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/* 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 #include #include #include #include #include #include #include #include namespace boost { namespace numeric { template inline interval exp(const interval& x) { typedef interval 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 inline interval log(const interval& x) { typedef interval 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 inline interval cos(const interval& x) { if (interval_lib::detail::test_input(x)) return interval::empty(); typename Policies::rounding rnd; typedef interval I; typedef typename interval_lib::unprotect::type R; // get lower bound within [0, pi] const R pi2 = interval_lib::pi_twice(); R tmp = fmod((const R&)x, pi2); if (width(tmp) >= pi2.lower()) return I(static_cast(-1), static_cast(1), true); // we are covering a full period if (tmp.lower() >= interval_lib::constants::pi_upper()) return -cos(tmp - interval_lib::pi()); T l = tmp.lower(); T u = tmp.upper(); BOOST_USING_STD_MIN(); // separate into monotone subintervals if (u <= interval_lib::constants::pi_lower()) return I(rnd.cos_down(u), rnd.cos_up(l), true); else if (u <= pi2.lower()) return I(static_cast(-1), rnd.cos_up(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.sub_down(pi2.lower(), u), l)), true); else return I(static_cast(-1), static_cast(1), true); } template inline interval sin(const interval& x) { typedef interval I; if (interval_lib::detail::test_input(x)) return I::empty(); typename Policies::rounding rnd; typedef typename interval_lib::unprotect::type R; I r = cos((const R&)x - interval_lib::pi_half()); (void)&rnd; return r; } template inline interval tan(const interval& x) { typedef interval I; if (interval_lib::detail::test_input(x)) return I::empty(); typename Policies::rounding rnd; typedef typename interval_lib::unprotect::type R; // get lower bound within [-pi/2, pi/2] const R pi = interval_lib::pi(); R tmp = fmod((const R&)x, pi); const T pi_half_d = interval_lib::constants::pi_half_lower(); 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 inline interval asin(const interval& x) { typedef interval I; if (interval_lib::detail::test_input(x) || x.upper() < static_cast(-1) || x.lower() > static_cast(1)) return I::empty(); typename Policies::rounding rnd; T l = (x.lower() <= static_cast(-1)) ? -interval_lib::constants::pi_half_upper() : rnd.asin_down(x.lower()); T u = (x.upper() >= static_cast(1) ) ? interval_lib::constants::pi_half_upper() : rnd.asin_up (x.upper()); return I(l, u, true); } template inline interval acos(const interval& x) { typedef interval I; if (interval_lib::detail::test_input(x) || x.upper() < static_cast(-1) || x.lower() > static_cast(1)) return I::empty(); typename Policies::rounding rnd; T l = (x.upper() >= static_cast(1) ) ? static_cast(0) : rnd.acos_down(x.upper()); T u = (x.lower() <= static_cast(-1)) ? interval_lib::constants::pi_upper() : rnd.acos_up (x.lower()); return I(l, u, true); } template inline interval atan(const interval& x) { typedef interval 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 inline interval sinh(const interval& x) { typedef interval 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 inline interval cosh(const interval& x) { typedef interval 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(1), rnd.cosh_up(-x.lower() > x.upper() ? x.lower() : x.upper()), true); } template inline interval tanh(const interval& x) { typedef interval 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 inline interval asinh(const interval& x) { typedef interval 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 inline interval acosh(const interval& x) { typedef interval I; if (interval_lib::detail::test_input(x) || x.upper() < static_cast(1)) return I::empty(); typename Policies::rounding rnd; T l = x.lower() <= static_cast(1) ? static_cast(0) : rnd.acosh_down(x.lower()); return I(l, rnd.acosh_up(x.upper()), true); } template inline interval atanh(const interval& x) { typedef interval I; if (interval_lib::detail::test_input(x) || x.upper() < static_cast(-1) || x.lower() > static_cast(1)) return I::empty(); typename Policies::rounding rnd; typedef typename Policies::checking checking; T l = (x.lower() <= static_cast(-1)) ? checking::neg_inf() : rnd.atanh_down(x.lower()); T u = (x.upper() >= static_cast(1) ) ? checking::pos_inf() : rnd.atanh_up (x.upper()); return I(l, u, true); } } // namespace numeric } // namespace boost #endif // BOOST_NUMERIC_INTERVAL_TRANSC_HPP