boost/math/special_functions/detail/fp_traits.hpp
// 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 <cstdint> #include <limits> #include <type_traits> #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 (__cplusplus >= 202002L || _MSVC_LANG >= 202002L) #if __has_include(<bit>) #include <bit> #define BOOST_MATH_ENDIAN_BIG_BYTE (std::endian::native == std::endian::big) #define BOOST_MATH_ENDIAN_LITTLE_BYTE (std::endian::native == std::endian::little) #else #error Missing <bit> header. Please disable standalone mode, and file an issue at https://github.com/boostorg/math #endif #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; static constexpr uint32_t sign = 0x80000000u; static constexpr uint32_t exponent = 0x7f800000; static constexpr uint32_t flag = 0x00000000; static constexpr 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(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; static constexpr uint64_t sign = static_cast<uint64_t>(0x80000000u) << 32; static constexpr uint64_t exponent = static_cast<uint64_t>(0x7ff00000) << 32; static constexpr uint64_t flag = 0; static constexpr uint64_t significand = (static_cast<uint64_t>(0x000fffff) << 32) + static_cast<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(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; static constexpr uint32_t sign = 0x80000000u; static constexpr uint32_t exponent = 0x7fff0000; static constexpr uint32_t flag = 0x00008000; 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; static constexpr uint32_t sign = 0x80000000u; static constexpr uint32_t exponent = 0x7ff00000; static constexpr uint32_t flag = 0x00000000; 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 : 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; static constexpr uint32_t sign = 0x80000000u; static constexpr uint32_t exponent = 0x7fff0000; static constexpr uint32_t flag = 0x00008000; 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; static constexpr uint32_t sign = 0x80000000u; static constexpr uint32_t exponent = 0x7fff0000; static constexpr uint32_t flag = 0x00000000; 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: 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<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 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__) # 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