| /* 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 |