200 lines
8.6 KiB
Plaintext
200 lines
8.6 KiB
Plaintext
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// Copyright (c) 2006 Xiaogang Zhang
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_BESSEL_J1_HPP
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#define BOOST_MATH_BESSEL_J1_HPP
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#ifdef _MSC_VER
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#pragma once
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#endif
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#include <boost/math/constants/constants.hpp>
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#include <boost/math/tools/rational.hpp>
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#include <boost/math/tools/big_constant.hpp>
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#include <boost/assert.hpp>
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// Bessel function of the first kind of order one
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// x <= 8, minimax rational approximations on root-bracketing intervals
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// x > 8, Hankel asymptotic expansion in Hart, Computer Approximations, 1968
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namespace boost { namespace math{ namespace detail{
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template <typename T>
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T bessel_j1(T x);
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template <class T>
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struct bessel_j1_initializer
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{
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struct init
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{
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init()
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{
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do_init();
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}
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static void do_init()
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{
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bessel_j1(T(1));
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}
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void force_instantiate()const{}
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};
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static const init initializer;
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static void force_instantiate()
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{
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initializer.force_instantiate();
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}
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};
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template <class T>
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const typename bessel_j1_initializer<T>::init bessel_j1_initializer<T>::initializer;
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template <typename T>
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T bessel_j1(T x)
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{
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bessel_j1_initializer<T>::force_instantiate();
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static const T P1[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4258509801366645672e+11)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6781041261492395835e+09)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.1548696764841276794e+08)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.8062904098958257677e+05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4615792982775076130e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0650724020080236441e+01)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0767857011487300348e-02))
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};
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static const T Q1[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.1868604460820175290e+12)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.2091902282580133541e+10)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.0228375140097033958e+08)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.9117614494174794095e+05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0742272239517380498e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
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};
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static const T P2[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.7527881995806511112e+16)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.6608531731299018674e+15)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.6658018905416665164e+13)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5580665670910619166e+11)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.8113931269860667829e+09)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5.0793266148011179143e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -7.5023342220781607561e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.6179191852758252278e+00))
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};
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static const T Q2[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7253905888447681194e+18)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7128800897135812012e+16)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.4899346165481429307e+13)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.7622777286244082666e+11)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.4872502899596389593e+08)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.1267125065029138050e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.3886978985861357615e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
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};
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static const T PC[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278571e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9422465050776411957e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.6033732483649391093e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5235293511811373833e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0982405543459346727e+05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.6116166443246101165e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
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};
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static const T QC[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -4.4357578167941278568e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -9.9341243899345856590e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -6.5853394797230870728e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.5118095066341608816e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.0726385991103820119e+05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -1.4550094401904961825e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
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};
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static const T PS[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.3220913409857223519e+04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.5145160675335701966e+04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6.6178836581270835179e+04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8494262873223866797e+04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7063754290207680021e+03)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.5265133846636032186e+01)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0))
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};
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static const T QS[] = {
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0871281941028743574e+05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.8194580422439972989e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.4194606696037208929e+06)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.0029443582266975117e+05)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.7890229745772202641e+04)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 8.6383677696049909675e+02)),
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static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.0))
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};
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static const T x1 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3.8317059702075123156e+00)),
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x2 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 7.0155866698156187535e+00)),
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x11 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.810e+02)),
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x12 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.2527979248768438556e-04)),
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x21 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.7960e+03)),
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x22 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -3.8330184381246462950e-05));
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T value, factor, r, rc, rs, w;
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BOOST_MATH_STD_USING
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using namespace boost::math::tools;
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using namespace boost::math::constants;
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w = abs(x);
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if (x == 0)
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{
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return static_cast<T>(0);
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}
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if (w <= 4) // w in (0, 4]
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{
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T y = x * x;
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BOOST_ASSERT(sizeof(P1) == sizeof(Q1));
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r = evaluate_rational(P1, Q1, y);
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factor = w * (w + x1) * ((w - x11/256) - x12);
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value = factor * r;
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}
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else if (w <= 8) // w in (4, 8]
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{
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T y = x * x;
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BOOST_ASSERT(sizeof(P2) == sizeof(Q2));
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r = evaluate_rational(P2, Q2, y);
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factor = w * (w + x2) * ((w - x21/256) - x22);
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value = factor * r;
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}
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else // w in (8, \infty)
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{
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T y = 8 / w;
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T y2 = y * y;
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BOOST_ASSERT(sizeof(PC) == sizeof(QC));
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BOOST_ASSERT(sizeof(PS) == sizeof(QS));
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rc = evaluate_rational(PC, QC, y2);
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rs = evaluate_rational(PS, QS, y2);
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factor = 1 / (sqrt(w) * constants::root_pi<T>());
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//
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// What follows is really just:
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//
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// T z = w - 0.75f * pi<T>();
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// value = factor * (rc * cos(z) - y * rs * sin(z));
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//
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// but using the sin/cos addition rules plus constants
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// for the values of sin/cos of 3PI/4 which then cancel
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// out with corresponding terms in "factor".
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//
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T sx = sin(x);
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T cx = cos(x);
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value = factor * (rc * (sx - cx) + y * rs * (sx + cx));
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}
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if (x < 0)
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{
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value *= -1; // odd function
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}
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return value;
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}
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}}} // namespaces
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#endif // BOOST_MATH_BESSEL_J1_HPP
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