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#ifndef NUMPY_CORE_SRC_COMMON_HALF_HPP
#define NUMPY_CORE_SRC_COMMON_HALF_HPP
#include "npstd.hpp"
#include "npy_cpu_dispatch.h" // NPY_HAVE_CPU_FEATURES
#include "half_private.hpp"
// TODO(@seiko2plus):
// - covers half-precision operations that being supported by numpy/halffloat.h
// - add support for arithmetic operations
// - enables __fp16 causes massive FP exceptions on aarch64,
// needs a deep investigation
namespace np {
/// @addtogroup cpp_core_types
/// @{
/// Provides a type that implements 16-bit floating point (half-precision).
/// This type is ensured to be 16-bit size.
#if 1 // ndef __ARM_FP16_FORMAT_IEEE
class Half final {
public:
/// Whether `Half` has a full native HW support.
static constexpr bool kNative = false;
/// Whether `Half` has a native HW support for single/double conversion.
template<typename T>
static constexpr bool kNativeConversion = (
(
std::is_same_v<T, float> &&
#if defined(NPY_HAVE_FP16) || defined(NPY_HAVE_VSX3)
true
#else
false
#endif
) || (
std::is_same_v<T, double> &&
#if defined(NPY_HAVE_AVX512FP16) || defined(NPY_HAVE_VSX3)
true
#else
false
#endif
)
);
/// Default constructor. initialize nothing.
Half() = default;
/// Constract from float
/// If there are no hardware optimization available, rounding will always
/// be set to ties to even.
explicit Half(float f)
{
#if defined(NPY_HAVE_FP16)
__m128 mf = _mm_load_ss(&f);
bits_ = static_cast<uint16_t>(_mm_cvtsi128_si32(_mm_cvtps_ph(mf, _MM_FROUND_TO_NEAREST_INT)));
#elif defined(NPY_HAVE_VSX3) && defined(NPY_HAVE_VSX_ASM)
__vector float vf32 = vec_splats(f);
__vector unsigned short vf16;
__asm__ __volatile__ ("xvcvsphp %x0,%x1" : "=wa" (vf16) : "wa" (vf32));
bits_ = vec_extract(vf16, 0);
#else
bits_ = half_private::FromFloatBits(BitCast<uint32_t>(f));
#endif
}
/// Construct from double.
/// If there are no hardware optimization available, rounding will always
/// be set to ties to even.
explicit Half(double f)
{
#if defined(NPY_HAVE_AVX512FP16)
__m128d md = _mm_load_sd(&f);
bits_ = static_cast<uint16_t>(_mm_cvtsi128_si32(_mm_castph_si128(_mm_cvtpd_ph(md))));
#elif defined(NPY_HAVE_VSX3) && defined(NPY_HAVE_VSX_ASM)
__vector double vf64 = vec_splats(f);
__vector unsigned short vf16;
__asm__ __volatile__ ("xvcvdphp %x0,%x1" : "=wa" (vf16) : "wa" (vf64));
bits_ = vec_extract(vf16, 0);
#else
bits_ = half_private::FromDoubleBits(BitCast<uint64_t>(f));
#endif
}
/// Cast to float
explicit operator float() const
{
#if defined(NPY_HAVE_FP16)
float ret;
_mm_store_ss(&ret, _mm_cvtph_ps(_mm_cvtsi32_si128(bits_)));
return ret;
#elif defined(NPY_HAVE_VSX3) && defined(vec_extract_fp_from_shorth)
return vec_extract(vec_extract_fp_from_shorth(vec_splats(bits_)), 0);
#elif defined(NPY_HAVE_VSX3) && defined(NPY_HAVE_VSX_ASM)
__vector float vf32;
__asm__ __volatile__("xvcvhpsp %x0,%x1"
: "=wa"(vf32)
: "wa"(vec_splats(bits_.u)));
return vec_extract(vf32, 0);
#else
return BitCast<float>(half_private::ToFloatBits(bits_));
#endif
}
/// Cast to double
explicit operator double() const
{
#if defined(NPY_HAVE_AVX512FP16)
double ret;
_mm_store_sd(&ret, _mm_cvtph_pd(_mm_castsi128_ph(_mm_cvtsi32_si128(bits_))));
return ret;
#elif defined(NPY_HAVE_VSX3) && defined(NPY_HAVE_VSX_ASM)
__vector float vf64;
__asm__ __volatile__("xvcvhpdp %x0,%x1"
: "=wa"(vf32)
: "wa"(vec_splats(bits_)));
return vec_extract(vf64, 0);
#else
return BitCast<double>(half_private::ToDoubleBits(bits_));
#endif
}
/// Returns a new Half constracted from the IEEE 754 binary16.
static constexpr Half FromBits(uint16_t bits)
{
Half h{};
h.bits_ = bits;
return h;
}
/// Returns the IEEE 754 binary16 representation.
constexpr uint16_t Bits() const
{
return bits_;
}
/// @name Comparison operators (orderd)
/// @{
constexpr bool operator==(Half r) const
{
return !(IsNaN() || r.IsNaN()) && Equal(r);
}
constexpr bool operator<(Half r) const
{
return !(IsNaN() || r.IsNaN()) && Less(r);
}
constexpr bool operator<=(Half r) const
{
return !(IsNaN() || r.IsNaN()) && LessEqual(r);
}
constexpr bool operator>(Half r) const
{
return r < *this;
}
constexpr bool operator>=(Half r) const
{
return r <= *this;
}
/// @}
/// @name Comparison operators (unorderd)
/// @{
constexpr bool operator!=(Half r) const
{
return !(*this == r);
}
/// @} Comparison operators
/// @name Comparison with no guarantee of NaN behavior
/// @{
constexpr bool Less(Half r) const
{
uint_fast16_t a = static_cast<uint_fast16_t>(bits_),
b = static_cast<uint_fast16_t>(r.bits_);
bool sign_a = (a & 0x8000u) == 0x8000u;
bool sign_b = (b & 0x8000u) == 0x8000u;
// if both `a` and `b` have same sign
// Test if `a` > `b` when `a` has the sign
// or `a` < `b` when is not.
// And make sure they are not equal to each other
// in case of both are equal to +-0
// else
// Test if `a` has the sign.
// and `a` != -0.0 and `b` != 0.0
return (sign_a == sign_b) ? (sign_a ^ (a < b)) && (a != b)
: sign_a && ((a | b) != 0x8000u);
}
constexpr bool LessEqual(Half r) const
{
uint_fast16_t a = static_cast<uint_fast16_t>(bits_),
b = static_cast<uint_fast16_t>(r.bits_);
bool sign_a = (a & 0x8000u) == 0x8000u;
bool sign_b = (b & 0x8000u) == 0x8000u;
// if both `a` and `b` have same sign
// Test if `a` > `b` when `a` has the sign
// or `a` < `b` when is not.
// or a == b (needed even if we used <= above instead
// since testing +-0 still required)
// else
// Test if `a` has the sign
// or `a` and `b` equal to +-0.0
return (sign_a == sign_b) ? (sign_a ^ (a < b)) || (a == b)
: sign_a || ((a | b) == 0x8000u);
}
constexpr bool Equal(Half r) const
{
// fast16 cast is not worth it, since unpack op should involved.
uint16_t a = bits_, b = r.bits_;
return a == b || ((a | b) == 0x8000u);
}
/// @} Comparison
/// @name Properties
// @{
constexpr bool IsNaN() const
{
return ((bits_ & 0x7c00u) == 0x7c00u) &&
((bits_ & 0x03ffu) != 0);
}
/// @} Properties
private:
uint16_t bits_;
};
#else // __ARM_FP16_FORMAT_IEEE
class Half final {
public:
static constexpr bool kNative = true;
template<typename T>
static constexpr bool kNativeConversion = (
std::is_same_v<T, float> || std::is_same_v<T, double>
);
Half() = default;
constexpr Half(__fp16 h) : half_(h)
{}
constexpr operator __fp16() const
{ return half_; }
static Half FromBits(uint16_t bits)
{
Half h;
h.half_ = BitCast<__fp16>(bits);
return h;
}
uint16_t Bits() const
{ return BitCast<uint16_t>(half_); }
constexpr bool Less(Half r) const
{ return half_ < r.half_; }
constexpr bool LessEqual(Half r) const
{ return half_ <= r.half_; }
constexpr bool Equal(Half r) const
{ return half_ == r.half_; }
constexpr bool IsNaN() const
{ return half_ != half_; }
private:
__fp16 half_;
};
#endif // __ARM_FP16_FORMAT_IEEE
/// @} cpp_core_types
} // namespace np
#endif // NUMPY_CORE_SRC_COMMON_HALF_HPP
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