[Deterministic] Optimize bmm_batch_invariant op (#12522)
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Minglei Zhu
@@ -559,19 +559,215 @@ def mean_batch_invariant(input, dim, keepdim=False, dtype: torch.dtype | None =
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return torch.sum(input, dim=dim, keepdim=keepdim, dtype=torch.float32) / n_elems
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@triton.jit
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def bmm_kernel_persistent(
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a_ptr,
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b_ptr,
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c_ptr, #
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B,
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M,
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N,
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K, #
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stride_ab,
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stride_am,
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stride_ak,
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stride_bb,
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stride_bk,
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stride_bn,
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stride_cb,
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stride_cm,
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stride_cn,
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BLOCK_SIZE_M: tl.constexpr, #
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BLOCK_SIZE_N: tl.constexpr, #
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BLOCK_SIZE_K: tl.constexpr, #
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GROUP_SIZE_M: tl.constexpr, #
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NUM_SMS: tl.constexpr, #
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A_LARGE: tl.constexpr,
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B_LARGE: tl.constexpr,
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C_LARGE: tl.constexpr,
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):
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"""
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Batched matrix multiplication kernel that processes batches in parallel.
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Each tile processes a (BLOCK_SIZE_M, BLOCK_SIZE_N) output block for a specific batch.
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"""
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start_pid = tl.program_id(axis=0)
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num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
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num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
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k_tiles = tl.cdiv(K, BLOCK_SIZE_K)
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num_tiles_per_batch = num_pid_m * num_pid_n
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num_tiles_total = B * num_tiles_per_batch
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offs_k_for_mask = tl.arange(0, BLOCK_SIZE_K)
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num_pid_in_group = GROUP_SIZE_M * num_pid_n
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# Process tiles in a deterministic order: batch-major ordering
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for tile_id in tl.range(start_pid, num_tiles_total, NUM_SMS, flatten=True):
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# Decompose tile_id into batch and within-batch tile
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batch_idx = tile_id // num_tiles_per_batch
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tile_in_batch = tile_id % num_tiles_per_batch
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pid_m, pid_n = _compute_pid(
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tile_in_batch, num_pid_in_group, num_pid_m, GROUP_SIZE_M, NUM_SMS
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)
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start_m = pid_m * BLOCK_SIZE_M
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start_n = pid_n * BLOCK_SIZE_N
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offs_am = start_m + tl.arange(0, BLOCK_SIZE_M)
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offs_bn = start_n + tl.arange(0, BLOCK_SIZE_N)
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if A_LARGE:
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offs_am = offs_am.to(tl.int64)
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if B_LARGE:
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offs_bn = offs_bn.to(tl.int64)
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offs_am = tl.where(offs_am < M, offs_am, 0)
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offs_bn = tl.where(offs_bn < N, offs_bn, 0)
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offs_am = tl.max_contiguous(tl.multiple_of(offs_am, BLOCK_SIZE_M), BLOCK_SIZE_M)
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offs_bn = tl.max_contiguous(tl.multiple_of(offs_bn, BLOCK_SIZE_N), BLOCK_SIZE_N)
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# Add batch offset
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if A_LARGE or B_LARGE:
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batch_idx_typed = batch_idx.to(tl.int64)
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else:
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batch_idx_typed = batch_idx
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accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
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for ki in range(k_tiles):
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if A_LARGE or B_LARGE:
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offs_k = ki * BLOCK_SIZE_K + tl.arange(0, BLOCK_SIZE_K).to(tl.int64)
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else:
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offs_k = ki * BLOCK_SIZE_K + tl.arange(0, BLOCK_SIZE_K)
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a_ptrs = a_ptr + (
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batch_idx_typed * stride_ab
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+ offs_am[:, None] * stride_am
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+ offs_k[None, :] * stride_ak
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)
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b_ptrs = b_ptr + (
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batch_idx_typed * stride_bb
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+ offs_k[:, None] * stride_bk
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+ offs_bn[None, :] * stride_bn
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)
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a = tl.load(
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a_ptrs, mask=offs_k_for_mask[None, :] < K - ki * BLOCK_SIZE_K, other=0.0
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)
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b = tl.load(
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b_ptrs, mask=offs_k_for_mask[:, None] < K - ki * BLOCK_SIZE_K, other=0.0
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)
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accumulator = tl.dot(a, b, accumulator)
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offs_cm = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
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offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
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if C_LARGE:
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offs_cm = offs_cm.to(tl.int64)
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offs_cn = offs_cn.to(tl.int64)
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c_ptrs = (
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c_ptr
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+ batch_idx_typed * stride_cb
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+ stride_cm * offs_cm[:, None]
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+ stride_cn * offs_cn[None, :]
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)
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c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
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if c_ptr.dtype.element_ty == tl.float8e4nv:
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c = accumulator.to(tl.float8e4nv)
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elif c_ptr.dtype.element_ty == tl.bfloat16:
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c = accumulator.to(tl.bfloat16)
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elif c_ptr.dtype.element_ty == tl.float32:
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c = accumulator.to(tl.float32)
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else:
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c = accumulator.to(tl.float16)
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tl.store(c_ptrs, c, mask=c_mask)
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def bmm_batch_invariant(a, b, *, out=None):
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# Batched matrix multiply: (B, M, K) x (B, K, N) -> (B, M, N)
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# Process each batch separately with our persistent kernel
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# Process batches in parallel with our persistent kernel
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if a.ndim == 3 and b.ndim == 3:
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results = []
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for i in range(a.shape[0]):
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results.append(matmul_persistent(a[i], b[i]))
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result = torch.stack(results, dim=0)
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# Check constraints
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assert a.shape[0] == b.shape[0], "Batch sizes must match"
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assert a.shape[2] == b.shape[1], "Incompatible dimensions"
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assert a.dtype == b.dtype, "Incompatible dtypes"
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if out is not None:
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out.copy_(result)
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return out
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return result
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B = a.shape[0]
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M = a.shape[1]
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K = a.shape[2]
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N = b.shape[2]
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dtype = a.dtype
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# Allocate output
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if out is None:
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c = torch.empty((B, M, N), device=a.device, dtype=dtype)
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else:
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c = out
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NUM_SMS = torch.cuda.get_device_properties("cuda").multi_processor_count
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# Use fixed kernel configuration for determinism
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configs = {
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torch.bfloat16: {
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"BLOCK_SIZE_M": 128,
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"BLOCK_SIZE_N": 128,
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"BLOCK_SIZE_K": 64,
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"GROUP_SIZE_M": 8,
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"num_stages": 3,
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"num_warps": 8,
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},
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torch.float16: {
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"BLOCK_SIZE_M": 128,
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"BLOCK_SIZE_N": 256,
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"BLOCK_SIZE_K": 64,
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"GROUP_SIZE_M": 8,
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"num_stages": 3,
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"num_warps": 8,
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},
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torch.float32: {
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"BLOCK_SIZE_M": 128,
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"BLOCK_SIZE_N": 128,
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"BLOCK_SIZE_K": 32,
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"GROUP_SIZE_M": 8,
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"num_stages": 3,
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"num_warps": 8,
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},
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}
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config = configs.get(dtype)
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if config is None:
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raise ValueError(
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f"Unsupported dtype {dtype} for bmm_batch_invariant. "
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f"Supported dtypes are: {list(configs.keys())}"
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)
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# Grid: limit by NUM_SMS for persistent kernel approach
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num_tiles_per_batch = triton.cdiv(M, config["BLOCK_SIZE_M"]) * triton.cdiv(
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N, config["BLOCK_SIZE_N"]
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)
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num_tiles_total = B * num_tiles_per_batch
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grid = (min(NUM_SMS, num_tiles_total),)
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bmm_kernel_persistent[grid](
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a,
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b,
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c, #
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B,
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M,
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N,
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K, #
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a.stride(0),
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a.stride(1),
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a.stride(2), #
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b.stride(0),
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b.stride(1),
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b.stride(2), #
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c.stride(0),
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c.stride(1),
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c.stride(2), #
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NUM_SMS=NUM_SMS, #
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A_LARGE=a.numel() > 2**31,
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B_LARGE=b.numel() > 2**31,
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C_LARGE=c.numel() > 2**31,
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**config,
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)
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return c
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else:
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raise ValueError(
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f"bmm_batch_invariant expects 3D tensors, "
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