334 lines
14 KiB
C++
334 lines
14 KiB
C++
// (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) BOOST_MATH_NOEXCEPT(U);
|
|
|
|
namespace detail{
|
|
|
|
template <class T, class V, class Tag>
|
|
inline V evaluate_polynomial_c_imp(const T* a, const V& val, const Tag*) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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_MATH_NOEXCEPT(U)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(U)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(U)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V);
|
|
|
|
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*) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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) BOOST_MATH_NOEXCEPT(V)
|
|
{
|
|
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
|
|
|
|
|
|
|
|
|