/* Boost interval/transc.hpp template implementation file

 *

 * Copyright 2000 Jens Maurer

 * Copyright 2002 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion

 *

 * Distributed under the Boost Software License, Version 1.0.

 * (See accompanying file LICENSE_1_0.txt or

 * copy at http://www.boost.org/LICENSE_1_0.txt)

 */

#ifndef BOOST_NUMERIC_INTERVAL_TRANSC_HPP

#define BOOST_NUMERIC_INTERVAL_TRANSC_HPP

#include <boost/config.hpp>

#include <boost/numeric/interval/detail/interval_prototype.hpp>

#include <boost/numeric/interval/detail/bugs.hpp>

#include <boost/numeric/interval/detail/test_input.hpp>

#include <boost/numeric/interval/rounding.hpp>

#include <boost/numeric/interval/constants.hpp>

#include <boost/numeric/interval/arith.hpp>

#include <boost/numeric/interval/arith2.hpp>

#include <algorithm>

namespace boost {

namespace numeric {

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);

}

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);

}

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);

}

template<class T, class Policies> inline

interval<T, Policies> sin(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;

  I r = cos((const R&)x - interval_lib::pi_half<R>());

  (void)&rnd;

  return r;

}

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);

}

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);

}

template<class T, class Policies> inline

interval<T, Policies> acos(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.upper() >= static_cast<T>(1) )

          ? static_cast<T>(0)

          : rnd.acos_down(x.upper());

  T u = (x.lower() <= static_cast<T>(-1))

          ? interval_lib::constants::pi_upper<T>()

          : rnd.acos_up  (x.lower());

  return I(l, u, true);

}

template<class T, class Policies> inline

interval<T, Policies> atan(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.atan_down(x.lower()), rnd.atan_up(x.upper()), true);

}

template<class T, class Policies> inline

interval<T, Policies> sinh(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.sinh_down(x.lower()), rnd.sinh_up(x.upper()), true);

}

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);

}

template<class T, class Policies> inline

interval<T, Policies> tanh(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.tanh_down(x.lower()), rnd.tanh_up(x.upper()), true);

}

template<class T, class Policies> inline

interval<T, Policies> asinh(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.asinh_down(x.lower()), rnd.asinh_up(x.upper()), true);

}

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);

}

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);

}

} // namespace numeric

} // namespace boost

#endif // BOOST_NUMERIC_INTERVAL_TRANSC_HPP