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float8.h
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/***************************************************************************************************
* Copyright (c) 2017 - 2023 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
* SPDX-License-Identifier: BSD-3-Clause
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* 3. Neither the name of the copyright holder nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
**************************************************************************************************/
/*!
\file
\brief Defines a class for using IEEE half-precision floating-point types in host or
device code.
*/
#pragma once
// FP8 types are available starting CUDA 11.8+
#if (__CUDACC_VER_MAJOR__ >= 12) || ((__CUDACC_VER_MAJOR__ == 11) && (__CUDACC_VER_MINOR__ >= 8))
#define CUDA_FP8_ENABLED 1
#endif
#if defined(__CUDA_ARCH__)
# if (__CUDA_ARCH__ >= 900)
# if (__CUDACC_VER_MAJOR__ >= 12) || ((__CUDACC_VER_MAJOR__ == 11) && (__CUDACC_VER_MINOR__ >= 8))
# define CUDA_PTX_FP8_CVT_ENABLED 1
# endif // (__CUDACC_VER_MAJOR__ >= 12) || ((__CUDACC_VER_MAJOR__ == 11) && (__CUDACC_VER_MINOR__ >= 8))
# endif // (__CUDA_ARCH__ >= 900)
#endif // defined(__CUDA_ARCH__)
#ifdef __GNUC__
// Ignore checks on reinterpret-casts that are being used for bitcasts.
#pragma GCC diagnostic ignored "-Wstrict-aliasing"
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////
#if defined(__CUDACC_RTC__)
#include "cutlass/floating_point_nvrtc.h"
#else
//
// Standard Library headers belong here to avoid conflicts with NVRTC.
//
#include <cmath>
#include <limits>
#include <cstdint>
#include <cstring>
#endif
#ifdef CUDA_FP8_ENABLED
#include <cuda_fp8.h>
#endif
#include <cuda_fp16.h>
#include "cutlass/cutlass.h"
///////////////////////////////////////////////////////////////////////////////////////////////////
namespace cutlass {
///////////////////////////////////////////////////////////////////////////////////////////////////
//
// FP8 Has 2 encodings possible : E4M3 and E5M2
//
// E4M3 : 7 | 6 5 4 3 | 2 1 0
// E5M2 : 7 | 6 5 4 3 2 | 1 0
//
///////////////////////////////////////////////////////////////////////////////////////////////////
enum class FloatEncoding {
E4M3,
E5M2
};
template<FloatEncoding T>
struct alignas(1) float8_base {
static constexpr bool IS_E4M3 = (T == FloatEncoding::E4M3);
static constexpr bool IS_E5M2 = (T == FloatEncoding::E5M2);
// Number of Bits representing mantissa and exponents
static constexpr int FP32_NUM_BITS = 32;
static constexpr int FP32_NUM_EXPONENT_BITS = 8;
static constexpr int FP32_NUM_MANTISSA_BITS = 23;
static constexpr uint32_t FP32_NAN = 0x7fffffff;
static constexpr uint32_t FP32_INFINITY_MASK = 0x7f800000;
static constexpr int FP32_MAX_EXPONENT = 127;
static constexpr int FP32_MIN_EXPONENT = -126;
static constexpr int FP32_EXPONENT_BIAS = 127;
static constexpr int FP16_NUM_BITS = 16;
static constexpr int FP16_NUM_EXPONENT_BITS = 5;
static constexpr int FP16_NUM_MANTISSA_BITS = 10;
static constexpr uint16_t FP16_NAN = 0x7fff;
static constexpr uint16_t FP16_INFINITY_MASK = 0x7c00;
static constexpr int FP16_MAX_EXPONENT = 15;
static constexpr int FP16_MIN_EXPONENT = -14;
static constexpr int FP16_EXPONENT_BIAS = 15;
static constexpr int FP8_NUM_BITS = 8;
static constexpr int FP8_NUM_EXPONENT_BITS = IS_E4M3 ? 4 : 5;
static constexpr int FP8_NUM_MANTISSA_BITS = IS_E4M3 ? 3 : 2;
static constexpr uint8_t FP8_NAN = 0x7f; // Also F8_INF
static constexpr uint8_t FP8_INFINITY_MASK = IS_E4M3 ? 0x78 : 0x7c;
static constexpr int FP8_MAX_EXPONENT = IS_E4M3 ? 7 : 15;
static constexpr int FP8_MIN_EXPONENT = IS_E4M3 ? -6 : -14;
static constexpr int FP8_EXPONENT_BIAS = IS_E4M3 ? 7 : 15;
static constexpr uint8_t FP8_EXPONENT_MASK = (1 << FP8_NUM_EXPONENT_BITS) - 1;
static constexpr uint8_t FP8_MANTISSA_MASK = (1 << FP8_NUM_MANTISSA_BITS) - 1;
static constexpr uint8_t FP8_MAX_FLT = (IS_E4M3 ? 0x7e : 0x7b);
// 256 in float
static constexpr uint32_t FP8_SAT_VAL_FP32 = 0x43800000;
//
// Data members
//
/// Data container
uint8_t storage;
/// Ctors.
CUTLASS_HOST_DEVICE
float8_base() : storage(0) { }
/// Is finite implementation
CUTLASS_HOST_DEVICE
static bool isfinite(float flt) {
uint32_t s;
#if defined(__CUDA_ARCH__)
s = reinterpret_cast<uint32_t const &>(flt);
#else
std::memcpy(&s, &flt, sizeof(s));
#endif
return (s & 0x7f800000) < 0x7f800000;
}
/// Is NaN implementation
CUTLASS_HOST_DEVICE
static bool isnan(float flt) {
uint32_t s;
#if defined(__CUDA_ARCH__)
s = reinterpret_cast<uint32_t const &>(flt);
#else
std::memcpy(&s, &flt, sizeof(s));
#endif
return (s & 0x7fffffff) > 0x7f800000;
}
/// Is infinite implementation
CUTLASS_HOST_DEVICE
static bool isinf(float flt) {
uint32_t s;
#if defined(__CUDA_ARCH__)
s = reinterpret_cast<uint32_t const &>(flt);
#else
std::memcpy(&s, &flt, sizeof(s));
#endif
// Sign = 0 for +inf, 1 for -inf
// Exponent = all ones
// Mantissa = all zeros
return (s == 0x7f800000) || (s == 0xff800000);
}
/// FP32 -> FP8 conversion - rounds to nearest even
CUTLASS_HOST_DEVICE
static uint8_t convert_float_to_fp8(float const& flt) {
// software implementation rounds toward nearest even
uint32_t s;
#if defined(__CUDA_ARCH__)
s = reinterpret_cast<uint32_t const &>(flt);
#else
std::memcpy(&s, &flt, sizeof(s));
#endif
// Extract the bits in the FP32 type
uint8_t sign = uint8_t((s >> 24 & 0x80));
int8_t exp = uint8_t(((s >> FP32_NUM_MANTISSA_BITS) & 0xff) - FP32_EXPONENT_BIAS);
int mantissa = s & 0x7fffff;
uint8_t u = 0;
uint8_t const kF8_NaN = 0x7f;
// NaN => NaN
if (isnan(flt)) {
return kF8_NaN;
}
// Inf => MAX_FLT (satfinite)
if (isinf(flt)) {
return sign | FP8_MAX_FLT;
}
// Special handling
if ( exp == -128 ) {
// int8 range is from -128 to 127
// So 255(inf) - 127(bias) = 128 - will show up as -128
// satfinite
return (sign | FP8_MAX_FLT);
}
int sticky_bit = 0;
bool skip_sign = false;
bool may_be_nan = false;
if ( (exp >= FP8_MIN_EXPONENT) && (exp <= FP8_MAX_EXPONENT) ) {
// normal fp32 to normal fp8
exp = uint8_t(exp + uint8_t(FP8_EXPONENT_BIAS));
u = uint8_t(((exp & FP8_EXPONENT_MASK) << FP8_NUM_MANTISSA_BITS));
u = uint8_t(u | (mantissa >> (FP32_NUM_MANTISSA_BITS - FP8_NUM_MANTISSA_BITS)));
} else if(exp < FP8_MIN_EXPONENT) {
// normal single-precision to subnormal float8-precision representation
int rshift = (FP8_MIN_EXPONENT - exp);
if (rshift < FP32_NUM_BITS) {
mantissa |= (1 << FP32_NUM_MANTISSA_BITS);
sticky_bit = ((mantissa & ((1 << rshift) - 1)) != 0);
mantissa = (mantissa >> rshift);
u = (uint8_t(mantissa >> (FP32_NUM_MANTISSA_BITS- FP8_NUM_MANTISSA_BITS)) & FP8_MANTISSA_MASK);
} else {
mantissa = 0;
u = 0;
}
// Exponent > FP8_MAX_EXPONENT - this is a special case done to match HW
// 0x4380_0000 to 0x43e0_0000 - maps from 256 to 448, and does not saturate / inf.
} else {
if( exp == (FP8_MAX_EXPONENT + 1) ) {
uint8_t mantissa_tmp = uint8_t(mantissa >> (FP32_NUM_MANTISSA_BITS - FP8_NUM_MANTISSA_BITS));
if( mantissa_tmp < FP8_MANTISSA_MASK) {
exp = uint8_t(exp + uint8_t(FP8_EXPONENT_BIAS));
u = uint8_t(exp << FP8_NUM_MANTISSA_BITS) | mantissa_tmp;
may_be_nan = (mantissa_tmp == (FP8_MANTISSA_MASK-1));
} else {
// satfinite
return (sign | FP8_MAX_FLT);
}
} else{
// satfinite
return (sign | FP8_MAX_FLT);
}
}
// round to nearest even
int NUM_BITS_SHIFT = FP32_NUM_MANTISSA_BITS - (FP8_NUM_MANTISSA_BITS + 1);
int round_bit = ((mantissa >> NUM_BITS_SHIFT) & 1);
sticky_bit |= ((mantissa & ((1 << NUM_BITS_SHIFT) - 1)) != 0);
if ((round_bit && sticky_bit) || (round_bit && (u & 1))) {
u = uint8_t(u + 1);
if( may_be_nan ) {
skip_sign = true;
}
}
if (u > FP8_MAX_FLT) {
// satfinite
u = (sign | FP8_MAX_FLT);
}
if( ! skip_sign ) {
u |= sign;
}
return u;
}
/// Converts a fp8 value stored as a uint8_t to a float
CUTLASS_HOST_DEVICE
static float convert_fp8_to_float(uint8_t const& x) {
uint32_t constexpr kF32_NaN = 0x7fffffff;
uint8_t const &f8 = x;
int sign = (f8 >> (FP8_NUM_BITS - 1)) & 1;
int exp = (f8 >> FP8_NUM_MANTISSA_BITS) & FP8_EXPONENT_MASK;
int mantissa = f8 & FP8_MANTISSA_MASK;
unsigned f = (sign << (FP32_NUM_BITS-1));
if (IS_E4M3 && exp == 15 && mantissa == 0x7) {
f = kF32_NaN;
}
else if (exp > 0 && (IS_E4M3 || exp < (FP8_MAX_EXPONENT + FP8_EXPONENT_BIAS + 1))) {
// normal
exp += (FP32_EXPONENT_BIAS - FP8_EXPONENT_BIAS);
f = f |
(exp << FP32_NUM_MANTISSA_BITS) |
(mantissa << (FP32_NUM_MANTISSA_BITS-FP8_NUM_MANTISSA_BITS));
} else if (exp == 0) {
if (mantissa) {
// subnormal
exp += (FP32_EXPONENT_BIAS - FP8_EXPONENT_BIAS) + 1;
while ((mantissa & (1 << FP8_NUM_MANTISSA_BITS)) == 0) {
mantissa <<= 1;
exp--;
}
mantissa &= FP8_MANTISSA_MASK;
f = f |
(exp << FP32_NUM_MANTISSA_BITS) |
(mantissa << (FP32_NUM_MANTISSA_BITS-FP8_NUM_MANTISSA_BITS));
} else {
// sign-preserving zero
}
} else {
if(mantissa == 0){
// Sign-preserving infinity
f = (f | 0x7f800000);
} else {
// Canonical NaN
f = kF32_NaN;
}
}
#if defined(__CUDA_ARCH__)
return reinterpret_cast<float const&>(f);
#else
float flt;
std::memcpy(&flt, &f, sizeof(flt));
return flt;
#endif
}
};
// Forward declaration of float_e5m2_t to define float_e4m3_t <=> float_e5m2_t
// conversions in class float_e4m3_t
struct float_e5m2_t;
///////////////////////////////////////////////////////////////
///
/// floating-point 8 type : E4M3
///
///////////////////////////////////////////////////////////////
struct alignas(1) float_e4m3_t : float8_base<FloatEncoding::E4M3> {
using Base = float8_base<FloatEncoding::E4M3>;
static constexpr int MAX_EXPONENT = Base::FP8_MAX_EXPONENT;
//
// Static conversion operators
//
/// Constructs from an uint8_t
CUTLASS_HOST_DEVICE
static float_e4m3_t bitcast(uint8_t x) {
float_e4m3_t f;
f.storage = x;
return f;
}
/// FP32 -> FP8 conversion - rounds to nearest even
CUTLASS_HOST_DEVICE
static float_e4m3_t from_float(float const& flt) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t tmp;
float y = float();
asm volatile("cvt.rn.satfinite.e4m3x2.f32 %0, %1, %2;" : "=h"(tmp) : "f"(y), "f"(flt));
return *reinterpret_cast<float_e4m3_t *>(&tmp);
#else
return bitcast(Base::convert_float_to_fp8(flt));
#endif
}
/// FP16 -> E5M2 conversion - rounds to nearest even
CUTLASS_HOST_DEVICE
static float_e4m3_t from_half(half const& flt) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t tmp = 0;
uint32_t bits = reinterpret_cast<uint16_t const &>(flt);
asm volatile("cvt.rn.satfinite.e4m3x2.f16x2 %0, %1;" : "=h"(tmp) : "r"(bits));
return *reinterpret_cast<float_e4m3_t *>(&tmp);
#else
return bitcast(Base::convert_float_to_fp8(__half2float(flt)));
#endif
}
// E4M3 -> half
CUTLASS_HOST_DEVICE
static half to_half(float_e4m3_t const& x) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t bits = x.storage;
uint32_t packed;
asm volatile("cvt.rn.f16x2.e4m3x2 %0, %1;\n" : "=r"(packed) : "h"(bits));
return reinterpret_cast<half2 const &>(packed).x;
#else
return __float2half(Base::convert_fp8_to_float(x.storage));
#endif
}
// E4M3 -> Float
CUTLASS_HOST_DEVICE
static float to_float(float_e4m3_t const& x) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t bits = x.storage;
uint32_t packed;
asm volatile("cvt.rn.f16x2.e4m3x2 %0, %1;\n" : "=r"(packed) : "h"(bits));
return __half2float(reinterpret_cast<half2 const &>(packed).x);
#else
return Base::convert_fp8_to_float(x.storage);
#endif
}
//
// Methods
//
/// Constructor inheritance
using Base::Base;
#ifdef CUDA_FP8_ENABLED
/// Conversion from CUDA's FP8 type
CUTLASS_HOST_DEVICE
explicit float_e4m3_t(__nv_fp8_e4m3 x) {
storage = x.__x;
}
#endif
/// Floating point conversion
CUTLASS_HOST_DEVICE
explicit float_e4m3_t(float x) {
storage = from_float(x).storage;
}
CUTLASS_HOST_DEVICE
explicit float_e4m3_t(half x) {
storage = from_half(x).storage;
}
/// Floating point conversion
CUTLASS_HOST_DEVICE
explicit float_e4m3_t(double x): float_e4m3_t(float(x)) {
}
/// Integer conversion
CUTLASS_HOST_DEVICE
explicit float_e4m3_t(int x): float_e4m3_t(float(x)) {
}
/// E5M2 conversion. Defined after float_e5m2_t is defined.
CUTLASS_HOST_DEVICE
explicit float_e4m3_t(float_e5m2_t x);
#ifdef CUDA_FP8_ENABLED
/// Assignment from CUDA's FP8 type
CUTLASS_HOST_DEVICE
float_e4m3_t & operator=(__nv_fp8_e4m3 x) {
storage = x.__x;
return *this;
}
#endif
/// Converts to float
CUTLASS_HOST_DEVICE
operator float() const {
return to_float(*this);
}
/// Converts to half
CUTLASS_HOST_DEVICE
operator half() const {
return to_half(*this);
}
/// Converts to float
CUTLASS_HOST_DEVICE
explicit operator double() const {
return double(to_float(*this));
}
/// Converts to int
CUTLASS_HOST_DEVICE
explicit operator int() const {
#if defined(__CUDA_ARCH__)
return __half2int_rn(to_half(*this));
#else
return int(to_float(*this));
#endif
}
/// Casts to bool
CUTLASS_HOST_DEVICE
explicit operator bool() const {
#if defined(__CUDA_ARCH__)
return bool(__half2int_rn(to_half(*this)));
#else
return bool(int(to_float(*this)));
#endif
}
/// Accesses raw internal state
CUTLASS_HOST_DEVICE
uint8_t& raw() {
return storage;
}
/// Accesses raw internal state
CUTLASS_HOST_DEVICE
uint8_t raw() const {
return storage;
}
/// Returns the sign bit
CUTLASS_HOST_DEVICE
bool signbit() const {
return ((storage & (1 << (Base::FP8_NUM_BITS - 1))) != 0);
}
/// Returns the biased exponent
CUTLASS_HOST_DEVICE
int exponent_biased() const {
return int((storage >> FP8_NUM_MANTISSA_BITS) & Base::FP8_EXPONENT_MASK);
}
/// Returns the unbiased exponent
CUTLASS_HOST_DEVICE
int exponent() const {
return exponent_biased() - 15;
}
/// Returns the mantissa
CUTLASS_HOST_DEVICE
int mantissa() const {
return int(storage & Base::FP8_MANTISSA_MASK);
}
};
///////////////////////////////////////////////////////////////
///
/// floating-point 8 type : E5M2
///
///////////////////////////////////////////////////////////////
struct alignas(1) float_e5m2_t : float8_base<FloatEncoding::E5M2> {
using Base = float8_base<FloatEncoding::E5M2>;
static constexpr int MAX_EXPONENT = Base::FP8_MAX_EXPONENT;
//
// Static conversion operators
//
/// Constructs from an uint8_t
CUTLASS_HOST_DEVICE
static float_e5m2_t bitcast(uint8_t x) {
float_e5m2_t f;
f.storage = x;
return f;
}
/// FP32 -> FP8 conversion - rounds to nearest even
CUTLASS_HOST_DEVICE
static float_e5m2_t from_float(float const& flt) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t tmp;
float y = float();
asm volatile("cvt.rn.satfinite.e5m2x2.f32 %0, %1, %2;" : "=h"(tmp) : "f"(y), "f"(flt));
return *reinterpret_cast<float_e5m2_t *>(&tmp);
#else
return bitcast(Base::convert_float_to_fp8(flt));
#endif
}
/// FP16 -> E5M2 conversion - rounds to nearest even
CUTLASS_HOST_DEVICE
static float_e5m2_t from_half(half const& flt) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t tmp = 0;
uint32_t bits = reinterpret_cast<uint16_t const &>(flt);
asm volatile("cvt.rn.satfinite.e5m2x2.f16x2 %0, %1;" : "=h"(tmp) : "r"(bits));
return *reinterpret_cast<float_e5m2_t *>(&tmp);
#else
return bitcast(Base::convert_float_to_fp8(__half2float(flt)));
#endif
}
// E5M2 -> half
CUTLASS_HOST_DEVICE
static half to_half(float_e5m2_t const& x) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t bits = x.storage;
uint32_t packed;
asm volatile("cvt.rn.f16x2.e5m2x2 %0, %1;\n" : "=r"(packed) : "h"(bits));
return reinterpret_cast<half2 const &>(packed).x;
#else
return __float2half(Base::convert_fp8_to_float(x.storage));
#endif
}
// E5M2 -> Float
CUTLASS_HOST_DEVICE
static float to_float(float_e5m2_t const& x) {
#if defined(CUDA_PTX_FP8_CVT_ENABLED)
uint16_t bits = x.storage;
uint32_t packed;
asm volatile("cvt.rn.f16x2.e5m2x2 %0, %1;\n" : "=r"(packed) : "h"(bits));
return __half2float(reinterpret_cast<half2 const &>(packed).x);
#else
return Base::convert_fp8_to_float(x.storage);
#endif
}
//
// Methods
//
/// Constructor inheritance
using Base::Base;
#ifdef CUDA_FP8_ENABLED
/// Conversion from CUDA's FP8 type
CUTLASS_HOST_DEVICE
explicit float_e5m2_t(__nv_fp8_e5m2 x) {
storage = x.__x;
}
#endif
/// Floating point conversion
CUTLASS_HOST_DEVICE
explicit float_e5m2_t(float x) {
storage = from_float(x).storage;
}
CUTLASS_HOST_DEVICE
explicit float_e5m2_t(half x) {
storage = from_half(x).storage;
}
/// Floating point conversion
CUTLASS_HOST_DEVICE
explicit float_e5m2_t(double x): float_e5m2_t(float(x)) {
}
/// Integer conversion
CUTLASS_HOST_DEVICE
explicit float_e5m2_t(int x): float_e5m2_t(float(x)) {
}
/// E4M3 conversion
CUTLASS_HOST_DEVICE
explicit float_e5m2_t(float_e4m3_t x);
#ifdef CUDA_FP8_ENABLED
/// Assignment from CUDA's FP8 type
CUTLASS_HOST_DEVICE
float_e5m2_t & operator=(__nv_fp8_e5m2 x) {
storage = x.__x;
return *this;
}
#endif
/// Converts to float
CUTLASS_HOST_DEVICE
operator float() const {
return to_float(*this);
}
/// Converts to half
CUTLASS_HOST_DEVICE
operator half() const {
return to_half(*this);
}
/// Converts to float
CUTLASS_HOST_DEVICE
explicit operator double() const {
return double(to_float(*this));
}
/// Converts to int
CUTLASS_HOST_DEVICE
explicit operator int() const {
#if defined(__CUDA_ARCH__)
return __half2int_rn(to_half(*this));
#else
return int(to_float(*this));
#endif
}
/// Casts to bool
CUTLASS_HOST_DEVICE
explicit operator bool() const {
#if defined(__CUDA_ARCH__)
return bool(__half2int_rn(to_half(*this)));
#else
return bool(int(to_float(*this)));
#endif
}
/// Accesses raw internal state
CUTLASS_HOST_DEVICE
uint8_t& raw() {
return storage;
}
/// Accesses raw internal state
CUTLASS_HOST_DEVICE
uint8_t raw() const {
return storage;
}
/// Returns the sign bit
CUTLASS_HOST_DEVICE
bool signbit() const {
return ((storage & (1 << (Base::FP8_NUM_BITS - 1))) != 0);
}
/// Returns the biased exponent
CUTLASS_HOST_DEVICE
int exponent_biased() const {
return int((storage >> FP8_NUM_MANTISSA_BITS) & Base::FP8_EXPONENT_MASK);
}
/// Returns the unbiased exponent
CUTLASS_HOST_DEVICE
int exponent() const {
return exponent_biased() - 15;
}
/// Returns the mantissa
CUTLASS_HOST_DEVICE
int mantissa() const {
return int(storage & Base::FP8_MANTISSA_MASK);
}
};
///////////////////////////////////////////////////////////////////////////////////////////////////
//
// Arithmetic operators
//
///////////////////////////////////////////////////////////////////////////////////////////////////
CUTLASS_HOST_DEVICE
bool operator==(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float(lhs) == float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator!=(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float(lhs) != float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator<(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float(lhs) < float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator<=(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float(lhs) <= float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator>(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float(lhs) > float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator>=(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float(lhs) >= float(rhs);
}
CUTLASS_HOST_DEVICE
float_e4m3_t operator+(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float_e4m3_t(float(lhs) + float(rhs));
}
CUTLASS_HOST_DEVICE
float_e4m3_t operator-(float_e4m3_t const& lhs) {
return float_e4m3_t(-float(lhs));
}
CUTLASS_HOST_DEVICE
float_e4m3_t operator-(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float_e4m3_t(float(lhs) - float(rhs));
}
CUTLASS_HOST_DEVICE
float_e4m3_t operator*(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float_e4m3_t(float(lhs) * float(rhs));
}
CUTLASS_HOST_DEVICE
float_e4m3_t operator/(float_e4m3_t const& lhs, float_e4m3_t const& rhs) {
return float_e4m3_t(float(lhs) / float(rhs));
}
CUTLASS_HOST_DEVICE
float_e4m3_t& operator+=(float_e4m3_t & lhs, float_e4m3_t const& rhs) {
lhs = float_e4m3_t(float(lhs) + float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e4m3_t& operator-=(float_e4m3_t & lhs, float_e4m3_t const& rhs) {
lhs = float_e4m3_t(float(lhs) - float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e4m3_t& operator*=(float_e4m3_t & lhs, float_e4m3_t const& rhs) {
lhs = float_e4m3_t(float(lhs) * float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e4m3_t& operator/=(float_e4m3_t & lhs, float_e4m3_t const& rhs) {
lhs = float_e4m3_t(float(lhs) / float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e4m3_t& operator++(float_e4m3_t & lhs) {
float tmp(lhs);
++tmp;
lhs = float_e4m3_t(tmp);
return lhs;
}
CUTLASS_HOST_DEVICE
float_e4m3_t& operator--(float_e4m3_t & lhs) {
float tmp(lhs);
--tmp;
lhs = float_e4m3_t(tmp);
return lhs;
}
CUTLASS_HOST_DEVICE
float_e4m3_t operator++(float_e4m3_t & lhs, int) {
float_e4m3_t ret(lhs);
float tmp(lhs);
tmp++;
lhs = float_e4m3_t(tmp);
return ret;
}
CUTLASS_HOST_DEVICE
float_e4m3_t operator--(float_e4m3_t & lhs, int) {
float_e4m3_t ret(lhs);
float tmp(lhs);
tmp--;
lhs = float_e4m3_t(tmp);
return ret;
}
CUTLASS_HOST_DEVICE
bool operator==(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float(lhs) == float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator!=(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float(lhs) != float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator<(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float(lhs) < float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator<=(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float(lhs) <= float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator>(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float(lhs) > float(rhs);
}
CUTLASS_HOST_DEVICE
bool operator>=(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float(lhs) >= float(rhs);
}
CUTLASS_HOST_DEVICE
float_e5m2_t operator+(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float_e5m2_t(float(lhs) + float(rhs));
}
CUTLASS_HOST_DEVICE
float_e5m2_t operator-(float_e5m2_t const& lhs) {
return float_e5m2_t(-float(lhs));
}
CUTLASS_HOST_DEVICE
float_e5m2_t operator-(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float_e5m2_t(float(lhs) - float(rhs));
}
CUTLASS_HOST_DEVICE
float_e5m2_t operator*(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float_e5m2_t(float(lhs) * float(rhs));
}
CUTLASS_HOST_DEVICE
float_e5m2_t operator/(float_e5m2_t const& lhs, float_e5m2_t const& rhs) {
return float_e5m2_t(float(lhs) / float(rhs));
}
CUTLASS_HOST_DEVICE
float_e5m2_t& operator+=(float_e5m2_t & lhs, float_e5m2_t const& rhs) {
lhs = float_e5m2_t(float(lhs) + float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e5m2_t& operator-=(float_e5m2_t & lhs, float_e5m2_t const& rhs) {
lhs = float_e5m2_t(float(lhs) - float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e5m2_t& operator*=(float_e5m2_t & lhs, float_e5m2_t const& rhs) {
lhs = float_e5m2_t(float(lhs) * float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e5m2_t& operator/=(float_e5m2_t & lhs, float_e5m2_t const& rhs) {
lhs = float_e5m2_t(float(lhs) / float(rhs));
return lhs;
}
CUTLASS_HOST_DEVICE
float_e5m2_t& operator++(float_e5m2_t & lhs) {
float tmp(lhs);
++tmp;
lhs = float_e5m2_t(tmp);
return lhs;
}
CUTLASS_HOST_DEVICE
float_e5m2_t& operator--(float_e5m2_t & lhs) {
float tmp(lhs);
--tmp;
lhs = float_e5m2_t(tmp);
return lhs;
}
CUTLASS_HOST_DEVICE
float_e5m2_t operator++(float_e5m2_t & lhs, int) {
float_e5m2_t ret(lhs);
float tmp(lhs);
tmp++;
lhs = float_e5m2_t(tmp);
return ret;
}
CUTLASS_HOST_DEVICE
float_e5m2_t operator--(float_e5m2_t & lhs, int) {
float_e5m2_t ret(lhs);
float tmp(lhs);
tmp--;
lhs = float_e5m2_t(tmp);
return ret;
}