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diff --git a/src/third_party/boost-1.56.0/boost/math/tools/detail/rational_horner3_16.hpp b/src/third_party/boost-1.56.0/boost/math/tools/detail/rational_horner3_16.hpp
new file mode 100644
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+++ b/src/third_party/boost-1.56.0/boost/math/tools/detail/rational_horner3_16.hpp
@@ -0,0 +1,1032 @@
+// (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_16_HPP
+#define BOOST_MATH_TOOLS_RAT_EVAL_16_HPP
+
+namespace boost{ namespace math{ namespace tools{ namespace detail{
+
+template <class T, class U, class V>
+inline V evaluate_rational_c_imp(const T*, const U*, 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]);
+ }
+}
+
+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_<13>*)
+{
+ if(x <= 1)
+ {
+ V x2 = x * x;
+ V t[4];
+ t[0] = a[12] * x2 + a[10];
+ t[1] = a[11] * x2 + a[9];
+ t[2] = b[12] * x2 + b[10];
+ t[3] = b[11] * x2 + b[9];
+ t[0] *= x2;
+ t[1] *= x2;
+ t[2] *= x2;
+ t[3] *= x2;
+ t[0] += static_cast<V>(a[8]);
+ t[1] += static_cast<V>(a[7]);
+ t[2] += static_cast<V>(b[8]);
+ t[3] += static_cast<V>(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[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] *= z2;
+ t[2] *= z2;
+ t[0] += static_cast<V>(a[12]);
+ t[2] += static_cast<V>(b[12]);
+ 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_<14>*)
+{
+ if(x <= 1)
+ {
+ V x2 = x * x;
+ V t[4];
+ t[0] = a[13] * x2 + a[11];
+ t[1] = a[12] * x2 + a[10];
+ t[2] = b[13] * x2 + b[11];
+ t[3] = b[12] * x2 + b[10];
+ t[0] *= x2;
+ t[1] *= x2;
+ t[2] *= x2;
+ t[3] *= x2;
+ t[0] += static_cast<V>(a[9]);
+ t[1] += static_cast<V>(a[8]);
+ t[2] += static_cast<V>(b[9]);
+ t[3] += static_cast<V>(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] *= z2;
+ t[1] *= z2;
+ t[2] *= z2;
+ t[3] *= z2;
+ t[0] += static_cast<V>(a[12]);
+ t[1] += static_cast<V>(a[13]);
+ t[2] += static_cast<V>(b[12]);
+ t[3] += static_cast<V>(b[13]);
+ 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_<15>*)
+{
+ if(x <= 1)
+ {
+ V x2 = x * x;
+ V t[4];
+ t[0] = a[14] * x2 + a[12];
+ t[1] = a[13] * x2 + a[11];
+ t[2] = b[14] * x2 + b[12];
+ t[3] = b[13] * x2 + b[11];
+ t[0] *= x2;
+ t[1] *= x2;
+ t[2] *= x2;
+ t[3] *= x2;
+ t[0] += static_cast<V>(a[10]);
+ t[1] += static_cast<V>(a[9]);
+ t[2] += static_cast<V>(b[10]);
+ t[3] += static_cast<V>(b[9]);
+ t[0] *= x2;
+ t[1] *= x2;
+ t[2] *= x2;
+ t[3] *= x2;
+ t[0] += static_cast<V>(a[8]);
+ t[1] += static_cast<V>(a[7]);
+ t[2] += static_cast<V>(b[8]);
+ t[3] += static_cast<V>(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[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] *= z2;
+ t[1] *= z2;
+ t[2] *= z2;
+ t[3] *= z2;
+ t[0] += static_cast<V>(a[12]);
+ t[1] += static_cast<V>(a[13]);
+ t[2] += static_cast<V>(b[12]);
+ t[3] += static_cast<V>(b[13]);
+ t[0] *= z2;
+ t[2] *= z2;
+ t[0] += static_cast<V>(a[14]);
+ t[2] += static_cast<V>(b[14]);
+ 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_<16>*)
+{
+ if(x <= 1)
+ {
+ V x2 = x * x;
+ V t[4];
+ t[0] = a[15] * x2 + a[13];
+ t[1] = a[14] * x2 + a[12];
+ t[2] = b[15] * x2 + b[13];
+ t[3] = b[14] * x2 + b[12];
+ t[0] *= x2;
+ t[1] *= x2;
+ t[2] *= x2;
+ t[3] *= x2;
+ t[0] += static_cast<V>(a[11]);
+ t[1] += static_cast<V>(a[10]);
+ t[2] += static_cast<V>(b[11]);
+ t[3] += static_cast<V>(b[10]);
+ t[0] *= x2;
+ t[1] *= x2;
+ t[2] *= x2;
+ t[3] *= x2;
+ t[0] += static_cast<V>(a[9]);
+ t[1] += static_cast<V>(a[8]);
+ t[2] += static_cast<V>(b[9]);
+ t[3] += static_cast<V>(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] *= z2;
+ t[1] *= z2;
+ t[2] *= z2;
+ t[3] *= z2;
+ t[0] += static_cast<V>(a[12]);
+ t[1] += static_cast<V>(a[13]);
+ t[2] += static_cast<V>(b[12]);
+ t[3] += static_cast<V>(b[13]);
+ t[0] *= z2;
+ t[1] *= z2;
+ t[2] *= z2;
+ t[3] *= z2;
+ t[0] += static_cast<V>(a[14]);
+ t[1] += static_cast<V>(a[15]);
+ t[2] += static_cast<V>(b[14]);
+ t[3] += static_cast<V>(b[15]);
+ t[0] *= z;
+ t[2] *= z;
+ return (t[0] + t[1]) / (t[2] + t[3]);
+ }
+}
+
+
+}}}} // namespaces
+
+#endif // include guard
+
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