matmul_triton.py

import torch
import triton
import triton.language as tl
from torch import Tensor


# fmt: off
# `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=[
        triton.Config({"BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64, "GROUP_SIZE_M": 8}, num_stages=3, num_warps=8),
        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_ref_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 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)
    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.
        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)
        # We accumulate along the K dimension.
        accumulator += tl.dot(a, b, allow_tf32=False)
        # Advance the ptrs to the next K block.
        a_ptrs += BLOCK_SIZE_K * stride_ak
        b_ptrs += BLOCK_SIZE_K * stride_bk

    c = accumulator

    # -----------------------------------------------------------
    # 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, :]
    c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
    tl.store(c_ptrs, c, mask=c_mask)


def matmul_ref(a, b):
    # 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"
    M, K = a.shape
    K, N = b.shape
    # 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_ref_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
# fmt: on


@triton.autotune(
    configs=[triton.Config({"BLOCK_SIZE": size}) for size in (16, 32, 64)],
    key=["m", "n", "k"],
)
@triton.jit
def matmul_kernel(a_ptr, b_ptr, c_ptr, m, n, k, BLOCK_SIZE: tl.constexpr):
    # A: (m, k), B: (k, n), C: (m, n)
    pid0 = tl.program_id(0)
    pid1 = tl.program_id(1)

    offsets_m = pid0 * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)
    offsets_n = pid1 * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)

    # each program calculate a block in C
    c = tl.zeros((BLOCK_SIZE, BLOCK_SIZE), dtype=tl.float32)

    # iterate over inner dim k
    for block_id_k in range(0, tl.cdiv(k, BLOCK_SIZE)):
        offsets_k = block_id_k * BLOCK_SIZE + tl.arange(0, BLOCK_SIZE)
        a_ptrs = a_ptr + offsets_m[:, None] * k + offsets_k[None, :]
        b_ptrs = b_ptr + offsets_k[:, None] * n + offsets_n[None, :]

        a = tl.load(a_ptrs, mask=(offsets_m[:, None] < m) & (offsets_k[None, :] < k), other=0.0)
        b = tl.load(b_ptrs, mask=(offsets_k[:, None] < k) & (offsets_n[None, :] < n), other=0.0)

        c += tl.dot(a, b, allow_tf32=False)

    c_ptrs = c_ptr + offsets_m[:, None] * n + offsets_n[None, :]
    tl.store(c_ptrs, c, mask=(offsets_m[:, None] < m) & (offsets_n[None, :] < n))


def matmul(a: Tensor, b: Tensor):
    assert a.is_cuda and b.is_cuda
    assert a.shape[1] == b.shape[0]
    assert a.is_contiguous() and b.is_contiguous()

    out = torch.empty((a.shape[0], b.shape[1]), device=a.device, dtype=a.dtype)

    def grid(meta):
        return (
            triton.cdiv(a.shape[0], meta["BLOCK_SIZE"]),
            triton.cdiv(b.shape[1], meta["BLOCK_SIZE"]),
        )

    matmul_kernel[grid](a, b, out, a.shape[0], b.shape[1], a.shape[1])
    return out


if __name__ == "__main__":
    n = 1000

    for dtype in (torch.float32, torch.float16, torch.bfloat16):
        print(dtype)
        a = torch.randn((n, n), device="cuda", dtype=dtype)
        b = torch.randn((n, n), device="cuda", dtype=dtype)
        out_torch = a @ b
        out_triton = matmul(a, b)

        try:
            torch.testing.assert_close(out_triton, out_torch)
        except Exception as e:
            print(e)