// (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 | |