OpenAI/Triton MLIR 第一章: Triton DSL¶

import triton
import triton.language as tl

__all__ = [
    "abs",
    "advance",
    "arange",
    "argmin",
    "argmax",
    "atomic_add",
    "atomic_and",
    "atomic_cas",
    "atomic_max",
    "atomic_min",
    "atomic_or",
    "atomic_xchg",
    "atomic_xor",
    "bfloat16",
    "block_type",
    "broadcast",
    "broadcast_to",
    "builtin",
    "cat",
    "cdiv",
    "constexpr",
    "cos",
    "debug_barrier",
    "device_assert",
    "device_print",
    "dot",
    "dtype",
    "exp",
    "expand_dims",
    "extra",
    "fdiv",
    "float16",
    "float32",
    "float64",
    "float8e4",
    "float8e5",
    "full",
    "function_type",
    "int1",
    "int16",
    "int32",
    "int64",
    "int8",
    "ir",
    "math",
    "load",
    "log",
    "make_block_ptr",
    "max",
    "max_contiguous",
    "maximum",
    "min",
    "minimum",
    "multiple_of",
    "num_programs",
    "pair_uniform_to_normal",
    "philox",
    "philox_impl",
    "pi32_t",
    "pointer_type",
    "program_id",
    "rand",
    "rand4x",
    "randint",
    "randint4x",
    "randn",
    "randn4x",
    "ravel",
    "reduce",
    "reshape",
    "sigmoid",
    "sin",
    "softmax",
    "sqrt",
    "static_range",
    "static_assert",
    "static_print",
    "store",
    "sum",
    "swizzle2d",
    "tensor",
    "trans",
    "triton",
    "uint16",
    "uint32",
    "uint32_to_uniform_float",
    "uint64",
    "uint8",
    "umulhi",
    "view",
    "void",
    "where",
    "xor_sum",
    "zeros",
    "zeros_like",
]

__all__ = [
    "autotune",
    "cdiv",
    "CompilationError",
    "compile",
    "Config",
    "heuristics",
    "impl",
    "jit",
    "JITFunction",
    "KernelInterface",
    "language",
    "MockTensor",
    "next_power_of_2",
    "ops",
    "OutOfResources",
    "reinterpret",
    "runtime",
    "TensorWrapper",
    "testing",
    "program_ids_from_grid",
]

def matmul(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_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),
        ACTIVATION=activation
    )
    return c

    grid = lambda META: (
        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),
        ACTIVATION=activation
    )

    dim3 block(BLOCK_SIZE_M, BLOCK_SIZE_N);  
    dim3 grid((M + BLOCK_SIZE_M - 1) / BLOCK_SIZE_M, (N + BLOCK_SIZE_N - 1) / BLOCK_SIZE_N);
    matmul_kernel<<<grid,block>>>(Ad, Bd, Cd, 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,
    ACTIVATION: 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)) % 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)
        # Advance the ptrs to the next K block.
        a_ptrs += BLOCK_SIZE_K * stride_ak
        b_ptrs += BLOCK_SIZE_K * stride_bk
    # You can fuse arbitrary activation functions here
    # while the accumulator is still in FP32!
    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, :]
    c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
    tl.store(c_ptrs, c, mask=c_mask)

torch.manual_seed(0)
a = torch.randn((512, 512), device='cuda', dtype=torch.float16)
b = torch.randn((512, 512), device='cuda', dtype=torch.float16)
triton_output = matmul(a, b)
torch_output = torch.matmul(a, b)
print(f"triton_output={triton_output}")
print(f"torch_output={torch_output}")
if torch.allclose(triton_output, torch_output, atol=1e-2, rtol=0):
    print("✅ Triton and Torch match")
else:
    print("❌ Triton and Torch differ")

@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.autotune(
    configs=[ 
        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.autotune(
    configs=[
        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2),
    ],
    key=['M', 'N', 'K'],
)

@triton.autotune(
    configs=[
        triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),
    ],
    key=['M', 'N', 'K'],
)