to_rational.h
// Copyright (c) 2002
// 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)
//
// $URL$
// $Id$
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Andreas Fabri, Susan Hert, Sylvain Pion
#ifndef CGAL_TO_RATIONAL_H
#define CGAL_TO_RATIONAL_H
#include <CGAL/number_type_basic.h>
#include <CGAL/Fraction_traits.h>
#include <cmath>
namespace CGAL {
template <class Rational>
Rational
to_rational(double x)
{
typedef Fraction_traits<Rational> FT;
typedef typename FT::Is_fraction Is_fraction;
typedef typename FT::Numerator_type Numerator_type;
typedef typename FT::Denominator_type Denominator_type;
typename FT::Compose compose;
CGAL_static_assertion((::std::is_same<Is_fraction,Tag_true>::value));
CGAL_USE_TYPE(Is_fraction);
CGAL_static_assertion((::std::is_same<Numerator_type,Denominator_type>::value));
CGAL_USE_TYPE(Denominator_type);
Numerator_type num(0),den(1);
if (x != 0.0)
{ bool neg = (x < 0);
if (neg) x = -x;
const unsigned shift = 15; // a safe shift per step
const int shift_pow = 32768; // = 2^shift
const double width = 32768; // = 2^shift
const int maxiter = 20; // ought not be necessary, but just in
// case, max 300 bits of precision
int expt;
double mantissa = std::frexp(x, &expt);
long exponent = expt;
double intpart;
int k = 0;
while (mantissa != 0.0 && k++ < maxiter)
{
mantissa *= width; // shift double mantissa
mantissa = std::modf(mantissa, &intpart);
num *= shift_pow;
num += (int)intpart;
exponent -= shift;
}
int expsign = (exponent>0 ? +1 : (exponent<0 ? -1 : 0));
exponent *= expsign;
Numerator_type twopot(2);
Numerator_type exppot(1);
while (exponent!=0) {
if (exponent & 1)
exppot *= twopot;
exponent >>= 1;
twopot *= twopot;
}
if (expsign > 0)
num *= exppot;
else if (expsign < 0)
den *= exppot;
if (neg)
num = -num;
}
return compose(num,den);
}
} //namespace CGAL
#endif // CGAL_TO_RATIONAL_H