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99eefd2ec0
mlx/mlx/backend/metal/kernels/steel/gemm/mma.h
Angelos Katharopoulos 99eefd2ec0
Gather mm new kernel and small refactoring (#2040)
2025-04-14 16:37:36 -07:00

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// Copyright © 2024 Apple Inc.
#pragma once
#include <metal_simdgroup>
#include <metal_simdgroup_matrix>
#include <metal_stdlib>
#include "mlx/backend/metal/kernels/steel/defines.h"
#include "mlx/backend/metal/kernels/steel/gemm/transforms.h"
#include "mlx/backend/metal/kernels/steel/utils/integral_constant.h"
using namespace metal;
///////////////////////////////////////////////////////////////////////////////
// MMA helper
///////////////////////////////////////////////////////////////////////////////
namespace mlx {
namespace steel {
template <typename T, int kFragRows_, int kFragCols_>
struct BaseMMAFrag {
static_assert(
kFragRows_ == 8,
"Only 8 x 8 fragment matrices are currently supported");
static_assert(
kFragCols_ == 8,
"Only 8 x 8 fragment matrices are currently supported");
};
template <typename T>
struct BaseMMAFrag<T, 8, 8> {
STEEL_CONST int kFragRows = 8;
STEEL_CONST int kFragCols = 8;
STEEL_CONST int kElemsPerFrag = (kFragRows * kFragCols) / 32;
STEEL_CONST int kElemRows = 1;
STEEL_CONST int kElemCols = 2;
static_assert(
kElemRows * kElemCols == kElemsPerFrag,
"MMAFrag shape is not consistent with MMAFrag size");
typedef metal::simdgroup_matrix<T, kFragRows, kFragCols> mat_type;
typedef metal::vec<T, kElemsPerFrag> frag_type;
METAL_FUNC static constexpr short2 get_coord(ushort simd_lane_id
[[thread_index_in_simdgroup]]) {
const short qid = simd_lane_id / 4;
const short fm = (qid & 4) + ((simd_lane_id / 2) % 4);
const short fn = (qid & 2) * 2 + (simd_lane_id % 2) * 2;
return short2{fn, fm};
}
template <typename SrcPtrType, typename StrX, typename StrY>
METAL_FUNC static constexpr void
load(thread frag_type& dst, SrcPtrType src, StrX str_x, StrY str_y) {
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kElemRows; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kElemCols; j++) {
dst[i * kElemCols + j] = static_cast<T>(src[i * str_x + j * str_y]);
}
}
}
template <
typename SrcPtrType,
typename StrX,
typename StrY,
typename LimX,
typename LimY,
typename OffX,
typename OffY>
METAL_FUNC static constexpr void load_safe(
thread frag_type& dst,
SrcPtrType src,
StrX str_x,
StrY str_y,
LimX lim_x,
LimY lim_y,
OffX off_x = Int<0>{},
OffY off_y = Int<0>{}) {
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kElemRows; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kElemCols; j++) {
if ((off_x + i) < lim_x && (off_y + j) < lim_y) {
dst[i * kElemCols + j] =
static_cast<T>(src[(off_x + i) * str_x + (off_x + j) * str_y]);
} else {
dst[i * kElemCols + j] = T(0);
}
}
}
}
template <typename DstPtrType, typename StrX, typename StrY>
METAL_FUNC static constexpr void
store(const thread frag_type& src, DstPtrType dst, StrX str_x, StrY str_y) {
using U = pointer_element_t<DstPtrType>;
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kElemRows; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kElemCols; j++) {
dst[i * str_x + j * str_y] = static_cast<U>(src[i * kElemCols + j]);
}
}
}
template <
typename DstPtrType,
typename StrX,
typename StrY,
typename LimX,
typename LimY,
typename OffX,
typename OffY>
METAL_FUNC static constexpr void store_safe(
const thread frag_type& src,
DstPtrType dst,
StrX str_x,
StrY str_y,
LimX lim_x,
LimY lim_y,
OffX off_x = Int<0>{},
OffY off_y = Int<0>{}) {
using U = pointer_element_t<DstPtrType>;
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kElemRows; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kElemCols; j++) {
if ((off_x + i) < lim_x && (off_y + j) < lim_y) {
dst[(off_x + i) * str_x + (off_y + j) * str_y] =
static_cast<U>(src[i * kElemCols + j]);
}
}
}
}
template <
typename DstPtrType,
typename StrX,
typename StrY,
typename StartX,
typename StopX,
typename StartY,
typename StopY,
typename OffX,
typename OffY>
METAL_FUNC static constexpr void store_slice(
const thread frag_type& src,
DstPtrType dst,
StrX str_x,
StrY str_y,
StartX start_x,
StopX stop_x,
StartY start_y,
StopY stop_y,
OffX off_x = Int<0>{},
OffY off_y = Int<0>{}) {
using U = pointer_element_t<DstPtrType>;
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kElemRows; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kElemCols; j++) {
if ((off_x + i) < stop_x && (off_x + i) >= start_x &&
(off_y + j) < stop_y && (off_y + j) >= start_y) {
dst[(off_x + i) * str_x + (off_y + j) * str_y] =
static_cast<U>(src[i * kElemCols + j]);
}
}
}
}
METAL_FUNC static constexpr void mma(
thread frag_type& D,
thread frag_type& A,
thread frag_type& B,
thread frag_type& C) {
mat_type D_mat;
mat_type A_mat;
mat_type B_mat;
mat_type C_mat;
reinterpret_cast<thread frag_type&>(A_mat.thread_elements()) = A;
reinterpret_cast<thread frag_type&>(B_mat.thread_elements()) = B;
reinterpret_cast<thread frag_type&>(C_mat.thread_elements()) = C;
mma(D_mat, A_mat, B_mat, C_mat);
D = reinterpret_cast<thread frag_type&>(D_mat.thread_elements());
}
METAL_FUNC static constexpr void mma(
thread mat_type& D,
thread mat_type& A,
thread mat_type& B,
thread mat_type& C) {
simdgroup_multiply_accumulate(D, A, B, C);
}
};
template <
typename T,
int kTileRows_,
int kTileCols_,
class MMAFrag_ = BaseMMAFrag<T, 8, 8>>
struct MMATile {
using MMAFrag_t = MMAFrag_;
using elem_type = T;
STEEL_CONST int kFragRows = MMAFrag_t::kFragRows;
STEEL_CONST int kFragCols = MMAFrag_t::kFragCols;
STEEL_CONST int kElemsPerFrag = MMAFrag_t::kElemsPerFrag;
STEEL_CONST int kTileRows = kTileRows_;
STEEL_CONST int kTileCols = kTileCols_;
STEEL_CONST int kRows = kTileRows * kFragRows;
STEEL_CONST int kCols = kTileCols * kFragCols;
STEEL_CONST int kNumFrags = kTileRows * kTileCols;
STEEL_CONST int kElemsPerTile = kNumFrags * kElemsPerFrag;
typedef typename MMAFrag_t::mat_type mat_type;
typedef typename MMAFrag_t::frag_type frag_type;
frag_type val_frags[kNumFrags] = {frag_type(0)};
METAL_FUNC MMATile() thread {}
METAL_FUNC constexpr void clear() {
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kNumFrags; ++i) {
val_frags[i] = frag_type(0);
}
}
METAL_FUNC constexpr thread frag_type& frag_at(const short i, const short j) {
return val_frags[i * kTileCols + j];
}
METAL_FUNC constexpr const thread frag_type& frag_at(
const short i,
const short j) const {
return val_frags[i * kTileCols + j];
}
METAL_FUNC mat_type mat_at(const short i, const short j) {
mat_type val_mat;
STEEL_PRAGMA_UNROLL
for (short ii = 0; ii < kElemsPerFrag; ++ii) {
val_mat.thread_elements()[ii] = frag_at(i, j)[ii];
}
return val_mat;
}
METAL_FUNC thread elem_type* elems() {
return reinterpret_cast<thread elem_type*>(val_frags);
}
METAL_FUNC const thread elem_type* elems() const {
return reinterpret_cast<const thread elem_type*>(val_frags);
}
template <typename U, int w_x, int w_y, int str_x, int str_y>
METAL_FUNC void load(const threadgroup U* src) {
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kTileRows; ++i) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kTileCols; ++j) {
MMAFrag_t::load(
frag_at(i, j),
&(
src[(i * kFragRows) * w_x * str_x +
(j * kFragCols) * w_y * str_y]),
Int<str_x>{},
Int<str_y>{});
}
}
}
template <typename U, int w_x, int w_y, int str_x, int str_y>
METAL_FUNC void store(threadgroup U* dst) const {
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kTileRows; ++i) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kTileCols; ++j) {
MMAFrag_t::store(
frag_at(i, j),
&(
dst[(i * kFragRows) * w_x * str_x +
(j * kFragCols) * w_y * str_y]),
Int<str_x>{},
Int<str_y>{});
}
}
}
template <typename U, int w_x, int w_y>
METAL_FUNC void load(const device U* src, const int ld) {
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kTileRows; ++i) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kTileCols; ++j) {
MMAFrag_t::load(
frag_at(i, j),
&(src[(i * kFragRows) * w_x * ld + (j * kFragCols) * w_y]),
ld,
Int<1>{});
}
}
}
template <typename U, int w_x, int w_y>
METAL_FUNC void store(device U* dst, const int ld) const {
STEEL_PRAGMA_UNROLL
for (short i = 0; i < kTileRows; ++i) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < kTileCols; ++j) {
MMAFrag_t::store(
frag_at(i, j),
&(dst[(i * kFragRows) * w_x * ld + (j * kFragCols) * w_y]),
ld,
Int<1>{});
}
}
}
template <typename U, int w_x, int w_y>
METAL_FUNC void
load_safe(const device U* src, const int ld, const short2 src_tile_dims) {
STEEL_PRAGMA_UNROLL
for (int i = 0; i < kTileRows; ++i) {
STEEL_PRAGMA_UNROLL
for (int j = 0; j < kTileCols; ++j) {
MMAFrag_t::load_safe(
frag_at(i, j),
src,
ld,
Int<1>{},
src_tile_dims.y,
src_tile_dims.x,
(i * kFragRows) * w_x,
(j * kFragCols) * w_y);
}
}
}
template <typename U, int w_x, int w_y>
METAL_FUNC void
store_safe(device U* dst, const int ld, const short2 dst_tile_dims) const {
STEEL_PRAGMA_UNROLL
for (int i = 0; i < kTileRows; ++i) {
STEEL_PRAGMA_UNROLL
for (int j = 0; j < kTileCols; ++j) {
MMAFrag_t::store_safe(
frag_at(i, j),
dst,
ld,
Int<1>{},
dst_tile_dims.y,
dst_tile_dims.x,
(i * kFragRows) * w_x,
(j * kFragCols) * w_y);
}
}
}
template <typename U, int w_x, int w_y>
METAL_FUNC void store_slice(
device U* dst,
const int ld,
const short2 start,
const short2 stop) const {
STEEL_PRAGMA_UNROLL
for (int i = 0; i < kTileRows; ++i) {
STEEL_PRAGMA_UNROLL
for (int j = 0; j < kTileCols; ++j) {
MMAFrag_t::store_slice(
frag_at(i, j),
dst,
ld,
Int<1>{},
start.y,
stop.y,
start.x,
stop.x,
(i * kFragRows) * w_x,
(j * kFragCols) * w_y);
}
}
}
};
template <typename T, typename U, int M, int N, int K>
METAL_FUNC void tile_matmad(
thread MMATile<T, M, N>& D,
thread MMATile<U, M, K>& A,
thread MMATile<U, K, N>& B,
thread MMATile<T, M, N>& C) {
STEEL_PRAGMA_UNROLL
for (short m = 0; m < M; ++m) {
STEEL_PRAGMA_UNROLL
for (short n = 0; n < N; ++n) {
short n_serp = (m % 2) ? (N - 1 - n) : n;
STEEL_PRAGMA_UNROLL
for (short k = 0; k < K; ++k) {
MMATile<T, M, N>::MMAFrag_t::mma(
D.frag_at(m, n_serp),
A.frag_at(m, k),
B.frag_at(k, n_serp),
C.frag_at(m, n_serp));
}
}
}
}
template <
typename T,
typename U,
int BM,
int BN,
int BK,
int WM,
int WN,
bool transpose_a,
bool transpose_b,
short lda_tgp,
short ldb_tgp,
typename AccumType = float,
typename Epilogue = TransformNone<U, AccumType>>
struct BlockMMA {
// MMAFrag size
STEEL_CONST short kFragSize = 8;
using MMAFrag_acc_t = BaseMMAFrag<AccumType, kFragSize, kFragSize>;
// Warp tile simdgroup matrix strides along M
STEEL_CONST short TM_stride = kFragSize * WM;
// Warp tile simdgroup matrix strides along M
STEEL_CONST short TN_stride = kFragSize * WN;
// Warp tile size along M
STEEL_CONST short TM = BM / (kFragSize * WM);
// Warp tile size along N
STEEL_CONST short TN = BN / (kFragSize * WN);
// Threadgroup A strides
STEEL_CONST short A_str_m = transpose_a ? 1 : lda_tgp; // M
STEEL_CONST short A_str_k = transpose_a ? lda_tgp : 1; // K
// Threadgroup B strides
STEEL_CONST short B_str_k = transpose_b ? 1 : ldb_tgp; // K
STEEL_CONST short B_str_n = transpose_b ? ldb_tgp : 1; // N
// Threadgroup strides along K
STEEL_CONST short tile_stride_a = kFragSize * A_str_k;
STEEL_CONST short tile_stride_b = kFragSize * B_str_k;
// Simdgroup matrices
MMATile<AccumType, TM, 1, MMAFrag_acc_t> Atile;
MMATile<AccumType, 1, TN, MMAFrag_acc_t> Btile;
MMATile<AccumType, TM, TN, MMAFrag_acc_t> Ctile;
// Offsets within threadgroup
short sm;
short sn;
short As_offset;
short Bs_offset;
/* Constructor */
METAL_FUNC BlockMMA(
ushort simd_group_id [[simdgroup_index_in_threadgroup]],
ushort simd_lane_id [[thread_index_in_simdgroup]]) {
// Determine thread position in simdgroup matrix
short tm = kFragSize * (simd_group_id / WN);
short tn = kFragSize * (simd_group_id % WN);
short2 simd_coord = MMAFrag_acc_t::get_coord(simd_lane_id);
sm = simd_coord.y;
sn = simd_coord.x;
// Determine thread and simdgroup offset
As_offset = (tm + sm) * A_str_m + (sn)*A_str_k; // M, K
Bs_offset = (sm)*B_str_k + (tn + sn) * B_str_n; // K, N
sm += tm;
sn += tn;
}
/* (BM, BK) X (BK, BN) multiply accumulate function */
METAL_FUNC void mma(const threadgroup T* As, const threadgroup T* Bs) {
// Adjust for simdgroup and thread location
As += As_offset;
Bs += Bs_offset;
// Iterate over BK in blocks of kFragSize
STEEL_PRAGMA_UNROLL
for (short kk = 0; kk < BK; kk += kFragSize) {
simdgroup_barrier(mem_flags::mem_none);
Atile.template load<T, WM, 1, A_str_m, A_str_k>(As);
simdgroup_barrier(mem_flags::mem_none);
Btile.template load<T, 1, WN, B_str_k, B_str_n>(Bs);
simdgroup_barrier(mem_flags::mem_none);
tile_matmad(Ctile, Atile, Btile, Ctile);
// Progress to next simdgroup tile
As += tile_stride_a;
Bs += tile_stride_b;
}
}
/* Store results from simdgroup_matrix results into device memory */
METAL_FUNC void store_result(device U* D, const int ldd) {
// Apply epilogue
STEEL_PRAGMA_UNROLL
for (short i = 0; i < decltype(Ctile)::kElemsPerTile; i++) {
Ctile.elems()[i] = Epilogue::apply(Ctile.elems()[i]);
}
// Adjust for simdgroup and thread location
D += sm * ldd + sn;
Ctile.template store<U, WM, WN>(D, ldd);
}
METAL_FUNC void
store_result_slice(device U* D, const int ldd, short2 start, short2 stop) {
// Apply epilogue
STEEL_PRAGMA_UNROLL
for (short i = 0; i < decltype(Ctile)::kElemsPerTile; i++) {
Ctile.elems()[i] = Epilogue::apply(Ctile.elems()[i]);
}
D += sm * ldd + sn;
start -= short2(sn, sm);
stop -= short2(sn, sm);
// TODO: Check the start as well
if (stop.y <= 0 || stop.x <= 0) {
return;
}
Ctile.template store_slice<U, WM, WN>(D, ldd, start, stop);
}
METAL_FUNC void
store_result_safe(device U* D, const int ldd, short2 dst_tile_dims) {
// Apply epilogue
STEEL_PRAGMA_UNROLL
for (short i = 0; i < decltype(Ctile)::kElemsPerTile; i++) {
Ctile.elems()[i] = Epilogue::apply(Ctile.elems()[i]);
}
// Adjust for simdgroup and thread location
D += sm * ldd + sn;
dst_tile_dims -= short2(sn, sm);
if (dst_tile_dims.x <= 0 || dst_tile_dims.y <= 0)
return;
Ctile.template store_safe<U, WM, WN>(D, ldd, dst_tile_dims);
}
/* Apply epilogue */
template <typename UnaryEpilogue>
METAL_FUNC void apply_epilogue(thread const UnaryEpilogue& epilogue_op) {
// Loop over all simdgroup tiles
STEEL_PRAGMA_UNROLL
for (short i = 0; i < decltype(Ctile)::kElemsPerTile; i++) {
Ctile.elems()[i] = epilogue_op.apply(Ctile.elems()[i]);
}
}
/* Apply epilogue */
template <typename BinaryEpilogue>
METAL_FUNC void apply_epilogue(
const device U* C,
const int ldc,
const int fdc,
thread const BinaryEpilogue& epilogue_op) {
// Adjust for simdgroup and thread location
C += (sm)*ldc + (sn)*fdc;
// Loop over all simdgroup tiles
STEEL_PRAGMA_UNROLL
for (short i = 0; i < TM; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < TN; j++) {
// Get accumulated result and associated offset in C
thread auto& accum = Ctile.frag_at(i, j);
int offset_c = (i * TM_stride) * ldc + (j * TN_stride) * fdc;
// Apply epilogue
STEEL_PRAGMA_UNROLL
for (short k = 0; k < decltype(Ctile)::kElemsPerFrag; k++) {
accum[k] = epilogue_op.apply(accum[k], C[offset_c + k * fdc]);
}
}
}
}
/* Apply epilogue */
template <typename BinaryEpilogue>
METAL_FUNC void apply_epilogue_safe(
const device U* C,
const int ldc,
const int fdc,
short2 dst_tile_dims,
thread const BinaryEpilogue& epilogue_op) {
// Adjust for simdgroup and thread location
C += (sm)*ldc + (sn)*fdc;
dst_tile_dims -= short2(sn, sm);
if (dst_tile_dims.x <= 0 || dst_tile_dims.y <= 0)
return;
// Loop over all simdgroup tiles
STEEL_PRAGMA_UNROLL
for (short i = 0; i < TM; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < TN; j++) {
// Get accumulated result and associated offset in C
thread auto& accum = Ctile.frag_at(i, j);
int offset_c = (i * TM_stride) * ldc + (j * TN_stride) * fdc;
constexpr short kelems = decltype(Ctile)::kElemsPerFrag;
// Read C
U c_elems[kelems] = {0};
STEEL_PRAGMA_UNROLL
for (short k = 0; k < kelems; k++) {
if ((j * TN_stride + k) < dst_tile_dims.x) {
c_elems[k] = C[offset_c + k * fdc];
}
}
// Apply epilogue
STEEL_PRAGMA_UNROLL
for (short k = 0; k < kelems; k++) {
accum[k] = epilogue_op.apply(accum[k], c_elems[k]);
}
}
}
}
/* Store results from simdgroup_matrix results into device memory */
METAL_FUNC void store_result(
device U* D,
const int ldd,
const device U* C,
const int ldc,
const int fdc,
thread const Epilogue& epilogue_op) const {
// Adjust for simdgroup and thread location
C += (sm)*ldc + (sn)*fdc;
D += (sm)*ldd + sn;
constexpr short kelems = decltype(Ctile)::kElemsPerFrag;
// Loop over all simdgroup tiles
STEEL_PRAGMA_UNROLL
for (short i = 0; i < TM; i++) {
STEEL_PRAGMA_UNROLL
for (short j = 0; j < TN; j++) {
// Get accumulated result and associated offset in C
thread const auto& accum = Ctile.frag_at(i, j);
int offset_c = (i * TM_stride) * ldc + (j * TN_stride) * fdc;
int offset_d = (i * TM_stride) * ldd + (j * TN_stride);
// Apply epilogue
STEEL_PRAGMA_UNROLL
for (short k = 0; k < kelems; k++) {
D[offset_d + k] = epilogue_op.apply(accum[k], C[offset_c + k * fdc]);
}
}
}
}
METAL_FUNC void store_result_safe(
device U* D,
const int ldd,
const device U* C,
const int ldc,
const int fdc,
short2 dst_tile_dims,
thread const Epilogue& epilogue_op) const {
// Adjust for simdgroup and thread location
C += (sm)*ldc + (sn)*fdc;
D += (sm)*ldd + sn;
dst_tile_dims -= short2(sn, sm);
if (dst_tile_dims.x <= 0 || dst_tile_dims.y <= 0)
return;
constexpr short kelems = decltype(Ctile)::kElemsPerFrag;
STEEL_PRAGMA_UNROLL
for (int i = 0; i < TM; i++) {
if (i * TM_stride < dst_tile_dims.y) {
STEEL_PRAGMA_UNROLL
for (int j = 0; j < TN; j++) {
// Get accumulated result and associated offset in C
thread const auto& accum = Ctile.frag_at(i, j);
int offset_c = (i * TM_stride) * ldc + (j * TN_stride) * fdc;
int offset_d = (i * TM_stride) * ldd + (j * TN_stride);
// Apply epilogue
STEEL_PRAGMA_UNROLL
for (short k = 0; k < kelems; k++) {
if ((j * TN_stride + k) < dst_tile_dims.x) {
D[offset_d + k] =
epilogue_op.apply(accum[k], C[offset_c + k * fdc]);
}
}
}
}
}
}
};
} // namespace steel
} // namespace mlx
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