| /* 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 |