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_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 Policies1, class Policies2> inline
bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
const T& yl = y.lower();
return xl > yl || (xl == yl && x.upper() >= y.upper());
}
template<class T, class Policies1, class Policies2> inline
logic::tribool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() == y.lower() && x.lower() == y.upper()) return true;
if (x.upper() < y.lower() || x.lower() > y.upper()) return false;
return logic::indeterminate;
}
template<class T, class Policies1, class Policies2> inline
bool overlap(const interval<T, Policies1>& x,
const interval<T, Policies2>& y)
{
if (interval_lib::detail::test_input(x, y)) return false;
return x.lower() <= y.lower() && y.lower() <= x.upper() ||
y.lower() <= x.lower() && x.lower() <= y.upper();
}
template<class T, class Policies1, class Policies2> inline
bool proper_subset(const interval<T, Policies1>& x,
const interval<T, Policies2>& y)
{
if (empty(y)) return false;
if (empty(x)) return true;
return y.lower() <= x.lower() && x.upper() <= y.upper() &&
(y.lower() != x.lower() || x.upper() != y.upper());
}
template<class T, class Policies> inline
interval<T, Policies> min(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
BOOST_NUMERIC_INTERVAL_using_max(min);
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x, y))
return I::empty();
return I(min(x.lower(), y.lower()), min(x.upper(), y.upper()), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator-(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
return interval<T,Policies>(rnd.sub_down(x.lower(), y.upper()),
rnd.sub_up (x.upper(), y.lower()), true);
}
template<class T, class Policies> inline
interval<T, Policies> acosh(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x) || x.upper() < static_cast<T>(1))
return I::empty();
typename Policies::rounding rnd;
T l = x.lower() <= static_cast<T>(1) ? static_cast<T>(0) : rnd.acosh_down(x.lower());
return I(l, rnd.acosh_up(x.upper()), true);
}
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> abs(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x))
return I::empty();
if (!interval_lib::user::is_neg(x.lower())) return x;
if (!interval_lib::user::is_pos(x.upper())) return -x;
BOOST_USING_STD_MAX();
return I(static_cast<T>(0), max BOOST_PREVENT_MACRO_SUBSTITUTION(-x.lower(), x.upper()), true);
}
template<class T, class Policies> inline
interval<T, Policies> abs(const interval<T, Policies>& x)
{
BOOST_NUMERIC_INTERVAL_using_max(max);
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x))
return I::empty();
if (!interval_lib::detail::is_neg(x.lower())) return x;
if (interval_lib::detail::is_neg(x.upper())) return -x;
return I(0, max(-x.lower(), x.upper()), true);
}
template<class T, class Policies> inline
interval<T, Policies> intersect(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
BOOST_NUMERIC_INTERVAL_using_max(min);
BOOST_NUMERIC_INTERVAL_using_max(max);
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
const T& l = max(x.lower(), y.lower());
const T& u = min(x.upper(), y.upper());
if (l <= u) return interval<T, Policies>(l, u, true);
else return interval<T, Policies>::empty();
}
template<class T, class Policies> inline
interval<T, Policies> intersect(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
const T& l = max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower());
const T& u = min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper());
if (l <= u) return interval<T, Policies>(l, u, true);
else return interval<T, Policies>::empty();
}
template<class T, class Policies> inline
interval<T, Policies> log(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x) ||
!interval_lib::user::is_pos(x.upper()))
return I::empty();
typename Policies::rounding rnd;
typedef typename Policies::checking checking;
T l = !interval_lib::user::is_pos(x.lower())
? checking::neg_inf() : rnd.log_down(x.lower());
return I(l, rnd.log_up(x.upper()), 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);
}
template<class T, class Policies> inline
interval<T, Policies> cosh(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x))
return I::empty();
typename Policies::rounding rnd;
if (interval_lib::user::is_neg(x.upper()))
return I(rnd.cosh_down(x.upper()), rnd.cosh_up(x.lower()), true);
else if (!interval_lib::user::is_neg(x.lower()))
return I(rnd.cosh_down(x.lower()), rnd.cosh_up(x.upper()), true);
else
return I(static_cast<T>(0), rnd.cosh_up(-x.lower() > x.upper() ? x.lower() : x.upper()), true);
}
template<class T, class Policies> inline
interval<T, Policies> div_zero_part2(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
// assert(y.lower() < 0 && y.upper() > 0 && (div_zero_part1(x, y, b), b));
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
typedef typename I::checking checking;
const T& inf = checking::inf();
if (is_neg(x.upper()))
return I(rnd.div_down(x.upper(), y.lower()), inf, true);
else
return I(rnd.div_down(x.lower(), y.upper()), inf, true);
}
template<class T, class Policies> inline
interval<T, Policies> atanh(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x)
|| x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
return I::empty();
typename Policies::rounding rnd;
typedef typename Policies::checking checking;
T l = (x.lower() <= static_cast<T>(-1))
? checking::neg_inf() : rnd.atanh_down(x.lower());
T u = (x.upper() >= static_cast<T>(1) )
? checking::pos_inf() : rnd.atanh_up (x.upper());
return I(l, u, true);
}
template<class T, class Policies> inline
bool zero_in(const interval<T, Policies>& x)
{
if (interval_lib::detail::test_input(x)) return false;
return (!interval_lib::user::is_pos(x.lower())) &&
(!interval_lib::user::is_neg(x.upper()));
}
template<class T, class Policies> inline
interval<T, Policies> asin(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x)
|| x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
return I::empty();
typename Policies::rounding rnd;
T l = (x.lower() <= static_cast<T>(-1))
? -interval_lib::constants::pi_half_upper<T>()
: rnd.asin_down(x.lower());
T u = (x.upper() >= static_cast<T>(1) )
? interval_lib::constants::pi_half_upper<T>()
: rnd.asin_up (x.upper());
return I(l, u, true);
}
template<class T, class Policies> inline
bool operator>(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
return xl > y || (xl == y && x.upper() > y);
}
template<class T, class Policies> inline
interval<T, Policies> operator-(const interval<T, Policies>& x)
{
if (interval_lib::detail::test_input(x))
return interval<T, Policies>::empty();
return interval<T, Policies>(-x.upper(), -x.lower(), true);
}
template<class T, class Policies> inline
interval<T, Policies> hull(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
BOOST_NUMERIC_INTERVAL_using_max(min);
BOOST_NUMERIC_INTERVAL_using_max(max);
bool bad_x = interval_lib::detail::test_input(x);
bool bad_y = interval_lib::detail::test_input(y);
if (bad_x)
if (bad_y) return interval<T, Policies>::empty();
else return y;
else
if (bad_y) return x;
return interval<T, Policies>(min(x.lower(), y.lower()),
max(x.upper(), y.upper()), true);
}
template<class T, class Policies> inline
T width(const interval<T, Policies>& x)
{
if (interval_lib::detail::test_input(x)) return static_cast<T>(0);
typename Policies::rounding rnd;
return rnd.sub_up(x.upper(), x.lower());
}
template<class T, class Policies> inline
interval<T, Policies> div_zero(const interval<T, Policies>& x)
{
if (is_zero(x.lower()) && is_zero(x.upper()))
return x;
else return interval<T, Policies>::whole();
}
template<class T, class Policies> inline
interval<T, Policies> hull(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
bool bad_x = interval_lib::detail::test_input(x);
bool bad_y = interval_lib::detail::test_input(y);
if (bad_x)
if (bad_y) return interval<T, Policies>::empty();
else return y;
else
if (bad_y) return x;
return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()),
max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true);
}
template<class T, class Policies> inline
logic::tribool operator>=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.lower() >= y) return true;
if (x.upper() < y) return false;
return logic::indeterminate;
}
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();
}