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exmy_base.h
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/***************************************************************************************************
* Copyright (c) 2023 - 2025 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 Generic floating-point type for ExMy format
*/
#pragma once
#include "cutlass/cutlass.h"
#include "cutlass/numeric_size.h"
#include "cutlass/platform/platform.h"
// #define CUTLASS_DEBUG_TRACE_LEVEL 2
///////////////////////////////////////////////////////////////////////////////////////////////////
namespace cutlass {
// Helper functions
namespace detail {
template <class Src, class Dst>
CUTLASS_HOST_DEVICE
Dst copy_bits(Src src)
{
Dst dst;
static_assert(sizeof(Src) <= sizeof(Dst), "Dst type should be at least the same size as Src type");
static_assert(cutlass::platform::is_trivially_copyable<Dst>::value, "Dst type should be trivially copyable");
static_assert(cutlass::platform::is_trivially_copyable<
/*cutlass::platform::remove_cvref_t< */ Dst /* > */ >::value, "Dst type should be trivially copyable");
memcpy(&dst, &src, sizeof(src));
return dst;
}
enum class NanInfEncoding
{
// IEEE-754 style NaN. Exponent bits are
// all ones, and at least one bit of mantissa is one
IEEE_754,
// Canonical NaN. There is only one value representing NaN and
// no Inf is defined.
CANONICAL_ONLY,
// No NaN or Inf encoded.
NONE
};
enum class FpEncoding
{
E11M52, // double
E8M23, // float
E5M2, // FP8
E4M3, // FP8
UE4M3, // FP8
UE8M0, // FP8
E3M2, // FP6
E2M3, // FP6
E2M1, // FP4
};
//////
#if (CUTLASS_CXX17_OR_LATER)
template<uint32_t NumExpBits, uint32_t NumMantissaBits>
constexpr int exponent_bias_cxx17() {
if CUTLASS_CONSTEXPR_IF_CXX17 (NumExpBits == 0) {
static_assert(NumMantissaBits <= static_cast<uint32_t>(cutlass::platform::numeric_limits<int32_t>::max()));
return -1 * static_cast<int>(NumMantissaBits);
}
else {
return static_cast<int>((1 << (NumExpBits - 1))) - 1;
}
CUTLASS_GCC_UNREACHABLE;
}
#endif
namespace impl {
template<uint32_t NumExpBitsMinusOne>
constexpr int shift_num_bits_expression_cxx11() {
#if (CUTLASS_CXX17_OR_LATER)
static_assert(NumExpBitsMinusOne <= 31u);
#endif
return NumExpBitsMinusOne > 31u ? 31u : NumExpBitsMinusOne;
}
template<uint32_t NumExpBitsMinusOne>
constexpr int inner_shift_expression_cxx11() {
return static_cast<int>((1u << shift_num_bits_expression_cxx11<NumExpBitsMinusOne>()) - 1u);
}
} // namespace impl
// C++11 equivalent of exponent_bias_cxx17()
template<uint32_t NumExpBits, uint32_t NumMantissaBits>
constexpr int exponent_bias_cxx11() {
#if (CUTLASS_CXX17_OR_LATER)
return exponent_bias_cxx17<NumExpBits, NumMantissaBits>();
#else
return (NumExpBits == 0) ?
-1 * static_cast<int>(NumMantissaBits) : impl::inner_shift_expression_cxx11<NumExpBits - 1u>();
#endif
}
// C++11 equivalent of maximum_exponent_cxx17()
template<uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr int maximum_exponent_cxx11() {
return
((NumExpBits == 0) ?
(0 - exponent_bias_cxx11<NumExpBits, NumMantissaBits>()) :
((NaNEncoding == NanInfEncoding::IEEE_754) ?
((static_cast<int>((1 << NumExpBits)) - 2) - exponent_bias_cxx11<NumExpBits, NumMantissaBits>()) :
((NaNEncoding == NanInfEncoding::CANONICAL_ONLY) ?
((NumMantissaBits > 0) ?
static_cast<int>((1 << NumExpBits)) - 1 - exponent_bias_cxx11<NumExpBits, NumMantissaBits>() :
static_cast<int>((1 << NumExpBits)) - 2 - exponent_bias_cxx11<NumExpBits, NumMantissaBits>()
) :
(static_cast<int>((1 << NumExpBits)) - 1 - exponent_bias_cxx11<NumExpBits, NumMantissaBits>())
)
)
);
}
#if (CUTLASS_CXX17_OR_LATER)
template<uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr int maximum_exponent_cxx17() {
constexpr int exp_bias = exponent_bias_cxx17<NumExpBits, NumMantissaBits>();
if CUTLASS_CONSTEXPR_IF_CXX17 (NumExpBits == 0) {
// If no exponent bits, return fixed hidden bias
return 0 - exp_bias;
}
else {
if CUTLASS_CONSTEXPR_IF_CXX17 (NaNEncoding == NanInfEncoding::IEEE_754) {
// We have IEEE style NaN and infinity
// All values when exp_bits = 1...1s are used.
int max_exp_bits = static_cast<int>((1 << NumExpBits)) - 2;
return max_exp_bits - exp_bias;
}
else {
// There are no cases where we have Inf without IEEE_754_Nan
// If we have a canonical NaN. Only exp=1..1 and mantissa=1..1
// value has a special meaning. If we also have at least one mantissa
// bit, then maximum exponent is 1...1 - exponent_bias
if CUTLASS_CONSTEXPR_IF_CXX17 (NaNEncoding == NanInfEncoding::CANONICAL_ONLY) {
if CUTLASS_CONSTEXPR_IF_CXX17 (NumMantissaBits > 0) {
int max_exp_bits = static_cast<int>((1 << NumExpBits)) - 1;
return max_exp_bits - exp_bias;
}
else { // no mantissa bits
int max_exp_bits = static_cast<int>((1 << NumExpBits)) - 2;
return max_exp_bits - exp_bias;
}
}
// No NaNs or infs
int max_exp_bits = static_cast<int>((1 << NumExpBits)) - 1;
return max_exp_bits - exp_bias;
}
}
CUTLASS_GCC_UNREACHABLE;
}
#endif
template<uint32_t NumExpBits, uint32_t NumMantissaBits>
constexpr int minimum_exponent_cxx11() {
return
((NumExpBits == 0) ?
0 - exponent_bias_cxx11<NumExpBits, NumMantissaBits>() :
((NumMantissaBits > 0) ?
1 - exponent_bias_cxx11<NumExpBits, NumMantissaBits>() :
0 - exponent_bias_cxx11<NumExpBits, NumMantissaBits>())
);
}
#if (CUTLASS_CXX17_OR_LATER)
template<uint32_t NumExpBits, uint32_t NumMantissaBits>
constexpr int minimum_exponent_cxx17() {
constexpr int exp_bias = exponent_bias_cxx17<NumExpBits, NumMantissaBits>();
constexpr bool has_denorm = (NumMantissaBits > 0);
if CUTLASS_CONSTEXPR_IF_CXX17 (NumExpBits == 0) {
// If no exponent bits, return fixed hidden bias
// Note that minimum and maximum exponents are the same.
return 0 - exp_bias;
}
if CUTLASS_CONSTEXPR_IF_CXX17 (has_denorm) {
// Exp = 0...0s is reserved for denorm values.
return 1 - exp_bias;
}
return 0 - exp_bias;
}
#endif
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage max_pos_denormal_value_cxx11() {
static_assert(NumExpBits > 0 || NumMantissaBits > 0, "Both NumExpBits and NumMantissaBits can't be zero");
return
(!(NumMantissaBits > 0) ? Storage(0) : Storage((1ull << NumMantissaBits) - 1));
}
#if (CUTLASS_CXX17_OR_LATER)
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage max_pos_denormal_value_cxx17() {
static_assert(NumExpBits > 0 || NumMantissaBits > 0, "Both NumExpBits and NumMantissaBits can't be zero");
constexpr bool has_denorm = (NumMantissaBits > 0);
if CUTLASS_CONSTEXPR_IF_CXX17 (!has_denorm) {
// If we don't have denormal values, return all 0s
return Storage(0);
}
else {
// Case: (NumExpBits > 0 && NumMantissaBits > 0) or (NumExpBits == 0 && NumMantissaBits > 0)
return Storage((1ull << NumMantissaBits) - 1);
}
CUTLASS_GCC_UNREACHABLE;
}
#endif
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage min_pos_denormal_value_cxx11() {
return (!(NumMantissaBits > 0) ? Storage(0) : Storage(1));
}
#if (CUTLASS_CXX17_OR_LATER)
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage min_pos_denormal_value_cxx17() {
constexpr bool has_denorm = (NumMantissaBits > 0);
if CUTLASS_CONSTEXPR_IF_CXX17 (!has_denorm) {
// If we don't have denormal values, return all 0s
return Storage(0);
}
// Case: (NumExpBits > 0 && NumMantissaBits > 0) or (NumExpBits == 0 && NumMantissaBits > 0)
return Storage(1);
}
#endif
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage max_pos_normal_value_cxx11() {
return
((NumExpBits == 0) ?
Storage(0) :
((NumMantissaBits == 0) ?
0 :
(((NaNEncoding == NanInfEncoding::IEEE_754 || NaNEncoding == NanInfEncoding::NONE) ?
((1ull << NumMantissaBits) - 1) :
((1ull << NumMantissaBits) - 2)))
) | (static_cast<Storage>(
maximum_exponent_cxx11<NumExpBits, NumMantissaBits, NaNEncoding>() +
exponent_bias_cxx11<NumExpBits, NumMantissaBits>()
) << NumMantissaBits)
);
}
#if (CUTLASS_CXX17_OR_LATER)
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage max_pos_normal_value_cxx17() {
if CUTLASS_CONSTEXPR_IF_CXX17 (NumExpBits == 0) {
// if there are no exponent bits, we don't have normal values.
return Storage(0);
}
constexpr int exp_bias = exponent_bias_cxx17<NumExpBits, NumMantissaBits>();
constexpr int max_exp = maximum_exponent_cxx17<NumExpBits, NumMantissaBits, NaNEncoding>();
constexpr int exp = max_exp + exp_bias;
// place the exponent
Storage val = static_cast<Storage>(exp) << NumMantissaBits;
// If there are no mantissa bits return the exponent
if CUTLASS_CONSTEXPR_IF_CXX17 (NumMantissaBits == 0) {
return val;
}
else {
// If the NaN Inf encoding follows IEEE 754 or there is no (NaN and Inf) then mantissa can be all 1..1s
if CUTLASS_CONSTEXPR_IF_CXX17 (NaNEncoding == NanInfEncoding::IEEE_754 ||
NaNEncoding == NanInfEncoding::NONE ) {
Storage mantissa = (1ull << NumMantissaBits) - 1;
val |= mantissa;
}
else {
// If we have a canonical NaN, then the exponent can be the maximum bit value
// but mantissa=1..1s is reserved for NaN.
Storage mantissa = (1ull << NumMantissaBits) - 2;
val |= mantissa;
}
return val;
}
CUTLASS_GCC_UNREACHABLE;
}
#endif
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage min_pos_normal_value_cxx11() {
return
((NumExpBits == 0) ?
Storage(0) :
(Storage((NumMantissaBits > 0) ? 1 : 0) << NumMantissaBits)
);
}
#if (CUTLASS_CXX17_OR_LATER)
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage min_pos_normal_value_cxx17() {
constexpr bool has_denorm = (NumMantissaBits > 0);
if CUTLASS_CONSTEXPR_IF_CXX17 (NumExpBits == 0) {
// if there are no exponent bits, we don't have normal values.
return Storage(0);
}
Storage exp = 0;
if CUTLASS_CONSTEXPR_IF_CXX17 (has_denorm) {
exp = 1;
}
return static_cast<Storage>(exp << NumMantissaBits);
}
#endif
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage max_value_cxx11() {
return
((NumExpBits > 0) ?
max_pos_normal_value_cxx11<Storage, NumExpBits, NumMantissaBits, NaNEncoding>() :
max_pos_denormal_value_cxx11<Storage, NumExpBits, NumMantissaBits, NaNEncoding>()
);
}
#if (CUTLASS_CXX17_OR_LATER)
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding>
constexpr Storage max_value_cxx17() {
constexpr bool has_normal = (NumExpBits > 0);
if CUTLASS_CONSTEXPR_IF_CXX17 (has_normal) {
return max_pos_normal_value_cxx17<Storage, NumExpBits, NumMantissaBits, NaNEncoding>();
}
else {
return max_pos_denormal_value_cxx17<Storage, NumExpBits, NumMantissaBits, NaNEncoding>();
}
CUTLASS_GCC_UNREACHABLE;
}
#endif
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding, bool IsSigned>
constexpr Storage min_value_cxx11() {
return
(IsSigned ?
Storage(1ull << (NumExpBits + NumMantissaBits)) | max_value_cxx11<Storage, NumExpBits, NumMantissaBits, NaNEncoding>() :
Storage(0)
);
}
#if (CUTLASS_CXX17_OR_LATER)
template<class Storage, uint32_t NumExpBits, uint32_t NumMantissaBits, NanInfEncoding NaNEncoding, bool IsSigned>
constexpr Storage min_value_cxx17() {
if (IsSigned) {
return Storage(1ull << (NumExpBits + NumMantissaBits)) | max_value_cxx17<Storage, NumExpBits, NumMantissaBits, NaNEncoding>();
}
else { // Unsigned number
return Storage(0);
}
CUTLASS_GCC_UNREACHABLE;
}
#endif
template <
class StorageType,
uint32_t NumBits, uint32_t NumExpBits, uint32_t NumMantissaBits,
NanInfEncoding Nan = NanInfEncoding::IEEE_754, bool IsSigned = true>
struct FpBitRepresentation {
public:
using Storage = StorageType;
#if (CUTLASS_CXX17_OR_LATER)
static_assert(cutlass::platform::is_unsigned_v<Storage>, "Use an unsigned integer for StorageType");
#endif
static constexpr bool IS_SIGNED = IsSigned;
// Canonical NaN is always represented as exponent=11...11 and mantissa=11...11, if it exists
static constexpr NanInfEncoding NAN_TYPE = Nan;
// Inf is always represented as exponent=11...11 and mantissa=00...00, if it exists
static constexpr bool HAS_INF = (NAN_TYPE == NanInfEncoding::IEEE_754);
static constexpr bool HAS_NAN = (NAN_TYPE != NanInfEncoding::NONE);
static constexpr bool HAS_DENORM = (NumMantissaBits > 0);
static constexpr bool HAS_NORMAL = !HAS_DENORM;
static constexpr uint32_t NUM_BITS = NumBits;
static constexpr uint32_t NUM_EXPONENT_BITS = NumExpBits;
static constexpr uint32_t NUM_MANTISSA_BITS = NumMantissaBits;
static_assert(NUM_BITS >= (NUM_EXPONENT_BITS + NUM_MANTISSA_BITS + uint32_t(IS_SIGNED)), "Number of bits do not match");
static constexpr Storage ONE = Storage(1);
static constexpr Storage ZERO = Storage(0);
// Note: Don't rely on operator precedence. Use parenthesis.
static constexpr Storage EXPONENT_MASK = (Storage(1) << Storage(NUM_EXPONENT_BITS)) - ONE;
static constexpr Storage MANTISSA_MASK = (Storage(1) << Storage(NUM_MANTISSA_BITS)) - ONE;
static constexpr Storage EXPONENT_SHIFT = Storage(NUM_MANTISSA_BITS);
static constexpr Storage SIGN_SHIFT = (IS_SIGNED) ? Storage(NUM_MANTISSA_BITS + NUM_EXPONENT_BITS) : Storage(0);
// Note: All biased/real exponent calculation are done with signed ints
// Use unsigned to represent data not exponent.
static constexpr int EXP_BIAS = detail::exponent_bias_cxx11<NUM_EXPONENT_BITS, NUM_MANTISSA_BITS>();
static constexpr int MAX_EXP = detail::maximum_exponent_cxx11<NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>();
static constexpr int MIN_EXP = detail::minimum_exponent_cxx11<NUM_EXPONENT_BITS, NUM_MANTISSA_BITS>();
// Floating-point Limits
static constexpr Storage MAX_POS_NORMAL_VAL = detail::max_pos_normal_value_cxx11<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>();
static constexpr Storage MAX_POS_DENORMAL_VAL = detail::max_pos_denormal_value_cxx11<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>();
static constexpr Storage MIN_POS_NORMAL_VAL = detail::min_pos_normal_value_cxx11<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>();
static constexpr Storage MIN_POS_DENORMAL_VAL = detail::min_pos_denormal_value_cxx11<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>();
static constexpr Storage MAX_VALUE = max_value_cxx11<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>();
static constexpr Storage MIN_VALUE = min_value_cxx11<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE, IS_SIGNED>();
//
// C++17 Verification
//
#if (CUTLASS_CXX17_OR_LATER)
static_assert(EXP_BIAS == detail::exponent_bias_cxx17<NUM_EXPONENT_BITS, NUM_MANTISSA_BITS>(), "Error");
static_assert(MAX_EXP == detail::maximum_exponent_cxx17<NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>(), "Error");
static_assert(MIN_EXP == detail::minimum_exponent_cxx17<NUM_EXPONENT_BITS, NUM_MANTISSA_BITS>(), "Error");
static_assert(MAX_POS_NORMAL_VAL == detail::max_pos_normal_value_cxx17<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>(), "Error");
static_assert(MAX_POS_DENORMAL_VAL == detail::max_pos_denormal_value_cxx17<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>(), "Error");
static_assert(MIN_POS_NORMAL_VAL == detail::min_pos_normal_value_cxx17<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>(), "Error");
static_assert(MIN_POS_DENORMAL_VAL == detail::min_pos_denormal_value_cxx17<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>(), "Error");
static_assert(MAX_VALUE == max_value_cxx17<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE>(), "Error");
static_assert(MIN_VALUE == min_value_cxx17<Storage, NUM_EXPONENT_BITS, NUM_MANTISSA_BITS, NAN_TYPE, IS_SIGNED>(), "Error");
#endif
// If we don't have INF defined, set the largest number. Gives us .satfinite behavior.
static constexpr Storage INF_MASK = (HAS_INF) ?
(Storage(EXPONENT_MASK) << Storage(NUM_MANTISSA_BITS)) : MAX_VALUE;
static constexpr Storage NAN_MASK = (Storage(EXPONENT_MASK) << Storage(NUM_MANTISSA_BITS)) | MANTISSA_MASK;
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 bool is_inf(Storage flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (!HAS_INF) {
return false;
}
bool exp_all_ones = (exponent_bits(flt) ^ EXPONENT_MASK) == 0;
bool mantissa_all_zeros = mantissa_bits(flt) == 0;
return exp_all_ones && mantissa_all_zeros;
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 bool is_canonical_nan(Storage flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (NAN_TYPE == NanInfEncoding::NONE) {
return false;
}
bool exp_all_ones = (exponent_bits(flt) ^ EXPONENT_MASK) == ZERO;
bool mantissa_all_ones = (mantissa_bits(flt) ^ MANTISSA_MASK) == ZERO;
return exp_all_ones && mantissa_all_ones;
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 bool is_nan(Storage flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (NAN_TYPE == NanInfEncoding::NONE) {
return false;
}
if CUTLASS_CONSTEXPR_IF_CXX17 (NAN_TYPE == NanInfEncoding::CANONICAL_ONLY) {
return is_canonical_nan(flt);
}
bool exp_all_ones = (exponent_bits(flt) ^ EXPONENT_MASK) == ZERO;
bool mantissa_has_ones = mantissa_bits(flt) > ZERO;
return exp_all_ones && mantissa_has_ones;
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 bool is_denorm(Storage flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (!HAS_DENORM) {
return false;
}
else if (exponent_bits(flt) == ZERO) {
// Exponent bits are all 0s
return true;
}
return false;
}
template<typename T = Storage>
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 T sign_bit(T flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (!IS_SIGNED) {
return T(0);
}
return static_cast<T>(flt >> T(SIGN_SHIFT));
}
template<typename T = Storage>
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 T set_sign_bit(T flt, T sign) {
if CUTLASS_CONSTEXPR_IF_CXX17 (!IS_SIGNED) {
return flt;
}
return static_cast<T>(flt | (sign << T(SIGN_SHIFT)));
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 Storage exponent_bits(Storage flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (NUM_EXPONENT_BITS == ZERO) {
return ZERO;
}
return (flt >> (NUM_MANTISSA_BITS)) & EXPONENT_MASK;
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 int exponent(Storage flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (NUM_EXPONENT_BITS == ZERO) {
return -int(EXP_BIAS);
}
if (HAS_DENORM && (exponent_bits(flt) == ZERO)) {
return 1 - int(EXP_BIAS);
}
return int(flt >> (NUM_MANTISSA_BITS) & EXPONENT_MASK) - int(EXP_BIAS);
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 Storage mantissa_bits(Storage flt) {
if CUTLASS_CONSTEXPR_IF_CXX17 (NUM_MANTISSA_BITS == ZERO) {
return ZERO;
}
return (flt & MANTISSA_MASK);
}
template <class FpType>
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 Storage to_bits(FpType flt) {
return copy_bits<FpType, Storage>(flt);
}
template <class DstFpBits>
CUTLASS_HOST_DEVICE static typename DstFpBits::Storage convert_to(
Storage src_val,
DstFpBits dst_encoding) {
return convert(FpBitRepresentation{}, src_val, dst_encoding);
}
template <class SrcFpBits>
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 Storage convert_from(
typename SrcFpBits::Storage src_val,
SrcFpBits src_encoding) {
return convert(src_encoding, src_val, FpBitRepresentation{});
}
private:
template<typename T = Storage>
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 T make_fp_from_bits(T sign, T exp, T mantissa) {
T fp_bits = T(ZERO);
CUTLASS_UNUSED(sign);
if CUTLASS_CONSTEXPR_IF_CXX17 (IS_SIGNED) {
fp_bits = sign << SIGN_SHIFT;
}
fp_bits |= (exp << T(NUM_MANTISSA_BITS));
fp_bits |= (mantissa);
return fp_bits;
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 Storage nan_with_sign(Storage sign) {
Storage fp_bits = NAN_MASK;
return set_sign_bit(fp_bits, sign);
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 Storage inf_with_sign(Storage sign) {
if CUTLASS_CONSTEXPR_IF_CXX17 (HAS_INF) {
Storage fp_bits = INF_MASK;
return set_sign_bit(fp_bits, sign);
}
else {
// If INF is not defined assume satfinite behavior
return (sign == ZERO) ? MAX_VALUE : MIN_VALUE;
}
CUTLASS_GCC_UNREACHABLE;
}
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 Storage significand(Storage flt) {
if (is_denorm(flt)) {
return mantissa_bits(flt);
}
else {
return (ONE << Storage(NUM_MANTISSA_BITS)) | mantissa_bits(flt);
}
CUTLASS_GCC_UNREACHABLE;
}
template<typename T>
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 T significand_hidden_bits(T significand) {
if CUTLASS_CONSTEXPR_IF_CXX17 (NUM_MANTISSA_BITS == 0) {
return T(1);
}
return ((T(0b11) << T(NUM_MANTISSA_BITS)) & significand) >> T(NUM_MANTISSA_BITS);
}
// Current assumption round to nearest even
template<class T>
CUTLASS_HOST_DEVICE
static CUTLASS_CONSTEXPR_IF_CXX17 T round_significand(T src, int shift_amount) {
T dst_mantissa = src;
// If the shift amount is positive, we are shifting left
// Type with less mantissa bits is rounded to a type with more
// mantissa bits.
if (shift_amount > 0) {
dst_mantissa = (dst_mantissa << (shift_amount));
}
else {
// There are fewer mantissa bits in the target type
// we need to round the destination number up for all
// lower precision bits removed.
// We assume round-to-nearest-even here.
int pos_shift_amount = -shift_amount;
// Too large shift return all zeros to prevent undefined behavior for shift.
if (pos_shift_amount >= static_cast<int>(sizeof(T) * 8)) {
return T(0);
}
T guard_bit_mask = (T(1) << T(pos_shift_amount)); // Last bit to remain in mantissa
T sticky_mask = (T(1) << T(pos_shift_amount - 1)) - T(1); // Remaining bits
T round_bit_mask = (T(1) << T(pos_shift_amount - 1)); // First bit removed from mantissa
bool sticky_bit = (src & sticky_mask) >= T(1); // ORing all sticky bits
bool round_bit = (src & round_bit_mask) >= T(1);
bool guard_bit = (src & guard_bit_mask) >= T(1);
// Shift mantissa bits to right to remove lowest precision bits
dst_mantissa = dst_mantissa >> pos_shift_amount;
if ((sticky_bit && round_bit) || (guard_bit && round_bit && !sticky_bit)) {
dst_mantissa += 1;
}
}
return dst_mantissa;
}
template <class SrcFpBits, class DstFpBits>
CUTLASS_HOST_DEVICE
static typename DstFpBits::Storage convert(
SrcFpBits src_encoding,
typename SrcFpBits::Storage src_val,
DstFpBits dst_encoding) {
using SrcT = typename SrcFpBits::Storage;
using DstT = typename DstFpBits::Storage;
using LargeStorage = typename cutlass::platform::conditional<(sizeof(SrcT) > sizeof(DstT)), SrcT, DstT>::type;
LargeStorage src_sign_bit = src_encoding.sign_bit(src_val);
// If the source is NaN, set the destination to NaN carrying the sign bit
if (src_encoding.is_nan(src_val)) {
return dst_encoding.nan_with_sign(DstT(src_sign_bit));
}
// If the source is INF, set the destination to INF carrying the sign bit
else if (src_encoding.is_inf(src_val)) {
return dst_encoding.set_sign_bit(DstFpBits::INF_MASK, DstT(src_sign_bit));
}
// Number is not NaN or INF: Zero and others
LargeStorage src_exp_bits = src_encoding.exponent_bits(src_val);
LargeStorage src_significand = src_encoding.significand(src_val);
int src_exp = src_encoding.exponent(src_val);
// The source value is 0. Return a signed 0.
if (src_exp_bits == LargeStorage(0) && src_significand == LargeStorage(0)) {
return dst_encoding.set_sign_bit(DstT(0), DstT(src_sign_bit));
}
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(1) src_sign: %llu src_exp_bits %llx src_exp %d src_significand %llx\n",
static_cast<unsigned long long>(src_sign_bit), static_cast<unsigned long long>(src_exp_bits), src_exp, static_cast<unsigned long long>(src_significand));
#endif
// Normalize the number: Left shift the significand bits until hidden "1" appears.
// Only needed if the src value is denormal.
// Conditions:
// If the exponent is 0, then the significand can't be 0 (src_val==0 case handled above):
// there is at least one "1" bit in the significand. Loop executes.
// If the exponent is not 0, then the number is normal:
// significand has hidden bit set. Loop doesn't execute.
// Assumption: Zero is always defined for the floating point types and detected above
while (src_encoding.significand_hidden_bits(src_significand) == LargeStorage(0)) {
src_significand <<= LargeStorage(1);
src_exp--;
}
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(2) src_sign: %llu src_exp_bits %llx src_exp %d src_significand %llx\n",
static_cast<unsigned long long>(src_sign_bit), static_cast<unsigned long long>(src_exp_bits), src_exp, static_cast<unsigned long long>(src_significand));
#endif
// The exponent exceeds DstFormat's exponent capacity
// Return positive/negative infinity.
// If no INF is defined, return positive/negative largest value.
if (src_exp > DstFpBits::MAX_EXP) {
return dst_encoding.set_sign_bit(DstFpBits::INF_MASK, DstT(src_sign_bit));
}
else if (src_exp <= DstFpBits::MAX_EXP && src_exp >= DstFpBits::MIN_EXP) {
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(3) Exp match: src_sign: %d src_exp_bits: %x src_exp: %d src_significand: %x\n",
src_sign_bit, src_exp_bits, src_exp, src_significand);
#endif
int shift_amount = int(DstFpBits::NUM_MANTISSA_BITS) - int(SrcFpBits::NUM_MANTISSA_BITS);
int dst_exponent = src_exp + DstFpBits::EXP_BIAS;
LargeStorage dst_mantissa = src_significand;
// if we have an M0 case, the floating point number is always denormal.
// Therefore, if exponents are equal, we need to check whether it is inf
if (DstFpBits::NUM_EXPONENT_BITS == 0) {
if (dst_mantissa > DstFpBits::INF_MASK) {
return dst_encoding.inf_with_sign(DstT(src_sign_bit));
}
}
// Round to nearest even
dst_mantissa = round_significand(dst_mantissa, shift_amount);
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(4) after rounding src_sign: %d dst_exponent: %d dst_mantissa: %x\n",
src_sign_bit, dst_exponent, dst_mantissa);
#endif
if (dst_encoding.significand_hidden_bits(dst_mantissa) > 0b1) {
// Significant became larger than 01.X...X. Divide significand by 2 and multiply exp by 2
while (dst_exponent < (DstFpBits::MAX_EXP+DstFpBits::EXP_BIAS) &&
dst_encoding.significand_hidden_bits(dst_mantissa) > LargeStorage(0b1)) {
dst_mantissa >>= LargeStorage(1);
dst_exponent++;
}
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(5) after rounding max_exp: %d src_sign: %d dst_exponent: %d dst_mantissa: %x\n",
DstFpBits::MAX_EXP,src_sign_bit, dst_exponent, dst_mantissa);
#endif
if (dst_encoding.significand_hidden_bits(dst_mantissa) > LargeStorage(0b1)) {
return dst_encoding.set_sign_bit(DstFpBits::INF_MASK, DstT(src_sign_bit));
}
}
dst_mantissa = dst_mantissa & DstFpBits::MANTISSA_MASK;
static_assert(sizeof(LargeStorage) >= sizeof(decltype(dst_exponent)),
"sizeof(LargeStorage) must be greater than or equal to sizeof(decltype(dst_exponent))");
LargeStorage dst_exponent_bits = static_cast<LargeStorage>(dst_exponent);
DstT final_val = static_cast<DstT>(dst_encoding.template make_fp_from_bits<LargeStorage>(src_sign_bit, dst_exponent_bits, dst_mantissa));
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(6) Final Value src_sign: %d dst_exp_bits: %x dst_mantissa: %x\n",
src_sign_bit, dst_exponent_bits, dst_mantissa);
#endif
if (DstFpBits::is_nan(final_val)) {
// This NAN is generated when:
// Src is not an Nan
// the exp of Src == the max_exp of Dst.
// The mantissa becomes all-1s after rounding.
// Return max value of Dst (not NAN) as it just couldn't be represented in the range of Dst.
return dst_encoding.set_sign_bit(DstFpBits::INF_MASK, DstT(src_sign_bit));
}
else {
return final_val;
}
}
else {
// Result is denormal
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(7) Denormal case src_sign: %d src_exp: %d src_significand: %x MIN_EXP: %d\n",
src_sign_bit, src_exp, src_significand, DstFpBits::MIN_EXP);
#endif
int exp_diff = src_exp - DstFpBits::MIN_EXP;
int shift_amount = int(DstFpBits::NUM_MANTISSA_BITS) - int(SrcFpBits::NUM_MANTISSA_BITS);
shift_amount += exp_diff;
LargeStorage dst_mantissa = src_significand;
dst_mantissa = round_significand(dst_mantissa, shift_amount);
if (dst_encoding.significand_hidden_bits(dst_mantissa) >= LargeStorage(0b1)) {
if CUTLASS_CONSTEXPR_IF_CXX17 (DstFpBits::NUM_EXPONENT_BITS == 0) {
return dst_encoding.inf_with_sign(DstT(src_sign_bit));
}
else {
LargeStorage dst_exp_bits = 1;
dst_mantissa &= DstFpBits::MANTISSA_MASK;
DstT final_val = static_cast<DstT>(dst_encoding.template make_fp_from_bits<LargeStorage>(src_sign_bit, dst_exp_bits, dst_mantissa));
return final_val;
}
}
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(7.1) Denormal case exp_diff: %d shift_amount: %d dst_mantissa %d\n", exp_diff, shift_amount, dst_mantissa);
#endif
dst_mantissa &= DstFpBits::MANTISSA_MASK;
#if (CUTLASS_DEBUG_TRACE_LEVEL > 1)
printf("(8) Final Value src_sign: %d src_exp: %d dst_mantissa: %x\n",
src_sign_bit, src_exp, dst_mantissa);
#endif
DstT final_val = static_cast<DstT>(dst_encoding.template make_fp_from_bits<LargeStorage>(src_sign_bit, LargeStorage(0), dst_mantissa));
return final_val;
}
return DstT(0);
}
template <class StorageType_, uint32_t NumBits_, uint32_t NumExpBits_,
uint32_t NumMantissaBits_, NanInfEncoding Nan_, bool IsSigned_>
friend struct FpBitRepresentation;
};
#if (CUTLASS_CXX17_OR_LATER)
template<FpEncoding FpExMyCode>
CUTLASS_CONSTEXPR_IF_CXX17 auto fp_encoding_selector() {
if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::E11M52) { // double
return cutlass::detail::FpBitRepresentation<uint64_t, 64, 11, 52, cutlass::detail::NanInfEncoding::IEEE_754>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::E8M23) { // float
return cutlass::detail::FpBitRepresentation<uint32_t, 32, 8, 23, cutlass::detail::NanInfEncoding::IEEE_754>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::E5M2) { // FP8
return cutlass::detail::FpBitRepresentation<uint8_t, 8, 5, 2, cutlass::detail::NanInfEncoding::IEEE_754>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::E4M3) { // FP8
return cutlass::detail::FpBitRepresentation<uint8_t, 8, 4, 3, cutlass::detail::NanInfEncoding::CANONICAL_ONLY>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::UE4M3) { // FP8
return cutlass::detail::FpBitRepresentation<uint8_t, 8, 4, 3, cutlass::detail::NanInfEncoding::CANONICAL_ONLY, false>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::UE8M0) { // FP8
return cutlass::detail::FpBitRepresentation<uint8_t, 8, 8, 0, cutlass::detail::NanInfEncoding::CANONICAL_ONLY, false>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::E3M2) { // FP6
return cutlass::detail::FpBitRepresentation<uint8_t, 6, 3, 2, cutlass::detail::NanInfEncoding::NONE>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::E2M3) { // FP6
return cutlass::detail::FpBitRepresentation<uint8_t, 6, 2, 3, cutlass::detail::NanInfEncoding::NONE>{};
}
else if CUTLASS_CONSTEXPR_IF_CXX17 (FpExMyCode == FpEncoding::E2M1) { // FP4
return cutlass::detail::FpBitRepresentation<uint8_t, 4, 2, 1, cutlass::detail::NanInfEncoding::NONE>{};
}
CUTLASS_GCC_UNREACHABLE;
}
#else
//
// Definitions for floating point encodings.
//
template <FpEncoding FpExMyCode> struct FpEncodingSelector {
using type = void;
};
template <> struct FpEncodingSelector<FpEncoding::E11M52> {
using type = cutlass::detail::FpBitRepresentation<uint64_t, 64, 11, 52, cutlass::detail::NanInfEncoding::IEEE_754>;
};
template <> struct FpEncodingSelector<FpEncoding::E8M23> {
using type = cutlass::detail::FpBitRepresentation<uint32_t, 32, 8, 23, cutlass::detail::NanInfEncoding::IEEE_754>;
};
template <> struct FpEncodingSelector<FpEncoding::E5M2> {
using type = cutlass::detail::FpBitRepresentation<uint8_t, 8, 5, 2, cutlass::detail::NanInfEncoding::IEEE_754>;
};
template <> struct FpEncodingSelector<FpEncoding::E4M3> {
using type = cutlass::detail::FpBitRepresentation<uint8_t, 8, 4, 3, cutlass::detail::NanInfEncoding::CANONICAL_ONLY>;
};
template <> struct FpEncodingSelector<FpEncoding::UE4M3> {
using type = cutlass::detail::FpBitRepresentation<uint8_t, 8, 4, 3, cutlass::detail::NanInfEncoding::CANONICAL_ONLY, false>;
};
template <> struct FpEncodingSelector<FpEncoding::UE8M0> {
using type = cutlass::detail::FpBitRepresentation<uint8_t, 8, 8, 0, cutlass::detail::NanInfEncoding::CANONICAL_ONLY, false>;
};
template <> struct FpEncodingSelector<FpEncoding::E3M2> {
using type = cutlass::detail::FpBitRepresentation<uint8_t, 6, 3, 2, cutlass::detail::NanInfEncoding::NONE>;
};
template <> struct FpEncodingSelector<FpEncoding::E2M3> {
using type = cutlass::detail::FpBitRepresentation<uint8_t, 6, 2, 3, cutlass::detail::NanInfEncoding::NONE>;
};
template <> struct FpEncodingSelector<FpEncoding::E2M1> {
using type = cutlass::detail::FpBitRepresentation<uint8_t, 4, 2, 1, cutlass::detail::NanInfEncoding::NONE>;
};
#endif
} // namespace detail
template <detail::FpEncoding T, class Derived>
struct float_exmy_base
{
static constexpr detail::FpEncoding Encoding = T;
using BitRepresentation =
#if (CUTLASS_CXX17_OR_LATER)
decltype(detail::fp_encoding_selector<T>())
#else
typename detail::FpEncodingSelector<T>::type
#endif
;
using FP32BitRepresentation =
#if (CUTLASS_CXX17_OR_LATER)
decltype(cutlass::detail::fp_encoding_selector<cutlass::detail::FpEncoding::E8M23>())
#else
typename detail::FpEncodingSelector<cutlass::detail::FpEncoding::E8M23>::type
#endif
;
using Storage = typename BitRepresentation::Storage;
//
// Data members
//
/// Data container
Storage storage;
/// Ctors.
float_exmy_base() = default;
CUTLASS_HOST_DEVICE
float_exmy_base(Storage s) : storage(s) {
}
/// Is finite implementation
CUTLASS_HOST_DEVICE
static bool isfinite(float_exmy_base flt) {
return !BitRepresentation::is_inf(flt.storage);
}
/// Is NaN implementation
CUTLASS_HOST_DEVICE
static bool isnan(float_exmy_base flt) {
return BitRepresentation::is_nan(flt.storage);
}
/// Is infinite implementation
CUTLASS_HOST_DEVICE
static bool isinf(float_exmy_base flt) {
return BitRepresentation::is_inf(flt.storage);
}
/// Is infinite implementation
CUTLASS_HOST_DEVICE
static bool isnormal(float_exmy_base flt) {
return !BitRepresentation::is_denorm(flt.storage);
}
CUTLASS_HOST_DEVICE
static float_exmy_base<T, Derived> bitcast(Storage x) {
float_exmy_base f;
f.storage = x;
return f;