195 lines
7.5 KiB
C++
195 lines
7.5 KiB
C++
/* Boost interval/detail/division.hpp file
|
|
*
|
|
* Copyright 2003 Guillaume Melquiond, Sylvain Pion
|
|
*
|
|
* Distributed under the Boost Software License, Version 1.0.
|
|
* (See accompanying file LICENSE_1_0.txt or
|
|
* copy at http://www.boost.org/LICENSE_1_0.txt)
|
|
*/
|
|
|
|
#ifndef BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
|
|
#define BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
|
|
|
|
#include <boost/numeric/interval/detail/interval_prototype.hpp>
|
|
#include <boost/numeric/interval/detail/bugs.hpp>
|
|
#include <boost/numeric/interval/detail/test_input.hpp>
|
|
#include <boost/numeric/interval/rounded_arith.hpp>
|
|
#include <algorithm>
|
|
|
|
namespace boost {
|
|
namespace numeric {
|
|
namespace interval_lib {
|
|
namespace detail {
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_non_zero(const interval<T, Policies>& x,
|
|
const interval<T, Policies>& y)
|
|
{
|
|
// assert(!in_zero(y));
|
|
typename Policies::rounding rnd;
|
|
typedef interval<T, Policies> I;
|
|
const T& xl = x.lower();
|
|
const T& xu = x.upper();
|
|
const T& yl = y.lower();
|
|
const T& yu = y.upper();
|
|
if (::boost::numeric::interval_lib::user::is_neg(xu))
|
|
if (::boost::numeric::interval_lib::user::is_neg(yu))
|
|
return I(rnd.div_down(xu, yl), rnd.div_up(xl, yu), true);
|
|
else
|
|
return I(rnd.div_down(xl, yl), rnd.div_up(xu, yu), true);
|
|
else if (::boost::numeric::interval_lib::user::is_neg(xl))
|
|
if (::boost::numeric::interval_lib::user::is_neg(yu))
|
|
return I(rnd.div_down(xu, yu), rnd.div_up(xl, yu), true);
|
|
else
|
|
return I(rnd.div_down(xl, yl), rnd.div_up(xu, yl), true);
|
|
else
|
|
if (::boost::numeric::interval_lib::user::is_neg(yu))
|
|
return I(rnd.div_down(xu, yu), rnd.div_up(xl, yl), true);
|
|
else
|
|
return I(rnd.div_down(xl, yu), rnd.div_up(xu, yl), true);
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_non_zero(const T& x, const interval<T, Policies>& y)
|
|
{
|
|
// assert(!in_zero(y));
|
|
typename Policies::rounding rnd;
|
|
typedef interval<T, Policies> I;
|
|
const T& yl = y.lower();
|
|
const T& yu = y.upper();
|
|
if (::boost::numeric::interval_lib::user::is_neg(x))
|
|
return I(rnd.div_down(x, yl), rnd.div_up(x, yu), true);
|
|
else
|
|
return I(rnd.div_down(x, yu), rnd.div_up(x, yl), true);
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_positive(const interval<T, Policies>& x, const T& yu)
|
|
{
|
|
// assert(::boost::numeric::interval_lib::user::is_pos(yu));
|
|
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
|
|
::boost::numeric::interval_lib::user::is_zero(x.upper()))
|
|
return x;
|
|
typename Policies::rounding rnd;
|
|
typedef interval<T, Policies> I;
|
|
const T& xl = x.lower();
|
|
const T& xu = x.upper();
|
|
typedef typename Policies::checking checking;
|
|
if (::boost::numeric::interval_lib::user::is_neg(xu))
|
|
return I(checking::neg_inf(), rnd.div_up(xu, yu), true);
|
|
else if (::boost::numeric::interval_lib::user::is_neg(xl))
|
|
return I(checking::neg_inf(), checking::pos_inf(), true);
|
|
else
|
|
return I(rnd.div_down(xl, yu), checking::pos_inf(), true);
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_positive(const T& x, const T& yu)
|
|
{
|
|
// assert(::boost::numeric::interval_lib::user::is_pos(yu));
|
|
typedef interval<T, Policies> I;
|
|
if (::boost::numeric::interval_lib::user::is_zero(x))
|
|
return I(static_cast<T>(0), static_cast<T>(0), true);
|
|
typename Policies::rounding rnd;
|
|
typedef typename Policies::checking checking;
|
|
if (::boost::numeric::interval_lib::user::is_neg(x))
|
|
return I(checking::neg_inf(), rnd.div_up(x, yu), true);
|
|
else
|
|
return I(rnd.div_down(x, yu), checking::pos_inf(), true);
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_negative(const interval<T, Policies>& x, const T& yl)
|
|
{
|
|
// assert(::boost::numeric::interval_lib::user::is_neg(yl));
|
|
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
|
|
::boost::numeric::interval_lib::user::is_zero(x.upper()))
|
|
return x;
|
|
typename Policies::rounding rnd;
|
|
typedef interval<T, Policies> I;
|
|
const T& xl = x.lower();
|
|
const T& xu = x.upper();
|
|
typedef typename Policies::checking checking;
|
|
if (::boost::numeric::interval_lib::user::is_neg(xu))
|
|
return I(rnd.div_down(xu, yl), checking::pos_inf(), true);
|
|
else if (::boost::numeric::interval_lib::user::is_neg(xl))
|
|
return I(checking::neg_inf(), checking::pos_inf(), true);
|
|
else
|
|
return I(checking::neg_inf(), rnd.div_up(xl, yl), true);
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_negative(const T& x, const T& yl)
|
|
{
|
|
// assert(::boost::numeric::interval_lib::user::is_neg(yl));
|
|
typedef interval<T, Policies> I;
|
|
if (::boost::numeric::interval_lib::user::is_zero(x))
|
|
return I(static_cast<T>(0), static_cast<T>(0), true);
|
|
typename Policies::rounding rnd;
|
|
typedef typename Policies::checking checking;
|
|
if (::boost::numeric::interval_lib::user::is_neg(x))
|
|
return I(rnd.div_down(x, yl), checking::pos_inf(), true);
|
|
else
|
|
return I(checking::neg_inf(), rnd.div_up(x, yl), true);
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_zero(const interval<T, Policies>& x)
|
|
{
|
|
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
|
|
::boost::numeric::interval_lib::user::is_zero(x.upper()))
|
|
return x;
|
|
else return interval<T, Policies>::whole();
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_zero(const T& x)
|
|
{
|
|
if (::boost::numeric::interval_lib::user::is_zero(x))
|
|
return interval<T, Policies>(static_cast<T>(0), static_cast<T>(0), true);
|
|
else return interval<T, Policies>::whole();
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_zero_part1(const interval<T, Policies>& x,
|
|
const interval<T, Policies>& y, bool& b)
|
|
{
|
|
// assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()));
|
|
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) && ::boost::numeric::interval_lib::user::is_zero(x.upper()))
|
|
{ b = false; return x; }
|
|
typename Policies::rounding rnd;
|
|
typedef interval<T, Policies> I;
|
|
const T& xl = x.lower();
|
|
const T& xu = x.upper();
|
|
const T& yl = y.lower();
|
|
const T& yu = y.upper();
|
|
typedef typename Policies::checking checking;
|
|
if (::boost::numeric::interval_lib::user::is_neg(xu))
|
|
{ b = true; return I(checking::neg_inf(), rnd.div_up(xu, yu), true); }
|
|
else if (::boost::numeric::interval_lib::user::is_neg(xl))
|
|
{ b = false; return I(checking::neg_inf(), checking::pos_inf(), true); }
|
|
else
|
|
{ b = true; return I(checking::neg_inf(), rnd.div_up(xl, yl), true); }
|
|
}
|
|
|
|
template<class T, class Policies> inline
|
|
interval<T, Policies> div_zero_part2(const interval<T, Policies>& x,
|
|
const interval<T, Policies>& y)
|
|
{
|
|
// assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()) && (div_zero_part1(x, y, b), b));
|
|
typename Policies::rounding rnd;
|
|
typedef interval<T, Policies> I;
|
|
typedef typename Policies::checking checking;
|
|
if (::boost::numeric::interval_lib::user::is_neg(x.upper()))
|
|
return I(rnd.div_down(x.upper(), y.lower()), checking::pos_inf(), true);
|
|
else
|
|
return I(rnd.div_down(x.lower(), y.upper()), checking::pos_inf(), true);
|
|
}
|
|
|
|
} // namespace detail
|
|
} // namespace interval_lib
|
|
} // namespace numeric
|
|
} // namespace boost
|
|
|
|
#endif // BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
|