/* 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