261 lines
7.9 KiB
C++
261 lines
7.9 KiB
C++
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// (C) Copyright John Maddock 2005-2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_TOOLS_FRACTION_INCLUDED
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#define BOOST_MATH_TOOLS_FRACTION_INCLUDED
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/config/no_tr1/cmath.hpp>
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#include <boost/cstdint.hpp>
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#include <boost/type_traits/integral_constant.hpp>
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#include <boost/mpl/if.hpp>
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#include <boost/math/tools/precision.hpp>
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namespace boost{ namespace math{ namespace tools{
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namespace detail
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{
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template <class T>
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struct is_pair : public boost::false_type{};
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template <class T, class U>
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struct is_pair<std::pair<T,U> > : public boost::true_type{};
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template <class Gen>
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struct fraction_traits_simple
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{
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typedef typename Gen::result_type result_type;
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typedef typename Gen::result_type value_type;
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static result_type a(const value_type&) BOOST_MATH_NOEXCEPT(value_type)
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{
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return 1;
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}
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static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
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{
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return v;
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}
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};
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template <class Gen>
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struct fraction_traits_pair
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{
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typedef typename Gen::result_type value_type;
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typedef typename value_type::first_type result_type;
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static result_type a(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
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{
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return v.first;
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}
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static result_type b(const value_type& v) BOOST_MATH_NOEXCEPT(value_type)
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{
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return v.second;
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}
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};
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template <class Gen>
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struct fraction_traits
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: public boost::mpl::if_c<
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is_pair<typename Gen::result_type>::value,
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fraction_traits_pair<Gen>,
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fraction_traits_simple<Gen> >::type
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{
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};
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} // namespace detail
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//
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// continued_fraction_b
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// Evaluates:
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//
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// b0 + a1
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// ---------------
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// b1 + a2
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// ----------
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// b2 + a3
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// -----
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// b3 + ...
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//
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// Note that the first a0 returned by generator Gen is disarded.
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//
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template <class Gen, class U>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor, boost::uintmax_t& max_terms)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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BOOST_MATH_STD_USING // ADL of std names
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typedef detail::fraction_traits<Gen> traits;
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typedef typename traits::result_type result_type;
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typedef typename traits::value_type value_type;
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result_type tiny = tools::min_value<result_type>();
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value_type v = g();
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result_type f, C, D, delta;
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f = traits::b(v);
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if(f == 0)
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f = tiny;
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C = f;
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D = 0;
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boost::uintmax_t counter(max_terms);
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do{
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v = g();
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D = traits::b(v) + traits::a(v) * D;
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if(D == 0)
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D = tiny;
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C = traits::b(v) + traits::a(v) / C;
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if(C == 0)
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C = tiny;
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D = 1/D;
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delta = C*D;
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f = f * delta;
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}while((fabs(delta - 1) > factor) && --counter);
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max_terms = max_terms - counter;
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return f;
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}
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template <class Gen, class U>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, const U& factor)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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boost::uintmax_t max_terms = (std::numeric_limits<boost::uintmax_t>::max)();
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return continued_fraction_b(g, factor, max_terms);
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}
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template <class Gen>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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BOOST_MATH_STD_USING // ADL of std names
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typedef detail::fraction_traits<Gen> traits;
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typedef typename traits::result_type result_type;
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result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
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boost::uintmax_t max_terms = (std::numeric_limits<boost::uintmax_t>::max)();
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return continued_fraction_b(g, factor, max_terms);
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}
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template <class Gen>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_b(Gen& g, int bits, boost::uintmax_t& max_terms)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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BOOST_MATH_STD_USING // ADL of std names
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typedef detail::fraction_traits<Gen> traits;
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typedef typename traits::result_type result_type;
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result_type factor = ldexp(1.0f, 1 - bits); // 1 / pow(result_type(2), bits);
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return continued_fraction_b(g, factor, max_terms);
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}
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//
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// continued_fraction_a
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// Evaluates:
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//
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// a1
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// ---------------
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// b1 + a2
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// ----------
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// b2 + a3
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// -----
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// b3 + ...
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//
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// Note that the first a1 and b1 returned by generator Gen are both used.
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//
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template <class Gen, class U>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor, boost::uintmax_t& max_terms)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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BOOST_MATH_STD_USING // ADL of std names
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typedef detail::fraction_traits<Gen> traits;
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typedef typename traits::result_type result_type;
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typedef typename traits::value_type value_type;
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result_type tiny = tools::min_value<result_type>();
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value_type v = g();
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result_type f, C, D, delta, a0;
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f = traits::b(v);
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a0 = traits::a(v);
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if(f == 0)
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f = tiny;
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C = f;
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D = 0;
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boost::uintmax_t counter(max_terms);
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do{
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v = g();
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D = traits::b(v) + traits::a(v) * D;
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if(D == 0)
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D = tiny;
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C = traits::b(v) + traits::a(v) / C;
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if(C == 0)
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C = tiny;
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D = 1/D;
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delta = C*D;
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f = f * delta;
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}while((fabs(delta - 1) > factor) && --counter);
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max_terms = max_terms - counter;
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return a0/f;
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}
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template <class Gen, class U>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, const U& factor)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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boost::uintmax_t max_iter = (std::numeric_limits<boost::uintmax_t>::max)();
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return continued_fraction_a(g, factor, max_iter);
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}
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template <class Gen>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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BOOST_MATH_STD_USING // ADL of std names
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typedef detail::fraction_traits<Gen> traits;
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typedef typename traits::result_type result_type;
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result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
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boost::uintmax_t max_iter = (std::numeric_limits<boost::uintmax_t>::max)();
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return continued_fraction_a(g, factor, max_iter);
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}
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template <class Gen>
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inline typename detail::fraction_traits<Gen>::result_type continued_fraction_a(Gen& g, int bits, boost::uintmax_t& max_terms)
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BOOST_NOEXCEPT_IF(BOOST_MATH_IS_FLOAT(typename detail::fraction_traits<Gen>::result_type) && noexcept(std::declval<Gen>()()))
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{
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BOOST_MATH_STD_USING // ADL of std names
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typedef detail::fraction_traits<Gen> traits;
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typedef typename traits::result_type result_type;
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result_type factor = ldexp(1.0f, 1-bits); // 1 / pow(result_type(2), bits);
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return continued_fraction_a(g, factor, max_terms);
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}
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} // namespace tools
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} // namespace math
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} // namespace boost
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#endif // BOOST_MATH_TOOLS_FRACTION_INCLUDED
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