text: //  Copyright John Maddock 2006.
  //  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)
  
  // Test real concept.
  
  // real_concept is an archetype for User defined Real types.
  
  // This file defines the features, constructors, operators, functions...
  // that are essential to use mathematical and statistical functions.
  // The template typename "RealType" is used where this type
  // (as well as the normal built-in types, float, double & long double)
  // can be used.
  // That this is the minimum set is confirmed by use as a type
  // in tests of all functions & distributions, for example:
  //   test_spots(0.F); & test_spots(0.);  for float and double, but also
  //   test_spots(boost::math::concepts::real_concept(0.));
  // NTL quad_float type is an example of a type meeting the requirements,
  // but note minor additions are needed - see ntl.diff and documentation
  // "Using With NTL - a High-Precision Floating-Point Library".
  
  #ifndef BOOST_MATH_REAL_CONCEPT_HPP
  #define BOOST_MATH_REAL_CONCEPT_HPP
  
  #include <boost/config.hpp>
  #include <boost/limits.hpp>
  #include <boost/math/special_functions/round.hpp>
  #include <boost/math/special_functions/trunc.hpp>
  #include <boost/math/special_functions/modf.hpp>
  #include <boost/math/tools/big_constant.hpp>
  #include <boost/math/tools/precision.hpp>
  #include <boost/math/policies/policy.hpp>
  #include <boost/math/special_functions/asinh.hpp>
  #include <boost/math/special_functions/atanh.hpp>
  #if defined(__SGI_STL_PORT)
  #  include <boost/math/tools/real_cast.hpp>
  #endif
  #include <ostream>
  #include <istream>
  #include <boost/config/no_tr1/cmath.hpp>
  #include <math.h> // fmodl
  
  #if defined(__SGI_STL_PORT) || defined(_RWSTD_VER) || defined(__LIBCOMO__)
  #  include <cstdio>
  #endif
  
  namespace boost{ namespace math{
  
  namespace concepts
  {
  
  #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
     typedef double real_concept_base_type;
  #else
     typedef long double real_concept_base_type;
  #endif
  
  class real_concept
  {
  public:
     // Constructors:
     real_concept() : m_value(0){}
     real_concept(char c) : m_value(c){}
  #ifndef BOOST_NO_INTRINSIC_WCHAR_T
     real_concept(wchar_t c) : m_value(c){}
  #endif
     real_concept(unsigned char c) : m_value(c){}
     real_concept(signed char c) : m_value(c){}
     real_concept(unsigned short c) : m_value(c){}
     real_concept(short c) : m_value(c){}
     real_concept(unsigned int c) : m_value(c){}
     real_concept(int c) : m_value(c){}
     real_concept(unsigned long c) : m_value(c){}
     real_concept(long c) : m_value(c){}
  #if defined(__DECCXX) || defined(__SUNPRO_CC)
     real_concept(unsigned long long c) : m_value(static_cast<real_concept_base_type>(c)){}
     real_concept(long long c) : m_value(static_cast<real_concept_base_type>(c)){}
  #elif defined(BOOST_HAS_LONG_LONG)
     real_concept(boost::ulong_long_type c) : m_value(static_cast<real_concept_base_type>(c)){}
     real_concept(boost::long_long_type c) : m_value(static_cast<real_concept_base_type>(c)){}
  #elif defined(BOOST_HAS_MS_INT64)
     real_concept(unsigned __int64 c) : m_value(static_cast<real_concept_base_type>(c)){}
     real_concept(__int64 c) : m_value(static_cast<real_concept_base_type>(c)){}
  #endif
     real_concept(float c) : m_value(c){}
     real_concept(double c) : m_value(c){}
     real_concept(long double c) : m_value(c){}
  #ifdef BOOST_MATH_USE_FLOAT128
     real_concept(BOOST_MATH_FLOAT128_TYPE c) : m_value(c){}
  #endif
  
     // Assignment:
     real_concept& operator=(char c) { m_value = c; return *this; }
     real_concept& operator=(unsigned char c) { m_value = c; return *this; }
     real_concept& operator=(signed char c) { m_value = c; return *this; }
  #ifndef BOOST_NO_INTRINSIC_WCHAR_T
     real_concept& operator=(wchar_t c) { m_value = c; return *this; }
  #endif
     real_concept& operator=(short c) { m_value = c; return *this; }
     real_concept& operator=(unsigned short c) { m_value = c; return *this; }
     real_concept& operator=(int c) { m_value = c; return *this; }
     real_concept& operator=(unsigned int c) { m_value = c; return *this; }
     real_concept& operator=(long c) { m_value = c; return *this; }
     real_concept& operator=(unsigned long c) { m_value = c; return *this; }
  #ifdef BOOST_HAS_LONG_LONG
     real_concept& operator=(boost::long_long_type c) { m_value = static_cast<real_concept_base_type>(c); return *this; }
     real_concept& operator=(boost::ulong_long_type c) { m_value = static_cast<real_concept_base_type>(c); return *this; }
  #endif
     real_concept& operator=(float c) { m_value = c; return *this; }
     real_concept& operator=(double c) { m_value = c; return *this; }
     real_concept& operator=(long double c) { m_value = c; return *this; }
  
     // Access:
     real_concept_base_type value()const{ return m_value; }
  
     // Member arithmetic:
     real_concept& operator+=(const real_concept& other)
     { m_value += other.value(); return *this; }
     real_concept& operator-=(const real_concept& other)
     { m_value -= other.value(); return *this; }
     real_concept& operator*=(const real_concept& other)
     { m_value *= other.value(); return *this; }
     real_concept& operator/=(const real_concept& other)
     { m_value /= other.value(); return *this; }
     real_concept operator-()const
     { return -m_value; }
     real_concept const& operator+()const
     { return *this; }
     real_concept& operator++()
     { ++m_value;  return *this; }
     real_concept& operator--()
     { --m_value;  return *this; }
  
  private:
     real_concept_base_type m_value;
  };
  
  // Non-member arithmetic:
  inline real_concept operator+(const real_concept& a, const real_concept& b)
  {
     real_concept result(a);
     result += b;
     return result;
  }
  inline real_concept operator-(const real_concept& a, const real_concept& b)
  {
     real_concept result(a);
     result -= b;
     return result;
  }
  inline real_concept operator*(const real_concept& a, const real_concept& b)
  {
     real_concept result(a);
     result *= b;
     return result;
  }
  inline real_concept operator/(const real_concept& a, const real_concept& b)
  {
     real_concept result(a);
     result /= b;
     return result;
  }
  
  // Comparison:
  inline bool operator == (const real_concept& a, const real_concept& b)
  { return a.value() == b.value(); }
  inline bool operator != (const real_concept& a, const real_concept& b)
  { return a.value() != b.value();}
  inline bool operator < (const real_concept& a, const real_concept& b)
  { return a.value() < b.value(); }
  inline bool operator <= (const real_concept& a, const real_concept& b)
  { return a.value() <= b.value(); }
  inline bool operator > (const real_concept& a, const real_concept& b)
  { return a.value() > b.value(); }
  inline bool operator >= (const real_concept& a, const real_concept& b)
  { return a.value() >= b.value(); }
  
  // Non-member functions:
  inline real_concept acos(real_concept a)
  { return std::acos(a.value()); }
  inline real_concept cos(real_concept a)
  { return std::cos(a.value()); }
  inline real_concept asin(real_concept a)
  { return std::asin(a.value()); }
  inline real_concept atan(real_concept a)
  { return std::atan(a.value()); }
  inline real_concept atan2(real_concept a, real_concept b)
  { return std::atan2(a.value(), b.value()); }
  inline real_concept ceil(real_concept a)
  { return std::ceil(a.value()); }
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  // I've seen std::fmod(long double) crash on some platforms
  // so use fmodl instead:
  #ifdef _WIN32_WCE
  //
  // Ugly workaround for macro fmodl:
  //
  inline long double call_fmodl(long double a, long double b)
  {  return fmodl(a, b); }
  inline real_concept fmod(real_concept a, real_concept b)
  { return call_fmodl(a.value(), b.value()); }
  #else
  inline real_concept fmod(real_concept a, real_concept b)
  { return fmodl(a.value(), b.value()); }
  #endif
  #endif
  inline real_concept cosh(real_concept a)
  { return std::cosh(a.value()); }
  inline real_concept exp(real_concept a)
  { return std::exp(a.value()); }
  inline real_concept fabs(real_concept a)
  { return std::fabs(a.value()); }
  inline real_concept abs(real_concept a)
  { return std::abs(a.value()); }
  inline real_concept floor(real_concept a)
  { return std::floor(a.value()); }
  inline real_concept modf(real_concept a, real_concept* ipart)
  {
  #ifdef __MINGW32__
     real_concept_base_type ip;
     real_concept_base_type result = boost::math::modf(a.value(), &ip);
     *ipart = ip;
     return result;
  #else
     real_concept_base_type ip;
     real_concept_base_type result = std::modf(a.value(), &ip);
     *ipart = ip;
     return result;
  #endif
  }
  inline real_concept frexp(real_concept a, int* expon)
  { return std::frexp(a.value(), expon); }
  inline real_concept ldexp(real_concept a, int expon)
  { return std::ldexp(a.value(), expon); }
  inline real_concept log(real_concept a)
  { return std::log(a.value()); }
  inline real_concept log10(real_concept a)
  { return std::log10(a.value()); }
  inline real_concept tan(real_concept a)
  { return std::tan(a.value()); }
  inline real_concept pow(real_concept a, real_concept b)
  { return std::pow(a.value(), b.value()); }
  #if !defined(__SUNPRO_CC)
  inline real_concept pow(real_concept a, int b)
  { return std::pow(a.value(), b); }
  #else
  inline real_concept pow(real_concept a, int b)
  { return std::pow(a.value(), static_cast<real_concept_base_type>(b)); }
  #endif
  inline real_concept sin(real_concept a)
  { return std::sin(a.value()); }
  inline real_concept sinh(real_concept a)
  { return std::sinh(a.value()); }
  inline real_concept sqrt(real_concept a)
  { return std::sqrt(a.value()); }
  inline real_concept tanh(real_concept a)
  { return std::tanh(a.value()); }
  
  //
  // C++11 ism's
  // Note that these must not actually call the std:: versions as that precludes using this
  // header to test in C++03 mode, call the Boost versions instead:
  //
  inline boost::math::concepts::real_concept asinh(boost::math::concepts::real_concept a)
  {
     return boost::math::asinh(a.value(), boost::math::policies::make_policy(boost::math::policies::overflow_error<boost::math::policies::ignore_error>()));
  }
  inline boost::math::concepts::real_concept acosh(boost::math::concepts::real_concept a)
  {
     return boost::math::acosh(a.value(), boost::math::policies::make_policy(boost::math::policies::overflow_error<boost::math::policies::ignore_error>()));
  }
  inline boost::math::concepts::real_concept atanh(boost::math::concepts::real_concept a)
  {
     return boost::math::atanh(a.value(), boost::math::policies::make_policy(boost::math::policies::overflow_error<boost::math::policies::ignore_error>()));
  }
  
  //
  // Conversion and truncation routines:
  //
  template <class Policy>
  inline int iround(const concepts::real_concept& v, const Policy& pol)
  { return boost::math::iround(v.value(), pol); }
  inline int iround(const concepts::real_concept& v)
  { return boost::math::iround(v.value(), policies::policy<>()); }
  template <class Policy>
  inline long lround(const concepts::real_concept& v, const Policy& pol)
  { return boost::math::lround(v.value(), pol); }
  inline long lround(const concepts::real_concept& v)
  { return boost::math::lround(v.value(), policies::policy<>()); }
  
  #ifdef BOOST_HAS_LONG_LONG
  template <class Policy>
  inline boost::long_long_type llround(const concepts::real_concept& v, const Policy& pol)
  { return boost::math::llround(v.value(), pol); }
  inline boost::long_long_type llround(const concepts::real_concept& v)
  { return boost::math::llround(v.value(), policies::policy<>()); }
  #endif
  
  template <class Policy>
  inline int itrunc(const concepts::real_concept& v, const Policy& pol)
  { return boost::math::itrunc(v.value(), pol); }
  inline int itrunc(const concepts::real_concept& v)
  { return boost::math::itrunc(v.value(), policies::policy<>()); }
  template <class Policy>
  inline long ltrunc(const concepts::real_concept& v, const Policy& pol)
  { return boost::math::ltrunc(v.value(), pol); }
  inline long ltrunc(const concepts::real_concept& v)
  { return boost::math::ltrunc(v.value(), policies::policy<>()); }
  
  #ifdef BOOST_HAS_LONG_LONG
  template <class Policy>
  inline boost::long_long_type lltrunc(const concepts::real_concept& v, const Policy& pol)
  { return boost::math::lltrunc(v.value(), pol); }
  inline boost::long_long_type lltrunc(const concepts::real_concept& v)
  { return boost::math::lltrunc(v.value(), policies::policy<>()); }
  #endif
  
  // Streaming:
  template <class charT, class traits>
  inline std::basic_ostream<charT, traits>& operator<<(std::basic_ostream<charT, traits>& os, const real_concept& a)
  {
     return os << a.value();
  }
  template <class charT, class traits>
  inline std::basic_istream<charT, traits>& operator>>(std::basic_istream<charT, traits>& is, real_concept& a)
  {
  #if defined(BOOST_MSVC) && defined(__SGI_STL_PORT)
     //
     // STLPort 5.1.4 has a problem reading long doubles from strings,
     // see http://sourceforge.net/tracker/index.php?func=detail&aid=1811043&group_id=146814&atid=766244
     //
     double v;
     is >> v;
     a = v;
     return is;
  #elif defined(__SGI_STL_PORT) || defined(_RWSTD_VER) || defined(__LIBCOMO__) || defined(_LIBCPP_VERSION)
     std::string s;
     real_concept_base_type d;
     is >> s;
     std::sscanf(s.c_str(), "%Lf", &d);
     a = d;
     return is;
  #else
     real_concept_base_type v;
     is >> v;
     a = v;
     return is;
  #endif
  }
  
  } // namespace concepts
  
  namespace tools
  {
  
  template <>
  inline concepts::real_concept make_big_value<concepts::real_concept>(boost::math::tools::largest_float val, const char* , mpl::false_ const&, mpl::false_ const&)
  {
     return val;  // Can't use lexical_cast here, sometimes it fails....
  }
  
  template <>
  inline concepts::real_concept max_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
  {
     return max_value<concepts::real_concept_base_type>();
  }
  
  template <>
  inline concepts::real_concept min_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
  {
     return min_value<concepts::real_concept_base_type>();
  }
  
  template <>
  inline concepts::real_concept log_max_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
  {
     return log_max_value<concepts::real_concept_base_type>();
  }
  
  template <>
  inline concepts::real_concept log_min_value<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
  {
     return log_min_value<concepts::real_concept_base_type>();
  }
  
  template <>
  inline concepts::real_concept epsilon<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
  {
  #ifdef __SUNPRO_CC
     return std::numeric_limits<concepts::real_concept_base_type>::epsilon();
  #else
     return tools::epsilon<concepts::real_concept_base_type>();
  #endif
  }
  
  template <>
  inline BOOST_MATH_CONSTEXPR int digits<concepts::real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept)) BOOST_NOEXCEPT
  {
     // Assume number of significand bits is same as real_concept_base_type,
     // unless std::numeric_limits<T>::is_specialized to provide digits.
     return tools::digits<concepts::real_concept_base_type>();
     // Note that if numeric_limits real concept is NOT specialized to provide digits10
     // (or max_digits10) then the default precision of 6 decimal digits will be used
     // by Boost test (giving misleading error messages like
     // "difference between {9.79796} and {9.79796} exceeds 5.42101e-19%"
     // and by Boost lexical cast and serialization causing loss of accuracy.
  }
  
  } // namespace tools
  /*
  namespace policies {
     namespace detail {
  
        template <class T>
        inline concepts::real_concept raise_rounding_error(
           const char*,
           const char*,
           const T& val,
           const concepts::real_concept&,
           const  ::boost::math::policies::rounding_error< ::boost::math::policies::errno_on_error>&) BOOST_MATH_NOEXCEPT(T)
        {
           errno = ERANGE;
           // This may or may not do the right thing, but the user asked for the error
           // to be silent so here we go anyway:
           return  val > 0 ? boost::math::tools::max_value<concepts::real_concept>() : -boost::math::tools::max_value<concepts::real_concept>();
        }
  
     }
  }*/
  
  #if defined(__SGI_STL_PORT) || defined(BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS)
  //
  // We shouldn't really need these type casts any more, but there are some
  // STLport iostream bugs we work around by using them....
  //
  namespace tools
  {
  // real_cast converts from T to integer and narrower floating-point types.
  
  // Convert from T to integer types.
  
  template <>
  inline unsigned int real_cast<unsigned int, concepts::real_concept>(concepts::real_concept r)
  {
     return static_cast<unsigned int>(r.value());
  }
  
  template <>
  inline int real_cast<int, concepts::real_concept>(concepts::real_concept r)
  {
     return static_cast<int>(r.value());
  }
  
  template <>
  inline long real_cast<long, concepts::real_concept>(concepts::real_concept r)
  {
     return static_cast<long>(r.value());
  }
  
  // Converts from T to narrower floating-point types, float, double & long double.
  
  template <>
  inline float real_cast<float, concepts::real_concept>(concepts::real_concept r)
  {
     return static_cast<float>(r.value());
  }
  template <>
  inline double real_cast<double, concepts::real_concept>(concepts::real_concept r)
  {
     return static_cast<double>(r.value());
  }
  template <>
  inline long double real_cast<long double, concepts::real_concept>(concepts::real_concept r)
  {
     return r.value();
  }
  
  } // STLPort
  
  #endif
  
  #if BOOST_WORKAROUND(BOOST_MSVC, <= 1310)
  //
  // For some strange reason ADL sometimes fails to find the
  // correct overloads, unless we bring these declarations into scope:
  //
  using concepts::itrunc;
  using concepts::iround;
  
  #endif
  
  } // namespace math
  } // namespace boost
  
  #endif // BOOST_MATH_REAL_CONCEPT_HPP
  
  
  