gemm.h

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// Copyright © 2024 Apple Inc.
 
#pragma once
 
#include "mlx/backend/metal/kernels/steel/gemm/loader.h"
#include "mlx/backend/metal/kernels/steel/gemm/mma.h"
#include "mlx/backend/metal/kernels/steel/gemm/params.h"
#include "mlx/backend/metal/kernels/steel/gemm/transforms.h"
#include "mlx/backend/metal/kernels/steel/utils.h"
 
using namespace metal;
 
// GEMM kernel class
 
namespace mlx {
namespace steel {
 
template <bool M_aligned, bool N_aligned, bool K_aligned>
struct LoopAlignment {};
 
template <
    typename T,
    typename U,
    int BM,
    int BN,
    int BK,
    int WM,
    int WN,
    bool transpose_a,
    bool transpose_b,
    bool MN_aligned,
    bool K_aligned,
    typename AccumType = typename AccumHelper<T>::accum_type,
    typename Epilogue = TransformNone<U, AccumType>>
struct GEMMKernel {
  STEEL_CONST short tgp_padding_a = 16 / sizeof(T);
  STEEL_CONST short tgp_padding_b = 16 / sizeof(T);
  STEEL_CONST short tgp_mem_size_a =
      transpose_a ? BK * (BM + tgp_padding_a) : BM * (BK + tgp_padding_a);
  STEEL_CONST short tgp_mem_size_b =
      transpose_b ? BN * (BK + tgp_padding_b) : BK * (BN + tgp_padding_b);
  STEEL_CONST short tgp_mem_size = tgp_mem_size_a + tgp_mem_size_b;
 
  STEEL_CONST short tgp_size = WM * WN * 32;
 
  using loader_a_t = BlockLoader<
      T,
      transpose_a ? BK : BM,
      transpose_a ? BM : BK,
      transpose_a ? BM + tgp_padding_a : BK + tgp_padding_a,
      !transpose_a,
      tgp_size>;
  using loader_b_t = BlockLoader<
      T,
      transpose_b ? BN : BK,
      transpose_b ? BK : BN,
      transpose_b ? BK + tgp_padding_b : BN + tgp_padding_b,
      transpose_b,
      tgp_size>;
  using mma_t = BlockMMA<
      T,
      U,
      BM,
      BN,
      BK,
      WM,
      WN,
      transpose_a,
      transpose_b,
      transpose_a ? BM + tgp_padding_a : BK + tgp_padding_a,
      transpose_b ? BK + tgp_padding_b : BN + tgp_padding_b,
      AccumType,
      Epilogue>;
 
  /* Main kernel function */
  template <bool M_aligned, bool N_aligned, bool K_aligned_>
  static METAL_FUNC void gemm_loop(
      threadgroup T* As [[threadgroup(0)]],
      threadgroup T* Bs [[threadgroup(1)]],
      const int gemm_k_iterations,
      thread loader_a_t& loader_a,
      thread loader_b_t& loader_b,
      thread mma_t& mma_op,
      thread const short& tgp_bm,
      thread const short& tgp_bn,
      thread const short& lbk,
      LoopAlignment<M_aligned, N_aligned, K_aligned_> l = {}) {
    // Appease the compiler
    (void)l;
 
    short2 tile_dims_A = transpose_a ? short2(tgp_bm, BK) : short2(BK, tgp_bm);
 
    short2 tile_dims_B = transpose_b ? short2(BK, tgp_bn) : short2(tgp_bn, BK);
 
    for (int k = 0; k < gemm_k_iterations; k++) {
      threadgroup_barrier(mem_flags::mem_threadgroup);
      // Load elements into threadgroup
      if (M_aligned) {
        loader_a.load_unsafe();
      } else {
        loader_a.load_safe(tile_dims_A);
      }
 
      if (N_aligned) {
        loader_b.load_unsafe();
      } else {
        loader_b.load_safe(tile_dims_B);
      }
 
      threadgroup_barrier(mem_flags::mem_threadgroup);
 
      // Multiply and accumulate threadgroup elements
      mma_op.mma(As, Bs);
 
      // Prepare for next iteration
      loader_a.next();
      loader_b.next();
    }
 
    if (!K_aligned_) {
      threadgroup_barrier(mem_flags::mem_threadgroup);
 
      short2 tile_dims_A_last =
          transpose_a ? short2(tgp_bm, lbk) : short2(lbk, tgp_bm);
      short2 tile_dims_B_last =
          transpose_b ? short2(lbk, tgp_bn) : short2(tgp_bn, lbk);
 
      loader_a.load_safe(tile_dims_A_last);
      loader_b.load_safe(tile_dims_B_last);
 
      threadgroup_barrier(mem_flags::mem_threadgroup);
 
      mma_op.mma(As, Bs);
    }
  }
 
  /* Main kernel function */
  static METAL_FUNC void run(
      const device T* A [[buffer(0)]],
      const device T* B [[buffer(1)]],
      device U* D [[buffer(2)]],
      const constant GEMMParams* params [[buffer(3)]],
      threadgroup T* As [[threadgroup(0)]],
      threadgroup T* Bs [[threadgroup(1)]],
      uint simd_lane_id [[thread_index_in_simdgroup]],
      uint simd_group_id [[simdgroup_index_in_threadgroup]],
      uint3 tid [[threadgroup_position_in_grid]],
      uint3 lid [[thread_position_in_threadgroup]]) {
    // Pacifying compiler
    (void)lid;
 
    const int tid_y = ((tid.y) << params->swizzle_log) +
        ((tid.x) & ((1 << params->swizzle_log) - 1));
    const int tid_x = (tid.x) >> params->swizzle_log;
 
    if (params->tiles_n <= tid_x || params->tiles_m <= tid_y) {
      return;
    }
 
    threadgroup_barrier(mem_flags::mem_none);
 
    // Find block in A, B, C
    const int c_row = tid_y * BM;
    const int c_col = tid_x * BN;
    const size_t c_row_long = size_t(c_row);
    const size_t c_col_long = size_t(c_col);
 
    A += transpose_a ? c_row_long : c_row_long * params->lda;
    B += transpose_b ? c_col_long * params->ldb : c_col_long;
    D += c_row_long * params->ldd + c_col_long;
 
    // Prepare threadgroup loading operations
    thread loader_a_t loader_a(A, params->lda, As, simd_group_id, simd_lane_id);
    thread loader_b_t loader_b(B, params->ldb, Bs, simd_group_id, simd_lane_id);
 
    // Prepare threadgroup mma operation
    thread mma_t mma_op(simd_group_id, simd_lane_id);
 
    int gemm_k_iterations = params->gemm_k_iterations_aligned;
 
    // MNK aligned loop
    if (MN_aligned) {
      for (int k = 0; k < gemm_k_iterations; k++) {
        threadgroup_barrier(mem_flags::mem_threadgroup);
        // Load elements into threadgroup
        loader_a.load_unsafe();
        loader_b.load_unsafe();
 
        threadgroup_barrier(mem_flags::mem_threadgroup);
 
        // Multiply and accumulate threadgroup elements
        mma_op.mma(As, Bs);
 
        // Prepare for next iteration
        loader_a.next();
        loader_b.next();
      }
 
      threadgroup_barrier(mem_flags::mem_none);
 
      // Loop tail
      if (!K_aligned) {
        int lbk = params->K - params->gemm_k_iterations_aligned * BK;
        short2 tile_dims_A = transpose_a ? short2(BM, lbk) : short2(lbk, BM);
        short2 tile_dims_B = transpose_b ? short2(lbk, BN) : short2(BN, lbk);
 
        loader_a.load_safe(tile_dims_A);
        loader_b.load_safe(tile_dims_B);
 
        threadgroup_barrier(mem_flags::mem_threadgroup);
 
        mma_op.mma(As, Bs);
      }
 
      // Store results to device memory
      mma_op.store_result(D, params->ldd);
      return;
 
    }
    // MN unaligned loop
    else { // Loop over K - unaligned case
      short tgp_bm = min(BM, params->M - c_row);
      short tgp_bn = min(BN, params->N - c_col);
      short leftover_bk = params->K - params->gemm_k_iterations_aligned * BK;
 
      if (tgp_bm == BM && tgp_bn == BN) {
        gemm_loop<true, true, K_aligned>(
            As,
            Bs,
            gemm_k_iterations,
            loader_a,
            loader_b,
            mma_op,
            tgp_bm,
            tgp_bn,
            leftover_bk);
 
        mma_op.store_result(D, params->ldd);
        return;
 
      } else if (tgp_bn == BN) {
        gemm_loop<false, true, K_aligned>(
            As,
            Bs,
            gemm_k_iterations,
            loader_a,
            loader_b,
            mma_op,
            tgp_bm,
            tgp_bn,
            leftover_bk);
 
        mma_op.store_result_safe(D, params->ldd, short2(tgp_bn, tgp_bm));
        return;
 
      } else if (tgp_bm == BM) {
        gemm_loop<true, false, K_aligned>(
            As,
            Bs,
            gemm_k_iterations,
            loader_a,
            loader_b,
            mma_op,
            tgp_bm,
            tgp_bn,
            leftover_bk);
 
        mma_op.store_result_safe(D, params->ldd, short2(tgp_bn, tgp_bm));
        return;
 
      } else {
        gemm_loop<false, false, K_aligned>(
            As,
            Bs,
            gemm_k_iterations,
            loader_a,
            loader_b,
            mma_op,
            tgp_bm,
            tgp_bn,
            leftover_bk);
 
        mma_op.store_result_safe(D, params->ldd, short2(tgp_bn, tgp_bm));
        return;
      }
    }
  }
};
 
} // namespace steel
} // namespace mlx