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// (C) Copyright John Maddock 2005-2006.
// Use, modification and distribution are subject to 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_MATH_TOOLS_FRACTION_INCLUDED
#define BOOST_MATH_TOOLS_FRACTION_INCLUDED
#ifdef _MSC_VER
#pragma once
#endif
#include <boost/config/no_tr1/cmath.hpp>
#include <boost/cstdint.hpp>
#include <boost/type_traits/integral_constant.hpp>
#include <boost/mpl/if.hpp>
#include <boost/math/tools/precision.hpp>
namespace boost{ namespace math{ namespace tools{
namespace detail
{
template <class T>
struct is_pair : public boost::false_type{};
template <class T, class U>
struct is_pair<std::pair<T,U> > : public boost::true_type{};
template <class Gen>
struct fraction_traits_simple
{
typedef typename Gen::result_type result_type;
typedef typename Gen::result_type value_type;
static result_type a(const value_type&)
{
return 1;
}
static result_type b(const value_type& v)
{
return v;
}
};
template <class Gen>
struct fraction_traits_pair
{
typedef typename Gen::result_type value_type;
typedef typename value_type::first_type result_type;
static result_type a(const value_type& v)
{
return v.first;
}
static result_type b(const value_type& v)
{
return v.second;
}
};
template <class Gen>
struct fraction_traits
: public boost::mpl::if_c<
is_pair<typename Gen::result_type>::value,
fraction_traits_pair<Gen>,
fraction_traits_simple<Gen> >::type
{
};
} // namespace detail
//
// continued_fraction_b
// Evaluates:
//
// b0 + a1
// ---------------
// b1 + a2
// ----------
// b2 + a3
// -----
// b3 + ...
//
// Note that the first a0 returned by generator Gen is disarded.
//
template <class Gen, class U>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor, boost::uintmax_t& max_terms)
{
BOOST_MATH_STD_USING // ADL of std names
typedef detail::fraction_traits<Gen> traits;
typedef typename traits::result_type result_type;
typedef typename traits::value_type value_type;
result_type tiny = tools::min_value<result_type>();
value_type v = g();
result_type f, C, D, delta;
f = traits::b(v);
if(f == 0)
f = tiny;
C = f;
D = 0;
boost::uintmax_t counter(max_terms);
do{
v = g();
D = traits::b(v) + traits::a(v) * D;
if(D == 0)
D = tiny;
C = traits::b(v) + traits::a(v) / C;
if(C == 0)
C = tiny;
D = 1/D;
delta = C*D;
f = f * delta;
}while((fabs(delta - 1) > factor) && --counter);
max_terms = max_terms - counter;
return f;
}
template <class Gen, class U>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor)
{
boost::uintmax_t max_terms = (std::numeric_limits<boost::uintmax_t>::max)();
return continued_fraction_b(g, factor, max_terms);
}
template <class Gen>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits)
{
BOOST_MATH_STD_USING // ADL of std names
typedef detail::fraction_traits<Gen> traits;
typedef typename traits::result_type result_type;
result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
boost::uintmax_t max_terms = (std::numeric_limits<boost::uintmax_t>::max)();
return continued_fraction_b(g, factor, max_terms);
}
template <class Gen>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits, boost::uintmax_t& max_terms)
{
BOOST_MATH_STD_USING // ADL of std names
typedef detail::fraction_traits<Gen> traits;
typedef typename traits::result_type result_type;
result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
return continued_fraction_b(g, factor, max_terms);
}
//
// continued_fraction_a
// Evaluates:
//
// a1
// ---------------
// b1 + a2
// ----------
// b2 + a3
// -----
// b3 + ...
//
// Note that the first a1 and b1 returned by generator Gen are both used.
//
template <class Gen, class U>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor, boost::uintmax_t& max_terms)
{
BOOST_MATH_STD_USING // ADL of std names
typedef detail::fraction_traits<Gen> traits;
typedef typename traits::result_type result_type;
typedef typename traits::value_type value_type;
result_type tiny = tools::min_value<result_type>();
value_type v = g();
result_type f, C, D, delta, a0;
f = traits::b(v);
a0 = traits::a(v);
if(f == 0)
f = tiny;
C = f;
D = 0;
boost::uintmax_t counter(max_terms);
do{
v = g();
D = traits::b(v) + traits::a(v) * D;
if(D == 0)
D = tiny;
C = traits::b(v) + traits::a(v) / C;
if(C == 0)
C = tiny;
D = 1/D;
delta = C*D;
f = f * delta;
}while((fabs(delta - 1) > factor) && --counter);
max_terms = max_terms - counter;
return a0/f;
}
template <class Gen, class U>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor)
{
boost::uintmax_t max_iter = (std::numeric_limits<boost::uintmax_t>::max)();
return continued_fraction_a(g, factor, max_iter);
}
template <class Gen>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits)
{
BOOST_MATH_STD_USING // ADL of std names
typedef detail::fraction_traits<Gen> traits;
typedef typename traits::result_type result_type;
result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
boost::uintmax_t max_iter = (std::numeric_limits<boost::uintmax_t>::max)();
return continued_fraction_a(g, factor, max_iter);
}
template <class Gen>
inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits, boost::uintmax_t& max_terms)
{
BOOST_MATH_STD_USING // ADL of std names
typedef detail::fraction_traits<Gen> traits;
typedef typename traits::result_type result_type;
result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
return continued_fraction_a(g, factor, max_terms);
}
} // namespace tools
} // namespace math
} // namespace boost
#endif // BOOST_MATH_TOOLS_FRACTION_INCLUDED
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