text: //  (C) Copyright John Maddock 2007.
  //  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)
  
  #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
  #include <boost/math/concepts/real_concept.hpp>
  #define BOOST_TEST_MAIN
  #include <boost/test/unit_test.hpp>
  #include <boost/test/tools/floating_point_comparison.hpp>
  #include <boost/math/special_functions/math_fwd.hpp>
  #include <boost/math/constants/constants.hpp>
  #include <boost/type_traits/is_floating_point.hpp>
  #include <boost/array.hpp>
  #include "functor.hpp"
  
  #include "handle_test_result.hpp"
  #include "table_type.hpp"
  
  #ifndef SC_
  #  define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
  #endif
  
  template <class Real, class T>
  void do_test_cyl_bessel_j(const T& data, const char* type_name, const char* test_name)
  {
  #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_J_FUNCTION_TO_TEST))
     typedef Real                   value_type;
  
     typedef value_type (*pg)(value_type, value_type);
  #ifdef BESSEL_J_FUNCTION_TO_TEST
     pg funcp = BESSEL_J_FUNCTION_TO_TEST;
  #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
     pg funcp = boost::math::cyl_bessel_j<value_type, value_type>;
  #else
     pg funcp = boost::math::cyl_bessel_j;
  #endif
  
     boost::math::tools::test_result<value_type> result;
  
     std::cout << "Testing " << test_name << " with type " << type_name
        << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  
     //
     // test cyl_bessel_j against data:
     //
     result = boost::math::tools::test_hetero<Real>(
        data, 
        bind_func<Real>(funcp, 0, 1), 
        extract_result<Real>(2));
     handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_j", test_name);
     std::cout << std::endl;
  
  #endif
  }
  
  template <class T>
  T cyl_bessel_j_int_wrapper(T v, T x)
  {
  #ifdef BESSEL_JN_FUNCTION_TO_TEST
     return static_cast<T>(BESSEL_JN_FUNCTION_TO_TEST(boost::math::itrunc(v), x));
  #else
     return static_cast<T>(boost::math::cyl_bessel_j(boost::math::itrunc(v), x));
  #endif
  }
  
  
  template <class Real, class T>
  void do_test_cyl_bessel_j_int(const T& data, const char* type_name, const char* test_name)
  {
  #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_JN_FUNCTION_TO_TEST))
     typedef Real                   value_type;
  
     typedef value_type (*pg)(value_type, value_type);
  #if defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
     pg funcp = cyl_bessel_j_int_wrapper<value_type>;
  #else
     pg funcp = cyl_bessel_j_int_wrapper;
  #endif
  
     boost::math::tools::test_result<value_type> result;
  
     std::cout << "Testing " << test_name << " with type " << type_name
        << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  
     //
     // test cyl_bessel_j against data:
     //
     result = boost::math::tools::test_hetero<Real>(
        data, 
        bind_func<Real>(funcp, 0, 1), 
        extract_result<Real>(2));
     handle_test_result(result, data[result.worst()], result.worst(), type_name, "cyl_bessel_j (integer orders)", test_name);
     std::cout << std::endl;
  #endif
  }
  
  template <class Real, class T>
  void do_test_sph_bessel_j(const T& data, const char* type_name, const char* test_name)
  {
  #if !(defined(ERROR_REPORTING_MODE) && !defined(BESSEL_JS_FUNCTION_TO_TEST))
     typedef Real                   value_type;
  
     typedef value_type (*pg)(unsigned, value_type);
  #ifdef BESSEL_JS_FUNCTION_TO_TEST
     pg funcp = BESSEL_JS_FUNCTION_TO_TEST;
  #elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
     pg funcp = boost::math::sph_bessel<value_type>;
  #else
     pg funcp = boost::math::sph_bessel;
  #endif
  
     boost::math::tools::test_result<value_type> result;
  
     std::cout << "Testing " << test_name << " with type " << type_name
        << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
  
     //
     // test sph_bessel against data:
     //
     result = boost::math::tools::test_hetero<Real>(
        data, 
        bind_func_int1<Real>(funcp, 0, 1), 
        extract_result<Real>(2));
     handle_test_result(result, data[result.worst()], result.worst(), type_name, "sph_bessel", test_name);
     std::cout << std::endl;
  #endif
  }
  
  template <class T>
  void test_bessel(T, const char* name)
  {
     //
     // The actual test data is rather verbose, so it's in a separate file
     //
     // The contents are as follows, each row of data contains
     // three items, input value a, input value b and erf(a, b):
     // 
      // function values calculated on http://functions.wolfram.com/
      static const std::array<std::array<typename table_type<T>::type, 3>, 8> j0_data = {{
         { { SC_(0.0), SC_(0.0), SC_(1.0) } },
         { { SC_(0.0), SC_(1.0), SC_(0.7651976865579665514497175261026632209093) } },
         { { SC_(0.0), SC_(-2.0), SC_(0.2238907791412356680518274546499486258252) } },
         { { SC_(0.0), SC_(4.0), SC_(-0.3971498098638473722865907684516980419756) } },
         { { SC_(0.0), SC_(-8.0), SC_(0.1716508071375539060908694078519720010684) } },
          {{ SC_(0.0), SC_(1e-05), SC_(0.999999999975000000000156249999999565972) }},
          {{ SC_(0.0), SC_(1e-10), SC_(0.999999999999999999997500000000000000000) }},
          {{ SC_(0.0), SC_(-1e+01), SC_(-0.2459357644513483351977608624853287538296) }},
      }};
      static const std::array<std::array<typename table_type<T>::type, 3>, 6> j0_tricky = {{
          // Big numbers make the accuracy of std::sin the limiting factor:
         { { SC_(0.0), SC_(1e+03), SC_(0.02478668615242017456133073111569370878617) } },
         { { SC_(0.0), SC_(1e+05), SC_(-0.001719201116235972192570601477073201747532) } },
          // test at the roots:
         { { SC_(0.0), SC_(2.4048252105712890625) /*T(2521642.0) / (1024 * 1024)*/, SC_(1.80208819970046790002973759410972422387259992955354630042138e-7) } },
         { { SC_(0.0), SC_(5.52007770538330078125) /*T(5788221.0) / (1024 * 1024)*/, SC_(-1.37774249380686777043369399806210229535671843632174587432454e-7) } },
         { { SC_(0.0), SC_(8.65372753143310546875) /*T(9074091.0) / (1024 * 1024)*/, SC_(1.03553057441100845081018471279571355857520645127532785991335e-7) } },
         { { SC_(0.0), SC_(11.791534423828125) /*T(12364320.0) / (1024 * 1024)*/, SC_(-3.53017140778223781420794006033810387155048392363051866610931e-9) } }
      }};    
  
      static const std::array<std::array<typename table_type<T>::type, 3>, 8> j1_data = {{
         { { SC_(1.0), SC_(0.0), SC_(0.0) } },
         { { SC_(1.0), SC_(1.0), SC_(0.4400505857449335159596822037189149131274) } },
         { { SC_(1.0), SC_(-2.0), SC_(-0.5767248077568733872024482422691370869203) } },
         { { SC_(1.0), SC_(4.0), SC_(-6.604332802354913614318542080327502872742e-02) } },
         { { SC_(1.0), SC_(-8.0), SC_(-0.2346363468539146243812766515904546115488) } },
         { { SC_(1.0), SC_(1e-05), SC_(4.999999999937500000000260416666666124132e-06) } },
         { { SC_(1.0), SC_(1e-10), SC_(4.999999999999999999993750000000000000000e-11) } },
         { { SC_(1.0), SC_(-1e+01), SC_(-4.347274616886143666974876802585928830627e-02) } },
      }};
      static const std::array<std::array<typename table_type<T>::type, 3>, 5> j1_tricky = {{
          // Big numbers make the accuracy of std::sin the limiting factor:
         { { SC_(1.0), SC_(1e+03), SC_(4.728311907089523917576071901216916285418e-03) } },
         { { SC_(1.0), SC_(1e+05), SC_(1.846757562882567716362123967114215743694e-03) } },
          // test zeros:
         { { SC_(1.0), SC_(3.8317050933837890625) /*T(4017834) / (1024 * 1024)*/, SC_(3.53149033321258645807835062770856949751958513973522222203044e-7) } },
         { { SC_(1.0), SC_(7.01558589935302734375) /*T(7356375) / (1024 * 1024)*/, SC_(-2.31227973111067286051984021150135526024117175836722748404342e-7) } },
         { { SC_(1.0), SC_(10.1734676361083984375) /*T(10667654) / (1024 * 1024)*/, SC_(1.24591331097191900488116495350277530373473085499043086981229e-7) } },
      }};
  
      static const std::array<std::array<typename table_type<T>::type, 3>, 17> jn_data = {{
          // This first one is a modified test case from https://svn.boost.org/trac/boost/ticket/2733
         { { SC_(-1.0), SC_(1.25), SC_(-0.510623260319880467069474837274910375352924050139633057168856) } },
         { { SC_(2.0), SC_(0.0), SC_(0.0) } },
         { { SC_(-2.0), SC_(0.0), SC_(0.0) } },
         { { SC_(2.0), SC_(1e-02), SC_(1.249989583365885362413250958437642113452e-05) } },
         { { SC_(5.0), SC_(10.0), SC_(-0.2340615281867936404436949416457777864635) } },
         { { SC_(5.0), SC_(-10.0), SC_(0.2340615281867936404436949416457777864635) } },
         { { SC_(-5.0), SC_(1e+06), SC_(7.259643842453285052375779970433848914846e-04) } },
         { { SC_(5.0), SC_(1e+06), SC_(-0.000725964384245328505237577997043384891484649290328285235308619) } },
         { { SC_(-5.0), SC_(-1.0), SC_(2.497577302112344313750655409880451981584e-04) } },
         { { SC_(10.0), SC_(10.0), SC_(0.2074861066333588576972787235187534280327) } },
         { { SC_(10.0), SC_(-10.0), SC_(0.2074861066333588576972787235187534280327) } },
         { { SC_(10.0), SC_(-5.0), SC_(1.467802647310474131107532232606627020895e-03) } },
         { { SC_(-10.0), SC_(1e+06), SC_(-3.310793117604488741264958559035744460210e-04) } },
         { { SC_(10.0), SC_(1e+06), SC_(-0.000331079311760448874126495855903574446020957243277028930713243) } },
          {{ SC_(1e+02), SC_(8e+01), SC_(4.606553064823477354141298259169874909670e-06) }},
          {{ SC_(1e+03), SC_(1e+05), SC_(1.283178112502480365195139312635384057363e-03) }},
          { { SC_(10.0), SC_(1e-100), SC_(2.69114445546737213403880070546737213403880070546737213403880e-1010) } },
      }};
      do_test_cyl_bessel_j<T>(j0_data, name, "Bessel J0: Mathworld Data");
      do_test_cyl_bessel_j<T>(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases)");
      do_test_cyl_bessel_j<T>(j1_data, name, "Bessel J1: Mathworld Data");
      do_test_cyl_bessel_j<T>(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases)");
      do_test_cyl_bessel_j<T>(jn_data, name, "Bessel JN: Mathworld Data");
  
      do_test_cyl_bessel_j_int<T>(j0_data, name, "Bessel J0: Mathworld Data (Integer Version)");
      do_test_cyl_bessel_j_int<T>(j0_tricky, name, "Bessel J0: Mathworld Data (Tricky cases) (Integer Version)");
      do_test_cyl_bessel_j_int<T>(j1_data, name, "Bessel J1: Mathworld Data (Integer Version)");
      do_test_cyl_bessel_j_int<T>(j1_tricky, name, "Bessel J1: Mathworld Data (tricky cases) (Integer Version)");
      do_test_cyl_bessel_j_int<T>(jn_data, name, "Bessel JN: Mathworld Data (Integer Version)");
  
      static const std::array<std::array<typename table_type<T>::type, 3>, 20> jv_data = {{
          //SC_(-2.4), {{ SC_(0.0), std::numeric_limits<T>::infinity() }},
         { { SC_(22.5), SC_(0.0), SC_(0.0) } },
         { { SC_(2.3994140625) /*2457.0 / 1024*/, SC_(0.0009765625) /* 1 / 1024*/, SC_(3.80739920118603335646474073457326714709615200130620574875292e-9) } },
          {{ SC_(5.5), SC_(3.1416015625) /* 3217/1024*/, SC_(0.0281933076257506091621579544064767140470089107926550720453038) }},
          {{ SC_(-5.5), SC_(3.1416015625) /* 3217/1024*/, SC_(-2.55820064470647911823175836997490971806135336759164272675969) }},
          {{ SC_(-5.5), SC_(1e+04), SC_(2.449843111985605522111159013846599118397e-03) }},
          {{ SC_(5.5), SC_(1e+04), SC_(0.00759343502722670361395585198154817047185480147294665270646578) }},
          {{ SC_(5.5), SC_(1e+06), SC_(-0.000747424248595630177396350688505919533097973148718960064663632) }},
          {{ SC_(5.125), SC_(1e+06), SC_(-0.000776600124835704280633640911329691642748783663198207360238214) }},
          {{ SC_(5.875), SC_(1e+06), SC_(-0.000466322721115193071631008581529503095819705088484386434589780) }},
          { { SC_(0.5), SC_(101.0), SC_(0.0358874487875643822020496677692429287863419555699447066226409) } },
          {{ SC_(-5.5), SC_(1e+04), SC_(0.00244984311198560552211115901384659911839737686676766460822577) }},
          {{ SC_(-5.5), SC_(1e+06), SC_(0.000279243200433579511095229508894156656558211060453622750659554) }},
          { { SC_(-0.5), SC_(101.0), SC_(0.0708184798097594268482290389188138201440114881159344944791454) } },
          {{ SC_(-10.0002994537353515625) /* -10486074 / (1024*1024)*/, SC_(0.0009765625) /* 1/1024*/, SC_(1.41474013160494695750009004222225969090304185981836460288562e35) }},
          { { SC_(-10.0002994537353515625) /* -10486074 / (1024*1024)*/, SC_(15.0), SC_(-0.0902239288885423309568944543848111461724911781719692852541489) } },
          {{ SC_(-10.0002994537353515625) /* -10486074 / (1024*1024)*/, SC_(100.0), SC_(-0.05476136603168065513386371539426045507795139476742228638) }},
          {{ SC_(-10.0002994537353515625) /* -10486074 / (1024*1024)*/, SC_(20000.0), SC_(-0.00556869085445857782456414284057389040183758546505700058) }},
          // Bug report https://svn.boost.org/trac/boost/ticket/4812:
          {{ SC_(1.5), SC_(7.845703125) /* 8034/1024*/, SC_(0.0339477646369710610146236955872928005087352629422508823945264) }},
          {{ SC_(8.5), SC_(12.566370614359172953850573533118011536788677597500423283899778369231265625144835994512139301368468271928592346053) /*Pi * 4*/, SC_(0.0436807946352780974532519564114026730332781693877984686758680) }},
          {{ SC_(-8.5), SC_(12.566370614359172953850573533118011536788677597500423283899778369231265625144835994512139301368468271928592346053) /*Pi * 4*/, SC_(-0.257086543428224355151772807588810984369026142375675714560864) }},
      }};
      do_test_cyl_bessel_j<T>(jv_data, name, "Bessel J: Mathworld Data");
      static const std::array<std::array<typename table_type<T>::type, 3>, 4> jv_large_data = {{
          // Bug report https://svn.boost.org/trac/boost/ticket/5560:
          {{ SC_(-0.5), SC_(1.2458993688871959419388378518880931736878259938089494331010226962863582408064841833232475731084062642684629e-206) /*static_cast<T>(std::ldexp(0.5, -683))*/, SC_(7.14823099969225685526188875418476476336424046896822867989728e102) }},
          { { SC_(256.0), SC_(512.0), SC_(0.00671672065717513246956991122723250578101154313313749938944675) } },
          { { SC_(-256.0), SC_(8.0), SC_(1.46866142030022704638298523775638527553596432641223316232692e-353) } },
          { { SC_(-2.5), SC_(4.0), SC_(-0.0145679476685218007666785535204236327832335803441449596297004) } },
      }};
      if(static_cast<T>(jv_large_data[0][1]) != 0)
        do_test_cyl_bessel_j<T>(jv_large_data, name, "Bessel J: Mathworld Data (large values)");
  
  #include "bessel_j_int_data.ipp"
      do_test_cyl_bessel_j<T>(bessel_j_int_data, name, "Bessel JN: Random Data");
  
  #include "bessel_j_data.ipp"
      do_test_cyl_bessel_j<T>(bessel_j_data, name, "Bessel J: Random Data");
  
  #include "bessel_j_large_data.ipp"
      do_test_cyl_bessel_j<T>(bessel_j_large_data, name, "Bessel J: Random Data (Tricky large values)");
  
  #include "sph_bessel_data.ipp"
      do_test_sph_bessel_j<T>(sph_bessel_data, name, "Bessel j: Random Data");
  
      //
      // Some special cases:
      //
      BOOST_CHECK_EQUAL(boost::math::sph_bessel(0, T(0)), T(1));
      BOOST_CHECK_EQUAL(boost::math::sph_bessel(1, T(0)), T(0));
      BOOST_CHECK_EQUAL(boost::math::sph_bessel(100000, T(0)), T(0));
  
      //
      // Special cases that are errors:
      //
      BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j(T(-2.5), T(0)), std::domain_error);
      BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j(T(-2.5), T(-2)), std::domain_error);
      BOOST_MATH_CHECK_THROW(boost::math::cyl_bessel_j(T(2.5), T(-2)), std::domain_error);
  }
  
  