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boost/numeric/interval/utility.hpp

/* Boost interval/utility.hpp template implementation file
 *
 * Copyright Jens Maurer 2000
 * Copyright Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion 2002-2003
 * Permission to use, copy, modify, sell, and distribute this software
 * is hereby granted without fee provided that the above copyright notice
 * appears in all copies and that both that copyright notice and this
 * permission notice appear in supporting documentation,
 *
 * None of the above authors nor Polytechnic University make any
 * representation about the suitability of this software for any
 * purpose. It is provided "as is" without express or implied warranty.
 *
 * $Id: utility.hpp,v 1.7 2003/09/12 06:06:12 gmelquio Exp $
 */

#ifndef BOOST_NUMERIC_INTERVAL_UTILITY_HPP
#define BOOST_NUMERIC_INTERVAL_UTILITY_HPP

#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
#include <boost/numeric/interval/detail/bugs.hpp>
#include <algorithm>
#include <utility>

/*
 * Implementation of simple functions
 */

namespace boost {
namespace numeric {

/*
 * Utility Functions
 */

template<class T, class Policies> inline
const T& lower(const interval<T, Policies>& x)
{
  return x.lower();
}

template<class T, class Policies> inline
const T& upper(const interval<T, Policies>& x)
{
  return x.upper();
}

template<class T, class Policies> inline
T checked_lower(const interval<T, Policies>& x)
{
  if (empty(x)) {
    typedef typename Policies::checking checking;
    return checking::nan();
  }
  return x.lower();
}

template<class T, class Policies> inline
T checked_upper(const interval<T, Policies>& x)
{
  if (empty(x)) {
    typedef typename Policies::checking checking;
    return checking::nan();
  }
  return x.upper();
}

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
T median(const interval<T, Policies>& x)
{
  if (interval_lib::detail::test_input(x)) {
    typedef typename Policies::checking checking;
    return checking::nan();
  }
  typename Policies::rounding rnd;
  return rnd.median(x.lower(), x.upper());
}

template<class T, class Policies> inline
interval<T, Policies> widen(const interval<T, Policies>& x, const T& v)
{
  if (interval_lib::detail::test_input(x))
    return interval<T, Policies>::empty();
  typename Policies::rounding rnd;
  return interval<T, Policies>(rnd.sub_down(x.lower(), v),
                               rnd.add_up  (x.upper(), v), true);
}

/*
 * Set-like operations
 */

template<class T, class Policies> inline
bool empty(const interval<T, Policies>& x)
{
  return interval_lib::detail::test_input(x);
}

template<class T, class Policies> inline
bool in_zero(const interval<T, Policies>& x)
{
  if (interval_lib::detail::test_input(x)) return false;
  return x.lower() <= static_cast<T>(0) && static_cast<T>(0) <= x.upper();
}

template<class T, class Policies> inline
bool in(const T& x, const interval<T, Policies>& y)
{
  if (interval_lib::detail::test_input(x, y)) return false;
  return y.lower() <= x && x <= y.upper();
}

template<class T, class Policies> inline
bool subset(const interval<T, Policies>& x,
            const interval<T, Policies>& y)
{
  if (empty(x)) return true;
  return !empty(y) && y.lower() <= x.lower() && x.upper() <= 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 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 Policies> inline
bool singleton(const interval<T, Policies>& x)
{
 return !empty(x) && x.lower() == x.upper();
}

template<class T, class Policies1, class Policies2> inline
bool equal(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
  if (empty(x)) return empty(y);
  return !empty(y) && x.lower() == y.lower() && x.upper() == y.upper();
}

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> 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
interval<T, Policies> hull(const interval<T, Policies>& x, const T& 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<T, Policies>(y);
  if (bad_y)
    if (bad_x) return interval<T, Policies>::empty();
    else       return x;
  else
    if (bad_x) return interval<T, Policies>(y, y, true);
  return interval<T, Policies>(min(x.lower(), y),
                               max(x.upper(), y), true);
}

template<class T, class Policies> inline
interval<T, Policies> hull(const T& 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<T, Policies>(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 interval<T, Policies>(x, x, true);
  return interval<T, Policies>(min(x, y.lower()),
                               max(x, y.upper()), true);
}

template<class T> inline
interval<T> hull(const T& x, const T& y)
{
  return interval<T>::hull(x, y);
}

template<class T, class Policies> inline
std::pair<interval<T, Policies>, interval<T, Policies> >
bisect(const interval<T, Policies>& x)
{
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x))
    return std::pair<I,I>(I::empty(), I::empty());
  const T m = median(x);
  return std::pair<I,I>(I(x.lower(), m, true), I(m, x.upper(), true));
}

/*
 * Elementary functions
 */

template<class T, class Policies> inline
T norm(const interval<T, Policies>& x)
{
  BOOST_NUMERIC_INTERVAL_using_max(max);
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x)) {
    typedef typename Policies::checking checking;
    return checking::nan();
  }
  return max(-x.lower(), x.upper());
}

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(static_cast<T>(0), max(-x.lower(), x.upper()), true);
}

template<class T, class Policies> inline
interval<T, Policies> max(const interval<T, Policies>& x,
                          const interval<T, Policies>& y)
{
  BOOST_NUMERIC_INTERVAL_using_max(max);
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x, y))
    return I::empty();
  return I(max(x.lower(), y.lower()), max(x.upper(), y.upper()), true);
}

template<class T, class Policies> inline
interval<T, Policies> max(const interval<T, Policies>& x, const T& y)
{
  BOOST_NUMERIC_INTERVAL_using_max(max);
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x, y))
    return I::empty();
  return I(max(x.lower(), y), max(x.upper(), y), true);
}

template<class T, class Policies> inline
interval<T, Policies> max(const T& x, const interval<T, Policies>& y)
{
  BOOST_NUMERIC_INTERVAL_using_max(max);
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x, y))
    return I::empty();
  return I(max(x, y.lower()), max(x, y.upper()), true);
}

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> min(const interval<T, Policies>& x, const T& 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), min(x.upper(), y), true);
}

template<class T, class Policies> inline
interval<T, Policies> min(const T& 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, y.lower()), min(x, y.upper()), true);
}

} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_INTERVAL_UTILITY_HPP