--- /dev/null
+// 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_J1_HPP
+#define BOOST_MATH_BESSEL_J1_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/constants/constants.hpp>
+#include <boost/math/tools/rational.hpp>
+#include <boost/math/tools/big_constant.hpp>
+#include <boost/assert.hpp>
+
+// Bessel function of the first kind of order one
+// x <= 8, minimax rational approximations on root-bracketing intervals
+// x > 8, Hankel asymptotic expansion in Hart, Computer Approximations, 1968
+
+namespace boost { namespace math{ namespace detail{
+
+template <typename T>
+T bessel_j1(T x);
+
+template <class T>
+struct bessel_j1_initializer
+{
+ struct init
+ {
+ init()
+ {
+ do_init();
+ }
+ static void do_init()
+ {
+ bessel_j1(T(1));
+ }
+ void force_instantiate()const{}
+ };
+ static const init initializer;
+ static void force_instantiate()
+ {
+ initializer.force_instantiate();
+ }
+};
+
+template <class T>
+const typename bessel_j1_initializer<T>::init bessel_j1_initializer<T>::initializer;
+
+template <typename T>
+T bessel_j1(T x)
+{
+ bessel_j1_initializer<T>::force_instantiate();
+
+ static const T P1[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4258509801366645672e+11)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6781041261492395835e+09)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1548696764841276794e+08)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.8062904098958257677e+05)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4615792982775076130e+03)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0650724020080236441e+01)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0767857011487300348e-02))
+ };
+ static const T Q1[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1868604460820175290e+12)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.2091902282580133541e+10)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0228375140097033958e+08)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9117614494174794095e+05)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0742272239517380498e+03)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
+ };
+ static const T P2[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7527881995806511112e+16)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.6608531731299018674e+15)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6658018905416665164e+13)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5580665670910619166e+11)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8113931269860667829e+09)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.0793266148011179143e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.5023342220781607561e+03)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6179191852758252278e+00))
+ };
+ static const T Q2[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7253905888447681194e+18)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7128800897135812012e+16)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.4899346165481429307e+13)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7622777286244082666e+11)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4872502899596389593e+08)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1267125065029138050e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3886978985861357615e+03)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
+ };
+ static const T PC[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278571e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9422465050776411957e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.6033732483649391093e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5235293511811373833e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0982405543459346727e+05)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6116166443246101165e+03)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
+ };
+ static const T QC[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278568e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9341243899345856590e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5853394797230870728e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5118095066341608816e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0726385991103820119e+05)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4550094401904961825e+03)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
+ };
+ static const T PS[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3220913409857223519e+04)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5145160675335701966e+04)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6178836581270835179e+04)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8494262873223866797e+04)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7063754290207680021e+03)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5265133846636032186e+01)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
+ };
+ static const T QS[] = {
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0871281941028743574e+05)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8194580422439972989e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4194606696037208929e+06)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.0029443582266975117e+05)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7890229745772202641e+04)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.6383677696049909675e+02)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
+ };
+ static const T x1 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.8317059702075123156e+00)),
+ x2 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0155866698156187535e+00)),
+ x11 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.810e+02)),
+ x12 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2527979248768438556e-04)),
+ x21 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7960e+03)),
+ x22 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8330184381246462950e-05));
+
+ T value, factor, r, rc, rs, w;
+
+ BOOST_MATH_STD_USING
+ using namespace boost::math::tools;
+ using namespace boost::math::constants;
+
+ w = abs(x);
+ if (x == 0)
+ {
+ return static_cast<T>(0);
+ }
+ if (w <= 4) // w in (0, 4]
+ {
+ T y = x * x;
+ BOOST_ASSERT(sizeof(P1) == sizeof(Q1));
+ r = evaluate_rational(P1, Q1, y);
+ factor = w * (w + x1) * ((w - x11/256) - x12);
+ value = factor * r;
+ }
+ else if (w <= 8) // w in (4, 8]
+ {
+ T y = x * x;
+ BOOST_ASSERT(sizeof(P2) == sizeof(Q2));
+ r = evaluate_rational(P2, Q2, y);
+ factor = w * (w + x2) * ((w - x21/256) - x22);
+ value = factor * r;
+ }
+ else // w in (8, \infty)
+ {
+ T y = 8 / w;
+ T y2 = y * y;
+ BOOST_ASSERT(sizeof(PC) == sizeof(QC));
+ BOOST_ASSERT(sizeof(PS) == sizeof(QS));
+ rc = evaluate_rational(PC, QC, y2);
+ rs = evaluate_rational(PS, QS, y2);
+ factor = 1 / (sqrt(w) * constants::root_pi<T>());
+ //
+ // What follows is really just:
+ //
+ // T z = w - 0.75f * pi<T>();
+ // value = factor * (rc * cos(z) - y * rs * sin(z));
+ //
+ // but using the sin/cos addition rules plus constants
+ // for the values of sin/cos of 3PI/4 which then cancel
+ // out with corresponding terms in "factor".
+ //
+ T sx = sin(x);
+ T cx = cos(x);
+ value = factor * (rc * (sx - cx) + y * rs * (sx + cx));
+ }
+
+ if (x < 0)
+ {
+ value *= -1; // odd function
+ }
+ return value;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_BESSEL_J1_HPP
+
projects / rsem.git / blobdiff