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IEC559 totalOrder
- From: Matthias Kretz <m dot kretz at gsi dot de>
- To: <libstdc++ at gcc dot gnu dot org>
- Date: Sat, 9 Nov 2019 08:40:40 +0100
- Subject: IEC559 totalOrder
Here's an IEC559 totalOrder implementation that works with clang and GCC, for
float, double, long double, and __float128 (at least the non-clang branch
should work with float16, too):
https://godbolt.org/z/QzGWdB
Note that I simplified the order reversal of negative values slightly, and
producing the bitmask for the sign is now "simpler".
As Jakub noted on IRC, 32-bit x86's long double is a problem. Since it has
sizeof == 12 there's no *constexpr* way to cast it to an integer.
std::bit_cast also wouldn't help. It seems there's no way around a builtin for
this function. (Besides that, I ignored the presence of unnormal values in
long double - you still get a totalOrder, but I'm not sure IEC559 requests a
different behavior.)
Cheers,
Matthias
--
#include <type_traits>
#include <limits>
#include <climits>
template <class T>
constexpr bool totalOrder(T xx, T yy)
{
//static_assert(std::numeric_limits<T>::is_iec559); // fails for __float128
constexpr int Bytes = sizeof(T) == 12 ? 16 : sizeof(T);
using II = std::conditional_t<Bytes == sizeof(signed char), signed char,
std::conditional_t<Bytes == sizeof(signed short), signed short,
std::conditional_t<Bytes == sizeof(signed int), signed int,
std::conditional_t<Bytes == sizeof(signed long), signed long,
std::conditional_t<Bytes == sizeof(signed long long), signed long
long,
__int128>>>>>;
#ifdef __clang__
constexpr int unused_bits = sizeof(T) <= 8 ? 0 :
(Bytes - 8) * CHAR_BIT - 1 -
__builtin_ctzll((__builtin_bit_cast(II, T(-0.)) >>
8 * CHAR_BIT));
const II xi = __builtin_bit_cast(II, xx) << unused_bits;
const II yi = __builtin_bit_cast(II, yy) << unused_bits;
constexpr II signbit = __builtin_bit_cast(II, T(-0.)) << unused_bits;
const auto x = xi < 0 ? ~(xi ^ signbit) : xi;
const auto y = yi < 0 ? ~(yi ^ signbit) : yi;
return x <= y;
#else
using F [[gnu::vector_size(Bytes)]] = T;
using I [[gnu::vector_size(Bytes)]] = II;
constexpr int unused_bits = sizeof(T) <= 8 ? 0 :
(Bytes - 8) * CHAR_BIT - 1 -
__builtin_ctzll((reinterpret_cast<I>(F{T(-0.)}) >>
8 * CHAR_BIT)[0]);
const I xi = reinterpret_cast<I>(F{xx}) << unused_bits;
const I yi = reinterpret_cast<I>(F{yy}) << unused_bits;
constexpr I signbit = reinterpret_cast<I>(F{T(-0.)}) << unused_bits;
const auto x = xi[0] < 0 ? (~(xi ^ signbit))[0] : xi[0];
const auto y = yi[0] < 0 ? (~(yi ^ signbit))[0] : yi[0];
return x <= y;
#endif
}
template <typename T> struct Test
{
// numeric_limits<__float128> produces bogus values
static constexpr auto qnan = std::numeric_limits<double>::quiet_NaN();
static constexpr auto snan = std::numeric_limits<double>::signaling_NaN();
static constexpr auto inf = std::numeric_limits<double>::infinity();
static_assert( totalOrder<T>( 0.0, 0.0));
static_assert( totalOrder<T>( 1.0, 1.0));
static_assert( totalOrder<T>(-1.0, -1.0));
static_assert( totalOrder<T>(-0.0, -0.0));
static_assert( totalOrder<T>(qnan, qnan));
static_assert( totalOrder<T>(snan, snan));
static_assert( totalOrder<T>( inf, inf));
static_assert( totalOrder<T>(-0.0, 0.0));
static_assert( totalOrder<T>(-0.0, +1.0));
static_assert( totalOrder<T>(-qnan, +0.0));
static_assert( totalOrder<T>(-qnan, -inf));
static_assert( totalOrder<T>(-3., -2.));
static_assert( totalOrder<T>(2., 3.));
static_assert( totalOrder<T>(2., inf));
static_assert( totalOrder<T>(0., qnan));
static_assert( totalOrder<T>(0., 2.));
static_assert( totalOrder<T>(2., qnan));
static_assert( totalOrder<T>(inf, qnan));
static_assert( totalOrder<T>(snan, qnan));
static_assert(!totalOrder<T>(snan, -qnan));
static_assert(!totalOrder<T>(0.0, -0.0));
static_assert(!totalOrder<T>(0.0, -qnan));
static_assert(!totalOrder<T>(0.0, -1.0));
static_assert(!totalOrder<T>(1.0, -1.0));
static_assert(!totalOrder<T>(qnan, -inf));
};
Test<float> a;
Test<double> b;
Test<long double> c;
Test<__float128> d;
--
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Dr. Matthias Kretz https://mattkretz.github.io
GSI Helmholtz Centre for Heavy Ion Research https://gsi.de
std::experimental::simd https://github.com/VcDevel/std-simd
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