comparison DEPENDENCIES/generic/include/boost/math/tools/rational.hpp @ 16:2665513ce2d3

Add boost headers

+//  (C) Copyright John Maddock 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_RATIONAL_HPP
+#define BOOST_MATH_TOOLS_RATIONAL_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/array.hpp>
+#include <boost/math/tools/config.hpp>
+#include <boost/mpl/int.hpp>
+
+#if BOOST_MATH_POLY_METHOD == 1
+#  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/polynomial_horner1_, BOOST_MATH_MAX_POLY_ORDER).hpp>
+#  include BOOST_HEADER()
+#  undef BOOST_HEADER
+#elif BOOST_MATH_POLY_METHOD == 2
+#  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/polynomial_horner2_, BOOST_MATH_MAX_POLY_ORDER).hpp>
+#  include BOOST_HEADER()
+#  undef BOOST_HEADER
+#elif BOOST_MATH_POLY_METHOD == 3
+#  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/polynomial_horner3_, BOOST_MATH_MAX_POLY_ORDER).hpp>
+#  include BOOST_HEADER()
+#  undef BOOST_HEADER
+#endif
+#if BOOST_MATH_RATIONAL_METHOD == 1
+#  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/rational_horner1_, BOOST_MATH_MAX_POLY_ORDER).hpp>
+#  include BOOST_HEADER()
+#  undef BOOST_HEADER
+#elif BOOST_MATH_RATIONAL_METHOD == 2
+#  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/rational_horner2_, BOOST_MATH_MAX_POLY_ORDER).hpp>
+#  include BOOST_HEADER()
+#  undef BOOST_HEADER
+#elif BOOST_MATH_RATIONAL_METHOD == 3
+#  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/rational_horner3_, BOOST_MATH_MAX_POLY_ORDER).hpp>
+#  include BOOST_HEADER()
+#  undef BOOST_HEADER
+#endif
+
+#if 0
+//
+// This just allows dependency trackers to find the headers
+// used in the above PP-magic.
+//
+#include <boost/math/tools/detail/polynomial_horner1_2.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_3.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_4.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_5.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_6.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_7.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_8.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_9.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_10.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_11.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_12.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_13.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_14.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_15.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_16.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_17.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_18.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_19.hpp>
+#include <boost/math/tools/detail/polynomial_horner1_20.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_2.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_3.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_4.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_5.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_6.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_7.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_8.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_9.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_10.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_11.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_12.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_13.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_14.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_15.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_16.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_17.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_18.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_19.hpp>
+#include <boost/math/tools/detail/polynomial_horner2_20.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_2.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_3.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_4.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_5.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_6.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_7.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_8.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_9.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_10.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_11.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_12.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_13.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_14.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_15.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_16.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_17.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_18.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_19.hpp>
+#include <boost/math/tools/detail/polynomial_horner3_20.hpp>
+#include <boost/math/tools/detail/rational_horner1_2.hpp>
+#include <boost/math/tools/detail/rational_horner1_3.hpp>
+#include <boost/math/tools/detail/rational_horner1_4.hpp>
+#include <boost/math/tools/detail/rational_horner1_5.hpp>
+#include <boost/math/tools/detail/rational_horner1_6.hpp>
+#include <boost/math/tools/detail/rational_horner1_7.hpp>
+#include <boost/math/tools/detail/rational_horner1_8.hpp>
+#include <boost/math/tools/detail/rational_horner1_9.hpp>
+#include <boost/math/tools/detail/rational_horner1_10.hpp>
+#include <boost/math/tools/detail/rational_horner1_11.hpp>
+#include <boost/math/tools/detail/rational_horner1_12.hpp>
+#include <boost/math/tools/detail/rational_horner1_13.hpp>
+#include <boost/math/tools/detail/rational_horner1_14.hpp>
+#include <boost/math/tools/detail/rational_horner1_15.hpp>
+#include <boost/math/tools/detail/rational_horner1_16.hpp>
+#include <boost/math/tools/detail/rational_horner1_17.hpp>
+#include <boost/math/tools/detail/rational_horner1_18.hpp>
+#include <boost/math/tools/detail/rational_horner1_19.hpp>
+#include <boost/math/tools/detail/rational_horner1_20.hpp>
+#include <boost/math/tools/detail/rational_horner2_2.hpp>
+#include <boost/math/tools/detail/rational_horner2_3.hpp>
+#include <boost/math/tools/detail/rational_horner2_4.hpp>
+#include <boost/math/tools/detail/rational_horner2_5.hpp>
+#include <boost/math/tools/detail/rational_horner2_6.hpp>
+#include <boost/math/tools/detail/rational_horner2_7.hpp>
+#include <boost/math/tools/detail/rational_horner2_8.hpp>
+#include <boost/math/tools/detail/rational_horner2_9.hpp>
+#include <boost/math/tools/detail/rational_horner2_10.hpp>
+#include <boost/math/tools/detail/rational_horner2_11.hpp>
+#include <boost/math/tools/detail/rational_horner2_12.hpp>
+#include <boost/math/tools/detail/rational_horner2_13.hpp>
+#include <boost/math/tools/detail/rational_horner2_14.hpp>
+#include <boost/math/tools/detail/rational_horner2_15.hpp>
+#include <boost/math/tools/detail/rational_horner2_16.hpp>
+#include <boost/math/tools/detail/rational_horner2_17.hpp>
+#include <boost/math/tools/detail/rational_horner2_18.hpp>
+#include <boost/math/tools/detail/rational_horner2_19.hpp>
+#include <boost/math/tools/detail/rational_horner2_20.hpp>
+#include <boost/math/tools/detail/rational_horner3_2.hpp>
+#include <boost/math/tools/detail/rational_horner3_3.hpp>
+#include <boost/math/tools/detail/rational_horner3_4.hpp>
+#include <boost/math/tools/detail/rational_horner3_5.hpp>
+#include <boost/math/tools/detail/rational_horner3_6.hpp>
+#include <boost/math/tools/detail/rational_horner3_7.hpp>
+#include <boost/math/tools/detail/rational_horner3_8.hpp>
+#include <boost/math/tools/detail/rational_horner3_9.hpp>
+#include <boost/math/tools/detail/rational_horner3_10.hpp>
+#include <boost/math/tools/detail/rational_horner3_11.hpp>
+#include <boost/math/tools/detail/rational_horner3_12.hpp>
+#include <boost/math/tools/detail/rational_horner3_13.hpp>
+#include <boost/math/tools/detail/rational_horner3_14.hpp>
+#include <boost/math/tools/detail/rational_horner3_15.hpp>
+#include <boost/math/tools/detail/rational_horner3_16.hpp>
+#include <boost/math/tools/detail/rational_horner3_17.hpp>
+#include <boost/math/tools/detail/rational_horner3_18.hpp>
+#include <boost/math/tools/detail/rational_horner3_19.hpp>
+#include <boost/math/tools/detail/rational_horner3_20.hpp>
+#endif
+
+namespace boost{ namespace math{ namespace tools{
+
+//
+// Forward declaration to keep two phase lookup happy:
+//
+template <class T, class U>
+U evaluate_polynomial(const T* poly, U const& z, std::size_t count);
+
+namespace detail{
+
+template <class T, class V, class Tag>
+inline V evaluate_polynomial_c_imp(const T* a, const V& val, const Tag*)
+{
+   return evaluate_polynomial(a, val, Tag::value);
+}
+
+} // namespace detail
+
+//
+// Polynomial evaluation with runtime size.
+// This requires a for-loop which may be more expensive than
+// the loop expanded versions above:
+//
+template <class T, class U>
+inline U evaluate_polynomial(const T* poly, U const& z, std::size_t count)
+{
+   BOOST_ASSERT(count > 0);
+   U sum = static_cast<U>(poly[count - 1]);
+   for(int i = static_cast<int>(count) - 2; i >= 0; --i)
+   {
+      sum *= z;
+      sum += static_cast<U>(poly[i]);
+   }
+   return sum;
+}
+//
+// Compile time sized polynomials, just inline forwarders to the
+// implementations above:
+//
+template <std::size_t N, class T, class V>
+inline V evaluate_polynomial(const T(&a)[N], const V& val)
+{
+   typedef mpl::int_<N> tag_type;
+   return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a), val, static_cast<tag_type const*>(0));
+}
+
+template <std::size_t N, class T, class V>
+inline V evaluate_polynomial(const boost::array<T,N>& a, const V& val)
+{
+   typedef mpl::int_<N> tag_type;
+   return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()), val, static_cast<tag_type const*>(0));
+}
+//
+// Even polynomials are trivial: just square the argument!
+//
+template <class T, class U>
+inline U evaluate_even_polynomial(const T* poly, U z, std::size_t count)
+{
+   return evaluate_polynomial(poly, U(z*z), count);
+}
+
+template <std::size_t N, class T, class V>
+inline V evaluate_even_polynomial(const T(&a)[N], const V& z)
+{
+   return evaluate_polynomial(a, V(z*z));
+}
+
+template <std::size_t N, class T, class V>
+inline V evaluate_even_polynomial(const boost::array<T,N>& a, const V& z)
+{
+   return evaluate_polynomial(a, V(z*z));
+}
+//
+// Odd polynomials come next:
+//
+template <class T, class U>
+inline U evaluate_odd_polynomial(const T* poly, U z, std::size_t count)
+{
+   return poly[0] + z * evaluate_polynomial(poly+1, U(z*z), count-1);
+}
+
+template <std::size_t N, class T, class V>
+inline V evaluate_odd_polynomial(const T(&a)[N], const V& z)
+{
+   typedef mpl::int_<N-1> tag_type;
+   return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a) + 1, V(z*z), static_cast<tag_type const*>(0));
+}
+
+template <std::size_t N, class T, class V>
+inline V evaluate_odd_polynomial(const boost::array<T,N>& a, const V& z)
+{
+   typedef mpl::int_<N-1> tag_type;
+   return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()) + 1, V(z*z), static_cast<tag_type const*>(0));
+}
+
+template <class T, class U, class V>
+V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count);
+
+namespace detail{
+
+template <class T, class U, class V, class Tag>
+inline V evaluate_rational_c_imp(const T* num, const U* denom, const V& z, const Tag*)
+{
+   return boost::math::tools::evaluate_rational(num, denom, z, Tag::value);
+}
+
+}
+//
+// Rational functions: numerator and denominator must be
+// equal in size.  These always have a for-loop and so may be less
+// efficient than evaluating a pair of polynomials. However, there
+// are some tricks we can use to prevent overflow that might otherwise
+// occur in polynomial evaluation, if z is large.  This is important
+// in our Lanczos code for example.
+//
+template <class T, class U, class V>
+V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count)
+{
+   V z(z_);
+   V s1, s2;
+   if(z <= 1)
+   {
+      s1 = static_cast<V>(num[count-1]);
+      s2 = static_cast<V>(denom[count-1]);
+      for(int i = (int)count - 2; i >= 0; --i)
+      {
+         s1 *= z;
+         s2 *= z;
+         s1 += num[i];
+         s2 += denom[i];
+      }
+   }
+   else
+   {
+      z = 1 / z;
+      s1 = static_cast<V>(num[0]);
+      s2 = static_cast<V>(denom[0]);
+      for(unsigned i = 1; i < count; ++i)
+      {
+         s1 *= z;
+         s2 *= z;
+         s1 += num[i];
+         s2 += denom[i];
+      }
+   }
+   return s1 / s2;
+}
+
+template <std::size_t N, class T, class U, class V>
+inline V evaluate_rational(const T(&a)[N], const U(&b)[N], const V& z)
+{
+   return detail::evaluate_rational_c_imp(a, b, z, static_cast<const mpl::int_<N>*>(0));
+}
+
+template <std::size_t N, class T, class U, class V>
+inline V evaluate_rational(const boost::array<T,N>& a, const boost::array<U,N>& b, const V& z)
+{
+   return detail::evaluate_rational_c_imp(a.data(), b.data(), z, static_cast<mpl::int_<N>*>(0));
+}
+
+} // namespace tools
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_TOOLS_RATIONAL_HPP
+
+
+
+