| // (C) Copyright John Maddock 2007. |
| // 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) |
| // |
| // This file is machine generated, do not edit by hand |
| |
| // Polynomial evaluation using second order Horners rule |
| #ifndef BOOST_MATH_TOOLS_RAT_EVAL_12_HPP |
| #define BOOST_MATH_TOOLS_RAT_EVAL_12_HPP |
| |
| namespace boost{ namespace math{ namespace tools{ namespace detail{ |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<0>*) |
| { |
| return static_cast<V>(0); |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V&, const mpl::int_<1>*) |
| { |
| return static_cast<V>(a[0]) / static_cast<V>(b[0]); |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<2>*) |
| { |
| return static_cast<V>((a[1] * x + a[0]) / (b[1] * x + b[0])); |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<3>*) |
| { |
| return static_cast<V>(((a[2] * x + a[1]) * x + a[0]) / ((b[2] * x + b[1]) * x + b[0])); |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<4>*) |
| { |
| return static_cast<V>((((a[3] * x + a[2]) * x + a[1]) * x + a[0]) / (((b[3] * x + b[2]) * x + b[1]) * x + b[0])); |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<5>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[4] * x2 + a[2]; |
| t[1] = a[3] * x2 + a[1]; |
| t[2] = b[4] * x2 + b[2]; |
| t[3] = b[3] * x2 + b[1]; |
| t[0] *= x2; |
| t[2] *= x2; |
| t[0] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[0]); |
| t[1] *= x; |
| t[3] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[2] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[2] += static_cast<V>(b[4]); |
| t[1] *= z; |
| t[3] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<6>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[5] * x2 + a[3]; |
| t[1] = a[4] * x2 + a[2]; |
| t[2] = b[5] * x2 + b[3]; |
| t[3] = b[4] * x2 + b[2]; |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[1]); |
| t[1] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[1]); |
| t[3] += static_cast<V>(b[0]); |
| t[0] *= x; |
| t[2] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= z; |
| t[2] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<7>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[6] * x2 + a[4]; |
| t[1] = a[5] * x2 + a[3]; |
| t[2] = b[6] * x2 + b[4]; |
| t[3] = b[5] * x2 + b[3]; |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[2]); |
| t[1] += static_cast<V>(a[1]); |
| t[2] += static_cast<V>(b[2]); |
| t[3] += static_cast<V>(b[1]); |
| t[0] *= x2; |
| t[2] *= x2; |
| t[0] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[0]); |
| t[1] *= x; |
| t[3] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= z2; |
| t[2] *= z2; |
| t[0] += static_cast<V>(a[6]); |
| t[2] += static_cast<V>(b[6]); |
| t[1] *= z; |
| t[3] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<8>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[7] * x2 + a[5]; |
| t[1] = a[6] * x2 + a[4]; |
| t[2] = b[7] * x2 + b[5]; |
| t[3] = b[6] * x2 + b[4]; |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[3]); |
| t[1] += static_cast<V>(a[2]); |
| t[2] += static_cast<V>(b[3]); |
| t[3] += static_cast<V>(b[2]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[1]); |
| t[1] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[1]); |
| t[3] += static_cast<V>(b[0]); |
| t[0] *= x; |
| t[2] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[6]); |
| t[1] += static_cast<V>(a[7]); |
| t[2] += static_cast<V>(b[6]); |
| t[3] += static_cast<V>(b[7]); |
| t[0] *= z; |
| t[2] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<9>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[8] * x2 + a[6]; |
| t[1] = a[7] * x2 + a[5]; |
| t[2] = b[8] * x2 + b[6]; |
| t[3] = b[7] * x2 + b[5]; |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[3]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[3]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[2]); |
| t[1] += static_cast<V>(a[1]); |
| t[2] += static_cast<V>(b[2]); |
| t[3] += static_cast<V>(b[1]); |
| t[0] *= x2; |
| t[2] *= x2; |
| t[0] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[0]); |
| t[1] *= x; |
| t[3] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[6]); |
| t[1] += static_cast<V>(a[7]); |
| t[2] += static_cast<V>(b[6]); |
| t[3] += static_cast<V>(b[7]); |
| t[0] *= z2; |
| t[2] *= z2; |
| t[0] += static_cast<V>(a[8]); |
| t[2] += static_cast<V>(b[8]); |
| t[1] *= z; |
| t[3] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<10>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[9] * x2 + a[7]; |
| t[1] = a[8] * x2 + a[6]; |
| t[2] = b[9] * x2 + b[7]; |
| t[3] = b[8] * x2 + b[6]; |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[5]); |
| t[1] += static_cast<V>(a[4]); |
| t[2] += static_cast<V>(b[5]); |
| t[3] += static_cast<V>(b[4]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[3]); |
| t[1] += static_cast<V>(a[2]); |
| t[2] += static_cast<V>(b[3]); |
| t[3] += static_cast<V>(b[2]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[1]); |
| t[1] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[1]); |
| t[3] += static_cast<V>(b[0]); |
| t[0] *= x; |
| t[2] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[6]); |
| t[1] += static_cast<V>(a[7]); |
| t[2] += static_cast<V>(b[6]); |
| t[3] += static_cast<V>(b[7]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[8]); |
| t[1] += static_cast<V>(a[9]); |
| t[2] += static_cast<V>(b[8]); |
| t[3] += static_cast<V>(b[9]); |
| t[0] *= z; |
| t[2] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<11>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[10] * x2 + a[8]; |
| t[1] = a[9] * x2 + a[7]; |
| t[2] = b[10] * x2 + b[8]; |
| t[3] = b[9] * x2 + b[7]; |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[6]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[6]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[3]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[3]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[2]); |
| t[1] += static_cast<V>(a[1]); |
| t[2] += static_cast<V>(b[2]); |
| t[3] += static_cast<V>(b[1]); |
| t[0] *= x2; |
| t[2] *= x2; |
| t[0] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[0]); |
| t[1] *= x; |
| t[3] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[6]); |
| t[1] += static_cast<V>(a[7]); |
| t[2] += static_cast<V>(b[6]); |
| t[3] += static_cast<V>(b[7]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[8]); |
| t[1] += static_cast<V>(a[9]); |
| t[2] += static_cast<V>(b[8]); |
| t[3] += static_cast<V>(b[9]); |
| t[0] *= z2; |
| t[2] *= z2; |
| t[0] += static_cast<V>(a[10]); |
| t[2] += static_cast<V>(b[10]); |
| t[1] *= z; |
| t[3] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| template <class T, class U, class V> |
| inline V evaluate_rational_c_imp(const T* a, const U* b, const V& x, const mpl::int_<12>*) |
| { |
| if(x <= 1) |
| { |
| V x2 = x * x; |
| V t[4]; |
| t[0] = a[11] * x2 + a[9]; |
| t[1] = a[10] * x2 + a[8]; |
| t[2] = b[11] * x2 + b[9]; |
| t[3] = b[10] * x2 + b[8]; |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[7]); |
| t[1] += static_cast<V>(a[6]); |
| t[2] += static_cast<V>(b[7]); |
| t[3] += static_cast<V>(b[6]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[5]); |
| t[1] += static_cast<V>(a[4]); |
| t[2] += static_cast<V>(b[5]); |
| t[3] += static_cast<V>(b[4]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[3]); |
| t[1] += static_cast<V>(a[2]); |
| t[2] += static_cast<V>(b[3]); |
| t[3] += static_cast<V>(b[2]); |
| t[0] *= x2; |
| t[1] *= x2; |
| t[2] *= x2; |
| t[3] *= x2; |
| t[0] += static_cast<V>(a[1]); |
| t[1] += static_cast<V>(a[0]); |
| t[2] += static_cast<V>(b[1]); |
| t[3] += static_cast<V>(b[0]); |
| t[0] *= x; |
| t[2] *= x; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| else |
| { |
| V z = 1 / x; |
| V z2 = 1 / (x * x); |
| V t[4]; |
| t[0] = a[0] * z2 + a[2]; |
| t[1] = a[1] * z2 + a[3]; |
| t[2] = b[0] * z2 + b[2]; |
| t[3] = b[1] * z2 + b[3]; |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[4]); |
| t[1] += static_cast<V>(a[5]); |
| t[2] += static_cast<V>(b[4]); |
| t[3] += static_cast<V>(b[5]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[6]); |
| t[1] += static_cast<V>(a[7]); |
| t[2] += static_cast<V>(b[6]); |
| t[3] += static_cast<V>(b[7]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[8]); |
| t[1] += static_cast<V>(a[9]); |
| t[2] += static_cast<V>(b[8]); |
| t[3] += static_cast<V>(b[9]); |
| t[0] *= z2; |
| t[1] *= z2; |
| t[2] *= z2; |
| t[3] *= z2; |
| t[0] += static_cast<V>(a[10]); |
| t[1] += static_cast<V>(a[11]); |
| t[2] += static_cast<V>(b[10]); |
| t[3] += static_cast<V>(b[11]); |
| t[0] *= z; |
| t[2] *= z; |
| return (t[0] + t[1]) / (t[2] + t[3]); |
| } |
| } |
| |
| |
| }}}} // namespaces |
| |
| #endif // include guard |
| |