Updated boost to v1.55.0

[rsem.git] / boost / math / special_functions / detail / bessel_i0.hpp

diff --git a/boost/math/special_functions/detail/bessel_i0.hpp b/boost/math/special_functions/detail/bessel_i0.hpp
new file mode 100644 (file)
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+++ b/boost/math/special_functions/detail/bessel_i0.hpp
@@ -0,0 +1,132 @@
+//  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_I0_HPP
+#define BOOST_MATH_BESSEL_I0_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/tools/rational.hpp>
+#include <boost/math/tools/big_constant.hpp>
+#include <boost/assert.hpp>
+
+// Modified Bessel function of the first kind of order zero
+// minimax rational approximations on intervals, see
+// Blair and Edwards, Chalk River Report AECL-4928, 1974
+
+namespace boost { namespace math { namespace detail{
+
+template <typename T>
+T bessel_i0(T x);
+
+template <class T>
+struct bessel_i0_initializer
+{
+   struct init
+   {
+      init()
+      {
+         do_init();
+      }
+      static void do_init()
+      {
+         bessel_i0(T(1));
+      }
+      void force_instantiate()const{}
+   };
+   static const init initializer;
+   static void force_instantiate()
+   {
+      initializer.force_instantiate();
+   }
+};
+
+template <class T>
+const typename bessel_i0_initializer<T>::init bessel_i0_initializer<T>::initializer;
+
+template <typename T>
+T bessel_i0(T x)
+{
+    bessel_i0_initializer<T>::force_instantiate();
+
+    static const T P1[] = {
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2335582639474375249e+15)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.5050369673018427753e+14)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2940087627407749166e+13)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.4925101247114157499e+11)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1912746104985237192e+10)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0313066708737980747e+08)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.9545626019847898221e+05)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.4125195876041896775e+03)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.0935347449210549190e+00)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5453977791786851041e-02)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.5172644670688975051e-05)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.0517226450451067446e-08)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.6843448573468483278e-11)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5982226675653184646e-14)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.2487866627945699800e-18)),
+    };
+    static const T Q1[] = {
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2335582639474375245e+15)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.8858692566751002988e+12)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.2207067397808979846e+10)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0377081058062166144e+07)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.8527560179962773045e+03)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
+    };
+    static const T P2[] = {
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2210262233306573296e-04)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3067392038106924055e-02)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4700805721174453923e-01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.5674518371240761397e+00)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.3517945679239481621e+01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.1611322818701131207e+01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.6090021968656180000e+00)),
+    };
+    static const T Q2[] = {
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.5194330231005480228e-04)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.2547697594819615062e-02)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1151759188741312645e+00)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3982595353892851542e+01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.0228002066743340583e+01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5539563258012929600e+01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.1446690275135491500e+01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
+    };
+    T value, factor, r;
+
+    BOOST_MATH_STD_USING
+    using namespace boost::math::tools;
+
+    if (x < 0)
+    {
+        x = -x;                         // even function
+    }
+    if (x == 0)
+    {
+        return static_cast<T>(1);
+    }
+    if (x <= 15)                        // x in (0, 15]
+    {
+        T y = x * x;
+        value = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
+    }
+    else                                // x in (15, \infty)
+    {
+        T y = 1 / x - T(1) / 15;
+        r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
+        factor = exp(x) / sqrt(x);
+        value = factor * r;
+    }
+
+    return value;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_BESSEL_I0_HPP
+