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