sl@0: /* Boost interval/transc.hpp template implementation file
sl@0:  *
sl@0:  * Copyright 2000 Jens Maurer
sl@0:  * Copyright 2002 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion
sl@0:  *
sl@0:  * Distributed under the Boost Software License, Version 1.0.
sl@0:  * (See accompanying file LICENSE_1_0.txt or
sl@0:  * copy at http://www.boost.org/LICENSE_1_0.txt)
sl@0:  */
sl@0: 
sl@0: #ifndef BOOST_NUMERIC_INTERVAL_TRANSC_HPP
sl@0: #define BOOST_NUMERIC_INTERVAL_TRANSC_HPP
sl@0: 
sl@0: #include <boost/config.hpp>
sl@0: #include <boost/numeric/interval/detail/interval_prototype.hpp>
sl@0: #include <boost/numeric/interval/detail/bugs.hpp>
sl@0: #include <boost/numeric/interval/detail/test_input.hpp>
sl@0: #include <boost/numeric/interval/rounding.hpp>
sl@0: #include <boost/numeric/interval/constants.hpp>
sl@0: #include <boost/numeric/interval/arith.hpp>
sl@0: #include <boost/numeric/interval/arith2.hpp>
sl@0: #include <algorithm>
sl@0: 
sl@0: namespace boost {
sl@0: namespace numeric {
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> exp(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   return I(rnd.exp_down(x.lower()), rnd.exp_up(x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> log(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x) ||
sl@0:       !interval_lib::user::is_pos(x.upper()))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   typedef typename Policies::checking checking;
sl@0:   T l = !interval_lib::user::is_pos(x.lower())
sl@0:              ? checking::neg_inf() : rnd.log_down(x.lower());
sl@0:   return I(l, rnd.log_up(x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> cos(const interval<T, Policies>& x)
sl@0: {
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return interval<T, Policies>::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   typedef interval<T, Policies> I;
sl@0:   typedef typename interval_lib::unprotect<I>::type R;
sl@0: 
sl@0:   // get lower bound within [0, pi]
sl@0:   const R pi2 = interval_lib::pi_twice<R>();
sl@0:   R tmp = fmod((const R&)x, pi2);
sl@0:   if (width(tmp) >= pi2.lower())
sl@0:     return I(static_cast<T>(-1), static_cast<T>(1), true); // we are covering a full period
sl@0:   if (tmp.lower() >= interval_lib::constants::pi_upper<T>())
sl@0:     return -cos(tmp - interval_lib::pi<R>());
sl@0:   T l = tmp.lower();
sl@0:   T u = tmp.upper();
sl@0: 
sl@0:   BOOST_USING_STD_MIN();
sl@0:   // separate into monotone subintervals
sl@0:   if (u <= interval_lib::constants::pi_lower<T>())
sl@0:     return I(rnd.cos_down(u), rnd.cos_up(l), true);
sl@0:   else if (u <= pi2.lower())
sl@0:     return I(static_cast<T>(-1), rnd.cos_up(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.sub_down(pi2.lower(), u), l)), true);
sl@0:   else
sl@0:     return I(static_cast<T>(-1), static_cast<T>(1), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> sin(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   typedef typename interval_lib::unprotect<I>::type R;
sl@0:   I r = cos((const R&)x - interval_lib::pi_half<R>());
sl@0:   (void)&rnd;
sl@0:   return r;
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> tan(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   typedef typename interval_lib::unprotect<I>::type R;
sl@0: 
sl@0:   // get lower bound within [-pi/2, pi/2]
sl@0:   const R pi = interval_lib::pi<R>();
sl@0:   R tmp = fmod((const R&)x, pi);
sl@0:   const T pi_half_d = interval_lib::constants::pi_half_lower<T>();
sl@0:   if (tmp.lower() >= pi_half_d)
sl@0:     tmp -= pi;
sl@0:   if (tmp.lower() <= -pi_half_d || tmp.upper() >= pi_half_d)
sl@0:     return I::whole();
sl@0:   return I(rnd.tan_down(tmp.lower()), rnd.tan_up(tmp.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> asin(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x)
sl@0:      || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   T l = (x.lower() <= static_cast<T>(-1))
sl@0:              ? -interval_lib::constants::pi_half_upper<T>()
sl@0:              : rnd.asin_down(x.lower());
sl@0:   T u = (x.upper() >= static_cast<T>(1) )
sl@0:              ?  interval_lib::constants::pi_half_upper<T>()
sl@0:              : rnd.asin_up  (x.upper());
sl@0:   return I(l, u, true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> acos(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x)
sl@0:      || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   T l = (x.upper() >= static_cast<T>(1) )
sl@0:           ? static_cast<T>(0)
sl@0:           : rnd.acos_down(x.upper());
sl@0:   T u = (x.lower() <= static_cast<T>(-1))
sl@0:           ? interval_lib::constants::pi_upper<T>()
sl@0:           : rnd.acos_up  (x.lower());
sl@0:   return I(l, u, true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> atan(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   return I(rnd.atan_down(x.lower()), rnd.atan_up(x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> sinh(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   return I(rnd.sinh_down(x.lower()), rnd.sinh_up(x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> cosh(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   if (interval_lib::user::is_neg(x.upper()))
sl@0:     return I(rnd.cosh_down(x.upper()), rnd.cosh_up(x.lower()), true);
sl@0:   else if (!interval_lib::user::is_neg(x.lower()))
sl@0:     return I(rnd.cosh_down(x.lower()), rnd.cosh_up(x.upper()), true);
sl@0:   else
sl@0:     return I(static_cast<T>(0), rnd.cosh_up(-x.lower() > x.upper() ? x.lower() : x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> tanh(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   return I(rnd.tanh_down(x.lower()), rnd.tanh_up(x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> asinh(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   return I(rnd.asinh_down(x.lower()), rnd.asinh_up(x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> acosh(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x) || x.upper() < static_cast<T>(1))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   T l = x.lower() <= static_cast<T>(1) ? static_cast<T>(0) : rnd.acosh_down(x.lower());
sl@0:   return I(l, rnd.acosh_up(x.upper()), true);
sl@0: }
sl@0: 
sl@0: template<class T, class Policies> inline
sl@0: interval<T, Policies> atanh(const interval<T, Policies>& x)
sl@0: {
sl@0:   typedef interval<T, Policies> I;
sl@0:   if (interval_lib::detail::test_input(x)
sl@0:       || x.upper() < static_cast<T>(-1) || x.lower() > static_cast<T>(1))
sl@0:     return I::empty();
sl@0:   typename Policies::rounding rnd;
sl@0:   typedef typename Policies::checking checking;
sl@0:   T l = (x.lower() <= static_cast<T>(-1))
sl@0:              ? checking::neg_inf() : rnd.atanh_down(x.lower());
sl@0:   T u = (x.upper() >= static_cast<T>(1) )
sl@0:              ? checking::pos_inf() : rnd.atanh_up  (x.upper());
sl@0:   return I(l, u, true);
sl@0: }
sl@0: 
sl@0: } // namespace numeric
sl@0: } // namespace boost
sl@0: 
sl@0: #endif // BOOST_NUMERIC_INTERVAL_TRANSC_HPP