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(y.lower() < 0 && y.upper() > 0); if (is_zero(x.lower()) && 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 I::checking checking; const T& inf = checking::inf(); if (is_neg(xu)) { b = true; return I(-inf, rnd.div_up(xu, yu), true); } else if (is_neg(xl)) { b = false; return I(-inf, inf, true); } else { b = true; return I(-inf, rnd.div_up(xl, 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> operator/(const interval<T, Policies>& x, const T& y) { if (interval_lib::detail::test_input(x, y) || interval_lib::user::is_zero(y)) return interval<T, Policies>::empty(); typename Policies::rounding rnd; const T& xl = x.lower(); const T& xu = x.upper(); if (interval_lib::user::is_neg(y)) return interval<T, Policies>(rnd.div_down(xu, y), rnd.div_up(xl, y), true); else return interval<T, Policies>(rnd.div_down(xl, y), rnd.div_up(xu, y), true); }
template<class I> inline I div(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) || user::is_zero(y)) return I::empty(); typename Policies::rounding rnd; return I(rnd.div_down(x, y), rnd.div_up(x, y), true); }
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_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 (is_neg(xu)) if (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 (is_neg(xl)) if (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 (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_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> multiplicative_inverse(const interval<T, Policies>& x) { typedef interval<T, Policies> I; if (detail::test_input(x)) return I::empty(); T one = static_cast<T>(1); typename Policies::rounding rnd; if (in_zero(x)) { typedef typename Policies::checking checking; if (!detail::is_zero(x.lower())) if (!detail::is_zero(x.upper())) return I::whole(); else return I(-checking::inf(), rnd.div_up(one, x.lower()), true); else if (!detail::is_zero(x.upper())) return I(rnd.div_down(one, x.upper()), checking::inf(), true); else return I::empty(); } else return I(rnd.div_down(one, x.upper()), rnd.div_up(one, x.lower()), true); }
template<class T, class Policies> inline interval<T, Policies> div_positive(const T& x, const T& yu) { // assert(yu > T(0)); typedef interval<T, Policies> I; if (is_zero(x)) return I(0, 0, true); typename Policies::rounding rnd; typedef typename Policies::checking checking; const T& inf = checking::inf(); if (is_neg(x)) return I(-inf, rnd.div_up(x, yu), true); else return I(rnd.div_down(x, yu), inf, 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_negative(const interval<T, Policies>& x, const T& yl) { // assert(yl < T(0)); if (is_zero(x.lower()) && 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; const T& inf = checking::inf(); if (is_neg(xu)) return I(rnd.div_down(xu, yl), inf, true); else if (is_neg(xl)) return I(-inf, inf, true); else return I(-inf, rnd.div_up(xl, yl), true); }