Ejemplo n.º 1
0
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);
}
Ejemplo n.º 2
0
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);
    }
}
Ejemplo n.º 3
0
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());
}
Ejemplo n.º 4
0
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;
}
Ejemplo n.º 5
0
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();
}
Ejemplo n.º 6
0
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());
}
Ejemplo n.º 7
0
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);
}
Ejemplo n.º 8
0
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);
}
Ejemplo n.º 9
0
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);
}
Ejemplo n.º 10
0
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);
}
Ejemplo n.º 11
0
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);
}
Ejemplo n.º 12
0
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);
}
Ejemplo n.º 13
0
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);
}
Ejemplo n.º 14
0
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();
}
Ejemplo n.º 15
0
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();
}
Ejemplo n.º 16
0
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);
}
Ejemplo n.º 17
0
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);
}
Ejemplo n.º 18
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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);
}
Ejemplo n.º 19
0
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);
}
Ejemplo n.º 20
0
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);
}
Ejemplo n.º 21
0
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()));
}
Ejemplo n.º 22
0
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);
}
Ejemplo n.º 23
0
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);
}
Ejemplo n.º 24
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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);
}
Ejemplo n.º 25
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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);
}
Ejemplo n.º 26
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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());
}
Ejemplo n.º 27
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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();
}
Ejemplo n.º 28
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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);
}
Ejemplo n.º 29
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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;
}
Ejemplo n.º 30
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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();
}