template<class T, class Policies> inline interval<T, Policies> operator*(const interval<T, Policies>& x, const interval<T, Policies>& y) { BOOST_USING_STD_MIN(); BOOST_USING_STD_MAX(); typedef interval<T, Policies> I; if (interval_lib::detail::test_input(x, y)) return I::empty(); typename Policies::rounding rnd; const T& xl = x.lower(); const T& xu = x.upper(); const T& yl = y.lower(); const T& yu = y.upper(); if (interval_lib::user::is_neg(xl)) if (interval_lib::user::is_pos(xu)) if (interval_lib::user::is_neg(yl)) if (interval_lib::user::is_pos(yu)) // M * M return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_down(xl, yu), rnd.mul_down(xu, yl)), max BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_up (xl, yl), rnd.mul_up (xu, yu)), true); else // M * N return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yl), true); else if (interval_lib::user::is_pos(yu)) // M * P return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yu), true); else // M * Z return I(static_cast<T>(0), static_cast<T>(0), true); else if (interval_lib::user::is_neg(yl)) if (interval_lib::user::is_pos(yu)) // N * M return I(rnd.mul_down(xl, yu), rnd.mul_up(xl, yl), true); else // N * N return I(rnd.mul_down(xu, yu), rnd.mul_up(xl, yl), true); else if (interval_lib::user::is_pos(yu)) // N * P return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yl), true); else // N * Z return I(static_cast<T>(0), static_cast<T>(0), true); else if (interval_lib::user::is_pos(xu)) if (interval_lib::user::is_neg(yl)) if (interval_lib::user::is_pos(yu)) // P * M return I(rnd.mul_down(xu, yl), rnd.mul_up(xu, yu), true); else // P * N return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yu), true); else if (interval_lib::user::is_pos(yu)) // P * P return I(rnd.mul_down(xl, yl), rnd.mul_up(xu, yu), true); else // P * Z return I(static_cast<T>(0), static_cast<T>(0), true); else // Z * ? return I(static_cast<T>(0), static_cast<T>(0), true); }
template<class T, class Policies> inline interval<T, Policies> operator*(const interval<T, Policies>& x, const interval<T, Policies>& y) { BOOST_NUMERIC_INTERVAL_using_max(min); BOOST_NUMERIC_INTERVAL_using_max(max); typedef interval<T, Policies> I; if (interval_lib::detail::test_input(x, y)) return I::empty(); typename Policies::rounding rnd; const T& xl = x.lower(); const T& xu = x.upper(); const T& yl = y.lower(); const T& yu = y.upper(); if (interval_lib::detail::is_neg(xl)) if (interval_lib::detail::is_pos(xu)) if (interval_lib::detail::is_neg(yl)) if (interval_lib::detail::is_pos(yu)) // M * M return I(min(rnd.mul_down(xl, yu), rnd.mul_down(xu, yl)), max(rnd.mul_up (xl, yl), rnd.mul_up (xu, yu)), true); else // M * N return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yl), true); else if (interval_lib::detail::is_pos(yu)) // M * P return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yu), true); else // M * Z return I(0, 0, true); else if (interval_lib::detail::is_neg(yl)) if (interval_lib::detail::is_pos(yu)) // N * M return I(rnd.mul_down(xl, yu), rnd.mul_up(xl, yl), true); else // N * N return I(rnd.mul_down(xu, yu), rnd.mul_up(xl, yl), true); else if (interval_lib::detail::is_pos(yu)) // N * P return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yl), true); else // N * Z return I(0, 0, true); else if (interval_lib::detail::is_pos(xu)) if (interval_lib::detail::is_neg(yl)) if (interval_lib::detail::is_pos(yu)) // P * M return I(rnd.mul_down(xu, yl), rnd.mul_up(xu, yu), true); else // P * N return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yu), true); else if (interval_lib::detail::is_pos(yu)) // P * P return I(rnd.mul_down(xl, yl), rnd.mul_up(xu, yu), true); else // P * Z return I(0, 0, true); else // Z * ? return I(0, 0, true); }
template<class T, class Policies> inline interval<T, Policies> operator*(const T& x, const interval<T, Policies>& y) { typedef interval<T, Policies> I; if (interval_lib::detail::test_input(x, y)) return I::empty(); typename Policies::rounding rnd; const T& yl = y.lower(); const T& yu = y.upper(); // x is supposed not to be infinite if (interval_lib::user::is_neg(x)) return I(rnd.mul_down(x, yu), rnd.mul_up(x, yl), true); else if (interval_lib::user::is_zero(x)) return I(static_cast<T>(0), static_cast<T>(0), true); else return I(rnd.mul_down(x, yl), rnd.mul_up(x, yu), true); }
template<class I> inline I mul(const typename I::base_type& x, const typename I::base_type& y) { typedef typename I::traits_type Policies; if (detail::test_input<typename I::base_type, Policies>(x, y)) return I::empty(); typename Policies::rounding rnd; return I(rnd.mul_down(x, y), rnd.mul_up(x, y), true); }