import torch import triton import triton.language as tl from .matmul_perf_model import early_config_prune, estimate_matmul_time def init_to_zero(name): return lambda nargs: nargs[name].zero_() def get_configs_io_bound(): configs = [] for num_stages in [2, 3, 4, 5, 6]: for block_m in [16, 32]: for block_k in [32, 64]: for block_n in [32, 64, 128, 256]: num_warps = 2 if block_n <= 64 else 4 configs.append( triton.Config({'BLOCK_M': block_m, 'BLOCK_N': block_n, 'BLOCK_K': block_k, 'SPLIT_K': 1}, num_stages=num_stages, num_warps=num_warps)) # split_k for split_k in [2, 4, 8, 16]: configs.append(triton.Config({'BLOCK_M': block_m, 'BLOCK_N': block_n, 'BLOCK_K': block_k, 'SPLIT_K': split_k}, num_stages=num_stages, num_warps=num_warps, pre_hook=init_to_zero('C'))) return configs @triton.autotune( configs=[ # basic configs for compute-bound matmuls triton.Config({'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=3, num_warps=8), triton.Config({'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=3, num_warps=8), triton.Config({'BLOCK_M': 256, 'BLOCK_N': 64, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 128, 'BLOCK_N': 64, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 128, 'BLOCK_N': 32, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 64, 'BLOCK_N': 32, 'BLOCK_K': 32, 'SPLIT_K': 1}, num_stages=5, num_warps=2), # good for int8 triton.Config({'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'SPLIT_K': 1}, num_stages=3, num_warps=8), triton.Config({'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 128, 'SPLIT_K': 1}, num_stages=3, num_warps=8), triton.Config({'BLOCK_M': 256, 'BLOCK_N': 64, 'BLOCK_K': 128, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 128, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 128, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 128, 'BLOCK_N': 64, 'BLOCK_K': 64, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 64, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 128, 'BLOCK_N': 32, 'BLOCK_K': 64, 'SPLIT_K': 1}, num_stages=4, num_warps=4), triton.Config({'BLOCK_M': 64, 'BLOCK_N': 32, 'BLOCK_K': 64, 'SPLIT_K': 1}, num_stages=5, num_warps=2), ] + get_configs_io_bound(), key=['M', 'N', 'K'], prune_configs_by={ 'early_config_prune': early_config_prune, 'perf_model': estimate_matmul_time, 'top_k': 10 }, ) @triton.heuristics({ 'EVEN_K': lambda args: args['K'] % (args['BLOCK_K'] * args['SPLIT_K']) == 0, }) @triton.jit def _kernel(A, B, C, M, N, K, stride_am, stride_ak, stride_bk, stride_bn, stride_cm, stride_cn, BLOCK_M: tl.constexpr, BLOCK_N: tl.constexpr, BLOCK_K: tl.constexpr, GROUP_M: tl.constexpr, SPLIT_K: tl.constexpr, EVEN_K: tl.constexpr, ACC_TYPE: tl.constexpr ): # matrix multiplication pid = tl.program_id(0) pid_z = tl.program_id(1) grid_m = (M + BLOCK_M - 1) // BLOCK_M grid_n = (N + BLOCK_N - 1) // BLOCK_N # re-order program ID for better L2 performance width = GROUP_M * grid_n group_id = pid // width group_size = min(grid_m - group_id * GROUP_M, GROUP_M) pid_m = group_id * GROUP_M + (pid % group_size) pid_n = (pid % width) // (group_size) # do matrix multiplication rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M) rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N) ram = tl.max_contiguous(tl.multiple_of(rm % M, BLOCK_M), BLOCK_M) rbn = tl.max_contiguous(tl.multiple_of(rn % N, BLOCK_N), BLOCK_N) rk = pid_z * BLOCK_K + tl.arange(0, BLOCK_K) # pointers A = A + (ram[:, None] * stride_am + rk[None, :] * stride_ak) B = B + (rk[:, None] * stride_bk + rbn[None, :] * stride_bn) acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=ACC_TYPE) for k in range(K, 0, -BLOCK_K * SPLIT_K): if EVEN_K: a = tl.load(A) b = tl.load(B) else: a = tl.load(A, mask=rk[None, :] < k, other=0.) b = tl.load(B, mask=rk[:, None] < k, other=0.) acc += tl.dot(a, b) A += BLOCK_K * SPLIT_K * stride_ak B += BLOCK_K * SPLIT_K * stride_bk acc = acc.to(C.dtype.element_ty) # rematerialize rm and rn to save registers rm = pid_m * BLOCK_M + tl.arange(0, BLOCK_M) rn = pid_n * BLOCK_N + tl.arange(0, BLOCK_N) C = C + (rm[:, None] * stride_cm + rn[None, :] * stride_cn) mask = (rm < M)[:, None] & (rn < N)[None, :] # handles write-back with reduction-splitting if SPLIT_K == 1: tl.store(C, acc, mask=mask) else: tl.atomic_add(C, acc, mask=mask) class _matmul(torch.autograd.Function): kernel = _kernel _locks = {} @staticmethod def _call(a, b): device = a.device # handle non-contiguous inputs if necessary if a.stride(0) > 1 and a.stride(1) > 1: a = a.contiguous() if b.stride(0) > 1 and b.stride(1) > 1: b = b.contiguous() # checks constraints assert a.shape[1] == b.shape[0], "incompatible dimensions" M, K = a.shape _, N = b.shape # allocates output c = torch.empty((M, N), device=device, dtype=a.dtype) # accumulator types ACC_TYPE = tl.float32 if a.dtype in [torch.float16, torch.bfloat16, torch.float32] else tl.int32 # launch kernel grid = lambda META: (triton.cdiv(M, META['BLOCK_M']) * triton.cdiv(N, META['BLOCK_N']), META['SPLIT_K']) _kernel[grid](a, b, c, M, N, K, a.stride(0), a.stride(1), b.stride(0), b.stride(1), c.stride(0), c.stride(1), GROUP_M=8, ACC_TYPE=ACC_TYPE) return c @staticmethod def forward(ctx, a, b): return _matmul._call(a, b) matmul = _matmul.apply