import triton import triton.language as tl import triton._C.libtriton.triton as _triton import torch @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, ): """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 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) a = torch.randn((512, 512), device='cuda', dtype=torch.float16) b = torch.randn((512, 512), device='cuda', dtype=torch.float16) c = torch.empty((512, 512), device='cuda', dtype=torch.float16) mod, ctx = matmul_kernel.compile_to_ttir( a, b, c, 512, 512, 512, a.stride(0), a.stride(1), b.stride(0), b.stride(1), c.stride(0), c.stride(1), 128, 128, 128, 8, grid=(2,) ) assert mod.verify() mod.dump() mod = matmul_kernel.compile_ttir_to_llir(mod, ctx) assert mod.verify() mod.dump()