306 lines
10 KiB
Plaintext
306 lines
10 KiB
Plaintext
/* Boost interval/arith.hpp template implementation file
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*
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* Copyright 2000 Jens Maurer
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* Copyright 2002-2003 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion
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*
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* Distributed under the Boost Software License, Version 1.0.
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* (See accompanying file LICENSE_1_0.txt or
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* copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_NUMERIC_INTERVAL_ARITH_HPP
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#define BOOST_NUMERIC_INTERVAL_ARITH_HPP
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#include <boost/config.hpp>
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#include <boost/numeric/interval/interval.hpp>
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#include <boost/numeric/interval/detail/bugs.hpp>
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#include <boost/numeric/interval/detail/test_input.hpp>
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#include <boost/numeric/interval/detail/division.hpp>
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#include <algorithm>
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namespace boost {
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namespace numeric {
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/*
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* Basic arithmetic operators
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*/
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template<class T, class Policies> inline
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const interval<T, Policies>& operator+(const interval<T, Policies>& x)
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{
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return x;
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator-(const interval<T, Policies>& x)
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{
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if (interval_lib::detail::test_input(x))
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return interval<T, Policies>::empty();
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return interval<T, Policies>(-x.upper(), -x.lower(), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator+=(const interval<T, Policies>& r)
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{
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if (interval_lib::detail::test_input(*this, r))
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set_empty();
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else {
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typename Policies::rounding rnd;
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set(rnd.add_down(low, r.low), rnd.add_up(up, r.up));
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}
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return *this;
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator+=(const T& r)
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{
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if (interval_lib::detail::test_input(*this, r))
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set_empty();
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else {
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typename Policies::rounding rnd;
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set(rnd.add_down(low, r), rnd.add_up(up, r));
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}
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return *this;
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator-=(const interval<T, Policies>& r)
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{
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if (interval_lib::detail::test_input(*this, r))
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set_empty();
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else {
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typename Policies::rounding rnd;
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set(rnd.sub_down(low, r.up), rnd.sub_up(up, r.low));
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}
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return *this;
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator-=(const T& r)
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{
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if (interval_lib::detail::test_input(*this, r))
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set_empty();
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else {
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typename Policies::rounding rnd;
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set(rnd.sub_down(low, r), rnd.sub_up(up, r));
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}
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return *this;
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator*=(const interval<T, Policies>& r)
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{
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return *this = *this * r;
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator*=(const T& r)
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{
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return *this = r * *this;
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator/=(const interval<T, Policies>& r)
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{
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return *this = *this / r;
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}
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template<class T, class Policies> inline
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interval<T, Policies>& interval<T, Policies>::operator/=(const T& r)
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{
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return *this = *this / r;
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator+(const interval<T, Policies>& x,
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const interval<T, Policies>& y)
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{
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if (interval_lib::detail::test_input(x, y))
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return interval<T, Policies>::empty();
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typename Policies::rounding rnd;
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return interval<T,Policies>(rnd.add_down(x.lower(), y.lower()),
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rnd.add_up (x.upper(), y.upper()), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator+(const T& x, const interval<T, Policies>& y)
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{
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if (interval_lib::detail::test_input(x, y))
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return interval<T, Policies>::empty();
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typename Policies::rounding rnd;
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return interval<T,Policies>(rnd.add_down(x, y.lower()),
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rnd.add_up (x, y.upper()), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator+(const interval<T, Policies>& x, const T& y)
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{ return y + x; }
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template<class T, class Policies> inline
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interval<T, Policies> operator-(const interval<T, Policies>& x,
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const interval<T, Policies>& y)
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{
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if (interval_lib::detail::test_input(x, y))
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return interval<T, Policies>::empty();
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typename Policies::rounding rnd;
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return interval<T,Policies>(rnd.sub_down(x.lower(), y.upper()),
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rnd.sub_up (x.upper(), y.lower()), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator-(const T& x, const interval<T, Policies>& y)
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{
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if (interval_lib::detail::test_input(x, y))
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return interval<T, Policies>::empty();
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typename Policies::rounding rnd;
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return interval<T,Policies>(rnd.sub_down(x, y.upper()),
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rnd.sub_up (x, y.lower()), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator-(const interval<T, Policies>& x, const T& y)
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{
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if (interval_lib::detail::test_input(x, y))
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return interval<T, Policies>::empty();
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typename Policies::rounding rnd;
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return interval<T,Policies>(rnd.sub_down(x.lower(), y),
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rnd.sub_up (x.upper(), y), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator*(const interval<T, Policies>& x,
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const interval<T, Policies>& y)
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{
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BOOST_USING_STD_MIN();
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BOOST_USING_STD_MAX();
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typedef interval<T, Policies> I;
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if (interval_lib::detail::test_input(x, y))
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return I::empty();
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typename Policies::rounding rnd;
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const T& xl = x.lower();
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const T& xu = x.upper();
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const T& yl = y.lower();
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const T& yu = y.upper();
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if (interval_lib::user::is_neg(xl))
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if (interval_lib::user::is_pos(xu))
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if (interval_lib::user::is_neg(yl))
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if (interval_lib::user::is_pos(yu)) // M * M
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return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_down(xl, yu), rnd.mul_down(xu, yl)),
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max BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_up (xl, yl), rnd.mul_up (xu, yu)), true);
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else // M * N
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return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yl), true);
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else
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if (interval_lib::user::is_pos(yu)) // M * P
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return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yu), true);
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else // M * Z
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return I(static_cast<T>(0), static_cast<T>(0), true);
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else
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if (interval_lib::user::is_neg(yl))
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if (interval_lib::user::is_pos(yu)) // N * M
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return I(rnd.mul_down(xl, yu), rnd.mul_up(xl, yl), true);
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else // N * N
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return I(rnd.mul_down(xu, yu), rnd.mul_up(xl, yl), true);
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else
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if (interval_lib::user::is_pos(yu)) // N * P
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return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yl), true);
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else // N * Z
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return I(static_cast<T>(0), static_cast<T>(0), true);
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else
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if (interval_lib::user::is_pos(xu))
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if (interval_lib::user::is_neg(yl))
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if (interval_lib::user::is_pos(yu)) // P * M
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return I(rnd.mul_down(xu, yl), rnd.mul_up(xu, yu), true);
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else // P * N
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return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yu), true);
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else
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if (interval_lib::user::is_pos(yu)) // P * P
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return I(rnd.mul_down(xl, yl), rnd.mul_up(xu, yu), true);
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else // P * Z
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return I(static_cast<T>(0), static_cast<T>(0), true);
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else // Z * ?
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return I(static_cast<T>(0), static_cast<T>(0), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator*(const T& x, const interval<T, Policies>& y)
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{
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typedef interval<T, Policies> I;
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if (interval_lib::detail::test_input(x, y))
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return I::empty();
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typename Policies::rounding rnd;
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const T& yl = y.lower();
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const T& yu = y.upper();
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// x is supposed not to be infinite
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if (interval_lib::user::is_neg(x))
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return I(rnd.mul_down(x, yu), rnd.mul_up(x, yl), true);
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else if (interval_lib::user::is_zero(x))
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return I(static_cast<T>(0), static_cast<T>(0), true);
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else
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return I(rnd.mul_down(x, yl), rnd.mul_up(x, yu), true);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator*(const interval<T, Policies>& x, const T& y)
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{ return y * x; }
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template<class T, class Policies> inline
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interval<T, Policies> operator/(const interval<T, Policies>& x,
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const interval<T, Policies>& y)
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{
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if (interval_lib::detail::test_input(x, y))
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return interval<T, Policies>::empty();
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if (zero_in(y))
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if (!interval_lib::user::is_zero(y.lower()))
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if (!interval_lib::user::is_zero(y.upper()))
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return interval_lib::detail::div_zero(x);
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else
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return interval_lib::detail::div_negative(x, y.lower());
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else
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if (!interval_lib::user::is_zero(y.upper()))
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return interval_lib::detail::div_positive(x, y.upper());
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else
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return interval<T, Policies>::empty();
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else
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return interval_lib::detail::div_non_zero(x, y);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator/(const T& x, const interval<T, Policies>& y)
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{
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if (interval_lib::detail::test_input(x, y))
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return interval<T, Policies>::empty();
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if (zero_in(y))
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if (!interval_lib::user::is_zero(y.lower()))
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if (!interval_lib::user::is_zero(y.upper()))
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return interval_lib::detail::div_zero<T, Policies>(x);
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else
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return interval_lib::detail::div_negative<T, Policies>(x, y.lower());
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else
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if (!interval_lib::user::is_zero(y.upper()))
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return interval_lib::detail::div_positive<T, Policies>(x, y.upper());
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else
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return interval<T, Policies>::empty();
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else
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return interval_lib::detail::div_non_zero(x, y);
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}
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template<class T, class Policies> inline
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interval<T, Policies> operator/(const interval<T, Policies>& x, const T& y)
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{
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if (interval_lib::detail::test_input(x, y) || interval_lib::user::is_zero(y))
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return interval<T, Policies>::empty();
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typename Policies::rounding rnd;
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const T& xl = x.lower();
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const T& xu = x.upper();
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if (interval_lib::user::is_neg(y))
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return interval<T, Policies>(rnd.div_down(xu, y), rnd.div_up(xl, y), true);
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else
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return interval<T, Policies>(rnd.div_down(xl, y), rnd.div_up(xu, y), true);
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}
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} // namespace numeric
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} // namespace boost
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#endif // BOOST_NUMERIC_INTERVAL_ARITH_HPP
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