/* 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>(1), 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 |