import torch import triton import triton.language as tl # % # :code:`triton.jit`'ed functions can be auto-tuned by using the `triton.autotune` # decorator, which consumes: # - A list of :code:`triton.Config` objects that define different configurations of # meta-parameters (e.g., BLOCK_SIZE_M) and compilation options (e.g., num_warps) to try # - An autotuning *key* whose change in values will trigger evaluation of all the # provided configs @triton.autotune( configs=[ triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8), triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8), triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2), triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2), ], key=['M', 'N', 'K'], ) @triton.jit def matmul_kernel( # Pointers to matrices a_ptr, b_ptr, c_ptr, # Matrix dimensions M, N, K, # The stride variables represent how much to increase the ptr by when moving by 1 # element in a particular dimension. E.g. stride_am is how much to increase a_ptr # by to get the element one row down (A has M rows) 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, ACTIVATION: 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 % 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 Arithmetics` section for details offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M) offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_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, K, BLOCK_SIZE_K): # Note that for simplicity, we don't apply a mask here. # This means that if K is not a multiple of BLOCK_SIZE_K, # this will access out-of-bounds memory and produce an # error or (worse!) incorrect results. a = tl.load(a_ptrs) b = tl.load(b_ptrs) # We accumulate along the K dimension accumulator += tl.dot(a, b) # Advance the ptrs to the next K block a_ptrs += BLOCK_SIZE_K * stride_ak b_ptrs += BLOCK_SIZE_K * stride_bk # you can fuse arbitrary activation functions here # while the accumulator is still in FP32! if ACTIVATION == "leaky_relu": accumulator = leaky_relu(accumulator) c = accumulator.to(tl.float16) # ----------------------------------------------------------- # Write back the block of the output matrix C 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) # we can fuse `leaky_relu` by providing it as an `ACTIVATION` meta-parameter in `_matmul` @triton.jit def leaky_relu(x): x = x + 1 return tl.where(x >= 0, x, 0.01 * x) def matmul(a, b, activation=""): # checks constraints assert a.shape[1] == b.shape[0], "incompatible dimensions" assert a.is_contiguous(), "matrix A must be contiguous" assert b.is_contiguous(), "matrix B must be contiguous" M, K = a.shape K, N = b.shape assert ( K % 32 == 0 ), "We don't check memory-out-of-bounds with K so K must be divisible by BLOCK_SIZE_K" # allocates output c = torch.empty((M, N), device=a.device, dtype=a.dtype) # 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), ACTIVATION=activation, ) return c torch.manual_seed(0) a = torch.randn((512, 512), device='cuda', dtype=torch.float16) b = torch.randn((512, 512), device='cuda', dtype=torch.float16) triton_output = matmul(a, b) torch_output = torch.matmul(a, b) print(f"triton_output={triton_output}") print(f"torch_output={torch_output}") if triton.testing.allclose(triton_output, torch_output): print("✅ Triton and Torch match") else: print("❌ Triton and Torch differ")