Chris@16: /* Boost interval/detail/division.hpp file
Chris@16:  *
Chris@16:  * Copyright 2003 Guillaume Melquiond, Sylvain Pion
Chris@16:  *
Chris@16:  * Distributed under the Boost Software License, Version 1.0.
Chris@16:  * (See accompanying file LICENSE_1_0.txt or
Chris@16:  * copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
Chris@16: #define BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP
Chris@16: 
Chris@16: #include <boost/numeric/interval/detail/interval_prototype.hpp>
Chris@16: #include <boost/numeric/interval/detail/bugs.hpp>
Chris@16: #include <boost/numeric/interval/detail/test_input.hpp>
Chris@16: #include <boost/numeric/interval/rounded_arith.hpp>
Chris@16: #include <algorithm>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace numeric {
Chris@16: namespace interval_lib {
Chris@16: namespace detail {
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_non_zero(const interval<T, Policies>& x,
Chris@16:                                    const interval<T, Policies>& y)
Chris@16: {
Chris@16:   // assert(!in_zero(y));
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   const T& xl = x.lower();
Chris@16:   const T& xu = x.upper();
Chris@16:   const T& yl = y.lower();
Chris@16:   const T& yu = y.upper();
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(xu))
Chris@16:     if (::boost::numeric::interval_lib::user::is_neg(yu))
Chris@16:       return I(rnd.div_down(xu, yl), rnd.div_up(xl, yu), true);
Chris@16:     else
Chris@16:       return I(rnd.div_down(xl, yl), rnd.div_up(xu, yu), true);
Chris@16:   else if (::boost::numeric::interval_lib::user::is_neg(xl))
Chris@16:     if (::boost::numeric::interval_lib::user::is_neg(yu))
Chris@16:       return I(rnd.div_down(xu, yu), rnd.div_up(xl, yu), true);
Chris@16:     else
Chris@16:       return I(rnd.div_down(xl, yl), rnd.div_up(xu, yl), true);
Chris@16:   else
Chris@16:     if (::boost::numeric::interval_lib::user::is_neg(yu))
Chris@16:       return I(rnd.div_down(xu, yu), rnd.div_up(xl, yl), true);
Chris@16:     else
Chris@16:       return I(rnd.div_down(xl, yu), rnd.div_up(xu, yl), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_non_zero(const T& x, const interval<T, Policies>& y)
Chris@16: {
Chris@16:   // assert(!in_zero(y));
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   const T& yl = y.lower();
Chris@16:   const T& yu = y.upper();
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(x))
Chris@16:     return I(rnd.div_down(x, yl), rnd.div_up(x, yu), true);
Chris@16:   else
Chris@16:     return I(rnd.div_down(x, yu), rnd.div_up(x, yl), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_positive(const interval<T, Policies>& x, const T& yu)
Chris@16: {
Chris@16:   // assert(::boost::numeric::interval_lib::user::is_pos(yu));
Chris@16:   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
Chris@16:       ::boost::numeric::interval_lib::user::is_zero(x.upper()))
Chris@16:     return x;
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   const T& xl = x.lower();
Chris@16:   const T& xu = x.upper();
Chris@16:   typedef typename Policies::checking checking;
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(xu))
Chris@16:     return I(checking::neg_inf(), rnd.div_up(xu, yu), true);
Chris@16:   else if (::boost::numeric::interval_lib::user::is_neg(xl))
Chris@16:     return I(checking::neg_inf(), checking::pos_inf(), true);
Chris@16:   else
Chris@16:     return I(rnd.div_down(xl, yu), checking::pos_inf(), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_positive(const T& x, const T& yu)
Chris@16: {
Chris@16:   // assert(::boost::numeric::interval_lib::user::is_pos(yu));
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (::boost::numeric::interval_lib::user::is_zero(x))
Chris@16:     return I(static_cast<T>(0), static_cast<T>(0), true);
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef typename Policies::checking checking;
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(x))
Chris@16:     return I(checking::neg_inf(), rnd.div_up(x, yu), true);
Chris@16:   else
Chris@16:     return I(rnd.div_down(x, yu), checking::pos_inf(), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_negative(const interval<T, Policies>& x, const T& yl)
Chris@16: {
Chris@16:   // assert(::boost::numeric::interval_lib::user::is_neg(yl));
Chris@16:   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
Chris@16:       ::boost::numeric::interval_lib::user::is_zero(x.upper()))
Chris@16:     return x;
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   const T& xl = x.lower();
Chris@16:   const T& xu = x.upper();
Chris@16:   typedef typename Policies::checking checking;
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(xu))
Chris@16:     return I(rnd.div_down(xu, yl), checking::pos_inf(), true);
Chris@16:   else if (::boost::numeric::interval_lib::user::is_neg(xl))
Chris@16:     return I(checking::neg_inf(), checking::pos_inf(), true);
Chris@16:   else
Chris@16:     return I(checking::neg_inf(), rnd.div_up(xl, yl), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_negative(const T& x, const T& yl)
Chris@16: {
Chris@16:   // assert(::boost::numeric::interval_lib::user::is_neg(yl));
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (::boost::numeric::interval_lib::user::is_zero(x))
Chris@16:     return I(static_cast<T>(0), static_cast<T>(0), true);
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef typename Policies::checking checking;
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(x))
Chris@16:     return I(rnd.div_down(x, yl), checking::pos_inf(), true);
Chris@16:   else
Chris@16:     return I(checking::neg_inf(), rnd.div_up(x, yl), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_zero(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
Chris@16:       ::boost::numeric::interval_lib::user::is_zero(x.upper()))
Chris@16:     return x;
Chris@16:   else return interval<T, Policies>::whole();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_zero(const T& x)
Chris@16: {
Chris@16:   if (::boost::numeric::interval_lib::user::is_zero(x))
Chris@16:     return interval<T, Policies>(static_cast<T>(0), static_cast<T>(0), true);
Chris@16:   else return interval<T, Policies>::whole();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_zero_part1(const interval<T, Policies>& x,
Chris@16:                                      const interval<T, Policies>& y, bool& b)
Chris@16: {
Chris@16:   // assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()));
Chris@16:   if (::boost::numeric::interval_lib::user::is_zero(x.lower()) && ::boost::numeric::interval_lib::user::is_zero(x.upper()))
Chris@16:     { b = false; return x; }
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   const T& xl = x.lower();
Chris@16:   const T& xu = x.upper();
Chris@16:   const T& yl = y.lower();
Chris@16:   const T& yu = y.upper();
Chris@16:   typedef typename Policies::checking checking;
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(xu))
Chris@16:     { b = true;  return I(checking::neg_inf(), rnd.div_up(xu, yu), true); }
Chris@16:   else if (::boost::numeric::interval_lib::user::is_neg(xl))
Chris@16:     { b = false; return I(checking::neg_inf(), checking::pos_inf(), true); }
Chris@16:   else
Chris@16:     { b = true;  return I(checking::neg_inf(), rnd.div_up(xl, yl), true); }
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> div_zero_part2(const interval<T, Policies>& x,
Chris@16:                                      const interval<T, Policies>& y)
Chris@16: {
Chris@16:   // 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));
Chris@16:   typename Policies::rounding rnd;
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   typedef typename Policies::checking checking;
Chris@16:   if (::boost::numeric::interval_lib::user::is_neg(x.upper()))
Chris@16:     return I(rnd.div_down(x.upper(), y.lower()), checking::pos_inf(), true);
Chris@16:   else
Chris@16:     return I(rnd.div_down(x.lower(), y.upper()), checking::pos_inf(), true);
Chris@16: }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: } // namespace interval_lib
Chris@16: } // namespace numeric
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP