Imported Upstream version 1.49.0upstream/1.49.0

1 files changed, 105 insertions, 0 deletions

diff --git a/boost/math/special_functions/detail/bessel_i1.hpp b/boost/math/special_functions/detail/bessel_i1.hpp
new file mode 100644
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+++ b/boost/math/special_functions/detail/bessel_i1.hpp
@@ -0,0 +1,105 @@
+//  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_I1_HPP
+#define BOOST_MATH_BESSEL_I1_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 one
+// 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_i1(T x)
+{
+    static const T P1[] = {
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4577180278143463643e+15)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7732037840791591320e+14)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.9876779648010090070e+12)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3357437682275493024e+11)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4828267606612366099e+09)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0588550724769347106e+07)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1894091982308017540e+04)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8225946631657315931e+02)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.7207090827310162436e-01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.1746443287817501309e-04)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.3466829827635152875e-06)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4831904935994647675e-09)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1928788903603238754e-12)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5245515583151902910e-16)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9705291802535139930e-19)),
+    };
+    static const T Q1[] = {
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.9154360556286927285e+15)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.7887501377547640438e+12)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4386907088588283434e+10)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1594225856856884006e+07)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -5.1326864679904189920e+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, 1.4582087408985668208e-05)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.9359825138577646443e-04)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.9204895411257790122e-02)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.4198728018058047439e-01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3960118277609544334e+00)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.9746376087200685843e+00)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5591872901933459000e-01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.0437159056137599999e-02)),
+    };
+    static const T Q2[] = {
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7510433111922824643e-05)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.2835624489492512649e-03)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.4212010813186530069e-02)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -8.5017476463217924408e-01)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.2593714889036996297e+00)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8806586721556593450e+00)),
+        static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
+    };
+    T value, factor, r, w;
+
+    BOOST_MATH_STD_USING
+    using namespace boost::math::tools;
+
+    w = abs(x);
+    if (x == 0)
+    {
+        return static_cast<T>(0);
+    }
+    if (w <= 15)                        // w in (0, 15]
+    {
+        T y = x * x;
+        r = evaluate_polynomial(P1, y) / evaluate_polynomial(Q1, y);
+        factor = w;
+        value = factor * r;
+    }
+    else                                // w in (15, \infty)
+    {
+        T y = 1 / w - T(1) / 15;
+        r = evaluate_polynomial(P2, y) / evaluate_polynomial(Q2, y);
+        factor = exp(w) / sqrt(w);
+        value = factor * r;
+    }
+
+    if (x < 0)
+    {
+        value *= -value;                 // odd function
+    }
+    return value;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_BESSEL_I1_HPP
+