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// fp_traits.hpp
#ifndef BOOST_SPIRIT_MATH_FP_TRAITS_HPP
#define BOOST_SPIRIT_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)
#if defined(__vms) && defined(__DECCXX) && !__IEEE_FLOAT
# error The VAX floating point mode on VMS is not supported.
#endif
#if defined(_MSC_VER)
#pragma once
#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>
//------------------------------------------------------------------------------
namespace boost {
namespace spirit {
namespace math {
namespace detail {
//------------------------------------------------------------------------------
/*
Most processors support three different floating point precisions:
single precision (32 bits), double precision (64 bits)
and extended double precision (>64 bits)
Note that the C++ type long double can be implemented
both as double precision and extended double precision.
*/
struct single_precision_tag {};
struct double_precision_tag {};
struct extended_double_precision_tag {};
//------------------------------------------------------------------------------
/*
template<class T, class U> struct fp_traits_impl;
This is traits class that describes the binary structure of floating
point numbers of C++ type T and precision U
Requirements:
T = float, double or long double
U = single_precision_tag, double_precision_tag
or extended_double_precision_tag
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.
coverage -- tells us whether all bytes are copied or not.
It is a typedef for all_bits or not_all_bits.
Static data members:
sign, exponent, flag, mantissa -- bit masks that give the meaning of the bits
in the leading bytes.
Static function members:
init() -- initializes the static data members, if needed.
(Is a no-op in the specialized versions of the template.)
get_bits(), set_bits() -- provide access to the leading bytes.
*/
struct all_bits {};
struct not_all_bits {};
// Generic version -------------------------------------------------------------
// The generic version uses run time initialization to determine the floating
// point format. It is capable of handling most formats,
// but not the Motorola 68K extended double precision format.
// Currently the generic version is used only for extended double precision
// on Itanium. In all other cases there are specializations of the template
// that use compile time initialization.
template<class T> struct uint32_t_coverage
{
typedef not_all_bits type;
};
template<> struct uint32_t_coverage<single_precision_tag>
{
typedef all_bits type;
};
template<class T, class U> struct fp_traits_impl
{
typedef uint32_t bits;
typedef BOOST_DEDUCED_TYPENAME uint32_t_coverage<U>::type coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
static uint32_t exponent;
static uint32_t flag;
static uint32_t mantissa;
static void init()
{
if(is_init_) return;
do_init_();
is_init_ = true;
}
static void get_bits(T x, uint32_t& a)
{
memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
}
static void set_bits(T& x, uint32_t a)
{
memcpy(reinterpret_cast<unsigned char*>(&x) + offset_, &a, 4);
}
private:
static size_t offset_;
static bool is_init_;
static void do_init_();
};
//..............................................................................
template<class T, class U> uint32_t fp_traits_impl<T,U>::exponent;
template<class T, class U> uint32_t fp_traits_impl<T,U>::flag;
template<class T, class U> uint32_t fp_traits_impl<T,U>::mantissa;
template<class T, class U> size_t fp_traits_impl<T,U>::offset_;
template<class T, class U> bool fp_traits_impl<T,U>::is_init_;
// In a single-threaded program, do_init will be called exactly once.
// In a multi-threaded program, do_init may be called simultaneously
// by more then one thread. That should not be a problem.
//..............................................................................
template<class T, class U> void fp_traits_impl<T,U>::do_init_()
{
T x = static_cast<T>(3) / static_cast<T>(4);
// sign bit = 0
// exponent: first and last bit = 0, all other bits = 1
// flag bit (if present) = 1
// mantissa: first bit = 1, all other bits = 0
uint32_t a;
for(size_t k = 0; k <= sizeof(T) - 4; ++k) {
memcpy(&a, reinterpret_cast<unsigned char*>(&x) + k, 4);
switch(a) {
case 0x3f400000: // IEEE single precision format
offset_ = k;
exponent = 0x7f800000;
flag = 0x00000000;
mantissa = 0x007fffff;
return;
case 0x3fe80000: // IEEE double precision format
// and PowerPC extended double precision format
offset_ = k;
exponent = 0x7ff00000;
flag = 0x00000000;
mantissa = 0x000fffff;
return;
case 0x3ffe0000: // Motorola extended double precision format
// Must not get here. Must be handled by specialization.
// To get accurate cutoff between normals and subnormals
// we must use the flag bit that is in the 5th byte.
// Otherwise this cutoff will be off by a factor 2.
// If we do get here, then we have failed to detect the Motorola
// processor at compile time.
BOOST_ASSERT(false &&
"Failed to detect the Motorola processor at compile time");
return;
case 0x3ffe8000: // IEEE extended double precision format
// with 15 exponent bits
offset_ = k;
exponent = 0x7fff0000;
flag = 0x00000000;
mantissa = 0x0000ffff;
return;
case 0x3ffec000: // Intel extended double precision format
offset_ = k;
exponent = 0x7fff0000;
flag = 0x00008000;
mantissa = 0x00007fff;
return;
default:
continue;
}
}
BOOST_ASSERT(false);
// Unknown format.
}
// float (32 bits) -------------------------------------------------------------
template<> struct fp_traits_impl<float, single_precision_tag>
{
typedef uint32_t bits;
typedef all_bits coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
BOOST_STATIC_CONSTANT(uint32_t, exponent = 0x7f800000);
BOOST_STATIC_CONSTANT(uint32_t, flag = 0x00000000);
BOOST_STATIC_CONSTANT(uint32_t, mantissa = 0x007fffff);
static void init() {}
static void get_bits(float x, uint32_t& a) { memcpy(&a, &x, 4); }
static void set_bits(float& x, uint32_t a) { memcpy(&x, &a, 4); }
};
// double (64 bits) ------------------------------------------------------------
#if defined(BOOST_NO_INT64_T) || defined(BOOST_NO_INCLASS_MEMBER_INITIALIZATION)
template<> struct fp_traits_impl<double, double_precision_tag>
{
typedef uint32_t bits;
typedef not_all_bits coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
BOOST_STATIC_CONSTANT(uint32_t, exponent = 0x7ff00000);
BOOST_STATIC_CONSTANT(uint32_t, flag = 0);
BOOST_STATIC_CONSTANT(uint32_t, mantissa = 0x000fffff);
static void init() {}
static void get_bits(double x, uint32_t& a)
{
memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
}
static void set_bits(double& x, uint32_t a)
{
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_impl<double, double_precision_tag>
{
typedef uint64_t bits;
typedef all_bits coverage;
static const uint64_t sign = (uint64_t)0x80000000 << 32;
static const uint64_t exponent = (uint64_t)0x7ff00000 << 32;
static const uint64_t flag = 0;
static const uint64_t mantissa
= ((uint64_t)0x000fffff << 32) + (uint64_t)0xffffffff;
static void init() {}
static void get_bits(double x, uint64_t& a) { memcpy(&a, &x, 8); }
static void set_bits(double& x, uint64_t a) { memcpy(&x, &a, 8); }
};
#endif
// long double (64 bits) -------------------------------------------------------
#if defined(BOOST_NO_INT64_T) || defined(BOOST_NO_INCLASS_MEMBER_INITIALIZATION)
template<> struct fp_traits_impl<long double, double_precision_tag>
{
typedef uint32_t bits;
typedef not_all_bits coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
BOOST_STATIC_CONSTANT(uint32_t, exponent = 0x7ff00000);
BOOST_STATIC_CONSTANT(uint32_t, flag = 0);
BOOST_STATIC_CONSTANT(uint32_t, mantissa = 0x000fffff);
static void init() {}
static void get_bits(long double x, uint32_t& a)
{
memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
}
static void set_bits(long double& x, uint32_t a)
{
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_impl<long double, double_precision_tag>
{
typedef uint64_t bits;
typedef all_bits coverage;
static const uint64_t sign = (uint64_t)0x80000000 << 32;
static const uint64_t exponent = (uint64_t)0x7ff00000 << 32;
static const uint64_t flag = 0;
static const uint64_t mantissa
= ((uint64_t)0x000fffff << 32) + (uint64_t)0xffffffff;
static void init() {}
static void get_bits(long double x, uint64_t& a) { memcpy(&a, &x, 8); }
static void set_bits(long double& x, uint64_t a) { 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_impl<long double, extended_double_precision_tag>
{
typedef uint32_t bits;
typedef not_all_bits coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
BOOST_STATIC_CONSTANT(uint32_t, exponent = 0x7fff0000);
BOOST_STATIC_CONSTANT(uint32_t, flag = 0x00008000);
BOOST_STATIC_CONSTANT(uint32_t, mantissa = 0x00007fff);
static void init() {}
static void get_bits(long double x, uint32_t& a)
{
memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + 6, 4);
}
static void set_bits(long double& x, uint32_t a)
{
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 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_impl<long double, extended_double_precision_tag>
{
typedef uint32_t bits;
typedef not_all_bits coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
BOOST_STATIC_CONSTANT(uint32_t, exponent = 0x7ff00000);
BOOST_STATIC_CONSTANT(uint32_t, flag = 0x00000000);
BOOST_STATIC_CONSTANT(uint32_t, mantissa = 0x000fffff);
static void init() {}
static void get_bits(long double x, uint32_t& a)
{
memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
}
static void set_bits(long double& x, uint32_t a)
{
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_impl<long double, extended_double_precision_tag>
{
typedef uint32_t bits;
typedef not_all_bits coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
BOOST_STATIC_CONSTANT(uint32_t, exponent = 0x7fff0000);
BOOST_STATIC_CONSTANT(uint32_t, flag = 0x00008000);
BOOST_STATIC_CONSTANT(uint32_t, mantissa = 0x00007fff);
static void init() {}
// copy 1st, 2nd, 5th and 6th byte. 3rd and 4th byte are padding.
static void get_bits(long double x, uint32_t& a)
{
memcpy(&a, &x, 2);
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)
{
memcpy(&x, &a, 2);
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_impl<long double, extended_double_precision_tag>
{
typedef uint32_t bits;
typedef not_all_bits coverage;
BOOST_STATIC_CONSTANT(uint32_t, sign = 0x80000000);
BOOST_STATIC_CONSTANT(uint32_t, exponent = 0x7fff0000);
BOOST_STATIC_CONSTANT(uint32_t, flag = 0x00000000);
BOOST_STATIC_CONSTANT(uint32_t, mantissa = 0x0000ffff);
static void init() {}
static void get_bits(long double x, uint32_t& a)
{
memcpy(&a, reinterpret_cast<const unsigned char*>(&x) + offset_, 4);
}
static void set_bits(long double& x, uint32_t a)
{
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> struct size_to_precision;
template<> struct size_to_precision<4>
{
typedef single_precision_tag type;
};
template<> struct size_to_precision<8>
{
typedef double_precision_tag type;
};
template<> struct size_to_precision<10>
{
typedef extended_double_precision_tag type;
};
template<> struct size_to_precision<12>
{
typedef extended_double_precision_tag type;
};
template<> struct size_to_precision<16>
{
typedef extended_double_precision_tag type;
};
// fp_traits is a type switch that selects the right fp_traits_impl
template<class T> struct fp_traits
{
BOOST_STATIC_ASSERT(boost::is_floating_point<T>::value);
typedef BOOST_DEDUCED_TYPENAME size_to_precision<sizeof(T)>::type precision;
typedef fp_traits_impl<T, precision> type;
};
//------------------------------------------------------------------------------
} // namespace detail
} // namespace math
} // namespace spirit
} // namespace boost
#endif