inf_ > d.sup_) return false;
overlap_action();
return false;
}
bool operator>= (const IA &d) const
{
return d <= *this;
}
bool operator== (const IA &d) const
{
if (d.inf_ > sup_ || d.sup_ < inf_) return false;
if (d.inf_ == sup_ && d.sup_ == inf_) return true;
overlap_action();
return false;
}
bool operator!= (const IA &d) const
{
return !(*this == d);
}
// TODO : Maybe I should suppress these : they are useless.
// 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_));
}
};
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 ?
}
#if 0 // TODO : Do this for the next release, same for is_one()
bool is_zero(const NT &n)
{
if (0 > n.sup_ || 0 < n.inf_) return false;
if (0 == n.sup_ && 0 == n.inf_) return true;
n.overlap_action();
}
#endif
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
namespace NTS {
#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
} // namespace NTS
inline
Interval_base
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_advanced approx ((double) l);
FPU_set_cw(CGAL_FE_UPWARD);
return approx + Interval_nt_advanced(Interval_base::Smallest);
}
else
#endif
return Interval_base(double(l));
}
// needed for making the testsuite pass for Intel7
namespace CGALi {
extern double zero();
}
CGAL_END_NAMESPACE
#endif // CGAL_INTERVAL_ARITHMETIC_H
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