/usr/include/boost/numeric/interval
Edit: /usr/include/boost/numeric/interval/transc.hpp (7917B)
/* 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