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+// 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).
+
+
+// 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(BOOST_MATH_DISABLE_STD_FPCLASSIFY)
+# 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