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)
  
  // std_real_concept is an archetype for built-in Real types.
  
  // The main purpose in providing this type is to verify
  // that std lib functions are found via a using declaration
  // bringing those functions into the current scope, and not
  // just because they happen to be in global scope.
  //
  // If ::pow is found rather than std::pow say, then the code
  // will silently compile, but truncation of long doubles to
  // double will cause a significant loss of precision.
  // A template instantiated with std_real_concept will *only*
  // compile if it std::whatever is in scope.
  
  #include <boost/config.hpp>
  #include <boost/limits.hpp>
  #include <boost/math/tools/real_cast.hpp>
  #include <boost/math/tools/precision.hpp>
  #include <boost/math/policies/policy.hpp>
  
  #include <ostream>
  #include <istream>
  #include <cmath>
  #include <math.h> // fmodl
  
  #ifndef BOOST_MATH_STD_REAL_CONCEPT_HPP
  #define BOOST_MATH_STD_REAL_CONCEPT_HPP
  
  namespace boost{ namespace math{
  
  namespace concepts
  {
  
  class std_real_concept
  {
  public:
     // Constructors:
     std_real_concept() : m_value(0){}
     std_real_concept(char c) : m_value(c){}
  #ifndef BOOST_NO_INTRINSIC_WCHAR_T
     std_real_concept(wchar_t c) : m_value(c){}
  #endif
     std_real_concept(unsigned char c) : m_value(c){}
     std_real_concept(signed char c) : m_value(c){}
     std_real_concept(unsigned short c) : m_value(c){}
     std_real_concept(short c) : m_value(c){}
     std_real_concept(unsigned int c) : m_value(c){}
     std_real_concept(int c) : m_value(c){}
     std_real_concept(unsigned long c) : m_value(c){}
     std_real_concept(long c) : m_value(c){}
  #if defined(BOOST_HAS_LONG_LONG) || defined(__DECCXX) || defined(__SUNPRO_CC)
     std_real_concept(unsigned long long c) : m_value(static_cast<long double>(c)){}
     std_real_concept(long long c) : m_value(static_cast<long double>(c)){}
  #endif
     std_real_concept(float c) : m_value(c){}
     std_real_concept(double c) : m_value(c){}
     std_real_concept(long double c) : m_value(c){}
  
     // Assignment:
     std_real_concept& operator=(char c) { m_value = c; return *this; }
     std_real_concept& operator=(unsigned char c) { m_value = c; return *this; }
     std_real_concept& operator=(signed char c) { m_value = c; return *this; }
  #ifndef BOOST_NO_INTRINSIC_WCHAR_T
     std_real_concept& operator=(wchar_t c) { m_value = c; return *this; }
  #endif
     std_real_concept& operator=(short c) { m_value = c; return *this; }
     std_real_concept& operator=(unsigned short c) { m_value = c; return *this; }
     std_real_concept& operator=(int c) { m_value = c; return *this; }
     std_real_concept& operator=(unsigned int c) { m_value = c; return *this; }
     std_real_concept& operator=(long c) { m_value = c; return *this; }
     std_real_concept& operator=(unsigned long c) { m_value = c; return *this; }
  #if defined(BOOST_HAS_LONG_LONG) || defined(__DECCXX) || defined(__SUNPRO_CC)
     std_real_concept& operator=(long long c) { m_value = static_cast<long double>(c); return *this; }
     std_real_concept& operator=(unsigned long long c) { m_value = static_cast<long double>(c); return *this; }
  #endif
     std_real_concept& operator=(float c) { m_value = c; return *this; }
     std_real_concept& operator=(double c) { m_value = c; return *this; }
     std_real_concept& operator=(long double c) { m_value = c; return *this; }
  
     // Access:
     long double value()const{ return m_value; }
  
     // Member arithmetic:
     std_real_concept& operator+=(const std_real_concept& other)
     { m_value += other.value(); return *this; }
     std_real_concept& operator-=(const std_real_concept& other)
     { m_value -= other.value(); return *this; }
     std_real_concept& operator*=(const std_real_concept& other)
     { m_value *= other.value(); return *this; }
     std_real_concept& operator/=(const std_real_concept& other)
     { m_value /= other.value(); return *this; }
     std_real_concept operator-()const
     { return -m_value; }
     std_real_concept const& operator+()const
     { return *this; }
  
  private:
     long double m_value;
  };
  
  // Non-member arithmetic:
  inline std_real_concept operator+(const std_real_concept& a, const std_real_concept& b)
  {
     std_real_concept result(a);
     result += b;
     return result;
  }
  inline std_real_concept operator-(const std_real_concept& a, const std_real_concept& b)
  {
     std_real_concept result(a);
     result -= b;
     return result;
  }
  inline std_real_concept operator*(const std_real_concept& a, const std_real_concept& b)
  {
     std_real_concept result(a);
     result *= b;
     return result;
  }
  inline std_real_concept operator/(const std_real_concept& a, const std_real_concept& b)
  {
     std_real_concept result(a);
     result /= b;
     return result;
  }
  
  // Comparison:
  inline bool operator == (const std_real_concept& a, const std_real_concept& b)
  { return a.value() == b.value(); }
  inline bool operator != (const std_real_concept& a, const std_real_concept& b)
  { return a.value() != b.value();}
  inline bool operator < (const std_real_concept& a, const std_real_concept& b)
  { return a.value() < b.value(); }
  inline bool operator <= (const std_real_concept& a, const std_real_concept& b)
  { return a.value() <= b.value(); }
  inline bool operator > (const std_real_concept& a, const std_real_concept& b)
  { return a.value() > b.value(); }
  inline bool operator >= (const std_real_concept& a, const std_real_concept& b)
  { return a.value() >= b.value(); }
  
  #if 0
  // Non-member mixed compare:
  template <class T>
  inline bool operator == (const T& a, const std_real_concept& b)
  {
     return a == b.value();
  }
  template <class T>
  inline bool operator != (const T& a, const std_real_concept& b)
  {
     return a != b.value();
  }
  template <class T>
  inline bool operator < (const T& a, const std_real_concept& b)
  {
     return a < b.value();
  }
  template <class T>
  inline bool operator > (const T& a, const std_real_concept& b)
  {
     return a > b.value();
  }
  template <class T>
  inline bool operator <= (const T& a, const std_real_concept& b)
  {
     return a <= b.value();
  }
  template <class T>
  inline bool operator >= (const T& a, const std_real_concept& b)
  {
     return a >= b.value();
  }
  #endif  // Non-member mixed compare:
  
  } // namespace concepts
  } // namespace math
  } // namespace boost
  
  namespace std{
  
  // Non-member functions:
  inline boost::math::concepts::std_real_concept acos(boost::math::concepts::std_real_concept a)
  { return std::acos(a.value()); }
  inline boost::math::concepts::std_real_concept cos(boost::math::concepts::std_real_concept a)
  { return std::cos(a.value()); }
  inline boost::math::concepts::std_real_concept asin(boost::math::concepts::std_real_concept a)
  { return std::asin(a.value()); }
  inline boost::math::concepts::std_real_concept atan(boost::math::concepts::std_real_concept a)
  { return std::atan(a.value()); }
  inline boost::math::concepts::std_real_concept atan2(boost::math::concepts::std_real_concept a, boost::math::concepts::std_real_concept b)
  { return std::atan2(a.value(), b.value()); }
  inline boost::math::concepts::std_real_concept ceil(boost::math::concepts::std_real_concept a)
  { return std::ceil(a.value()); }
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  inline boost::math::concepts::std_real_concept fmod(boost::math::concepts::std_real_concept a, boost::math::concepts::std_real_concept b)
  { return fmodl(a.value(), b.value()); }
  #else
  inline boost::math::concepts::std_real_concept fmod(boost::math::concepts::std_real_concept a, boost::math::concepts::std_real_concept b)
  { return std::fmod(a.value(), b.value()); }
  #endif
  inline boost::math::concepts::std_real_concept cosh(boost::math::concepts::std_real_concept a)
  { return std::cosh(a.value()); }
  inline boost::math::concepts::std_real_concept exp(boost::math::concepts::std_real_concept a)
  { return std::exp(a.value()); }
  inline boost::math::concepts::std_real_concept fabs(boost::math::concepts::std_real_concept a)
  { return std::fabs(a.value()); }
  inline boost::math::concepts::std_real_concept abs(boost::math::concepts::std_real_concept a)
  { return std::abs(a.value()); }
  inline boost::math::concepts::std_real_concept floor(boost::math::concepts::std_real_concept a)
  { return std::floor(a.value()); }
  inline boost::math::concepts::std_real_concept modf(boost::math::concepts::std_real_concept a, boost::math::concepts::std_real_concept* ipart)
  {
     long double ip;
     long double result = std::modf(a.value(), &ip);
     *ipart = ip;
     return result;
  }
  inline boost::math::concepts::std_real_concept frexp(boost::math::concepts::std_real_concept a, int* expon)
  { return std::frexp(a.value(), expon); }
  inline boost::math::concepts::std_real_concept ldexp(boost::math::concepts::std_real_concept a, int expon)
  { return std::ldexp(a.value(), expon); }
  inline boost::math::concepts::std_real_concept log(boost::math::concepts::std_real_concept a)
  { return std::log(a.value()); }
  inline boost::math::concepts::std_real_concept log10(boost::math::concepts::std_real_concept a)
  { return std::log10(a.value()); }
  inline boost::math::concepts::std_real_concept tan(boost::math::concepts::std_real_concept a)
  { return std::tan(a.value()); }
  inline boost::math::concepts::std_real_concept pow(boost::math::concepts::std_real_concept a, boost::math::concepts::std_real_concept b)
  { return std::pow(a.value(), b.value()); }
  #if !defined(__SUNPRO_CC)
  inline boost::math::concepts::std_real_concept pow(boost::math::concepts::std_real_concept a, int b)
  { return std::pow(a.value(), b); }
  #else
  inline boost::math::concepts::std_real_concept pow(boost::math::concepts::std_real_concept a, int b)
  { return std::pow(a.value(), static_cast<long double>(b)); }
  #endif
  inline boost::math::concepts::std_real_concept sin(boost::math::concepts::std_real_concept a)
  { return std::sin(a.value()); }
  inline boost::math::concepts::std_real_concept sinh(boost::math::concepts::std_real_concept a)
  { return std::sinh(a.value()); }
  inline boost::math::concepts::std_real_concept sqrt(boost::math::concepts::std_real_concept a)
  { return std::sqrt(a.value()); }
  inline boost::math::concepts::std_real_concept tanh(boost::math::concepts::std_real_concept a)
  { return std::tanh(a.value()); }
  
  } // namespace std
  
  namespace boost{ namespace math{ namespace concepts{
  
  // Streaming:
  template <class charT, class traits>
  inline std::basic_ostream<charT, traits>& operator<<(std::basic_ostream<charT, traits>& os, const std_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, std_real_concept& a)
  {
     long double v;
     is >> v;
     a = v;
     return is;
  }
  
  } // namespace concepts
  
  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::std_real_concept>(concepts::std_real_concept r)
  {
     return static_cast<unsigned int>(r.value());
  }
  
  template <>
  inline int real_cast<int, concepts::std_real_concept>(concepts::std_real_concept r)
  {
     return static_cast<int>(r.value());
  }
  
  template <>
  inline long real_cast<long, concepts::std_real_concept>(concepts::std_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::std_real_concept>(concepts::std_real_concept r)
  {
     return static_cast<float>(r.value());
  }
  template <>
  inline double real_cast<double, concepts::std_real_concept>(concepts::std_real_concept r)
  {
     return static_cast<double>(r.value());
  }
  template <>
  inline long double real_cast<long double, concepts::std_real_concept>(concepts::std_real_concept r)
  {
     return r.value();
  }
  
  template <>
  inline concepts::std_real_concept max_value<concepts::std_real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
  {
     return max_value<long double>();
  }
  
  template <>
  inline concepts::std_real_concept min_value<concepts::std_real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
  {
     return min_value<long double>();
  }
  
  template <>
  inline concepts::std_real_concept log_max_value<concepts::std_real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
  {
     return log_max_value<long double>();
  }
  
  template <>
  inline concepts::std_real_concept log_min_value<concepts::std_real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
  {
     return log_min_value<long double>();
  }
  
  template <>
  inline concepts::std_real_concept epsilon<concepts::std_real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
  {
     return tools::epsilon<long double>();
  }
  
  template <>
  inline int digits<concepts::std_real_concept>(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
  { // Assume number of significand bits is same as long double,
    // unless std::numeric_limits<T>::is_specialized to provide digits.
     return digits<long double>();
  }
  
  } // namespace tools
  } // namespace math
  } // namespace boost
  
  #endif // BOOST_MATH_STD_REAL_CONCEPT_HPP
  
  
  