Exemplo n.º 1
0
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());
}
Exemplo 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);
    }
}
Exemplo n.º 3
0
template<class T, class Policies> inline
interval<T, Policies> cos(const interval<T, Policies>& x)
{
  if (interval_lib::detail::test_input(x))
    return interval<T, Policies>::empty();
  typename Policies::rounding rnd;
  typedef interval<T, Policies> I;
  typedef typename interval_lib::unprotect<I>::type R;

  // get lower bound within [0, pi]
  const R pi2 = interval_lib::pi_twice<R>();
  R tmp = fmod((const R&)x, pi2);
  if (width(tmp) >= pi2.lower())
    return I(static_cast<T>(-1), static_cast<T>(1), true); // we are covering a full period
  if (tmp.lower() >= interval_lib::constants::pi_upper<T>())
    return -cos(tmp - interval_lib::pi<R>());
  T l = tmp.lower();
  T u = tmp.upper();

  BOOST_USING_STD_MIN();
  // separate into monotone subintervals
  if (u <= interval_lib::constants::pi_lower<T>())
    return I(rnd.cos_down(u), rnd.cos_up(l), true);
  else if (u <= pi2.lower())
    return I(static_cast<T>(-1), rnd.cos_up(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.sub_down(pi2.lower(), u), l)), true);
  else
    return I(static_cast<T>(-1), static_cast<T>(1), true);
}
Exemplo n.º 4
0
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);
}
Exemplo n.º 5
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template<class T, class Policies> inline
interval<T, Policies> operator-(const T& 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, y.upper()),
                              rnd.sub_up  (x, y.lower()), true);
}
Exemplo n.º 6
0
template<class T, class Policies> inline
interval<T, Policies> exp(const interval<T, Policies>& x)
{
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x))
    return I::empty();
  typename Policies::rounding rnd;
  return I(rnd.exp_down(x.lower()), rnd.exp_up(x.upper()), true);
}
Exemplo n.º 7
0
template<class I> inline
I div(const typename I::base_type& x, const typename I::base_type& y)
{
  typedef typename I::traits_type Policies;
  if (detail::test_input<typename I::base_type, Policies>(x, y) || user::is_zero(y))
    return I::empty();
  typename Policies::rounding rnd;
  return I(rnd.div_down(x, y), rnd.div_up(x, y), true);
}
Exemplo n.º 8
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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);
}
Exemplo n.º 9
0
template<class T, class Policies> inline
interval<T, Policies> fmod(const interval<T, Policies>& x, const T& y)
{
  if (interval_lib::detail::test_input(x, y))
    return interval<T, Policies>::empty();
  typename Policies::rounding rnd;
  typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
  T n = rnd.int_down(rnd.div_down(x.lower(), y));
  return (const I&)x - n * I(y);
}
Exemplo n.º 10
0
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());
}
Exemplo n.º 11
0
template<class T, class Policies> inline
interval<T, Policies> fmod(const T& x, const interval<T, Policies>& y)
{
  if (interval_lib::detail::test_input(x, y))
    return interval<T, Policies>::empty();
  typename Policies::rounding rnd;
  typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
  const T& yb = interval_lib::detail::is_neg(x) ? y.lower() : y.upper();
  T n = rnd.int_down(rnd.div_down(x, yb));
  return x - n * (const I&)y;
}
Exemplo n.º 12
0
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator-=(const T& r)
{
  if (interval_lib::detail::test_input(*this, r))
    set_empty();
  else {
    typename Policies::rounding rnd;
    set(rnd.sub_down(low, r), rnd.sub_up(up, r));
  }
  return *this;
}
Exemplo n.º 13
0
template<class T, class Policies> inline
interval<T, Policies> div_non_zero(const T& x, const interval<T, Policies>& y)
{
  // assert(!in_zero(y));
  typename Policies::rounding rnd;
  typedef interval<T, Policies> I;
  const T& yl = y.lower();
  const T& yu = y.upper();
  if (::boost::numeric::interval_lib::user::is_neg(x))
    return I(rnd.div_down(x, yl), rnd.div_up(x, yu), true);
  else
    return I(rnd.div_down(x, yu), rnd.div_up(x, yl), true);
}
Exemplo n.º 14
0
template<class T, class Policies> inline
interval<T, Policies> operator/(const interval<T, Policies>& x, const T& y)
{
  if (interval_lib::detail::test_input(x, y) || interval_lib::user::is_zero(y))
    return interval<T, Policies>::empty();
  typename Policies::rounding rnd;
  const T& xl = x.lower();
  const T& xu = x.upper();
  if (interval_lib::user::is_neg(y))
    return interval<T, Policies>(rnd.div_down(xu, y), rnd.div_up(xl, y), true);
  else
    return interval<T, Policies>(rnd.div_down(xl, y), rnd.div_up(xu, y), true);
}
Exemplo n.º 15
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);
}
Exemplo 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);
}
Exemplo n.º 17
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template<class T, class Policies> inline
interval<T, Policies> div_positive(const T& x, const T& yu)
{
    // assert(yu > T(0));
    typedef interval<T, Policies> I;
    if (is_zero(x)) return I(0, 0, true);
    typename Policies::rounding rnd;
    typedef typename Policies::checking checking;
    const T& inf = checking::inf();
    if (is_neg(x))
        return I(-inf, rnd.div_up(x, yu), true);
    else
        return I(rnd.div_down(x, yu), inf, true);
}
Exemplo n.º 18
0
template<class T, class Policies> inline
interval<T, Policies> div_positive(const T& x, const T& yu)
{
  // assert(::boost::numeric::interval_lib::user::is_pos(yu));
  typedef interval<T, Policies> I;
  if (::boost::numeric::interval_lib::user::is_zero(x))
    return I(static_cast<T>(0), static_cast<T>(0), true);
  typename Policies::rounding rnd;
  typedef typename Policies::checking checking;
  if (::boost::numeric::interval_lib::user::is_neg(x))
    return I(checking::neg_inf(), rnd.div_up(x, yu), true);
  else
    return I(rnd.div_down(x, yu), checking::pos_inf(), true);
}
Exemplo 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);
}
Exemplo 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);
}
Exemplo n.º 21
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);
}
Exemplo n.º 22
0
template<class T, class Policies> inline
interval<T, Policies> operator*(const T& x, const interval<T, Policies>& y)
{ 
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x, y))
    return I::empty();
  typename Policies::rounding rnd;
  const T& yl = y.lower();
  const T& yu = y.upper();
  // x is supposed not to be infinite
  if (interval_lib::user::is_neg(x))
    return I(rnd.mul_down(x, yu), rnd.mul_up(x, yl), true);
  else if (interval_lib::user::is_zero(x))
    return I(static_cast<T>(0), static_cast<T>(0), true);
  else
    return I(rnd.mul_down(x, yl), rnd.mul_up(x, yu), true);
}
Exemplo n.º 23
0
template<class T, class Policies> inline
interval<T, Policies> tan(const interval<T, Policies>& x)
{
  typedef interval<T, Policies> I;
  if (interval_lib::detail::test_input(x))
    return I::empty();
  typename Policies::rounding rnd;
  typedef typename interval_lib::unprotect<I>::type R;

  // get lower bound within [-pi/2, pi/2]
  const R pi = interval_lib::pi<R>();
  R tmp = fmod((const R&)x, pi);
  const T pi_half_d = interval_lib::constants::pi_half_lower<T>();
  if (tmp.lower() >= pi_half_d)
    tmp -= pi;
  if (tmp.lower() <= -pi_half_d || tmp.upper() >= pi_half_d)
    return I::whole();
  return I(rnd.tan_down(tmp.lower()), rnd.tan_up(tmp.upper()), true);
}
Exemplo n.º 24
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template<class T, class Policies> inline
interval<T, Policies> div_negative(const interval<T, Policies>& x, const T& yl)
{
    // assert(yl < T(0));
    if (is_zero(x.lower()) && is_zero(x.upper()))
        return x;
    typename Policies::rounding rnd;
    typedef interval<T, Policies> I;
    const T& xl = x.lower();
    const T& xu = x.upper();
    typedef typename Policies::checking checking;
    const T& inf = checking::inf();
    if (is_neg(xu))
        return I(rnd.div_down(xu, yl), inf, true);
    else if (is_neg(xl))
        return I(-inf, inf, true);
    else
        return I(-inf, rnd.div_up(xl, yl), true);
}
Exemplo n.º 25
0
template<class T, class Policies> inline
interval<T, Policies> div_positive(const interval<T, Policies>& x, const T& yu)
{
  // assert(::boost::numeric::interval_lib::user::is_pos(yu));
  if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
      ::boost::numeric::interval_lib::user::is_zero(x.upper()))
    return x;
  typename Policies::rounding rnd;
  typedef interval<T, Policies> I;
  const T& xl = x.lower();
  const T& xu = x.upper();
  typedef typename Policies::checking checking;
  if (::boost::numeric::interval_lib::user::is_neg(xu))
    return I(checking::neg_inf(), rnd.div_up(xu, yu), true);
  else if (::boost::numeric::interval_lib::user::is_neg(xl))
    return I(checking::neg_inf(), checking::pos_inf(), true);
  else
    return I(rnd.div_down(xl, yu), checking::pos_inf(), true);
}
Exemplo n.º 26
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(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()));
  if (::boost::numeric::interval_lib::user::is_zero(x.lower()) && ::boost::numeric::interval_lib::user::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 Policies::checking checking;
  if (::boost::numeric::interval_lib::user::is_neg(xu))
    { b = true;  return I(checking::neg_inf(), rnd.div_up(xu, yu), true); }
  else if (::boost::numeric::interval_lib::user::is_neg(xl))
    { b = false; return I(checking::neg_inf(), checking::pos_inf(), true); }
  else
    { b = true;  return I(checking::neg_inf(), rnd.div_up(xl, yl), true); }
}
Exemplo n.º 27
0
template<class T, class Policies> inline
interval<T, Policies> multiplicative_inverse(const interval<T, Policies>& x)
{
  typedef interval<T, Policies> I;
  if (detail::test_input(x))
    return I::empty();
  T one = static_cast<T>(1);
  typename Policies::rounding rnd;
  if (in_zero(x)) {
    typedef typename Policies::checking checking;
    if (!detail::is_zero(x.lower()))
      if (!detail::is_zero(x.upper()))
        return I::whole();
      else
        return I(-checking::inf(), rnd.div_up(one, x.lower()), true);
    else
      if (!detail::is_zero(x.upper()))
        return I(rnd.div_down(one, x.upper()), checking::inf(), true);
      else
        return I::empty();
  } else 
    return I(rnd.div_down(one, x.upper()), rnd.div_up(one, x.lower()), true);
}
Exemplo n.º 28
0
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);
}
Exemplo n.º 29
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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);
}
Exemplo n.º 30
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);
}