matmul_sparse.py

# Original kernel from Chao Xu (Dustinpro) and Yuanwei Fang (fywkevin)
#
# Triton official: https://triton-lang.org/main/getting-started/tutorials/03-matrix-multiplication.html
# scatter2scatter: https://github.com/shawntan/scattermoe/blob/main/scattermoe/kernels/ops.py#L58
# OpenAI sparse-autoencoder: https://github.com/openai/sparse_autoencoder/blob/main/sparse_autoencoder/kernels.py#L220
# Apple sparse-CCE: https://github.com/apple/ml-cross-entropy/blob/e43af99cb21ea27e4afe0c90c04e66f9abfd47c6/cut_cross_entropy/cce_lse_forward.py#L26
# Sparse Toolkit: https://github.com/stanford-futuredata/stk/blob/736313768ef697ce13a0594a41b2512a0fbc9884/stk/backend/triton_kernels.py#L34
import torch

# @manual=//triton:triton
import triton

# @manual=//triton:triton
import triton.language as tl


def is_cuda():
    return triton.runtime.driver.active.get_current_target().backend == "cuda"


def is_hip_mi200():
    target = triton.runtime.driver.active.get_current_target()
    return target.backend == "hip" and target.arch == "gfx90a"


def get_cuda_autotune_config(sparse: bool):
    # keep a simple config for simplicity
    return [
        triton.Config(
            {
                "BLOCK_SIZE_M": 128,
                "BLOCK_SIZE_N": 256,
                "BLOCK_SIZE_K": 64,
                "GROUP_SIZE_M": 8,
            },
            num_stages=6 if sparse else 3,
            num_warps=8,
        )
    ]


def get_autotune_config(sparse: bool):
    return get_cuda_autotune_config(sparse)


# `triton.jit`'ed functions can be auto-tuned by using the `triton.autotune` decorator, which consumes:
#   - A list of `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 auto-tuning *key* whose change in values will trigger evaluation of all the
#       provided configs
@triton.autotune(
    configs=get_autotune_config(sparse=False),
    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,  #
):
    """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 the `L2 Cache Optimizations` section for details.

    ## This section can reduce 10% runtime but let's comment it out for now for simplicity
    # 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

    pid_m = tl.program_id(axis=0)
    pid_n = tl.program_id(axis=1)

    # ----------------------------------------------------------
    # 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)
    # offs_k = tl.max_contiguous(tl.load(idx_ptr + offs_k), BLOCK_SIZE_K)
    # offs_k = tl.arange(0, BLOCK_SIZE_K)
    # offs_am = tl.load(idx_ptr + tl.arange(0, BLOCK_SIZE_M) * )
    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.
        # For simplicity, I assume the dimensions are always divisible by BLOCK_SIZE_K
        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)

        # [Failed Attempt] If we only load half values, a @ b will be much slower.
        # a = tl.load(a_ptrs, mask=offs_k[None, :] % 2 == 0, other=0.0)
        # b = tl.load(b_ptrs, mask=offs_k[:, None] % 2 == 0, 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
    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, :]
    # this mask is somehow necessary for accurate match
    c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
    tl.store(c_ptrs, c, mask=c_mask)


@triton.autotune(
    configs=get_autotune_config(sparse=True),
    key=["M", "N", "K"],
)
@triton.jit
def matmul_sparse_kernel(
    # Pointers to matrices
    a_ptr,
    b_ptr,
    c_ptr,
    idx_ptr,
    # Matrix dimensions
    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,  #
):
    """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)
    """
    pid_m = tl.program_id(axis=0)
    pid_n = tl.program_id(axis=1)

    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_bn[None, :] * stride_bn  # + offs_k[:, None] * stride_bk

    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
    for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
        # Load idx_ptr to get the indices
        selected_idx = tl.max_contiguous(
            tl.load(idx_ptr + k * BLOCK_SIZE_K + offs_k), BLOCK_SIZE_K
        )
        # Only load the selected rows and cols
        a = tl.load(a_ptrs + selected_idx[None, :] * stride_ak)
        b = tl.load(b_ptrs + selected_idx[:, None] * stride_bk)

        # We accumulate along the K dimension.
        accumulator = tl.dot(a, b, 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, :]
    # this mask is somehow necessary for accurate match
    c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
    tl.store(c_ptrs, c, mask=c_mask)


def matmul(a, b):
    # Check constraints.
    assert a.shape[1] == b.shape[0], "Incompatible dimensions"
    # assert a.is_contiguous(), "Matrix A must be contiguous"
    M, K = a.shape
    K, N = b.shape
    b = b.contiguous()
    # Allocates output.
    c = torch.empty((M, N), device=a.device, dtype=torch.float16)
    # 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"]),
        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


def matmul_sparse(a, b, step_size=1):
    # NOTE: may set the step_size as 1, 2, 4 ... for different sparsity levels

    # Check constraints.
    assert a.shape[1] == b.shape[0], "Incompatible dimensions"
    # assert a.is_contiguous(), "Matrix A must be contiguous"
    M, K = a.shape
    K, N = b.shape
    b = b.contiguous()
    # Allocates output.
    c = torch.empty((M, N), device=a.device, dtype=torch.float16)
    # 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"]),
        triton.cdiv(M, META["BLOCK_SIZE_M"]),
        triton.cdiv(N, META["BLOCK_SIZE_N"]),
    )

    # One more arg for idx_ptr
    selected_k_idx = torch.arange(0, K, step_size, device=a.device)

    matmul_sparse_kernel[grid](
        a,
        b,
        c,
        selected_k_idx,
        M,
        N,
        K // step_size,
        a.stride(0),
        a.stride(1),  #
        b.stride(0),
        b.stride(1),  #
        c.stride(0),
        c.stride(1),  #
    )

    return c


TORCH_HAS_FP8 = False
ref_lib = "cuBLAS" if is_cuda() else "rocBLAS"
configs = []
for fp8_inputs in [False, True]:
    if fp8_inputs and (not TORCH_HAS_FP8 or not is_cuda()):
        continue
    configs.append(
        triton.testing.Benchmark(
            x_names=["M", "N", "K"],  # Argument names to use as an x-axis for the plot
            # NOTE: I fixed the input M, N, K to be 5120, 13824, 5120
            x_vals=[(8192, 13824, 5120)] * 3,  # Different possible values for `x_name`
            line_arg="provider",  # Argument name whose value corresponds to a different line in the plot
            # Possible values for `line_arg`
            # Don't compare to cublas for fp8 cases as torch.matmul doesn't support fp8 at the moment.
            line_vals=["triton"]
            if fp8_inputs
            else [
                ref_lib.lower(),
                "triton",
                "triton_sparse",
            ],  # Label name for the lines
            line_names=["Triton"]
            if fp8_inputs
            else [ref_lib, "Triton", "Triton_Sparse"],  # Line styles
            styles=[("green", "-"), ("blue", "-"), ("red", "-")],  # Line styles
            ylabel="TFLOPS",  # Label name for the y-axis
            plot_name="matmul-performance-"
            + (
                "fp16" if not fp8_inputs else "fp8"
            ),  # Name for the plot, used also as a file name for saving the plot.
            args={"fp8_inputs": fp8_inputs},
        )
    )


@triton.testing.perf_report(configs)
def benchmark(M, N, K, provider, fp8_inputs):
    a = torch.randn((M, K), device="cuda", dtype=torch.float16)
    b = torch.randn((K, N), device="cuda", dtype=torch.float16)

    a = a.T.contiguous().T

    quantiles = [0.5, 0.2, 0.8]
    if provider == ref_lib.lower():
        ms, min_ms, max_ms = triton.testing.do_bench(
            lambda: torch.matmul(a, b), quantiles=quantiles
        )
    if provider == "triton":
        ms, min_ms, max_ms = triton.testing.do_bench(
            lambda: matmul(a, b), quantiles=quantiles
        )
        print(matmul_kernel.best_config, ms)
    if provider == "triton_sparse":
        ms, min_ms, max_ms = triton.testing.do_bench(
            lambda: matmul_sparse(a, b), quantiles=quantiles
        )
        print(matmul_sparse_kernel.best_config, ms)
    # The higher, the better
    perf = lambda ms: 2 * M * N * K * 1e-12 / (ms * 1e-3)
    return perf(ms), perf(max_ms), perf(min_ms)


def main() -> None:
    global a, b
    # Unit Test
    torch.manual_seed(0)
    step_size = 2
    # both are row-majored
    # pyre-fixme[10]: Name `a` is used but not defined.
    a = torch.randn((256, 128), device="cuda", dtype=torch.float16)
    # pyre-fixme[10]: Name `b` is used but not defined.
    b = torch.randn((128, 512), device="cuda", dtype=torch.float16)

    a = a.T.contiguous().T

    triton_output = matmul_sparse(a, b, step_size=step_size)
    torch_output = a[:, ::step_size] @ b[::step_size, :]
    print(f"triton_output_with_fp16_inputs={triton_output}")
    print(f"torch_output_with_fp16_inputs={torch_output}")
    # Bigger tolerance for AMD MI200 devices.
    # MI200 devices use reduced precision fp16 and bf16 and flush input and
    # output denormal values to zero. Detailed info is at: https://pytorch.org/docs/stable/notes/numerical_accuracy.html#reduced-precision-fp16-and-bf16-gemms-and-convolutions-on-amd-instinct-mi200-devices
    rtol = 1e-2 if is_hip_mi200() else 0
    if torch.allclose(triton_output, torch_output, atol=1e-2, rtol=rtol):
        print("✅ Triton and Torch match")
    else:
        print("❌ Triton and Torch differ")

    # Benchmark
    benchmark.run(show_plots=True, print_data=True)


if __name__ == "__main__":
    # Do not add code here, it won't be run. Add them to the function called below.
    main()  # pragma: no cover

# Expected Output on an H100:
# for the default: step_size = 1
# $ python matmul_sparse.py
# Monkey patched Triton's _build! See /packages/xlformers_emu_conda_unified/conda/lib/python3.10/site-packages/patch_triton.py
# Monkey patched Triton's nvsmi! See /packages/xlformers_emu_conda_unified/conda/lib/python3.10/site-packages/patch_triton.py
# triton_output_with_fp16_inputs=tensor([[  2.7754,  -0.1849,  -1.8604,  ..., -12.0938,  16.1406, -14.7500],
#         [ 14.5234,  16.6719, -10.4844,  ...,  -6.0742, -17.8906,  -0.6675],
#         [-15.9922,   6.3867,   5.9883,  ...,  -1.6328,  -7.3750,  18.0625],
#         ...,
#         [ 10.7422,   2.3633,  -4.8203,  ...,   4.7578,   1.4883,  -2.9141],
#         [ 20.5312,   6.5547,   9.5156,  ...,   7.6758,  11.3359,   4.1211],
#         [ 10.8359,  -2.3418,  -1.1533,  ...,   3.5332,   8.2109, -10.4531]],
#        device='cuda:0', dtype=torch.float16)
# torch_output_with_fp16_inputs=tensor([[  2.7754,  -0.1849,  -1.8604,  ..., -12.0938,  16.1406, -14.7500],
#         [ 14.5234,  16.6719, -10.4844,  ...,  -6.0742, -17.8906,  -0.6675],
#         [-15.9922,   6.3867,   5.9883,  ...,  -1.6328,  -7.3750,  18.0625],
#         ...,
#         [ 10.7422,   2.3633,  -4.8203,  ...,   4.7578,   1.4883,  -2.9141],
#         [ 20.5312,   6.5547,   9.5156,  ...,   7.6758,  11.3359,   4.1211],
#         [ 10.8359,  -2.3418,  -1.1533,  ...,   3.5332,   8.2109, -10.4531]],
#        device='cuda:0', dtype=torch.float16)
# ✅ Triton and Torch match
# BLOCK_SIZE_M: 128, BLOCK_SIZE_N: 256, BLOCK_SIZE_K: 64, GROUP_SIZE_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None 1.920896053314209
# BLOCK_SIZE_M: 128, BLOCK_SIZE_N: 256, BLOCK_SIZE_K: 64, GROUP_SIZE_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None 6.49567985534668
# BLOCK_SIZE_M: 128, BLOCK_SIZE_N: 256, BLOCK_SIZE_K: 64, GROUP_SIZE_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None 1.9256799221038818
# BLOCK_SIZE_M: 128, BLOCK_SIZE_N: 256, BLOCK_SIZE_K: 64, GROUP_SIZE_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None 6.48799991607666
# BLOCK_SIZE_M: 128, BLOCK_SIZE_N: 256, BLOCK_SIZE_K: 64, GROUP_SIZE_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None 1.9171359539031982
# BLOCK_SIZE_M: 128, BLOCK_SIZE_N: 256, BLOCK_SIZE_K: 64, GROUP_SIZE_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None 6.476831912994385
# matmul-performance-fp16:
#         M        N       K      cuBLAS      Triton  Triton_Sparse
# 0  8192.0  13824.0  5120.0  605.427753  603.698033     178.524988
# 1  8192.0  13824.0  5120.0  598.325609  602.198297     178.736311
# 2  8192.0  13824.0  5120.0  598.049139  604.882073     179.044506