Added boost header

test/external/boost/math/special_functions/detail/bessel_k0.hpp

@@ -0,0 +1,121 @@
+//  Copyright (c) 2006 Xiaogang Zhang
+//  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_BESSEL_K0_HPP
+#define BOOST_MATH_BESSEL_K0_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/tools/rational.hpp>
+#include <boost/math/policies/error_handling.hpp>
+#include <boost/assert.hpp>
+
+// Modified Bessel function of the second kind of order zero
+// minimax rational approximations on intervals, see
+// Russon and Blair, Chalk River Report AECL-3461, 1969
+
+namespace boost { namespace math { namespace detail{
+
+template <typename T, typename Policy>
+T bessel_k0(T x, const Policy& pol)
+{
+    BOOST_MATH_INSTRUMENT_CODE(x);
+
+    static const T P1[] = {
+         static_cast<T>(2.4708152720399552679e+03L),
+         static_cast<T>(5.9169059852270512312e+03L),
+         static_cast<T>(4.6850901201934832188e+02L),
+         static_cast<T>(1.1999463724910714109e+01L),
+         static_cast<T>(1.3166052564989571850e-01L),
+         static_cast<T>(5.8599221412826100000e-04L)
+    };
+    static const T Q1[] = {
+         static_cast<T>(2.1312714303849120380e+04L),
+        static_cast<T>(-2.4994418972832303646e+02L),
+         static_cast<T>(1.0L)
+    };
+    static const T P2[] = {
+        static_cast<T>(-1.6128136304458193998e+06L),
+        static_cast<T>(-3.7333769444840079748e+05L),
+        static_cast<T>(-1.7984434409411765813e+04L),
+        static_cast<T>(-2.9501657892958843865e+02L),
+        static_cast<T>(-1.6414452837299064100e+00L)
+    };
+    static const T Q2[] = {
+        static_cast<T>(-1.6128136304458193998e+06L),
+        static_cast<T>(2.9865713163054025489e+04L),
+        static_cast<T>(-2.5064972445877992730e+02L),
+        static_cast<T>(1.0L)
+    };
+    static const T P3[] = {
+         static_cast<T>(1.1600249425076035558e+02L),
+         static_cast<T>(2.3444738764199315021e+03L),
+         static_cast<T>(1.8321525870183537725e+04L),
+         static_cast<T>(7.1557062783764037541e+04L),
+         static_cast<T>(1.5097646353289914539e+05L),
+         static_cast<T>(1.7398867902565686251e+05L),
+         static_cast<T>(1.0577068948034021957e+05L),
+         static_cast<T>(3.1075408980684392399e+04L),
+         static_cast<T>(3.6832589957340267940e+03L),
+         static_cast<T>(1.1394980557384778174e+02L)
+    };
+    static const T Q3[] = {
+         static_cast<T>(9.2556599177304839811e+01L),
+         static_cast<T>(1.8821890840982713696e+03L),
+         static_cast<T>(1.4847228371802360957e+04L),
+         static_cast<T>(5.8824616785857027752e+04L),
+         static_cast<T>(1.2689839587977598727e+05L),
+         static_cast<T>(1.5144644673520157801e+05L),
+         static_cast<T>(9.7418829762268075784e+04L),
+         static_cast<T>(3.1474655750295278825e+04L),
+         static_cast<T>(4.4329628889746408858e+03L),
+         static_cast<T>(2.0013443064949242491e+02L),
+         static_cast<T>(1.0L)
+    };
+    T value, factor, r, r1, r2;
+
+    BOOST_MATH_STD_USING
+    using namespace boost::math::tools;
+
+    static const char* function = "boost::math::bessel_k0<%1%>(%1%,%1%)";
+
+    if (x < 0)
+    {
+       return policies::raise_domain_error<T>(function,
+            "Got x = %1%, but argument x must be non-negative, complex number result not supported", x, pol);
+    }
+    if (x == 0)
+    {
+       return policies::raise_overflow_error<T>(function, 0, pol);
+    }
+    if (x <= 1)                         // x in (0, 1]
+    {
+        T y = x * x;
+        r1 = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
+        r2 = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
+        factor = log(x);
+        value = r1 - factor * r2;
+    }
+    else                                // x in (1, \infty)
+    {
+        T y = 1 / x;
+        r = evaluate_polynomial(P3, y) / evaluate_polynomial(Q3, y);
+        factor = exp(-x) / sqrt(x);
+        value = factor * r;
+        BOOST_MATH_INSTRUMENT_CODE("y = " << y);
+        BOOST_MATH_INSTRUMENT_CODE("r = " << r);
+        BOOST_MATH_INSTRUMENT_CODE("factor = " << factor);
+        BOOST_MATH_INSTRUMENT_CODE("value = " << value);
+    }
+
+    return value;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_BESSEL_K0_HPP
+