Chris@16: /* Boost interval/utility.hpp template implementation file
Chris@16:  *
Chris@16:  * Copyright 2000 Jens Maurer
Chris@16:  * Copyright 2002-2003 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion
Chris@16:  *
Chris@16:  * Distributed under the Boost Software License, Version 1.0.
Chris@16:  * (See accompanying file LICENSE_1_0.txt or
Chris@16:  * copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_NUMERIC_INTERVAL_UTILITY_HPP
Chris@16: #define BOOST_NUMERIC_INTERVAL_UTILITY_HPP
Chris@16: 
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/numeric/interval/detail/interval_prototype.hpp>
Chris@16: #include <boost/numeric/interval/detail/test_input.hpp>
Chris@16: #include <boost/numeric/interval/detail/bugs.hpp>
Chris@16: #include <algorithm>
Chris@16: #include <utility>
Chris@16: 
Chris@16: /*
Chris@16:  * Implementation of simple functions
Chris@16:  */
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace numeric {
Chris@16: 
Chris@16: /*
Chris@16:  * Utility Functions
Chris@16:  */
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: const T& lower(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   return x.lower();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: const T& upper(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   return x.upper();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: T checked_lower(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   if (empty(x)) {
Chris@16:     typedef typename Policies::checking checking;
Chris@16:     return checking::nan();
Chris@16:   }
Chris@16:   return x.lower();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: T checked_upper(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   if (empty(x)) {
Chris@16:     typedef typename Policies::checking checking;
Chris@16:     return checking::nan();
Chris@16:   }
Chris@16:   return x.upper();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: T width(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   if (interval_lib::detail::test_input(x)) return static_cast<T>(0);
Chris@16:   typename Policies::rounding rnd;
Chris@16:   return rnd.sub_up(x.upper(), x.lower());
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: T median(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   if (interval_lib::detail::test_input(x)) {
Chris@16:     typedef typename Policies::checking checking;
Chris@16:     return checking::nan();
Chris@16:   }
Chris@16:   typename Policies::rounding rnd;
Chris@16:   return rnd.median(x.lower(), x.upper());
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> widen(const interval<T, Policies>& x, const T& v)
Chris@16: {
Chris@16:   if (interval_lib::detail::test_input(x))
Chris@16:     return interval<T, Policies>::empty();
Chris@16:   typename Policies::rounding rnd;
Chris@16:   return interval<T, Policies>(rnd.sub_down(x.lower(), v),
Chris@16:                                rnd.add_up  (x.upper(), v), true);
Chris@16: }
Chris@16: 
Chris@16: /*
Chris@16:  * Set-like operations
Chris@16:  */
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: bool empty(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   return interval_lib::detail::test_input(x);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: bool zero_in(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   if (interval_lib::detail::test_input(x)) return false;
Chris@16:   return (!interval_lib::user::is_pos(x.lower())) &&
Chris@16:          (!interval_lib::user::is_neg(x.upper()));
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: bool in_zero(const interval<T, Policies>& x) // DEPRECATED
Chris@16: {
Chris@16:   return zero_in<T, Policies>(x);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: bool in(const T& x, const interval<T, Policies>& y)
Chris@16: {
Chris@16:   if (interval_lib::detail::test_input(x, y)) return false;
Chris@16:   return y.lower() <= x && x <= y.upper();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: bool subset(const interval<T, Policies>& x,
Chris@16:             const interval<T, Policies>& y)
Chris@16: {
Chris@16:   if (empty(x)) return true;
Chris@16:   return !empty(y) && y.lower() <= x.lower() && x.upper() <= y.upper();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies1, class Policies2> inline
Chris@16: bool proper_subset(const interval<T, Policies1>& x,
Chris@16:                    const interval<T, Policies2>& y)
Chris@16: {
Chris@16:   if (empty(y)) return false;
Chris@16:   if (empty(x)) return true;
Chris@16:   return y.lower() <= x.lower() && x.upper() <= y.upper() &&
Chris@16:          (y.lower() != x.lower() || x.upper() != y.upper());
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies1, class Policies2> inline
Chris@16: bool overlap(const interval<T, Policies1>& x,
Chris@16:              const interval<T, Policies2>& y)
Chris@16: {
Chris@16:   if (interval_lib::detail::test_input(x, y)) return false;
Chris@16:   return (x.lower() <= y.lower() && y.lower() <= x.upper()) ||
Chris@16:          (y.lower() <= x.lower() && x.lower() <= y.upper());
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: bool singleton(const interval<T, Policies>& x)
Chris@16: {
Chris@16:  return !empty(x) && x.lower() == x.upper();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies1, class Policies2> inline
Chris@16: bool equal(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
Chris@16: {
Chris@16:   if (empty(x)) return empty(y);
Chris@16:   return !empty(y) && x.lower() == y.lower() && x.upper() == y.upper();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> intersect(const interval<T, Policies>& x,
Chris@16:                                 const interval<T, Policies>& y)
Chris@16: {
Chris@16:   BOOST_USING_STD_MIN();
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   if (interval_lib::detail::test_input(x, y))
Chris@16:     return interval<T, Policies>::empty();
Chris@16:   const T& l = max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower());
Chris@16:   const T& u = min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper());
Chris@16:   if (l <= u) return interval<T, Policies>(l, u, true);
Chris@16:   else        return interval<T, Policies>::empty();
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> hull(const interval<T, Policies>& x,
Chris@16:                            const interval<T, Policies>& y)
Chris@16: {
Chris@16:   BOOST_USING_STD_MIN();
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   bool bad_x = interval_lib::detail::test_input(x);
Chris@16:   bool bad_y = interval_lib::detail::test_input(y);
Chris@16:   if (bad_x)
Chris@16:     if (bad_y) return interval<T, Policies>::empty();
Chris@16:     else       return y;
Chris@16:   else
Chris@16:     if (bad_y) return x;
Chris@16:   return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()),
Chris@16:                                max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> hull(const interval<T, Policies>& x, const T& y)
Chris@16: {
Chris@16:   BOOST_USING_STD_MIN();
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   bool bad_x = interval_lib::detail::test_input(x);
Chris@16:   bool bad_y = interval_lib::detail::test_input<T, Policies>(y);
Chris@16:   if (bad_y)
Chris@16:     if (bad_x) return interval<T, Policies>::empty();
Chris@16:     else       return x;
Chris@16:   else
Chris@16:     if (bad_x) return interval<T, Policies>(y, y, true);
Chris@16:   return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y),
Chris@16:                                max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> hull(const T& x, const interval<T, Policies>& y)
Chris@16: {
Chris@16:   BOOST_USING_STD_MIN();
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   bool bad_x = interval_lib::detail::test_input<T, Policies>(x);
Chris@16:   bool bad_y = interval_lib::detail::test_input(y);
Chris@16:   if (bad_x)
Chris@16:     if (bad_y) return interval<T, Policies>::empty();
Chris@16:     else       return y;
Chris@16:   else
Chris@16:     if (bad_y) return interval<T, Policies>(x, x, true);
Chris@16:   return interval<T, Policies>(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()),
Chris@16:                                max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T> inline
Chris@16: interval<T> hull(const T& x, const T& y)
Chris@16: {
Chris@16:   return interval<T>::hull(x, y);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: std::pair<interval<T, Policies>, interval<T, Policies> >
Chris@16: bisect(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x))
Chris@16:     return std::pair<I,I>(I::empty(), I::empty());
Chris@16:   const T m = median(x);
Chris@16:   return std::pair<I,I>(I(x.lower(), m, true), I(m, x.upper(), true));
Chris@16: }
Chris@16: 
Chris@16: /*
Chris@16:  * Elementary functions
Chris@16:  */
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: T norm(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x)) {
Chris@16:     typedef typename Policies::checking checking;
Chris@16:     return checking::nan();
Chris@16:   }
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   return max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper());
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> abs(const interval<T, Policies>& x)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x))
Chris@16:     return I::empty();
Chris@16:   if (!interval_lib::user::is_neg(x.lower())) return x;
Chris@16:   if (!interval_lib::user::is_pos(x.upper())) return -x;
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   return I(static_cast<T>(0), max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast<T>(-x.lower()), x.upper()), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x,
Chris@16:                                                             const interval<T, Policies>& y)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x, y))
Chris@16:     return I::empty();
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x, y))
Chris@16:     return I::empty();
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), max BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> max BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x, y))
Chris@16:     return I::empty();
Chris@16:   BOOST_USING_STD_MAX();
Chris@16:   return I(max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), max BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x,
Chris@16:                                                             const interval<T, Policies>& y)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x, y))
Chris@16:     return I::empty();
Chris@16:   BOOST_USING_STD_MIN();
Chris@16:   return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y.lower()), min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y.upper()), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const interval<T, Policies>& x, const T& y)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x, y))
Chris@16:     return I::empty();
Chris@16:   BOOST_USING_STD_MIN();
Chris@16:   return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x.lower(), y), min BOOST_PREVENT_MACRO_SUBSTITUTION(x.upper(), y), true);
Chris@16: }
Chris@16: 
Chris@16: template<class T, class Policies> inline
Chris@16: interval<T, Policies> min BOOST_PREVENT_MACRO_SUBSTITUTION (const T& x, const interval<T, Policies>& y)
Chris@16: {
Chris@16:   typedef interval<T, Policies> I;
Chris@16:   if (interval_lib::detail::test_input(x, y))
Chris@16:     return I::empty();
Chris@16:   BOOST_USING_STD_MIN();
Chris@16:   return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.lower()), min BOOST_PREVENT_MACRO_SUBSTITUTION(x, y.upper()), true);
Chris@16: }
Chris@16: 
Chris@16: } // namespace numeric
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_NUMERIC_INTERVAL_UTILITY_HPP