Triton Partition K gemm to TritonBench

Summary: This an early exploration. Triton Partition K ([link](https://github.com/NVIDIA/cutlass/blob/main/media/docs/efficient_gemm.md#parallelized-reductions)) used two kernels (gemm + reduce) to achieve the goal of splitK. Comparing with the `atomic_add` Triton GEMM, the partitionK is more friendly to epilogue fusion

Reviewed By: bertmaher, chenyang78

Differential Revision: D59948589

fbshipit-source-id: a2118947f8e20ab17d26843fd263b83e22f58541

torchbenchmark/operators/gemm/operator.py

@@ -23,7 +23,7 @@
 from .triton_matmul import matmul as triton_tutorial_matmul
 from .triton_matmul import matmul_kernel as triton_tutorial_matmul_kernel
 from .persistent_matmul import matmul_persistent, matmul_tma_persistent, matmul_tma_persistent_cached
-
+from .partition_k import matmul_partition_k
 import torch._inductor.config as inductor_config
 
 if inductor_config.is_fbcode():
@@ -74,12 +74,12 @@
 
 SPLIT_K_SHAPES = [
     (m, m, k, None)
-    for m in [128 * i for i in range(1, 5)]
-    for k in [2048 * i for i in range(1, 9)]
+    for m in [16 * i for i in range(1, 5)]
+    for k in [4096 * i for i in range(1, 9)]
 ]
 
 class Operator(BenchmarkOperator):
-    DEFAULT_METRICS = ["latency", "speedup", "accuracy", "tflops", "best_config"]
+    DEFAULT_METRICS = ["speedup", "tflops"]
     DEFAULT_PRECISION = "fp16"
 
     def __init__(self, tb_args: argparse.Namespace, extra_args: Optional[List[str]] = None):
@@ -106,6 +106,13 @@ def triton_tutorial_matmul(self, a, b, bias) -> Callable:
         else:
             return lambda: triton_tutorial_matmul(a, b)
 
+    @register_benchmark()
+    def matmul_partition_k(self, a, b, bias) -> Callable:
+        if not bias == None:
+            return lambda: matmul_partition_k(a, b) + bias
+        else:
+            return lambda: matmul_partition_k(a, b)
+
     @register_benchmark()
     def triton_persistent_matmul(self, a, b, bias) -> Callable:
         if not bias == None:

torchbenchmark/operators/gemm/partition_k.py

@@ -0,0 +1,255 @@
+import torch
+
+import triton
+import triton.language as tl
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {
+                "BLOCK_SIZE_M": 32,
+                "BLOCK_SIZE_N": 32,
+                "BLOCK_SIZE_K": 64,
+            },
+            num_stages=4,
+            num_warps=2,
+        ),
+        triton.Config(
+            {
+                "BLOCK_SIZE_M": 32,
+                "BLOCK_SIZE_N": 32,
+                "BLOCK_SIZE_K": 64,
+            },
+            num_stages=5,
+            num_warps=2,
+        ),
+        triton.Config(
+            {
+                "BLOCK_SIZE_M": 32,
+                "BLOCK_SIZE_N": 32,
+                "BLOCK_SIZE_K": 64,
+            },
+            num_stages=6,
+            num_warps=2,
+        ),
+        triton.Config(
+            {
+                "BLOCK_SIZE_M": 32,
+                "BLOCK_SIZE_N": 32,
+                "BLOCK_SIZE_K": 128,
+            },
+            num_stages=4,
+            num_warps=2,
+        ),
+        triton.Config(
+            {
+                "BLOCK_SIZE_M": 32,
+                "BLOCK_SIZE_N": 32,
+                "BLOCK_SIZE_K": 128,
+            },
+            num_stages=5,
+            num_warps=2,
+        ),
+        triton.Config(
+            {
+                "BLOCK_SIZE_M": 32,
+                "BLOCK_SIZE_N": 32,
+                "BLOCK_SIZE_K": 128,
+            },
+            num_stages=6,
+            num_warps=2,
+        ),
+    ],
+    key=["M", "N", "K", "PK"],
+)
+@triton.jit
+def _matmul_partition_k(
+    # Pointers to matrices
+    a_ptr,
+    b_ptr,
+    c_buf_ptr,
+    # Matrix dimensions
+    M,
+    N,
+    K,
+    PK,
+    PK_SIZE,
+    # 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_cb_m,
+    stride_cb_n,
+    stride_cb_k,
+    # Meta-parameters
+    BLOCK_SIZE_M: tl.constexpr,
+    BLOCK_SIZE_N: tl.constexpr,
+    BLOCK_SIZE_K: 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_m = tl.program_id(axis=0)
+    pid_n = tl.program_id(axis=1)
+    pid_pk = tl.program_id(axis=2)
+    # num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
+    # num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
+    # num_pid_pk = PK
+    # num_pid_nk = num_pid_n * num_pid_pk
+    # num_pid_in_group = GROUP_SIZE_M * num_pid_nk
+    # 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_nk = (pid % num_pid_in_group) // group_size_m
+    # pid_n = pid_nk // num_pid_n
+    # pid_pk = pid_nk % num_pid_n
+
+    # ----------------------------------------------------------
+    # 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 = (pid_pk * PK_SIZE + tl.arange(0, BLOCK_SIZE_K)) % 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(PK_SIZE, 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)
+        a = tl.load(a_ptrs)
+        b = tl.load(b_ptrs)
+        accumulator += tl.dot(a, b)
+        a_ptrs += BLOCK_SIZE_K * stride_ak
+        b_ptrs += BLOCK_SIZE_K * stride_bk
+    acc = accumulator.to(tl.float16)
+
+    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)
+    offs_ck = pid_pk
+    c_buf_ptrs = (
+        c_buf_ptr
+        + stride_cb_m * offs_cm[:, None, None]
+        + stride_cb_n * offs_cn[None, :, None]
+        + stride_cb_k * offs_ck[None, None, :]
+    )
+    tl.store(c_buf_ptrs, acc[:, :, None])
+
+
+@triton.jit
+def _reduce(
+    c_ptr,
+    c_buf_ptr,
+    M,
+    N,
+    stride_cm,
+    stride_cn,
+    stride_cb_m,
+    stride_cb_n,
+    stride_cb_k,
+    PK: tl.constexpr,
+    BLOCK_SIZE_M: tl.constexpr,
+    BLOCK_SIZE_N: tl.constexpr,
+):
+    pid = tl.program_id(0)
+    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
+    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
+    pid_m = pid // num_pid_m
+    pid_n = pid % num_pid_n
+
+    offs_m = (pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)) % M
+    offs_n = (pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)) % N
+    offs_k = tl.arange(0, PK)
+    c_buf_ptrs = c_buf_ptr + (
+        offs_m[:, None, None] * stride_cb_m
+        + offs_n[None, :, None] * stride_cb_n
+        + offs_k[None, None, :] * stride_cb_k
+    )
+    c_buf = tl.load(c_buf_ptrs)
+    reduced_k = tl.sum(c_buf, axis=2)
+
+    c_ptrs = c_ptr + (offs_m[:, None] * stride_cm + offs_n[None, :] * stride_cn)
+    tl.store(c_ptrs, reduced_k)
+
+def matmul_partition_k(a, b, triton_reduce=False):
+    # Check 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"
+
+    partitionK = 64
+
+    M, K = a.shape
+    K, N = b.shape
+    # Allocates output.
+    partitionK_SIZE = K // partitionK
+
+    c_buf = torch.empty((M, N, partitionK), device=a.device, dtype=a.dtype)
+    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"]),
+        partitionK,
+    )
+    _matmul_partition_k[grid](
+        a,
+        b,
+        c_buf,  #
+        M,
+        N,
+        K,  #
+        partitionK,
+        partitionK_SIZE,  #
+        a.stride(0),
+        a.stride(1),  #
+        b.stride(0),
+        b.stride(1),  #
+        c_buf.stride(0),  #
+        c_buf.stride(1),
+        c_buf.stride(2),
+    )
+    if triton_reduce:
+        BLOCK_M = 32
+        BLOCK_N = 32
+
+        grid_reduce = lambda META: (triton.cdiv(M, BLOCK_M) * triton.cdiv(N, BLOCK_N),)
+
+        _reduce[grid_reduce](
+            c,
+            c_buf,
+            M,
+            N,
+            c.stride(0),
+            c.stride(1),
+            c_buf.stride(0),
+            c_buf.stride(1),
+            c_buf.stride(2),
+            partitionK,
+            BLOCK_M,
+            BLOCK_N,
+        )
+        return c
+    else:
+        return c_buf.sum(dim=2)