text: // fp_traits.hpp
  
  #ifndef BOOST_MATH_FP_TRAITS_HPP
  #define BOOST_MATH_FP_TRAITS_HPP
  
  // Copyright (c) 2006 Johan Rade
  
  // Distributed under 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)
  
  /*
  To support old compilers, care has been taken to avoid partial template
  specialization and meta function forwarding.
  With these techniques, the code could be simplified.
  */
  
  #if defined(__vms) && defined(__DECCXX) && !__IEEE_FLOAT
  // The VAX floating point formats are used (for float and double)
  #   define BOOST_FPCLASSIFY_VAX_FORMAT
  #endif
  
  #include <cstring>
  
  #include <boost/assert.hpp>
  #include <boost/cstdint.hpp>
  #include <boost/detail/endian.hpp>
  #include <boost/static_assert.hpp>
  #include <boost/type_traits/is_floating_point.hpp>
  
  #ifdef BOOST_NO_STDC_NAMESPACE
    namespace std{ using ::memcpy; }
  #endif
  
  #ifndef FP_NORMAL
  
  #define FP_ZERO        0
  #define FP_NORMAL      1
  #define FP_INFINITE    2
  #define FP_NAN         3
  #define FP_SUBNORMAL   4
  
  #else
  
  #define BOOST_HAS_FPCLASSIFY
  
  #ifndef fpclassify
  #  if (defined(__GLIBCPP__) || defined(__GLIBCXX__)) \
           && defined(_GLIBCXX_USE_C99_MATH) \
           && !(defined(_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) \
           && (_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC != 0))
  #     ifdef _STLP_VENDOR_CSTD
  #        if _STLPORT_VERSION >= 0x520
  #           define BOOST_FPCLASSIFY_PREFIX ::__std_alias:: 
  #        else
  #           define BOOST_FPCLASSIFY_PREFIX ::_STLP_VENDOR_CSTD:: 
  #        endif
  #     else
  #        define BOOST_FPCLASSIFY_PREFIX ::std::
  #     endif
  #  else
  #     undef BOOST_HAS_FPCLASSIFY
  #     define BOOST_FPCLASSIFY_PREFIX
  #  endif
  #elif (defined(__HP_aCC) && !defined(__hppa))
  // aCC 6 appears to do "#define fpclassify fpclassify" which messes us up a bit!
  #  define BOOST_FPCLASSIFY_PREFIX ::
  #else
  #  define BOOST_FPCLASSIFY_PREFIX
  #endif
  
  #ifdef __MINGW32__
  #  undef BOOST_HAS_FPCLASSIFY
  #endif
  
  #endif
  
  
  //------------------------------------------------------------------------------
  
  namespace boost {
  namespace math {
  namespace detail {
  
  //------------------------------------------------------------------------------
  
  /* 
  The following classes are used to tag the different methods that are used
  for floating point classification
  */
  
  struct native_tag {};
  template <bool has_limits>
  struct generic_tag {};
  struct ieee_tag {};
  struct ieee_copy_all_bits_tag : public ieee_tag {};
  struct ieee_copy_leading_bits_tag : public ieee_tag {};
  
  #ifdef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
  //
  // These helper functions are used only when numeric_limits<>
  // members are not compile time constants:
  //
  inline bool is_generic_tag_false(const generic_tag<false>*)
  {
     return true;
  }
  inline bool is_generic_tag_false(const void*)
  {
     return false;
  }
  #endif
  
  //------------------------------------------------------------------------------
  
  /*
  Most processors support three different floating point precisions:
  single precision (32 bits), double precision (64 bits)
  and extended double precision (80 - 128 bits, depending on the processor)
  
  Note that the C++ type long double can be implemented
  both as double precision and extended double precision.
  */
  
  struct unknown_precision{};
  struct single_precision {};
  struct double_precision {};
  struct extended_double_precision {};
  
  // native_tag version --------------------------------------------------------------
  
  template<class T> struct fp_traits_native
  {
      typedef native_tag method;
  };
  
  // generic_tag version -------------------------------------------------------------
  
  template<class T, class U> struct fp_traits_non_native
  {
  #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
     typedef generic_tag<std::numeric_limits<T>::is_specialized> method;
  #else
     typedef generic_tag<false> method;
  #endif
  };
  
  // ieee_tag versions ---------------------------------------------------------------
  
  /*
  These specializations of fp_traits_non_native contain information needed
  to "parse" the binary representation of a floating point number.
  
  Typedef members:
  
    bits -- the target type when copying the leading bytes of a floating
        point number. It is a typedef for uint32_t or uint64_t.
  
    method -- tells us whether all bytes are copied or not.
        It is a typedef for ieee_copy_all_bits_tag or ieee_copy_leading_bits_tag.
  
  Static data members:
  
    sign, exponent, flag, significand -- bit masks that give the meaning of the
    bits in the leading bytes.
  
  Static function members:
  
    get_bits(), set_bits() -- provide access to the leading bytes.
  
  */
  
  // ieee_tag version, float (32 bits) -----------------------------------------------
  
  #ifndef BOOST_FPCLASSIFY_VAX_FORMAT
  
  template<> struct fp_traits_non_native<float, single_precision>
  {
      typedef ieee_copy_all_bits_tag method;
  
      BOOST_STATIC_CONSTANT(uint32_t, sign        = 0x80000000u);
      BOOST_STATIC_CONSTANT(uint32_t, exponent    = 0x7f800000);
      BOOST_STATIC_CONSTANT(uint32_t, flag        = 0x00000000);
      BOOST_STATIC_CONSTANT(uint32_t, significand = 0x007fffff);
  
      typedef uint32_t bits;
      static void get_bits(float x, uint32_t& a) { std::memcpy(&a, &x, 4); }
      static void set_bits(float& x, uint32_t a) { std::memcpy(&x, &a, 4); }
  };
  
  // ieee_tag version, double (64 bits) ----------------------------------------------
  
  #if defined(BOOST_NO_INT64_T) || defined(BOOST_NO_INCLASS_MEMBER_INITIALIZATION) \
     || defined(__BORLANDC__) || defined(__CODEGEAR__)
  
  template<> struct fp_traits_non_native<double, double_precision>
  {
      typedef ieee_copy_leading_bits_tag method;
  
      BOOST_STATIC_CONSTANT(uint32_t, sign        = 0x80000000u);
      BOOST_STATIC_CONSTANT(uint32_t, exponent    = 0x7ff00000);
      BOOST_STATIC_CONSTANT(uint32_t, flag        = 0);
      BOOST_STATIC_CONSTANT(uint32_t, significand = 0x000fffff);
  
      typedef uint32_t bits;
  
      static void get_bits(double x, uint32_t& a)
      {
          std::memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
      }
  
      static void set_bits(double& x, uint32_t a)
      {
          std::memcpy(reinterpret_cast<unsigned char*>(&x) + offset_, &a, 4);
      }
  
  private:
  
  #if defined(BOOST_BIG_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 0);
  #elif defined(BOOST_LITTLE_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 4);
  #else
      BOOST_STATIC_ASSERT(false);
  #endif
  };
  
  //..............................................................................
  
  #else
  
  template<> struct fp_traits_non_native<double, double_precision>
  {
      typedef ieee_copy_all_bits_tag method;
  
      static const uint64_t sign     = ((uint64_t)0x80000000u) << 32;
      static const uint64_t exponent = ((uint64_t)0x7ff00000) << 32;
      static const uint64_t flag     = 0;
      static const uint64_t significand
          = (((uint64_t)0x000fffff) << 32) + ((uint64_t)0xffffffffu);
  
      typedef uint64_t bits;
      static void get_bits(double x, uint64_t& a) { std::memcpy(&a, &x, 8); }
      static void set_bits(double& x, uint64_t a) { std::memcpy(&x, &a, 8); }
  };
  
  #endif
  
  #endif  // #ifndef BOOST_FPCLASSIFY_VAX_FORMAT
  
  // long double (64 bits) -------------------------------------------------------
  
  #if defined(BOOST_NO_INT64_T) || defined(BOOST_NO_INCLASS_MEMBER_INITIALIZATION)\
     || defined(__BORLANDC__) || defined(__CODEGEAR__)
  
  template<> struct fp_traits_non_native<long double, double_precision>
  {
      typedef ieee_copy_leading_bits_tag method;
  
      BOOST_STATIC_CONSTANT(uint32_t, sign        = 0x80000000u);
      BOOST_STATIC_CONSTANT(uint32_t, exponent    = 0x7ff00000);
      BOOST_STATIC_CONSTANT(uint32_t, flag        = 0);
      BOOST_STATIC_CONSTANT(uint32_t, significand = 0x000fffff);
  
      typedef uint32_t bits;
  
      static void get_bits(long double x, uint32_t& a)
      {
          std::memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
      }
  
      static void set_bits(long double& x, uint32_t a)
      {
          std::memcpy(reinterpret_cast<unsigned char*>(&x) + offset_, &a, 4);
      }
  
  private:
  
  #if defined(BOOST_BIG_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 0);
  #elif defined(BOOST_LITTLE_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 4);
  #else
      BOOST_STATIC_ASSERT(false);
  #endif
  };
  
  //..............................................................................
  
  #else
  
  template<> struct fp_traits_non_native<long double, double_precision>
  {
      typedef ieee_copy_all_bits_tag method;
  
      static const uint64_t sign     = (uint64_t)0x80000000u << 32;
      static const uint64_t exponent = (uint64_t)0x7ff00000 << 32;
      static const uint64_t flag     = 0;
      static const uint64_t significand
          = ((uint64_t)0x000fffff << 32) + (uint64_t)0xffffffffu;
  
      typedef uint64_t bits;
      static void get_bits(long double x, uint64_t& a) { std::memcpy(&a, &x, 8); }
      static void set_bits(long double& x, uint64_t a) { std::memcpy(&x, &a, 8); }
  };
  
  #endif
  
  
  // long double (>64 bits), x86 and x64 -----------------------------------------
  
  #if defined(__i386) || defined(__i386__) || defined(_M_IX86) \
      || defined(__amd64) || defined(__amd64__)  || defined(_M_AMD64) \
      || defined(__x86_64) || defined(__x86_64__) || defined(_M_X64)
  
  // Intel extended double precision format (80 bits)
  
  template<>
  struct fp_traits_non_native<long double, extended_double_precision>
  {
      typedef ieee_copy_leading_bits_tag method;
  
      BOOST_STATIC_CONSTANT(uint32_t, sign        = 0x80000000u);
      BOOST_STATIC_CONSTANT(uint32_t, exponent    = 0x7fff0000);
      BOOST_STATIC_CONSTANT(uint32_t, flag        = 0x00008000);
      BOOST_STATIC_CONSTANT(uint32_t, significand = 0x00007fff);
  
      typedef uint32_t bits;
  
      static void get_bits(long double x, uint32_t& a)
      {
          std::memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + 6, 4);
      }
  
      static void set_bits(long double& x, uint32_t a)
      {
          std::memcpy(reinterpret_cast<unsigned char*>(&x) + 6, &a, 4);
      }
  };
  
  
  // long double (>64 bits), Itanium ---------------------------------------------
  
  #elif defined(__ia64) || defined(__ia64__) || defined(_M_IA64)
  
  // The floating point format is unknown at compile time
  // No template specialization is provided.
  // The generic_tag definition is used.
  
  // The Itanium supports both
  // the Intel extended double precision format (80 bits) and
  // the IEEE extended double precision format with 15 exponent bits (128 bits).
  
  #elif defined(__GNUC__) && (LDBL_MANT_DIG == 106)
  
  //
  // Define nothing here and fall though to generic_tag:
  // We have GCC's "double double" in effect, and any attempt
  // to handle it via bit-fiddling is pretty much doomed to fail...
  //
  
  // long double (>64 bits), PowerPC ---------------------------------------------
  
  #elif defined(__powerpc) || defined(__powerpc__) || defined(__POWERPC__) \
      || defined(__ppc) || defined(__ppc__) || defined(__PPC__)
  
  // PowerPC extended double precision format (128 bits)
  
  template<>
  struct fp_traits_non_native<long double, extended_double_precision>
  {
      typedef ieee_copy_leading_bits_tag method;
  
      BOOST_STATIC_CONSTANT(uint32_t, sign        = 0x80000000u);
      BOOST_STATIC_CONSTANT(uint32_t, exponent    = 0x7ff00000);
      BOOST_STATIC_CONSTANT(uint32_t, flag        = 0x00000000);
      BOOST_STATIC_CONSTANT(uint32_t, significand = 0x000fffff);
  
      typedef uint32_t bits;
  
      static void get_bits(long double x, uint32_t& a)
      {
          std::memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
      }
  
      static void set_bits(long double& x, uint32_t a)
      {
          std::memcpy(reinterpret_cast<unsigned char*>(&x) + offset_, &a, 4);
      }
  
  private:
  
  #if defined(BOOST_BIG_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 0);
  #elif defined(BOOST_LITTLE_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 12);
  #else
      BOOST_STATIC_ASSERT(false);
  #endif
  };
  
  
  // long double (>64 bits), Motorola 68K ----------------------------------------
  
  #elif defined(__m68k) || defined(__m68k__) \
      || defined(__mc68000) || defined(__mc68000__) \
  
  // Motorola extended double precision format (96 bits)
  
  // It is the same format as the Intel extended double precision format,
  // except that 1) it is big-endian, 2) the 3rd and 4th byte are padding, and
  // 3) the flag bit is not set for infinity
  
  template<>
  struct fp_traits_non_native<long double, extended_double_precision>
  {
      typedef ieee_copy_leading_bits_tag method;
  
      BOOST_STATIC_CONSTANT(uint32_t, sign        = 0x80000000u);
      BOOST_STATIC_CONSTANT(uint32_t, exponent    = 0x7fff0000);
      BOOST_STATIC_CONSTANT(uint32_t, flag        = 0x00008000);
      BOOST_STATIC_CONSTANT(uint32_t, significand = 0x00007fff);
  
      // copy 1st, 2nd, 5th and 6th byte. 3rd and 4th byte are padding.
  
      typedef uint32_t bits;
  
      static void get_bits(long double x, uint32_t& a)
      {
          std::memcpy(&a, &x, 2);
          std::memcpy(reinterpret_cast<unsigned char*>(&a) + 2,
                 reinterpret_cast<const unsigned char*>(&x) + 4, 2);
      }
  
      static void set_bits(long double& x, uint32_t a)
      {
          std::memcpy(&x, &a, 2);
          std::memcpy(reinterpret_cast<unsigned char*>(&x) + 4,
                 reinterpret_cast<const unsigned char*>(&a) + 2, 2);
      }
  };
  
  
  // long double (>64 bits), All other processors --------------------------------
  
  #else
  
  // IEEE extended double precision format with 15 exponent bits (128 bits)
  
  template<>
  struct fp_traits_non_native<long double, extended_double_precision>
  {
      typedef ieee_copy_leading_bits_tag method;
  
      BOOST_STATIC_CONSTANT(uint32_t, sign        = 0x80000000u);
      BOOST_STATIC_CONSTANT(uint32_t, exponent    = 0x7fff0000);
      BOOST_STATIC_CONSTANT(uint32_t, flag        = 0x00000000);
      BOOST_STATIC_CONSTANT(uint32_t, significand = 0x0000ffff);
  
      typedef uint32_t bits;
  
      static void get_bits(long double x, uint32_t& a)
      {
          std::memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
      }
  
      static void set_bits(long double& x, uint32_t a)
      {
          std::memcpy(reinterpret_cast<unsigned char*>(&x) + offset_, &a, 4);
      }
  
  private:
  
  #if defined(BOOST_BIG_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 0);
  #elif defined(BOOST_LITTLE_ENDIAN)
      BOOST_STATIC_CONSTANT(int, offset_ = 12);
  #else
      BOOST_STATIC_ASSERT(false);
  #endif
  };
  
  #endif
  
  //------------------------------------------------------------------------------
  
  // size_to_precision is a type switch for converting a C++ floating point type
  // to the corresponding precision type.
  
  template<int n, bool fp> struct size_to_precision
  {
     typedef unknown_precision type;
  };
  
  template<> struct size_to_precision<4, true>
  {
      typedef single_precision type;
  };
  
  template<> struct size_to_precision<8, true>
  {
      typedef double_precision type;
  };
  
  template<> struct size_to_precision<10, true>
  {
      typedef extended_double_precision type;
  };
  
  template<> struct size_to_precision<12, true>
  {
      typedef extended_double_precision type;
  };
  
  template<> struct size_to_precision<16, true>
  {
      typedef extended_double_precision type;
  };
  
  //------------------------------------------------------------------------------
  //
  // Figure out whether to use native classification functions based on
  // whether T is a built in floating point type or not:
  //
  template <class T>
  struct select_native
  {
      typedef BOOST_DEDUCED_TYPENAME size_to_precision<sizeof(T), ::boost::is_floating_point<T>::value>::type precision;
      typedef fp_traits_non_native<T, precision> type;
  };
  template<>
  struct select_native<float>
  {
      typedef fp_traits_native<float> type;
  };
  template<>
  struct select_native<double>
  {
      typedef fp_traits_native<double> type;
  };
  template<>
  struct select_native<long double>
  {
      typedef fp_traits_native<long double> type;
  };
  
  //------------------------------------------------------------------------------
  
  // fp_traits is a type switch that selects the right fp_traits_non_native
  
  #if (defined(BOOST_MATH_USE_C99) && !(defined(__GNUC__) && (__GNUC__ < 4))) \
     && !defined(__hpux) \
     && !defined(__DECCXX)\
     && !defined(__osf__) \
     && !defined(__SGI_STL_PORT) && !defined(_STLPORT_VERSION)\
     && !defined(__FAST_MATH__)\
     && !defined(BOOST_MATH_DISABLE_STD_FPCLASSIFY)\
     && !defined(BOOST_INTEL)\
     && !defined(sun)\
     && !defined(__VXWORKS__)   
  #  define BOOST_MATH_USE_STD_FPCLASSIFY
  #endif
  
  template<class T> struct fp_traits
  {
      typedef BOOST_DEDUCED_TYPENAME size_to_precision<sizeof(T), ::boost::is_floating_point<T>::value>::type precision;
  #if defined(BOOST_MATH_USE_STD_FPCLASSIFY) && !defined(BOOST_MATH_DISABLE_STD_FPCLASSIFY)
      typedef typename select_native<T>::type type;
  #else
      typedef fp_traits_non_native<T, precision> type;
  #endif
      typedef fp_traits_non_native<T, precision> sign_change_type;
  };
  
  //------------------------------------------------------------------------------
  
  }   // namespace detail
  }   // namespace math
  }   // namespace boost
  
  #endif
  