Chris@16: //  (C) Copyright John Maddock 2006.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_TOOLS_RATIONAL_HPP
Chris@16: #define BOOST_MATH_TOOLS_RATIONAL_HPP
Chris@16: 
Chris@16: #ifdef _MSC_VER
Chris@16: #pragma once
Chris@16: #endif
Chris@16: 
Chris@16: #include <boost/array.hpp>
Chris@16: #include <boost/math/tools/config.hpp>
Chris@16: #include <boost/mpl/int.hpp>
Chris@16: 
Chris@16: #if BOOST_MATH_POLY_METHOD == 1
Chris@16: #  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/polynomial_horner1_, BOOST_MATH_MAX_POLY_ORDER).hpp>
Chris@16: #  include BOOST_HEADER()
Chris@16: #  undef BOOST_HEADER
Chris@16: #elif BOOST_MATH_POLY_METHOD == 2
Chris@16: #  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/polynomial_horner2_, BOOST_MATH_MAX_POLY_ORDER).hpp>
Chris@16: #  include BOOST_HEADER()
Chris@16: #  undef BOOST_HEADER
Chris@16: #elif BOOST_MATH_POLY_METHOD == 3
Chris@16: #  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/polynomial_horner3_, BOOST_MATH_MAX_POLY_ORDER).hpp>
Chris@16: #  include BOOST_HEADER()
Chris@16: #  undef BOOST_HEADER
Chris@16: #endif
Chris@16: #if BOOST_MATH_RATIONAL_METHOD == 1
Chris@16: #  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/rational_horner1_, BOOST_MATH_MAX_POLY_ORDER).hpp>
Chris@16: #  include BOOST_HEADER()
Chris@16: #  undef BOOST_HEADER
Chris@16: #elif BOOST_MATH_RATIONAL_METHOD == 2
Chris@16: #  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/rational_horner2_, BOOST_MATH_MAX_POLY_ORDER).hpp>
Chris@16: #  include BOOST_HEADER()
Chris@16: #  undef BOOST_HEADER
Chris@16: #elif BOOST_MATH_RATIONAL_METHOD == 3
Chris@16: #  define BOOST_HEADER() <BOOST_JOIN(boost/math/tools/detail/rational_horner3_, BOOST_MATH_MAX_POLY_ORDER).hpp>
Chris@16: #  include BOOST_HEADER()
Chris@16: #  undef BOOST_HEADER
Chris@16: #endif
Chris@16: 
Chris@16: #if 0
Chris@16: //
Chris@16: // This just allows dependency trackers to find the headers
Chris@16: // used in the above PP-magic.
Chris@16: //
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_2.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_3.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_4.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_5.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_6.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_7.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_8.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_9.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_10.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_11.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_12.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_13.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_14.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_15.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_16.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_17.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_18.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_19.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner1_20.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_2.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_3.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_4.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_5.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_6.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_7.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_8.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_9.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_10.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_11.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_12.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_13.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_14.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_15.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_16.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_17.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_18.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_19.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner2_20.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_2.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_3.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_4.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_5.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_6.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_7.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_8.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_9.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_10.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_11.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_12.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_13.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_14.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_15.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_16.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_17.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_18.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_19.hpp>
Chris@16: #include <boost/math/tools/detail/polynomial_horner3_20.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_2.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_3.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_4.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_5.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_6.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_7.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_8.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_9.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_10.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_11.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_12.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_13.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_14.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_15.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_16.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_17.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_18.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_19.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner1_20.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_2.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_3.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_4.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_5.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_6.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_7.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_8.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_9.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_10.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_11.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_12.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_13.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_14.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_15.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_16.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_17.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_18.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_19.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner2_20.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_2.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_3.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_4.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_5.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_6.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_7.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_8.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_9.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_10.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_11.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_12.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_13.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_14.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_15.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_16.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_17.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_18.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_19.hpp>
Chris@16: #include <boost/math/tools/detail/rational_horner3_20.hpp>
Chris@16: #endif
Chris@16: 
Chris@16: namespace boost{ namespace math{ namespace tools{
Chris@16: 
Chris@16: //
Chris@16: // Forward declaration to keep two phase lookup happy:
Chris@16: //
Chris@16: template <class T, class U>
Chris@16: U evaluate_polynomial(const T* poly, U const& z, std::size_t count);
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: template <class T, class V, class Tag>
Chris@16: inline V evaluate_polynomial_c_imp(const T* a, const V& val, const Tag*)
Chris@16: {
Chris@16:    return evaluate_polynomial(a, val, Tag::value);
Chris@16: }
Chris@16: 
Chris@16: } // namespace detail
Chris@16: 
Chris@16: //
Chris@16: // Polynomial evaluation with runtime size.
Chris@16: // This requires a for-loop which may be more expensive than
Chris@16: // the loop expanded versions above:
Chris@16: //
Chris@16: template <class T, class U>
Chris@16: inline U evaluate_polynomial(const T* poly, U const& z, std::size_t count)
Chris@16: {
Chris@16:    BOOST_ASSERT(count > 0);
Chris@16:    U sum = static_cast<U>(poly[count - 1]);
Chris@16:    for(int i = static_cast<int>(count) - 2; i >= 0; --i)
Chris@16:    {
Chris@16:       sum *= z;
Chris@16:       sum += static_cast<U>(poly[i]);
Chris@16:    }
Chris@16:    return sum;
Chris@16: }
Chris@16: //
Chris@16: // Compile time sized polynomials, just inline forwarders to the
Chris@16: // implementations above:
Chris@16: //
Chris@16: template <std::size_t N, class T, class V>
Chris@16: inline V evaluate_polynomial(const T(&a)[N], const V& val)
Chris@16: {
Chris@16:    typedef mpl::int_<N> tag_type;
Chris@16:    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a), val, static_cast<tag_type const*>(0));
Chris@16: }
Chris@16: 
Chris@16: template <std::size_t N, class T, class V>
Chris@16: inline V evaluate_polynomial(const boost::array<T,N>& a, const V& val)
Chris@16: {
Chris@16:    typedef mpl::int_<N> tag_type;
Chris@16:    return detail::evaluate_polynomial_c_imp(static_cast<const T*>(a.data()), val, static_cast<tag_type const*>(0));
Chris@16: }
Chris@16: //
Chris@16: // Even polynomials are trivial: just square the argument!
Chris@16: //
Chris@16: template <class T, class U>
Chris@16: inline U evaluate_even_polynomial(const T* poly, U z, std::size_t count)
Chris@16: {
Chris@16:    return evaluate_polynomial(poly, U(z*z), count);
Chris@16: }
Chris@16: 
Chris@16: template <std::size_t N, class T, class V>
Chris@16: inline V evaluate_even_polynomial(const T(&a)[N], const V& z)
Chris@16: {
Chris@16:    return evaluate_polynomial(a, V(z*z));
Chris@16: }
Chris@16: 
Chris@16: template <std::size_t N, class T, class V>
Chris@16: inline V evaluate_even_polynomial(const boost::array<T,N>& a, const V& z)
Chris@16: {
Chris@16:    return evaluate_polynomial(a, V(z*z));
Chris@16: }
Chris@16: //
Chris@16: // Odd polynomials come next:
Chris@16: //
Chris@16: template <class T, class U>
Chris@16: inline U evaluate_odd_polynomial(const T* poly, U z, std::size_t count)
Chris@16: {
Chris@16:    return poly[0] + z * evaluate_polynomial(poly+1, U(z*z), count-1);
Chris@16: }
Chris@16: 
Chris@16: template <std::size_t N, class T, class V>
Chris@16: inline V evaluate_odd_polynomial(const T(&a)[N], const V& z)
Chris@16: {
Chris@16:    typedef mpl::int_<N-1> tag_type;
Chris@16:    return a[0] + z * detail::evaluate_polynomial_c_imp(static_cast<const T*>(a) + 1, V(z*z), static_cast<tag_type const*>(0));
Chris@16: }
Chris@16: 
Chris@16: template <std::size_t N, class T, class V>
Chris@16: inline V evaluate_odd_polynomial(const boost::array<T,N>& a, const V& z)
Chris@16: {
Chris@16:    typedef mpl::int_<N-1> tag_type;
Chris@16:    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));
Chris@16: }
Chris@16: 
Chris@16: template <class T, class U, class V>
Chris@16: V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count);
Chris@16: 
Chris@16: namespace detail{
Chris@16: 
Chris@16: template <class T, class U, class V, class Tag>
Chris@16: inline V evaluate_rational_c_imp(const T* num, const U* denom, const V& z, const Tag*)
Chris@16: {
Chris@16:    return boost::math::tools::evaluate_rational(num, denom, z, Tag::value);
Chris@16: }
Chris@16: 
Chris@16: }
Chris@16: //
Chris@16: // Rational functions: numerator and denominator must be
Chris@16: // equal in size.  These always have a for-loop and so may be less
Chris@16: // efficient than evaluating a pair of polynomials. However, there
Chris@16: // are some tricks we can use to prevent overflow that might otherwise
Chris@16: // occur in polynomial evaluation, if z is large.  This is important
Chris@16: // in our Lanczos code for example.
Chris@16: //
Chris@16: template <class T, class U, class V>
Chris@16: V evaluate_rational(const T* num, const U* denom, const V& z_, std::size_t count)
Chris@16: {
Chris@16:    V z(z_);
Chris@16:    V s1, s2;
Chris@16:    if(z <= 1)
Chris@16:    {
Chris@16:       s1 = static_cast<V>(num[count-1]);
Chris@16:       s2 = static_cast<V>(denom[count-1]);
Chris@16:       for(int i = (int)count - 2; i >= 0; --i)
Chris@16:       {
Chris@16:          s1 *= z;
Chris@16:          s2 *= z;
Chris@16:          s1 += num[i];
Chris@16:          s2 += denom[i];
Chris@16:       }
Chris@16:    }
Chris@16:    else
Chris@16:    {
Chris@16:       z = 1 / z;
Chris@16:       s1 = static_cast<V>(num[0]);
Chris@16:       s2 = static_cast<V>(denom[0]);
Chris@16:       for(unsigned i = 1; i < count; ++i)
Chris@16:       {
Chris@16:          s1 *= z;
Chris@16:          s2 *= z;
Chris@16:          s1 += num[i];
Chris@16:          s2 += denom[i];
Chris@16:       }
Chris@16:    }
Chris@16:    return s1 / s2;
Chris@16: }
Chris@16: 
Chris@16: template <std::size_t N, class T, class U, class V>
Chris@16: inline V evaluate_rational(const T(&a)[N], const U(&b)[N], const V& z)
Chris@16: {
Chris@16:    return detail::evaluate_rational_c_imp(a, b, z, static_cast<const mpl::int_<N>*>(0));
Chris@16: }
Chris@16: 
Chris@16: template <std::size_t N, class T, class U, class V>
Chris@16: inline V evaluate_rational(const boost::array<T,N>& a, const boost::array<U,N>& b, const V& z)
Chris@16: {
Chris@16:    return detail::evaluate_rational_c_imp(a.data(), b.data(), z, static_cast<mpl::int_<N>*>(0));
Chris@16: }
Chris@16: 
Chris@16: } // namespace tools
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #endif // BOOST_MATH_TOOLS_RATIONAL_HPP
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: