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 // fp_traits.hpp
 
 #ifndef BOOST_MATH_FP_TRAITS_HPP
 #define BOOST_MATH_FP_TRAITS_HPP
 
 // Copyright (c) 2006 Johan Rade
 // Copyright (c) 2024 Matt Borland
 
 // 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 <cstdint>
 #include <limits>
 #include <type_traits>
 #include <boost/math/tools/config.hpp>
 #include <boost/math/tools/is_standalone.hpp>
 #include <boost/math/tools/assert.hpp>
 
 // Determine endianness
 #ifndef BOOST_MATH_STANDALONE
 
 #include <boost/predef/other/endian.h>
 #define BOOST_MATH_ENDIAN_BIG_BYTE BOOST_ENDIAN_BIG_BYTE
 #define BOOST_MATH_ENDIAN_LITTLE_BYTE BOOST_ENDIAN_LITTLE_BYTE
 
 #elif defined(_WIN32)
 
 #define BOOST_MATH_ENDIAN_BIG_BYTE 0
 #define BOOST_MATH_ENDIAN_LITTLE_BYTE 1
 
 #elif defined(__BYTE_ORDER__)
 
 #define BOOST_MATH_ENDIAN_BIG_BYTE (__BYTE_ORDER__ == __ORDER_BIG_ENDIAN__)
 #define BOOST_MATH_ENDIAN_LITTLE_BYTE (__BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__)
 
 #else
 #error Could not determine endian type. Please disable standalone mode, and file an issue at https://github.com/boostorg/math
 #endif // Determine endianness
 
 static_assert((BOOST_MATH_ENDIAN_BIG_BYTE || BOOST_MATH_ENDIAN_LITTLE_BYTE)
     && !(BOOST_MATH_ENDIAN_BIG_BYTE && BOOST_MATH_ENDIAN_LITTLE_BYTE),
     "Inconsistent endianness detected. Please disable standalone mode, and file an issue at https://github.com/boostorg/math");
 
 #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_MATH_STATIC constexpr uint32_t sign        = 0x80000000u;
     BOOST_MATH_STATIC constexpr uint32_t exponent    = 0x7f800000;
     BOOST_MATH_STATIC constexpr uint32_t flag        = 0x00000000;
     BOOST_MATH_STATIC constexpr uint32_t significand = 0x007fffff;
 
     typedef uint32_t bits;
     BOOST_MATH_GPU_ENABLED static void get_bits(float x, uint32_t& a) { std::memcpy(&a, &x, 4); }
     BOOST_MATH_GPU_ENABLED 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(BOOST_BORLANDC) || defined(__CODEGEAR__)
 
 template<> struct fp_traits_non_native<double, double_precision>
 {
     typedef ieee_copy_leading_bits_tag method;
 
     static constexpr uint32_t sign        = 0x80000000u;
     static constexpr uint32_t exponent    = 0x7ff00000;
     static constexpr uint32_t flag        = 0;
     static constexpr 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:
     static constexpr int offset_ = BOOST_MATH_ENDIAN_BIG_BYTE ? 0 : 4;
 };
 
 //..............................................................................
 
 #else
 
 template<> struct fp_traits_non_native<double, double_precision>
 {
     typedef ieee_copy_all_bits_tag method;
 
     BOOST_MATH_STATIC constexpr uint64_t sign     = static_cast<uint64_t>(0x80000000u) << 32;
     BOOST_MATH_STATIC constexpr uint64_t exponent = static_cast<uint64_t>(0x7ff00000) << 32;
     BOOST_MATH_STATIC constexpr uint64_t flag     = 0;
     BOOST_MATH_STATIC constexpr uint64_t significand
         = (static_cast<uint64_t>(0x000fffff) << 32) + static_cast<uint64_t>(0xffffffffu);
 
     typedef uint64_t bits;
     BOOST_MATH_GPU_ENABLED static void get_bits(double x, uint64_t& a) { std::memcpy(&a, &x, 8); }
     BOOST_MATH_GPU_ENABLED 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(BOOST_BORLANDC) || defined(__CODEGEAR__)
 
 template<> struct fp_traits_non_native<long double, double_precision>
 {
     typedef ieee_copy_leading_bits_tag method;
 
     static constexpr uint32_t sign        = 0x80000000u;
     static constexpr uint32_t exponent    = 0x7ff00000;
     static constexpr uint32_t flag        = 0;
     static constexpr 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:
     static constexpr int offset_ = BOOST_MATH_ENDIAN_BIG_BYTE ? 0 : 4;
 };
 
 //..............................................................................
 
 #else
 
 template<> struct fp_traits_non_native<long double, double_precision>
 {
     typedef ieee_copy_all_bits_tag method;
 
     static const uint64_t sign     = static_cast<uint64_t>(0x80000000u) << 32;
     static const uint64_t exponent = static_cast<uint64_t>(0x7ff00000) << 32;
     static const uint64_t flag     = 0;
     static const uint64_t significand
         = (static_cast<uint64_t>(0x000fffff) << 32) + static_cast<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_MATH_STATIC constexpr uint32_t sign        = 0x80000000u;
     BOOST_MATH_STATIC constexpr uint32_t exponent    = 0x7fff0000;
     BOOST_MATH_STATIC constexpr uint32_t flag        = 0x00008000;
     BOOST_MATH_STATIC constexpr 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_MATH_STATIC constexpr uint32_t sign        = 0x80000000u;
     BOOST_MATH_STATIC constexpr uint32_t exponent    = 0x7ff00000;
     BOOST_MATH_STATIC constexpr uint32_t flag        = 0x00000000;
     BOOST_MATH_STATIC constexpr 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:
     BOOST_MATH_STATIC constexpr int offset_ = BOOST_MATH_ENDIAN_BIG_BYTE ? 0 : 12;
 };
 
 
 // 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_MATH_STATIC constexpr uint32_t sign        = 0x80000000u;
     BOOST_MATH_STATIC constexpr uint32_t exponent    = 0x7fff0000;
     BOOST_MATH_STATIC constexpr uint32_t flag        = 0x00008000;
     BOOST_MATH_STATIC constexpr 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_MATH_STATIC constexpr uint32_t sign        = 0x80000000u;
     BOOST_MATH_STATIC constexpr uint32_t exponent    = 0x7fff0000;
     BOOST_MATH_STATIC constexpr uint32_t flag        = 0x00000000;
     BOOST_MATH_STATIC constexpr 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:
     BOOST_MATH_STATIC constexpr int offset_ = BOOST_MATH_ENDIAN_BIG_BYTE ? 0 : 12;
 };
 
 #endif
 
 //------------------------------------------------------------------------------
 
 // size_to_precision is a type switch for converting a C++ floating point type
 // to the corresponding precision type.
 
 template<size_t 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 typename size_to_precision<sizeof(T), ::std::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(__INTEL_COMPILER)\
    && !defined(sun)\
    && !defined(__VXWORKS__)\
    && !defined(BOOST_MATH_HAS_GPU_SUPPORT)
 #  define BOOST_MATH_USE_STD_FPCLASSIFY
 #endif
 
 template<class T> struct fp_traits
 {
     typedef typename size_to_precision<sizeof(T), ::std::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

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