import torch import triton import triton.language as tl # Ensure CUDA is available and properly initialize device if not torch.cuda.is_available(): raise RuntimeError("CUDA is not available. This benchmark requires a CUDA-enabled GPU.") DEVICE = torch.device("cuda:0") torch.cuda.set_device(DEVICE) @triton.jit def gelu(x): return x * 0.5 * (1.0 + tl.extra.cuda.libdevice.erf(x * 0.7071067811865476)) @triton.autotune( configs=[ triton.Config( { "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 128, "BLOCK_SIZE_K": 64, "GROUP_SIZE_M": 8, "NUM_STAGES": 4, }, num_stages=4, num_warps=8, ), ], key=["M", "N", "K"], use_cuda_graph=True, ) @triton.jit def matmul_kernel( a_ptr, b_ptr, c_ptr, M, N, K, stride_am, stride_ak, # stride_bk, stride_bn, # stride_cm, stride_cn, # Meta-parameters BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr, # GROUP_SIZE_M: tl.constexpr, # NUM_STAGES: tl.constexpr, ): """Kernel for computing the matmul C = A x B. A has shape (M, K), B has shape (K, N) and C has shape (M, N) """ # ----------------------------------------------------------- # Map program ids `pid` to the block of C it should compute. # This is done in a grouped ordering to promote L2 data reuse. # See above `L2 Cache Optimizations` section for details. pid = tl.program_id(axis=0) num_pid_m = tl.cdiv(M, BLOCK_SIZE_M) num_pid_n = tl.cdiv(N, BLOCK_SIZE_N) num_pid_in_group = GROUP_SIZE_M * num_pid_n group_id = pid // num_pid_in_group first_pid_m = group_id * GROUP_SIZE_M group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M) pid_m = first_pid_m + ((pid % num_pid_in_group) % group_size_m) pid_n = (pid % num_pid_in_group) // group_size_m # ---------------------------------------------------------- # Create pointers for the first blocks of A and B. # We will advance this pointer as we move in the K direction # and accumulate # `a_ptrs` is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers # `b_ptrs` is a block of [BLOCK_SIZE_K, BLOCK_SIZE_N] pointers # See above `Pointer Arithmetic` section for details offs_am = (pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)) % M offs_bn = (pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)) % N offs_k = tl.arange(0, BLOCK_SIZE_K) a_ptrs = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak) b_ptrs = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn) # ----------------------------------------------------------- # Iterate to compute a block of the C matrix. # We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block # of fp32 values for higher accuracy. # `accumulator` will be converted back to fp16 after the loop. accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32) for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)): # Load the next block of A and B, generate a mask by checking the K dimension. # If it is out of bounds, set it to 0. a = tl.load(a_ptrs, mask=offs_k[None, :] < K - k * BLOCK_SIZE_K, other=0.0) b = tl.load(b_ptrs, mask=offs_k[:, None] < K - k * BLOCK_SIZE_K, other=0.0) # We accumulate along the K dimension. accumulator = tl.dot(a, b, accumulator) # Advance the ptrs to the next K block. a_ptrs += BLOCK_SIZE_K * stride_ak b_ptrs += BLOCK_SIZE_K * stride_bk accumulator = gelu(accumulator) c = accumulator.to(tl.float16) # ----------------------------------------------------------- # Write back the block of the output matrix C with masks. offs_cm = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M) offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N) c_ptrs = c_ptr + stride_cm * offs_cm[:, None] + stride_cn * offs_cn[None, :] c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N) tl.store(c_ptrs, c, mask=c_mask) def matmul(a, b): assert a.shape[1] == b.shape[0], "Illegal dimensions of input operands" assert a.is_contiguous(), "Matrix A must be contiguous" (M, N, K) = (a.shape[0], b.shape[1], a.shape[1]) c = torch.zeros((M, N), dtype=torch.float16, device=DEVICE) # 1D launch kernel where each block gets its own program. grid = lambda META: ( triton.cdiv(M, META["BLOCK_SIZE_M"]) * triton.cdiv(N, META["BLOCK_SIZE_N"]), ) matmul_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), # ) return c