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