Added boost header

test/external/boost/math/tools/series.hpp

@@ -0,0 +1,158 @@
+//  (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
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/config/no_tr1/cmath.hpp>
+#include <boost/cstdint.hpp>
+#include <boost/limits.hpp>
+#include <boost/math/tools/config.hpp>
+
+namespace boost{ namespace math{ namespace tools{
+
+//
+// Simple series summation come first:
+//
+template <class Functor, class U, class V>
+inline typename Functor::result_type sum_series(Functor& func, const U& factor, boost::uintmax_t& max_terms, const V& init_value)
+{
+   BOOST_MATH_STD_USING
+
+   typedef typename Functor::result_type result_type;
+
+   boost::uintmax_t counter = max_terms;
+
+   result_type result = init_value;
+   result_type next_term;
+   do{
+      next_term = func();
+      result += next_term;
+   }
+   while((fabs(factor * result) < fabs(next_term)) && --counter);
+
+   // set max_terms to the actual number of terms of the series evaluated:
+   max_terms = max_terms - counter;
+
+   return result;
+}
+
+template <class Functor, class U>
+inline typename Functor::result_type sum_series(Functor& func, const U& factor, boost::uintmax_t& max_terms)
+{
+   typename Functor::result_type init_value = 0;
+   return sum_series(func, factor, max_terms, init_value);
+}
+
+template <class Functor, class U>
+inline typename Functor::result_type sum_series(Functor& func, int bits, boost::uintmax_t& max_terms, const U& init_value)
+{
+   BOOST_MATH_STD_USING
+   typedef typename Functor::result_type result_type;
+   result_type factor = ldexp(result_type(1), 1 - bits);
+   return sum_series(func, factor, max_terms, init_value);
+}
+
+template <class Functor>
+inline typename Functor::result_type sum_series(Functor& func, int bits)
+{
+   BOOST_MATH_STD_USING
+   typedef typename Functor::result_type result_type;
+   boost::uintmax_t iters = (std::numeric_limits<boost::uintmax_t>::max)();
+   result_type init_val = 0;
+   return sum_series(func, bits, iters, init_val);
+}
+
+template <class Functor>
+inline 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;
+   result_type init_val = 0;
+   return sum_series(func, bits, max_terms, init_val);
+}
+
+template <class Functor, class U>
+inline typename Functor::result_type sum_series(Functor& func, int bits, const U& init_value)
+{
+   BOOST_MATH_STD_USING
+   boost::uintmax_t iters = (std::numeric_limits<boost::uintmax_t>::max)();
+   return sum_series(func, bits, iters, init_value);
+}
+
+//
+// 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 <class Functor>
+inline 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 <class Functor>
+inline 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
+