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Added mathsym+tcc and boost against all advice

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maartenkeijzer 2005-10-06 12:13:53 +00:00
commit 90702a435d
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32
eo/contrib/boost/numeric/interval.hpp Normal file
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/* Boost interval.hpp header 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_HPP
#define BOOST_NUMERIC_INTERVAL_HPP
#include <boost/limits.hpp>
#include <boost/numeric/interval/interval.hpp>
#include <boost/numeric/interval/policies.hpp>
#include <boost/numeric/interval/hw_rounding.hpp>
#include <boost/numeric/interval/rounded_arith.hpp>
#include <boost/numeric/interval/rounded_transc.hpp>
#include <boost/numeric/interval/constants.hpp>
#include <boost/numeric/interval/checking.hpp>
#include <boost/numeric/interval/compare.hpp>
#include <boost/numeric/interval/utility.hpp>
#include <boost/numeric/interval/arith.hpp>
#include <boost/numeric/interval/arith2.hpp>
#include <boost/numeric/interval/arith3.hpp>
#include <boost/numeric/interval/transc.hpp>
#endif // BOOST_NUMERIC_INTERVAL_HPP

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/* Boost interval/arith.hpp template implementation file
*
* Copyright 2000 Jens Maurer
* Copyright 2002-2003 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_ARITH_HPP
#define BOOST_NUMERIC_INTERVAL_ARITH_HPP
#include <boost/config.hpp>
#include <boost/numeric/interval/interval.hpp>
#include <boost/numeric/interval/detail/bugs.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
#include <boost/numeric/interval/detail/division.hpp>
#include <algorithm>
namespace boost {
namespace numeric {
/*
* Basic arithmetic operators
*/
template<class T, class Policies> inline
const interval<T, Policies>& operator+(const interval<T, Policies>& x)
{
return x;
}
template<class T, class Policies> inline
interval<T, Policies> operator-(const interval<T, Policies>& x)
{
if (interval_lib::detail::test_input(x))
return interval<T, Policies>::empty();
return interval<T, Policies>(-x.upper(), -x.lower(), true);
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator+=(const interval<T, Policies>& r)
{
if (interval_lib::detail::test_input(*this, r))
set_empty();
else {
typename Policies::rounding rnd;
set(rnd.add_down(low, r.low), rnd.add_up(up, r.up));
}
return *this;
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator+=(const T& r)
{
if (interval_lib::detail::test_input(*this, r))
set_empty();
else {
typename Policies::rounding rnd;
set(rnd.add_down(low, r), rnd.add_up(up, r));
}
return *this;
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator-=(const interval<T, Policies>& r)
{
if (interval_lib::detail::test_input(*this, r))
set_empty();
else {
typename Policies::rounding rnd;
set(rnd.sub_down(low, r.up), rnd.sub_up(up, r.low));
}
return *this;
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator-=(const T& r)
{
if (interval_lib::detail::test_input(*this, r))
set_empty();
else {
typename Policies::rounding rnd;
set(rnd.sub_down(low, r), rnd.sub_up(up, r));
}
return *this;
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator*=(const interval<T, Policies>& r)
{
return *this = *this * r;
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator*=(const T& r)
{
return *this = r * *this;
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator/=(const interval<T, Policies>& r)
{
return *this = *this / r;
}
template<class T, class Policies> inline
interval<T, Policies>& interval<T, Policies>::operator/=(const T& r)
{
return *this = *this / r;
}
template<class T, class Policies> inline
interval<T, Policies> operator+(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
return interval<T,Policies>(rnd.add_down(x.lower(), y.lower()),
rnd.add_up (x.upper(), y.upper()), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator+(const T& x, const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
return interval<T,Policies>(rnd.add_down(x, y.lower()),
rnd.add_up (x, y.upper()), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator+(const interval<T, Policies>& x, const T& y)
{ return y + x; }
template<class T, class Policies> inline
interval<T, Policies> operator-(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
return interval<T,Policies>(rnd.sub_down(x.lower(), y.upper()),
rnd.sub_up (x.upper(), y.lower()), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator-(const T& x, const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
return interval<T,Policies>(rnd.sub_down(x, y.upper()),
rnd.sub_up (x, y.lower()), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator-(const interval<T, Policies>& x, const T& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
return interval<T,Policies>(rnd.sub_down(x.lower(), y),
rnd.sub_up (x.upper(), y), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator*(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x, y))
return I::empty();
typename Policies::rounding rnd;
const T& xl = x.lower();
const T& xu = x.upper();
const T& yl = y.lower();
const T& yu = y.upper();
if (interval_lib::user::is_neg(xl))
if (interval_lib::user::is_pos(xu))
if (interval_lib::user::is_neg(yl))
if (interval_lib::user::is_pos(yu)) // M * M
return I(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_down(xl, yu), rnd.mul_down(xu, yl)),
max BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.mul_up (xl, yl), rnd.mul_up (xu, yu)), true);
else // M * N
return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yl), true);
else
if (interval_lib::user::is_pos(yu)) // M * P
return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yu), true);
else // M * Z
return I(static_cast<T>(0), static_cast<T>(0), true);
else
if (interval_lib::user::is_neg(yl))
if (interval_lib::user::is_pos(yu)) // N * M
return I(rnd.mul_down(xl, yu), rnd.mul_up(xl, yl), true);
else // N * N
return I(rnd.mul_down(xu, yu), rnd.mul_up(xl, yl), true);
else
if (interval_lib::user::is_pos(yu)) // N * P
return I(rnd.mul_down(xl, yu), rnd.mul_up(xu, yl), true);
else // N * Z
return I(static_cast<T>(0), static_cast<T>(0), true);
else
if (interval_lib::user::is_pos(xu))
if (interval_lib::user::is_neg(yl))
if (interval_lib::user::is_pos(yu)) // P * M
return I(rnd.mul_down(xu, yl), rnd.mul_up(xu, yu), true);
else // P * N
return I(rnd.mul_down(xu, yl), rnd.mul_up(xl, yu), true);
else
if (interval_lib::user::is_pos(yu)) // P * P
return I(rnd.mul_down(xl, yl), rnd.mul_up(xu, yu), true);
else // P * Z
return I(static_cast<T>(0), static_cast<T>(0), true);
else // Z * ?
return I(static_cast<T>(0), static_cast<T>(0), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator*(const T& x, const interval<T, Policies>& y)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x, y))
return I::empty();
typename Policies::rounding rnd;
const T& yl = y.lower();
const T& yu = y.upper();
// x is supposed not to be infinite
if (interval_lib::user::is_neg(x))
return I(rnd.mul_down(x, yu), rnd.mul_up(x, yl), true);
else if (interval_lib::user::is_zero(x))
return I(static_cast<T>(0), static_cast<T>(0), true);
else
return I(rnd.mul_down(x, yl), rnd.mul_up(x, yu), true);
}
template<class T, class Policies> inline
interval<T, Policies> operator*(const interval<T, Policies>& x, const T& y)
{ return y * x; }
template<class T, class Policies> inline
interval<T, Policies> operator/(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
if (in_zero(y))
if (!interval_lib::user::is_zero(y.lower()))
if (!interval_lib::user::is_zero(y.upper()))
return interval_lib::detail::div_zero(x);
else
return interval_lib::detail::div_negative(x, y.lower());
else
if (!interval_lib::user::is_zero(y.upper()))
return interval_lib::detail::div_positive(x, y.upper());
else
return interval<T, Policies>::empty();
else
return interval_lib::detail::div_non_zero(x, y);
}
template<class T, class Policies> inline
interval<T, Policies> operator/(const T& x, const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
if (in_zero(y))
if (!interval_lib::user::is_zero(y.lower()))
if (!interval_lib::user::is_zero(y.upper()))
return interval_lib::detail::div_zero<T, Policies>(x);
else
return interval_lib::detail::div_negative<T, Policies>(x, y.lower());
else
if (!interval_lib::user::is_zero(y.upper()))
return interval_lib::detail::div_positive<T, Policies>(x, y.upper());
else
return interval<T, Policies>::empty();
else
return interval_lib::detail::div_non_zero(x, y);
}
template<class T, class Policies> inline
interval<T, Policies> operator/(const interval<T, Policies>& x, const T& y)
{
if (interval_lib::detail::test_input(x, y) || interval_lib::user::is_zero(y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
const T& xl = x.lower();
const T& xu = x.upper();
if (interval_lib::user::is_neg(y))
return interval<T, Policies>(rnd.div_down(xu, y), rnd.div_up(xl, y), true);
else
return interval<T, Policies>(rnd.div_down(xl, y), rnd.div_up(xu, y), true);
}
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_ARITH_HPP

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/* Boost interval/arith2.hpp template implementation file
*
* This header provides some auxiliary arithmetic
* functions: fmod, sqrt, square, pov, inverse and
* a multi-interval division.
*
* Copyright 2002-2003 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_ARITH2_HPP
#define BOOST_NUMERIC_INTERVAL_ARITH2_HPP
#include <boost/config.hpp>
#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
#include <boost/numeric/interval/detail/bugs.hpp>
#include <boost/numeric/interval/detail/division.hpp>
#include <boost/numeric/interval/arith.hpp>
#include <boost/numeric/interval/policies.hpp>
#include <algorithm>
#include <cmath>
namespace boost {
namespace numeric {
template<class T, class Policies> inline
interval<T, Policies> fmod(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
T const &yb = interval_lib::user::is_neg(x.lower()) ? y.lower() : y.upper();
T n = rnd.int_down(rnd.div_down(x.lower(), yb));
return (const I&)x - n * (const I&)y;
}
template<class T, class Policies> inline
interval<T, Policies> fmod(const interval<T, Policies>& x, const T& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
T n = rnd.int_down(rnd.div_down(x.lower(), y));
return (const I&)x - n * I(y);
}
template<class T, class Policies> inline
interval<T, Policies> fmod(const T& x, const interval<T, Policies>& y)
{
if (interval_lib::detail::test_input(x, y))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
typedef typename interval_lib::unprotect<interval<T, Policies> >::type I;
T const &yb = interval_lib::user::is_neg(x) ? y.lower() : y.upper();
T n = rnd.int_down(rnd.div_down(x, yb));
return x - n * (const I&)y;
}
namespace interval_lib {
template<class T, class Policies> inline
interval<T, Policies> division_part1(const interval<T, Policies>& x,
const interval<T, Policies>& y, bool& b)
{
typedef interval<T, Policies> I;
b = false;
if (detail::test_input(x, y))
return I::empty();
if (in_zero(y))
if (!user::is_zero(y.lower()))
if (!user::is_zero(y.upper()))
return detail::div_zero_part1(x, y, b);
else
return detail::div_negative(x, y.lower());
else
if (!user::is_zero(y.upper()))
return detail::div_positive(x, y.upper());
else
return I::empty();
else
return detail::div_non_zero(x, y);
}
template<class T, class Policies> inline
interval<T, Policies> division_part2(const interval<T, Policies>& x,
const interval<T, Policies>& y, bool b = true)
{
if (!b) return interval<T, Policies>::empty();
return detail::div_zero_part2(x, y);
}
template<class T, class Policies> inline
interval<T, Policies> multiplicative_inverse(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (detail::test_input(x))
return I::empty();
T one = static_cast<T>(1);
typename Policies::rounding rnd;
if (in_zero(x)) {
typedef typename Policies::checking checking;
if (!user::is_zero(x.lower()))
if (!user::is_zero(x.upper()))
return I::whole();
else
return I(checking::neg_inf(), rnd.div_up(one, x.lower()), true);
else
if (!user::is_zero(x.upper()))
return I(rnd.div_down(one, x.upper()), checking::pos_inf(), true);
else
return I::empty();
} else
return I(rnd.div_down(one, x.upper()), rnd.div_up(one, x.lower()), true);
}
namespace detail {
template<class T, class Rounding> inline
T pow_aux(const T& x_, int pwr, Rounding& rnd) // x and pwr are positive
{
T x = x_;
T y = (pwr & 1) ? x_ : static_cast<T>(1);
pwr >>= 1;
while (pwr > 0) {
x = rnd.mul_up(x, x);
if (pwr & 1) y = rnd.mul_up(x, y);
pwr >>= 1;
}
return y;
}
} // namespace detail
} // namespace interval_lib
template<class T, class Policies> inline
interval<T, Policies> pow(const interval<T, Policies>& x, int pwr)
{
BOOST_USING_STD_MAX();
using interval_lib::detail::pow_aux;
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x))
return I::empty();
if (pwr == 0)
if (interval_lib::user::is_zero(x.lower())
&& interval_lib::user::is_zero(x.upper()))
return I::empty();
else
return I(static_cast<T>(1));
else if (pwr < 0)
return interval_lib::multiplicative_inverse(pow(x, -pwr));
typename Policies::rounding rnd;
if (interval_lib::user::is_neg(x.upper())) { // [-2,-1]
T yl = pow_aux(-x.upper(), pwr, rnd);
T yu = pow_aux(-x.lower(), pwr, rnd);
if (pwr & 1) // [-2,-1]^1
return I(-yu, -yl, true);
else // [-2,-1]^2
return I(yl, yu, true);
} else if (interval_lib::user::is_neg(x.lower())) { // [-1,1]
if (pwr & 1) { // [-1,1]^1
return I(-pow_aux(-x.lower(), pwr, rnd), pow_aux(x.upper(), pwr, rnd), true);
} else { // [-1,1]^2
return I(static_cast<T>(0), pow_aux(max BOOST_PREVENT_MACRO_SUBSTITUTION(-x.lower(), x.upper()), pwr, rnd), true);
}
} else { // [1,2]
return I(pow_aux(x.lower(), pwr, rnd), pow_aux(x.upper(), pwr, rnd), true);
}
}
template<class T, class Policies> inline
interval<T, Policies> sqrt(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x) || interval_lib::user::is_neg(x.upper()))
return I::empty();
typename Policies::rounding rnd;
T l = !interval_lib::user::is_pos(x.lower()) ? static_cast<T>(0) : rnd.sqrt_down(x.lower());
return I(l, rnd.sqrt_up(x.upper()), true);
}
template<class T, class Policies> inline
interval<T, Policies> square(const interval<T, Policies>& x)
{
typedef interval<T, Policies> I;
if (interval_lib::detail::test_input(x))
return I::empty();
typename Policies::rounding rnd;
const T& xl = x.lower();
const T& xu = x.upper();
if (interval_lib::user::is_neg(xu))
return I(rnd.mul_down(xu, xu), rnd.mul_up(xl, xl), true);
else if (interval_lib::user::is_pos(x.lower()))
return I(rnd.mul_down(xl, xl), rnd.mul_up(xu, xu), true);
else
return I(static_cast<T>(0), (-xl > xu ? rnd.mul_up(xl, xl) : rnd.mul_up(xu, xu)), true);
}
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_ARITH2_HPP

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/* Boost interval/arith3.hpp template implementation file
*
* This headers provides arithmetical functions
* which compute an interval given some base
* numbers. The resulting interval encloses the
* real result of the arithmetic operation.
*
* Copyright 2003 Guillaume Melquiond
*
* 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_ARITH3_HPP
#define BOOST_NUMERIC_INTERVAL_ARITH3_HPP
#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
template<class I> inline
I add(const typename I::base_type& x, const typename I::base_type& y)
{
typedef typename I::traits_type Policies;
if (detail::test_input<typename I::base_type, Policies>(x, y))
return I::empty();
typename Policies::rounding rnd;
return I(rnd.add_down(x, y), rnd.add_up(x, y), true);
}
template<class I> inline
I sub(const typename I::base_type& x, const typename I::base_type& y)
{
typedef typename I::traits_type Policies;
if (detail::test_input<typename I::base_type, Policies>(x, y))
return I::empty();
typename Policies::rounding rnd;
return I(rnd.sub_down(x, y), rnd.sub_up(x, y), true);
}
template<class I> inline
I mul(const typename I::base_type& x, const typename I::base_type& y)
{
typedef typename I::traits_type Policies;
if (detail::test_input<typename I::base_type, Policies>(x, y))
return I::empty();
typename Policies::rounding rnd;
return I(rnd.mul_down(x, y), rnd.mul_up(x, y), true);
}
template<class I> inline
I div(const typename I::base_type& x, const typename I::base_type& y)
{
typedef typename I::traits_type Policies;
if (detail::test_input<typename I::base_type, Policies>(x, y) || user::is_zero(y))
return I::empty();
typename Policies::rounding rnd;
return I(rnd.div_down(x, y), rnd.div_up(x, y), true);
}
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_ARITH3_HPP

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/* Boost interval/checking.hpp template implementation file
*
* 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_CHECKING_HPP
#define BOOST_NUMERIC_INTERVAL_CHECKING_HPP
#include <stdexcept>
#include <string>
#include <cassert>
#include <boost/limits.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
struct exception_create_empty
{
void operator()()
{
throw std::runtime_error("boost::interval: empty interval created");
}
};
struct exception_invalid_number
{
void operator()()
{
throw std::invalid_argument("boost::interval: invalid number");
}
};
template<class T>
struct checking_base
{
static T pos_inf()
{
assert(std::numeric_limits<T>::has_infinity);
return std::numeric_limits<T>::infinity();
}
static T neg_inf()
{
assert(std::numeric_limits<T>::has_infinity);
return -std::numeric_limits<T>::infinity();
}
static T nan()
{
assert(std::numeric_limits<T>::has_quiet_NaN);
return std::numeric_limits<T>::quiet_NaN();
}
static bool is_nan(const T& x)
{
return std::numeric_limits<T>::has_quiet_NaN && (x != x);
}
static T empty_lower()
{
return (std::numeric_limits<T>::has_quiet_NaN ?
std::numeric_limits<T>::quiet_NaN() : static_cast<T>(1));
}
static T empty_upper()
{
return (std::numeric_limits<T>::has_quiet_NaN ?
std::numeric_limits<T>::quiet_NaN() : static_cast<T>(0));
}
static bool is_empty(const T& l, const T& u)
{
return !(l <= u); // safety for partial orders
}
};
template<class T, class Checking = checking_base<T>,
class Exception = exception_create_empty>
struct checking_no_empty: Checking
{
static T nan()
{
assert(false);
return Checking::nan();
}
static T empty_lower()
{
Exception()();
return Checking::empty_lower();
}
static T empty_upper()
{
Exception()();
return Checking::empty_upper();
}
static bool is_empty(const T&, const T&)
{
return false;
}
};
template<class T, class Checking = checking_base<T> >
struct checking_no_nan: Checking
{
static bool is_nan(const T&)
{
return false;
}
};
template<class T, class Checking = checking_base<T>,
class Exception = exception_invalid_number>
struct checking_catch_nan: Checking
{
static bool is_nan(const T& x)
{
if (Checking::is_nan(x)) Exception()();
return false;
}
};
template<class T>
struct checking_strict:
checking_no_nan<T, checking_no_empty<T> >
{};
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_CHECKING_HPP

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/* Boost interval/compare.hpp template implementation file
*
* 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_COMPARE_HPP
#define BOOST_NUMERIC_INTERVAL_COMPARE_HPP
#include <boost/numeric/interval/compare/certain.hpp>
#include <boost/numeric/interval/compare/possible.hpp>
#include <boost/numeric/interval/compare/explicit.hpp>
#include <boost/numeric/interval/compare/lexicographic.hpp>
#include <boost/numeric/interval/compare/set.hpp>
#endif // BOOST_NUMERIC_INTERVAL_COMPARE_HPP

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/* Boost interval/compare/certain.hpp template implementation file
*
* Copyright 2003 Guillaume Melquiond
*
* 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_COMPARE_CERTAIN_HPP
#define BOOST_NUMERIC_INTERVAL_COMPARE_CERTAIN_HPP
#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
namespace compare {
namespace certain {
template<class T, class Policies1, class Policies2> inline
bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() < y.lower();
}
template<class T, class Policies> inline
bool operator<(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() < y;
}
template<class T, class Policies1, class Policies2> inline
bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() <= y.lower();
}
template<class T, class Policies> inline
bool operator<=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() <= y;
}
template<class T, class Policies1, class Policies2> inline
bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() > y.upper();
}
template<class T, class Policies> inline
bool operator>(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() > y;
}
template<class T, class Policies1, class Policies2> inline
bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() >= y.upper();
}
template<class T, class Policies> inline
bool operator>=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() >= y;
}
template<class T, class Policies1, class Policies2> inline
bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() == y.lower() && x.lower() == y.upper();
}
template<class T, class Policies> inline
bool operator==(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() == y && x.lower() == y;
}
template<class T, class Policies1, class Policies2> inline
bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() < y.lower() || x.lower() > y.upper();
}
template<class T, class Policies> inline
bool operator!=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() < y || x.lower() > y;
}
} // namespace certain
} // namespace compare
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_COMPARE_CERTAIN_HPP

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/* Boost interval/compare/explicit.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_COMPARE_EXPLICIT_HPP
#define BOOST_NUMERIC_INTERVAL_COMPARE_EXPLICIT_HPP
#include <boost/numeric/interval/detail/interval_prototype.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
/*
* Certainly... operations
*/
template<class T, class Policies1, class Policies2> inline
bool cerlt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.upper() < y.lower();
}
template<class T, class Policies> inline
bool cerlt(const interval<T, Policies>& x, const T& y)
{
return x.upper() < y;
}
template<class T, class Policies> inline
bool cerlt(const T& x, const interval<T, Policies>& y)
{
return x < y.lower();
}
template<class T, class Policies1, class Policies2> inline
bool cerle(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.upper() <= y.lower();
}
template<class T, class Policies> inline
bool cerle(const interval<T, Policies>& x, const T& y)
{
return x.upper() <= y;
}
template<class T, class Policies> inline
bool cerle(const T& x, const interval<T, Policies>& y)
{
return x <= y.lower();
}
template<class T, class Policies1, class Policies2> inline
bool cergt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.lower() > y.upper();
}
template<class T, class Policies> inline
bool cergt(const interval<T, Policies>& x, const T& y)
{
return x.lower() > y;
}
template<class T, class Policies> inline
bool cergt(const T& x, const interval<T, Policies>& y)
{
return x > y.upper();
}
template<class T, class Policies1, class Policies2> inline
bool cerge(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.lower() >= y.upper();
}
template<class T, class Policies> inline
bool cerge(const interval<T, Policies>& x, const T& y)
{
return x.lower() >= y;
}
template<class T, class Policies> inline
bool cerge(const T& x, const interval<T, Policies>& y)
{
return x >= y.upper();
}
template<class T, class Policies1, class Policies2> inline
bool cereq(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.lower() == y.upper() && y.lower() == x.upper();
}
template<class T, class Policies> inline
bool cereq(const interval<T, Policies>& x, const T& y)
{
return x.lower() == y && x.upper() == y;
}
template<class T, class Policies> inline
bool cereq(const T& x, const interval<T, Policies>& y)
{
return x == y.lower() && x == y.upper();
}
template<class T, class Policies1, class Policies2> inline
bool cerne(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.upper() < y.lower() || y.upper() < x.lower();
}
template<class T, class Policies> inline
bool cerne(const interval<T, Policies>& x, const T& y)
{
return x.upper() < y || y < x.lower();
}
template<class T, class Policies> inline
bool cerne(const T& x, const interval<T, Policies>& y)
{
return x < y.lower() || y.upper() < x;
}
/*
* Possibly... comparisons
*/
template<class T, class Policies1, class Policies2> inline
bool poslt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.lower() < y.upper();
}
template<class T, class Policies> inline
bool poslt(const interval<T, Policies>& x, const T& y)
{
return x.lower() < y;
}
template<class T, class Policies> inline
bool poslt(const T& x, const interval<T, Policies>& y)
{
return x < y.upper();
}
template<class T, class Policies1, class Policies2> inline
bool posle(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.lower() <= y.upper();
}
template<class T, class Policies> inline
bool posle(const interval<T, Policies>& x, const T& y)
{
return x.lower() <= y;
}
template<class T, class Policies> inline
bool posle(const T& x, const interval<T, Policies>& y)
{
return x <= y.upper();
}
template<class T, class Policies1, class Policies2> inline
bool posgt(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.upper() > y.lower();
}
template<class T, class Policies> inline
bool posgt(const interval<T, Policies>& x, const T& y)
{
return x.upper() > y;
}
template<class T, class Policies> inline
bool posgt(const T& x, const interval<T, Policies> & y)
{
return x > y.lower();
}
template<class T, class Policies1, class Policies2> inline
bool posge(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.upper() >= y.lower();
}
template<class T, class Policies> inline
bool posge(const interval<T, Policies>& x, const T& y)
{
return x.upper() >= y;
}
template<class T, class Policies> inline
bool posge(const T& x, const interval<T, Policies>& y)
{
return x >= y.lower();
}
template<class T, class Policies1, class Policies2> inline
bool poseq(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.upper() >= y.lower() && y.upper() >= x.lower();
}
template<class T, class Policies> inline
bool poseq(const interval<T, Policies>& x, const T& y)
{
return x.upper() >= y && y >= x.lower();
}
template<class T, class Policies> inline
bool poseq(const T& x, const interval<T, Policies>& y)
{
return x >= y.lower() && y.upper() >= x;
}
template<class T, class Policies1, class Policies2> inline
bool posne(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return x.upper() != y.lower() || y.upper() != x.lower();
}
template<class T, class Policies> inline
bool posne(const interval<T, Policies>& x, const T& y)
{
return x.upper() != y || y != x.lower();
}
template<class T, class Policies> inline
bool posne(const T& x, const interval<T, Policies>& y)
{
return x != y.lower() || y.upper() != x;
}
} // namespace interval_lib
} // namespace numeric
} //namespace boost
#endif // BOOST_NUMERIC_INTERVAL_COMPARE_EXPLICIT_HPP

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/* Boost interval/compare/lexicographic.hpp template implementation file
*
* Copyright 2002-2003 Guillaume Melquiond
*
* 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_COMPARE_LEXICOGRAPHIC_HPP
#define BOOST_NUMERIC_INTERVAL_COMPARE_LEXICOGRAPHIC_HPP
#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
namespace compare {
namespace lexicographic {
template<class T, class Policies1, class Policies2> inline
bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
const T& yl = y.lower();
return xl < yl || (xl == yl && x.upper() < y.upper());
}
template<class T, class Policies> inline
bool operator<(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() < y;
}
template<class T, class Policies1, class Policies2> inline
bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
const T& yl = y.lower();
return xl < yl || (xl == yl && x.upper() <= y.upper());
}
template<class T, class Policies> inline
bool operator<=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
return xl < y || (xl == y && x.upper() <= y);
}
template<class T, class Policies1, class Policies2> inline
bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
const T& yl = y.lower();
return xl > yl || (xl == yl && x.upper() > y.upper());
}
template<class T, class Policies> inline
bool operator>(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
return xl > y || (xl == y && x.upper() > y);
}
template<class T, class Policies1, class Policies2> inline
bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
const T& xl = x.lower();
const T& yl = y.lower();
return xl > yl || (xl == yl && x.upper() >= y.upper());
}
template<class T, class Policies> inline
bool operator>=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() >= y;
}
template<class T, class Policies1, class Policies2> inline
bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() == y.lower() && x.upper() == y.upper();
}
template<class T, class Policies> inline
bool operator==(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() == y && x.upper() == y;
}
template<class T, class Policies1, class Policies2> inline
bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() != y.lower() || x.upper() != y.upper();
}
template<class T, class Policies> inline
bool operator!=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() != y || x.upper() != y;
}
} // namespace lexicographic
} // namespace compare
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_COMPARE_LEXICOGRAPHIC_HPP

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/* Boost interval/compare/possible.hpp template implementation file
*
* Copyright 2003 Guillaume Melquiond
*
* 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_COMPARE_POSSIBLE_HPP
#define BOOST_NUMERIC_INTERVAL_COMPARE_POSSIBLE_HPP
#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
namespace compare {
namespace possible {
template<class T, class Policies1, class Policies2> inline
bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() < y.upper();
}
template<class T, class Policies> inline
bool operator<(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() < y;
}
template<class T, class Policies1, class Policies2> inline
bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() <= y.upper();
}
template<class T, class Policies> inline
bool operator<=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() <= y;
}
template<class T, class Policies1, class Policies2> inline
bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() > y.lower();
}
template<class T, class Policies> inline
bool operator>(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() > y;
}
template<class T, class Policies1, class Policies2> inline
bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() >= y.lower();
}
template<class T, class Policies> inline
bool operator>=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.upper() >= y;
}
template<class T, class Policies1, class Policies2> inline
bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() <= y.upper() && x.upper() >= y.lower();
}
template<class T, class Policies> inline
bool operator==(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() <= y && x.upper() >= y;
}
template<class T, class Policies1, class Policies2> inline
bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() != y.upper() || x.upper() != y.lower();
}
template<class T, class Policies> inline
bool operator!=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
return x.lower() != y || x.upper() != y;
}
} // namespace possible
} // namespace compare
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_COMPARE_POSSIBLE_HPP

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/* Boost interval/compare/set.hpp template implementation file
*
* Copyright 2002-2003 Guillaume Melquiond
*
* 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_COMPARE_SET_HPP
#define BOOST_NUMERIC_INTERVAL_COMPARE_SET_HPP
#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
#include <boost/numeric/interval/utility.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
namespace compare {
namespace set {
template<class T, class Policies1, class Policies2> inline
bool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return proper_subset(x, y);
}
template<class T, class Policies> inline
bool operator<(const interval<T, Policies>& x, const T& y)
{
throw comparison_error();
}
template<class T, class Policies1, class Policies2> inline
bool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return subset(x, y);
}
template<class T, class Policies> inline
bool operator<=(const interval<T, Policies>& x, const T& y)
{
throw comparison_error();
}
template<class T, class Policies1, class Policies2> inline
bool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return proper_subset(y, x);
}
template<class T, class Policies> inline
bool operator>(const interval<T, Policies>& x, const T& y)
{
throw comparison_error();
}
template<class T, class Policies1, class Policies2> inline
bool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return subset(y, x);
}
template<class T, class Policies> inline
bool operator>=(const interval<T, Policies>& x, const T& y)
{
throw comparison_error();
}
template<class T, class Policies1, class Policies2> inline
bool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return equal(y, x);
}
template<class T, class Policies> inline
bool operator==(const interval<T, Policies>& x, const T& y)
{
throw comparison_error();
}
template<class T, class Policies1, class Policies2> inline
bool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
return !equal(y, x);
}
template<class T, class Policies> inline
bool operator!=(const interval<T, Policies>& x, const T& y)
{
throw comparison_error();
}
} // namespace set
} // namespace compare
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_COMPARE_SET_HPP

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/* Boost interval/compare/tribool.hpp template implementation file
*
* Copyright 2002-2003 Guillaume Melquiond
*
* 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_COMPARE_TRIBOOL_HPP
#define BOOST_NUMERIC_INTERVAL_COMPARE_TRIBOOL_HPP
#include <boost/numeric/interval/detail/interval_prototype.hpp>
#include <boost/numeric/interval/detail/test_input.hpp>
#include <boost/logic/tribool.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
namespace compare {
namespace tribool {
template<class T, class Policies1, class Policies2> inline
logic::tribool operator<(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() < y.lower()) return true;
if (x.lower() >= y.upper()) return false;
return logic::indeterminate;
}
template<class T, class Policies> inline
logic::tribool operator<(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() < y) return true;
if (x.lower() >= y) return false;
return logic::indeterminate;
}
template<class T, class Policies1, class Policies2> inline
logic::tribool operator<=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() <= y.lower()) return true;
if (x.lower() > y.upper()) return false;
return logic::indeterminate;
}
template<class T, class Policies> inline
logic::tribool operator<=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() <= y) return true;
if (x.lower() > y) return false;
return logic::indeterminate;
}
template<class T, class Policies1, class Policies2> inline
logic::tribool operator>(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.lower() > y.upper()) return true;
if (x.upper() <= y.lower()) return false;
return logic::indeterminate;
}
template<class T, class Policies> inline
logic::tribool operator>(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.lower() > y) return true;
if (x.upper() <= y) return false;
return logic::indeterminate;
}
template<class T, class Policies1, class Policies2> inline
logic::tribool operator>=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.lower() >= y.upper()) return true;
if (x.upper() < y.lower()) return false;
return logic::indeterminate;
}
template<class T, class Policies> inline
logic::tribool operator>=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.lower() >= y) return true;
if (x.upper() < y) return false;
return logic::indeterminate;
}
template<class T, class Policies1, class Policies2> inline
logic::tribool operator==(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() == y.lower() && x.lower() == y.upper()) return true;
if (x.upper() < y.lower() || x.lower() > y.upper()) return false;
return logic::indeterminate;
}
template<class T, class Policies> inline
logic::tribool operator==(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() == y && x.lower() == y) return true;
if (x.upper() < y || x.lower() > y) return false;
return logic::indeterminate;
}
template<class T, class Policies1, class Policies2> inline
logic::tribool operator!=(const interval<T, Policies1>& x, const interval<T, Policies2>& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() < y.lower() || x.lower() > y.upper()) return true;
if (x.upper() == y.lower() && x.lower() == y.upper()) return false;
return logic::indeterminate;
}
template<class T, class Policies> inline
logic::tribool operator!=(const interval<T, Policies>& x, const T& y)
{
if (detail::test_input(x, y)) throw comparison_error();
if (x.upper() < y || x.lower() > y) return true;
if (x.upper() == y && x.lower() == y) return false;
return logic::indeterminate;
}
} // namespace tribool
} // namespace compare
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_COMPARE_TRIBOOL_HPP

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/* Boost interval/constants.hpp template implementation file
*
* 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_CONSTANTS_HPP
#define BOOST_NUMERIC_INTERVAL_CONSTANTS_HPP
namespace boost {
namespace numeric {
namespace interval_lib {
namespace constants {
// These constants should be exactly computed.
// Decimal representations wouldn't do it since the standard doesn't
// specify the rounding (even nearest) that should be used.
static const float pi_f_l = 13176794.0f/(1<<22);
static const float pi_f_u = 13176795.0f/(1<<22);
static const double pi_d_l = (3373259426.0 + 273688.0 / (1<<21)) / (1<<30);
static const double pi_d_u = (3373259426.0 + 273689.0 / (1<<21)) / (1<<30);
template<class T> inline T pi_lower() { return 3; }
template<class T> inline T pi_upper() { return 4; }
template<class T> inline T pi_half_lower() { return 1; }
template<class T> inline T pi_half_upper() { return 2; }
template<class T> inline T pi_twice_lower() { return 6; }
template<class T> inline T pi_twice_upper() { return 7; }
template<> inline float pi_lower<float>() { return pi_f_l; }
template<> inline float pi_upper<float>() { return pi_f_u; }
template<> inline float pi_half_lower<float>() { return pi_f_l / 2; }
template<> inline float pi_half_upper<float>() { return pi_f_u / 2; }
template<> inline float pi_twice_lower<float>() { return pi_f_l * 2; }
template<> inline float pi_twice_upper<float>() { return pi_f_u * 2; }
template<> inline double pi_lower<double>() { return pi_d_l; }
template<> inline double pi_upper<double>() { return pi_d_u; }
template<> inline double pi_half_lower<double>() { return pi_d_l / 2; }
template<> inline double pi_half_upper<double>() { return pi_d_u / 2; }
template<> inline double pi_twice_lower<double>() { return pi_d_l * 2; }
template<> inline double pi_twice_upper<double>() { return pi_d_u * 2; }
template<> inline long double pi_lower<long double>() { return pi_d_l; }
template<> inline long double pi_upper<long double>() { return pi_d_u; }
template<> inline long double pi_half_lower<long double>() { return pi_d_l / 2; }
template<> inline long double pi_half_upper<long double>() { return pi_d_u / 2; }
template<> inline long double pi_twice_lower<long double>() { return pi_d_l * 2; }
template<> inline long double pi_twice_upper<long double>() { return pi_d_u * 2; }
} // namespace constants
template<class I> inline
I pi()
{
typedef typename I::base_type T;
return I(constants::pi_lower<T>(),
constants::pi_upper<T>(), true);
}
template<class I> inline
I pi_half()
{
typedef typename I::base_type T;
return I(constants::pi_half_lower<T>(),
constants::pi_half_upper<T>(), true);
}
template<class I> inline
I pi_twice()
{
typedef typename I::base_type T;
return I(constants::pi_twice_lower<T>(),
constants::pi_twice_upper<T>(), true);
}
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_CONSTANTS_HPP

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/* Boost interval/detail/bcc_rounding_control.hpp 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_DETAIL_BCC_ROUNDING_CONTROL_HPP
#define BOOST_NUMERIC_INTERVAL_DETAIL_BCC_ROUNDING_CONTROL_HPP
#ifndef __BORLANDC__
# error This header is only intended for Borland C++.
#endif
#ifndef _M_IX86
# error This header only works on x86 CPUs.
#endif
#include <float.h> // Borland C++ rounding control
namespace boost {
namespace numeric {
namespace interval_lib {
namespace detail {
#ifndef BOOST_NUMERIC_INTERVAL_KEEP_EXCEPTIONS_FOR_BCC
extern "C" { unsigned int _RTLENTRY _fm_init(void); }
struct borland_workaround {
borland_workaround() { _fm_init(); }
};
static borland_workaround borland_workaround_exec;
#endif // BOOST_NUMERIC_INTERVAL_KEEP_EXCEPTIONS_FOR_BCC
__inline double rint(double)
{ __emit__(0xD9); __emit__(0xFC); /* asm FRNDINT */ }
struct x86_rounding
{
typedef unsigned int rounding_mode;
static void get_rounding_mode(rounding_mode& mode)
{ mode = _control87(0, 0); }
static void set_rounding_mode(const rounding_mode mode)
{ _control87(mode, 0xffff); }
static double to_int(const double& x) { return rint(x); }
};
} // namespace detail
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_BCC_ROUNDING_CONTROL_HPP */

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/* Boost interval/detail/bugs.hpp 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_DETAIL_BUGS
#define BOOST_NUMERIC_INTERVAL_DETAIL_BUGS
#include <boost/config.hpp>
#if defined(__GLIBC__) && (defined(__USE_MISC) || defined(__USE_XOPEN_EXTENDED) || defined(__USE_ISOC99)) && !defined(__ICC)
# define BOOST_HAS_INV_HYPERBOLIC
#endif
#ifdef BOOST_NO_STDC_NAMESPACE
# define BOOST_NUMERIC_INTERVAL_using_math(a) using ::a
# ifdef BOOST_HAS_INV_HYPERBOLIC
# define BOOST_NUMERIC_INTERVAL_using_ahyp(a) using ::a
# endif
#else
# define BOOST_NUMERIC_INTERVAL_using_math(a) using std::a
# if defined(BOOST_HAS_INV_HYPERBOLIC)
# if defined(__GLIBCPP__) || defined(__GLIBCXX__)
# define BOOST_NUMERIC_INTERVAL_using_ahyp(a) using ::a
# else
# define BOOST_NUMERIC_INTERVAL_using_ahyp(a) using std::a
# endif
# endif
#endif
#if defined(__COMO__) || defined(BOOST_INTEL)
# define BOOST_NUMERIC_INTERVAL_using_max(a) using std::a
#elif defined(BOOST_NO_STDC_NAMESPACE)
# define BOOST_NUMERIC_INTERVAL_using_max(a) using ::a
#else
# define BOOST_NUMERIC_INTERVAL_using_max(a) using std::a
#endif
#ifndef BOOST_NUMERIC_INTERVAL_using_ahyp
# define BOOST_NUMERIC_INTERVAL_using_ahyp(a)
#endif
#if defined(__GNUC__) && (__GNUC__ <= 2)
// cf PR c++/1981 for a description of the bug
#include <algorithm>
#include <cmath>
namespace boost {
namespace numeric {
using std::min;
using std::max;
using std::sqrt;
using std::exp;
using std::log;
using std::cos;
using std::tan;
using std::asin;
using std::acos;
using std::atan;
using std::ceil;
using std::floor;
using std::sinh;
using std::cosh;
using std::tanh;
# undef BOOST_NUMERIC_INTERVAL_using_max
# undef BOOST_NUMERIC_INTERVAL_using_math
# define BOOST_NUMERIC_INTERVAL_using_max(a)
# define BOOST_NUMERIC_INTERVAL_using_math(a)
# undef BOOST_NUMERIC_INTERVAL_using_ahyp
# define BOOST_NUMERIC_INTERVAL_using_ahyp(a)
} // namespace numeric
} // namespace boost
#endif
#endif // BOOST_NUMERIC_INTERVAL_DETAIL_BUGS

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/* Boost interval/detail/c99_rounding_control.hpp 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_DETAIL_C99_ROUNDING_CONTROL_HPP
#define BOOST_NUMERIC_INTERVAL_DETAIL_C99_ROUNDING_CONTROL_HPP
#include <boost/numeric/interval/detail/c99sub_rounding_control.hpp>
namespace boost {
namespace numeric {
namespace interval_lib {
namespace detail {
struct c99_rounding_control: c99_rounding
{
template<class T>
static T force_rounding(const T& r) { volatile T r_ = r; return r_; }
};
} // namespace detail
template<>
struct rounding_control<float>:
detail::c99_rounding_control { };
template<>
struct rounding_control<double>:
detail::c99_rounding_control { };
template<>
struct rounding_control<long double>:
detail::c99_rounding_control { };
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#undef BOOST_NUMERIC_INTERVAL_NO_HARDWARE
#endif // BOOST_NUMERIC_INTERVAL_DETAIL_C99_ROUNDING_CONTROL_HPP

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/* Boost interval/detail/c99sub_rounding_control.hpp 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_DETAIL_C99SUB_ROUNDING_CONTROL_HPP
#define BOOST_NUMERIC_INTERVAL_DETAIL_C99SUB_ROUNDING_CONTROL_HPP
#include <fenv.h> // ISO C 99 rounding mode control
namespace boost {
namespace numeric {
namespace interval_lib {
namespace detail {
extern "C" { double rint(double); }
struct c99_rounding
{
typedef int rounding_mode;
static void set_rounding_mode(const rounding_mode mode) { fesetround(mode); }
static void get_rounding_mode(rounding_mode &mode) { mode = fegetround(); }
static void downward() { set_rounding_mode(FE_DOWNWARD); }
static void upward() { set_rounding_mode(FE_UPWARD); }
static void to_nearest() { set_rounding_mode(FE_TONEAREST); }
static void toward_zero() { set_rounding_mode(FE_TOWARDZERO); }
template<class T>
static T to_int(const T& r) { return rint(r); }
};
} // namespace detail
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_DETAIL_C99SUB_ROUBDING_CONTROL_HPP

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/* Boost interval/detail/division.hpp file
*
* Copyright 2003 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_DETAIL_DIVISION_HPP
#define BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_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/rounded_arith.hpp>
#include <algorithm>
namespace boost {
namespace numeric {
namespace interval_lib {
namespace detail {
template<class T, class Policies> inline
interval<T, Policies> div_non_zero(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
// assert(!in_zero(y));
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
const T& xl = x.lower();
const T& xu = x.upper();
const T& yl = y.lower();
const T& yu = y.upper();
if (::boost::numeric::interval_lib::user::is_neg(xu))
if (::boost::numeric::interval_lib::user::is_neg(yu))
return I(rnd.div_down(xu, yl), rnd.div_up(xl, yu), true);
else
return I(rnd.div_down(xl, yl), rnd.div_up(xu, yu), true);
else if (::boost::numeric::interval_lib::user::is_neg(xl))
if (::boost::numeric::interval_lib::user::is_neg(yu))
return I(rnd.div_down(xu, yu), rnd.div_up(xl, yu), true);
else
return I(rnd.div_down(xl, yl), rnd.div_up(xu, yl), true);
else
if (::boost::numeric::interval_lib::user::is_neg(yu))
return I(rnd.div_down(xu, yu), rnd.div_up(xl, yl), true);
else
return I(rnd.div_down(xl, yu), rnd.div_up(xu, yl), true);
}
template<class T, class Policies> inline
interval<T, Policies> div_non_zero(const T& x, const interval<T, Policies>& y)
{
// assert(!in_zero(y));
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
const T& yl = y.lower();
const T& yu = y.upper();
if (::boost::numeric::interval_lib::user::is_neg(x))
return I(rnd.div_down(x, yl), rnd.div_up(x, yu), true);
else
return I(rnd.div_down(x, yu), rnd.div_up(x, yl), true);
}
template<class T, class Policies> inline
interval<T, Policies> div_positive(const interval<T, Policies>& x, const T& yu)
{
// assert(::boost::numeric::interval_lib::user::is_pos(yu));
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
::boost::numeric::interval_lib::user::is_zero(x.upper()))
return x;
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
const T& xl = x.lower();
const T& xu = x.upper();
typedef typename Policies::checking checking;
if (::boost::numeric::interval_lib::user::is_neg(xu))
return I(checking::neg_inf(), rnd.div_up(xu, yu), true);
else if (::boost::numeric::interval_lib::user::is_neg(xl))
return I(checking::neg_inf(), checking::pos_inf(), true);
else
return I(rnd.div_down(xl, yu), checking::pos_inf(), true);
}
template<class T, class Policies> inline
interval<T, Policies> div_positive(const T& x, const T& yu)
{
// assert(::boost::numeric::interval_lib::user::is_pos(yu));
typedef interval<T, Policies> I;
if (::boost::numeric::interval_lib::user::is_zero(x))
return I(static_cast<T>(0), static_cast<T>(0), true);
typename Policies::rounding rnd;
typedef typename Policies::checking checking;
if (::boost::numeric::interval_lib::user::is_neg(x))
return I(checking::neg_inf(), rnd.div_up(x, yu), true);
else
return I(rnd.div_down(x, yu), checking::pos_inf(), true);
}
template<class T, class Policies> inline
interval<T, Policies> div_negative(const interval<T, Policies>& x, const T& yl)
{
// assert(::boost::numeric::interval_lib::user::is_neg(yl));
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
::boost::numeric::interval_lib::user::is_zero(x.upper()))
return x;
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
const T& xl = x.lower();
const T& xu = x.upper();
typedef typename Policies::checking checking;
if (::boost::numeric::interval_lib::user::is_neg(xu))
return I(rnd.div_down(xu, yl), checking::pos_inf(), true);
else if (::boost::numeric::interval_lib::user::is_neg(xl))
return I(checking::neg_inf(), checking::pos_inf(), true);
else
return I(checking::neg_inf(), rnd.div_up(xl, yl), true);
}
template<class T, class Policies> inline
interval<T, Policies> div_negative(const T& x, const T& yl)
{
// assert(::boost::numeric::interval_lib::user::is_neg(yl));
typedef interval<T, Policies> I;
if (::boost::numeric::interval_lib::user::is_zero(x))
return I(static_cast<T>(0), static_cast<T>(0), true);
typename Policies::rounding rnd;
typedef typename Policies::checking checking;
if (::boost::numeric::interval_lib::user::is_neg(x))
return I(rnd.div_down(x, yl), checking::pos_inf(), true);
else
return I(checking::neg_inf(), rnd.div_up(x, yl), true);
}
template<class T, class Policies> inline
interval<T, Policies> div_zero(const interval<T, Policies>& x)
{
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) &&
::boost::numeric::interval_lib::user::is_zero(x.upper()))
return x;
else return interval<T, Policies>::whole();
}
template<class T, class Policies> inline
interval<T, Policies> div_zero(const T& x)
{
if (::boost::numeric::interval_lib::user::is_zero(x))
return interval<T, Policies>(static_cast<T>(0), static_cast<T>(0), true);
else return interval<T, Policies>::whole();
}
template<class T, class Policies> inline
interval<T, Policies> div_zero_part1(const interval<T, Policies>& x,
const interval<T, Policies>& y, bool& b)
{
// assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()));
if (::boost::numeric::interval_lib::user::is_zero(x.lower()) && ::boost::numeric::interval_lib::user::is_zero(x.upper()))
{ b = false; return x; }
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
const T& xl = x.lower();
const T& xu = x.upper();
const T& yl = y.lower();
const T& yu = y.upper();
typedef typename Policies::checking checking;
if (::boost::numeric::interval_lib::user::is_neg(xu))
{ b = true; return I(checking::neg_inf(), rnd.div_up(xu, yu), true); }
else if (::boost::numeric::interval_lib::user::is_neg(xl))
{ b = false; return I(checking::neg_inf(), checking::pos_inf(), true); }
else
{ b = true; return I(checking::neg_inf(), rnd.div_up(xl, yl), true); }
}
template<class T, class Policies> inline
interval<T, Policies> div_zero_part2(const interval<T, Policies>& x,
const interval<T, Policies>& y)
{
// assert(::boost::numeric::interval_lib::user::is_neg(y.lower()) && ::boost::numeric::interval_lib::user::is_pos(y.upper()) && (div_zero_part1(x, y, b), b));
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
typedef typename Policies::checking checking;
if (::boost::numeric::interval_lib::user::is_neg(x.upper()))
return I(rnd.div_down(x.upper(), y.lower()), checking::pos_inf(), true);
else
return I(rnd.div_down(x.lower(), y.upper()), checking::pos_inf(), true);
}
} // namespace detail
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_DETAIL_DIVISION_HPP

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/* Boost interval/detail/interval_prototype.hpp file
*
* 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_DETAIL_INTERVAL_PROTOTYPE_HPP
#define BOOST_NUMERIC_INTERVAL_DETAIL_INTERVAL_PROTOTYPE_HPP
namespace boost {
namespace numeric {
namespace interval_lib {
template<class T> struct rounded_math;
template<class T> struct checking_strict;
class comparison_error;
template<class Rounding, class Checking> struct policies;
/*
* default policies class
*/
template<class T>
struct default_policies
{
typedef policies<rounded_math<T>, checking_strict<T> > type;
};
} // namespace interval_lib
template<class T, class Policies = typename interval_lib::default_policies<T>::type >
class interval;
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_INTERVAL_DETAIL_INTERVAL_PROTOTYPE_HPP

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eo/contrib/boost/numeric/interval/detail/msvc_rounding_control.hpp Normal file
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/* Boost interval/detail/msvc_rounding_control.hpp file
*
* Copyright 2000 Maarten Keijzer
* 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_DETAIL_MSVC_ROUNDING_CONTROL_HPP
#define BOOST_NUMERIC_INTERVAL_DETAIL_MSVC_ROUNDING_CONTROL_HPP
#ifndef _MSC_VER
# error This header is only intended for MSVC, but might work for Borland as well
#endif
#include <float.h> // MSVC rounding control
namespace boost {
namespace numeric {
namespace interval_lib {
namespace detail {
extern "C" { double rint(double); }
struct x86_rounding
{
static unsigned int hard2msvc(unsigned short m) {
unsigned int n = 0;
if (m & 0x01) n |= _EM_INVALID;
if (m & 0x02) n |= _EM_DENORMAL;
if (m & 0x04) n |= _EM_ZERODIVIDE;
if (m & 0x08) n |= _EM_OVERFLOW;
if (m & 0x10) n |= _EM_UNDERFLOW;
if (m & 0x20) n |= _EM_INEXACT;
switch (m & 0x300) {
case 0x000: n |= _PC_24; break;
case 0x200: n |= _PC_53; break;
case 0x300: n |= _PC_64; break;
}
switch (m & 0xC00) {
case 0x000: n |= _RC_NEAR; break;
case 0x400: n |= _RC_DOWN; break;
case 0x800: n |= _RC_UP; break;
case 0xC00: n |= _RC_CHOP; break;
}
if (m & 0x1000) n |= _IC_AFFINE; // only useful on 287
return n;
}
static unsigned short msvc2hard(unsigned int n) {
unsigned short m = 0;
if (n & _EM_INVALID) m |= 0x01;
if (n & _EM_DENORMAL) m |= 0x02;
if (n & _EM_ZERODIVIDE) m |= 0x04;
if (n & _EM_OVERFLOW) m |= 0x08;
if (n & _EM_UNDERFLOW) m |= 0x10;
if (n & _EM_INEXACT) m |= 0x20;
switch (n & _MCW_RC) {
case _RC_NEAR: m |= 0x000; break;
case _RC_DOWN: m |= 0x400; break;
case _RC_UP: m |= 0x800; break;
case _RC_CHOP: m |= 0xC00; break;
}
switch (n & _MCW_PC) {
case _PC_24: m |= 0x000; break;
case _PC_53: m |= 0x200; break;
case _PC_64: m |= 0x300; break;
}
if ((n & _MCW_IC) == _IC_AFFINE) m |= 0x1000;
return m;
}
typedef unsigned short rounding_mode;
static void get_rounding_mode(rounding_mode& mode)
{ mode = msvc2hard(_control87(0, 0)); }
static void set_rounding_mode(const rounding_mode mode)
{ _control87(hard2msvc(mode), _MCW_EM | _MCW_RC | _MCW_PC | _MCW_IC); }
static double to_int(const double& x) { return rint(x); }
};
} // namespace detail
} // namespace interval_lib
} // namespace numeric
} // namespace boost
#endif /* BOOST_NUMERIC_INTERVAL_DETAIL_MSVC_ROUNDING_CONTROL_HPP */

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