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路径: \\game3dprogramming\materials\GameFactory\GameFactoryDemo\references\boost_1_35_0\boost\math\tools\series.hpp
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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_SERIES_INCLUDED #define BOOST_MATH_TOOLS_SERIES_INCLUDED #include
#include
#include
namespace boost{ namespace math{ namespace tools{ // // Simple series summation come first: // template
typename Functor::result_type sum_series(Functor& func, int bits) { BOOST_MATH_STD_USING typedef typename Functor::result_type result_type; result_type factor = pow(result_type(2), bits); result_type result = func(); result_type next_term; do{ next_term = func(); result += next_term; } while(fabs(result) < fabs(factor * next_term)); return result; } template
typename Functor::result_type sum_series(Functor& func, int bits, boost::uintmax_t& max_terms) { BOOST_MATH_STD_USING typedef typename Functor::result_type result_type; boost::uintmax_t counter = max_terms; result_type factor = ldexp(result_type(1), bits); result_type result = func(); result_type next_term; do{ next_term = func(); result += next_term; } while((fabs(result) < fabs(factor * next_term)) && --counter); // set max_terms to the actual number of terms of the series evaluated: max_terms = max_terms - counter; return result; } template
typename Functor::result_type sum_series(Functor& func, int bits, U init_value) { BOOST_MATH_STD_USING typedef typename Functor::result_type result_type; result_type factor = ldexp(result_type(1), bits); result_type result = static_cast
(init_value); result_type next_term; do{ next_term = func(); result += next_term; } while(fabs(result) < fabs(factor * next_term)); return result; } template
typename Functor::result_type sum_series(Functor& func, int bits, boost::uintmax_t& max_terms, U init_value) { BOOST_MATH_STD_USING typedef typename Functor::result_type result_type; boost::uintmax_t counter = max_terms; result_type factor = ldexp(result_type(1), bits); result_type result = init_value; result_type next_term; do{ next_term = func(); result += next_term; } while((fabs(result) < fabs(factor * next_term)) && --counter); // set max_terms to the actual number of terms of the series evaluated: max_terms = max_terms - counter; return result; } // // Algorithm kahan_sum_series invokes Functor func until the N'th // term is too small to have any effect on the total, the terms // are added using the Kahan summation method. // // CAUTION: Optimizing compilers combined with extended-precision // machine registers conspire to render this algorithm partly broken: // double rounding of intermediate terms (first to a long double machine // register, and then to a double result) cause the rounding error computed // by the algorithm to be off by up to 1ulp. However this occurs rarely, and // in any case the result is still much better than a naive summation. // template
typename Functor::result_type kahan_sum_series(Functor& func, int bits) { BOOST_MATH_STD_USING typedef typename Functor::result_type result_type; result_type factor = pow(result_type(2), bits); result_type result = func(); result_type next_term, y, t; result_type carry = 0; do{ next_term = func(); y = next_term - carry; t = result + y; carry = t - result; carry -= y; result = t; } while(fabs(result) < fabs(factor * next_term)); return result; } template
typename Functor::result_type kahan_sum_series(Functor& func, int bits, boost::uintmax_t& max_terms) { BOOST_MATH_STD_USING typedef typename Functor::result_type result_type; boost::uintmax_t counter = max_terms; result_type factor = ldexp(result_type(1), bits); result_type result = func(); result_type next_term, y, t; result_type carry = 0; do{ next_term = func(); y = next_term - carry; t = result + y; carry = t - result; carry -= y; result = t; } while((fabs(result) < fabs(factor * next_term)) && --counter); // set max_terms to the actual number of terms of the series evaluated: max_terms = max_terms - counter; return result; } } // namespace tools } // namespace math } // namespace boost #endif // BOOST_MATH_TOOLS_SERIES_INCLUDED
series.hpp
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