template<class T, class Policies> inline
interval<T, Policies> operator/(const T& x, const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
if (zero_in(y))
if (!interval_lib::user::is_zero(y.lower()))
if (!interval_lib::user::is_zero(y.upper()))
return interval_lib::detail::div_zero<T, Policies>(x);
else
return interval_lib::detail::div_negative<T, Policies>(x, y.lower());
else
if (!interval_lib::user::is_zero(y.upper()))
return interval_lib::detail::div_positive<T, Policies>(x, y.upper());
else
return interval<T, Policies>::empty();
else
return interval_lib::detail::div_non_zero(x, y);
}
template<class T, class Policies> inline
interval<T, Policies> division_part1(const interval<T, Policies>& x,
const interval<T, Policies>& y, bool& b)
{
typedef interval<T, Policies> I;
b = false;
if (detail::test_input(x, y))
return I::empty();
if (zero_in(y))
if (!user::is_zero(y.lower()))
if (!user::is_zero(y.upper()))
return detail::div_zero_part1(x, y, b);
else
return detail::div_negative(x, y.lower());
else
if (!user::is_zero(y.upper()))
return detail::div_positive(x, y.upper());
else
return I::empty();
else
return detail::div_non_zero(x, y);
}
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 (zero_in(x)) {
typedef typename Policies::checking checking;
if (!user::is_zero(x.lower()))
if (!user::is_zero(x.upper()))
return I::whole();
else
return I(checking::neg_inf(), rnd.div_up(one, x.lower()), true);
else
if (!user::is_zero(x.upper()))
return I(rnd.div_down(one, x.upper()), checking::pos_inf(), true);
else
return I::empty();
} else
return I(rnd.div_down(one, x.upper()), rnd.div_up(one, x.lower()), true);
}