Persistent Matmul

This script demonstrates persistent kernel implementations of matrix multiplication using Triton. Various matmul methods are included, such as naive, persistent, and TMA (Tensor Memory Accelerator) based approaches. The kernels support both FP16 and FP8 data types but the FP8 implementation is only available on CUDA devices with compute capability >= 9.0.

Triton and cuBLAS implementations are benchmarked under different configurations and evaluated using the proton profiler. Users can pass command-line arguments to specify matrix dimensions and iteration steps flexibly.

# FP8
python 09-persistent-matmul.py --prec fp8 --K_range 128 1024 --K_step 128

# FP16
python 09-persistent-matmul.py --prec fp16 --K_range 128 1024 --K_step 128

Note that currently this tutorial will fail on devices with a small shared memory size, such as RTX-4090.

M=32, N=32, K=32 verification naive vs: torch: ✅ cublas: ✅ persistent: ✅
M=8192, N=8192, K=512 verification naive vs: torch: ✅ cublas: ✅ persistent: ✅
176.702 5444.602 ROOT
├─ nan 0.049 _ZN2at6native18elementwise_kernelILi128ELi4EZNS0_22gpu_kernel_impl_nocastIZZZNS0_23direct_copy_kernel_cudaERNS_18TensorIteratorBaseEENKUlvE1_clEvENKUlvE8_clEvEUlN3c104HalfEE_EEvS4_RKT_EUliE_EEviT1_
├─ nan 0.044 _ZN2at6native54_GLOBAL__N__d8ceb000_21_DistributionNormal_cu_0c5b6e8543distribution_elementwise_grid_stride_kernelIfLi4EZNS0_9templates4cuda20normal_and_transformIN3c104HalfEfPNS_17CUDAGeneratorImplEZZZNS4_13normal_kernelIS9_EEvRKNS_10TensorBaseEddT_ENKUlvE_clEvENKUlvE1_clEvEUlfE_EEvRNS_18TensorIteratorBaseET1_T2_EUlP24curandStatePhilox4_32_10E0_ZNS1_27distribution_nullary_kernelIS7_f6float4S9_SO_SH_EEvSJ_SL_RKT3_T4_EUlifE_EEviNS_15PhiloxCudaStateESK_SL_
├─ 177.329 4262.779 cublas [M=8192, N=8192, K=512]
│  └─ nan 4262.779 ampere_fp16_s16816gemm_fp16_128x128_ldg8_f2f_stages_32x5_tn
├─ 170.290 403.545 matmul_kernel [M=8192, N=8192, K=512]
├─ 172.997 397.229 matmul_kernel_persistent [M=8192, N=8192, K=512]
└─ 180.387 380.956 torch [M=8192, N=8192, K=512]
   └─ nan 380.956 ampere_fp16_s16816gemm_fp16_128x128_ldg8_f2f_stages_32x5_tn

import argparse

import torch
import triton
import triton.language as tl
import triton.tools.experimental_descriptor
import triton.profiler as proton
from contextlib import contextmanager

from typing import Optional

if torch.cuda.is_available():
    from triton._C.libtriton import nvidia
    cublas_workspace = torch.empty(32 * 1024 * 1024, device="cuda", dtype=torch.uint8)
    cublas = nvidia.cublas.CublasLt(cublas_workspace)
else:
    cublas = None


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


def supports_tma():
    return is_cuda() and torch.cuda.get_device_capability()[0] >= 9


def _matmul_launch_metadata(grid, kernel, args):
    ret = {}
    M, N, K = args["M"], args["N"], args["K"]
    ret["name"] = f"{kernel.name} [M={M}, N={N}, K={K}]"
    if "c_ptr" in args:
        bytes_per_elem = args["c_ptr"].element_size()
    else:
        bytes_per_elem = 1 if args["FP8_OUTPUT"] else 2
    ret[f"flops{bytes_per_elem * 8}"] = 2. * M * N * K
    ret["bytes"] = bytes_per_elem * (M * K + N * K + M * N)
    return ret


@triton.jit(launch_metadata=_matmul_launch_metadata)
def matmul_kernel(a_ptr, b_ptr, c_ptr,  #
                  M, N, K,  #
                  stride_am, stride_ak,  #
                  stride_bk, stride_bn,  #
                  stride_cm, stride_cn,  #
                  BLOCK_SIZE_M: tl.constexpr,  #
                  BLOCK_SIZE_N: tl.constexpr,  #
                  BLOCK_SIZE_K: tl.constexpr,  #
                  GROUP_SIZE_M: tl.constexpr,  #
                  ):
    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

    start_m = pid_m * BLOCK_SIZE_M
    start_n = pid_n * BLOCK_SIZE_N

    offs_am = start_m + tl.arange(0, BLOCK_SIZE_M)
    offs_bn = start_n + tl.arange(0, BLOCK_SIZE_N)
    offs_am = tl.where(offs_am < M, offs_am, 0)
    offs_bn = tl.where(offs_bn < N, offs_bn, 0)

    offs_am = tl.max_contiguous(tl.multiple_of(offs_am, BLOCK_SIZE_M), BLOCK_SIZE_M)
    offs_bn = tl.max_contiguous(tl.multiple_of(offs_bn, BLOCK_SIZE_N), BLOCK_SIZE_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)

    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)

    for k in range(0, tl.cdiv(K, 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)
        accumulator = tl.dot(a, b, accumulator)
        a_ptrs += BLOCK_SIZE_K * stride_ak
        b_ptrs += BLOCK_SIZE_K * stride_bk

    if (c_ptr.dtype.element_ty == tl.float8e4nv):
        c = accumulator.to(tl.float8e4nv)
    else:
        c = 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)
    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(a, b):
    configs = {
        torch.float8_e4m3fn: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 128, "GROUP_SIZE_M": 8, "num_stages": 4,
            "num_warps": 8
        }, torch.float16: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64, "GROUP_SIZE_M": 8, "num_stages": 3,
            "num_warps": 8
        }
    }
    # Check constraints.
    assert a.shape[1] == b.shape[0], "Incompatible dimensions"
    assert a.dtype == b.dtype, "Incompatible dtypes"
    M, K = a.shape
    K, N = b.shape
    dtype = a.dtype

    c = torch.empty((M, N), device=a.device, dtype=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),  #
        BLOCK_SIZE_M=configs[dtype]["BLOCK_SIZE_M"],  #
        BLOCK_SIZE_N=configs[dtype]["BLOCK_SIZE_N"],  #
        BLOCK_SIZE_K=configs[dtype]["BLOCK_SIZE_K"],  #
        GROUP_SIZE_M=configs[dtype]["GROUP_SIZE_M"],  #
        num_stages=configs[dtype]["num_stages"],  #
        num_warps=configs[dtype]["num_warps"],  #
    )
    return c


@triton.jit(launch_metadata=_matmul_launch_metadata)
def matmul_kernel_persistent(a_ptr, b_ptr, c_ptr,  #
                             M, N, K,  #
                             stride_am, stride_ak,  #
                             stride_bk, stride_bn,  #
                             stride_cm, stride_cn,  #
                             BLOCK_SIZE_M: tl.constexpr,  #
                             BLOCK_SIZE_N: tl.constexpr,  #
                             BLOCK_SIZE_K: tl.constexpr,  #
                             GROUP_SIZE_M: tl.constexpr,  #
                             NUM_SMS: tl.constexpr,  #
                             ):
    start_pid = tl.program_id(axis=0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    k_tiles = tl.cdiv(K, BLOCK_SIZE_K)
    num_tiles = num_pid_m * num_pid_n

    tiles_per_SM = num_tiles // NUM_SMS
    if start_pid < num_tiles % NUM_SMS:
        tiles_per_SM += 1

    tile_id = start_pid - NUM_SMS
    ki = -1

    offs_k_for_mask = tl.arange(0, BLOCK_SIZE_K)

    num_pid_in_group = GROUP_SIZE_M * num_pid_n

    pid_m = 0
    pid_n = 0
    offs_am = tl.arange(0, BLOCK_SIZE_M)
    offs_bn = tl.arange(0, BLOCK_SIZE_N)

    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)

    for _ in range(0, k_tiles * tiles_per_SM):
        ki = tl.where(ki == k_tiles - 1, 0, ki + 1)
        if ki == 0:
            tile_id += NUM_SMS
            group_id = tile_id // 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 + (tile_id % group_size_m)
            pid_n = (tile_id % num_pid_in_group) // group_size_m

            start_m = pid_m * BLOCK_SIZE_M
            start_n = pid_n * BLOCK_SIZE_N
            offs_am = start_m + tl.arange(0, BLOCK_SIZE_M)
            offs_bn = start_n + tl.arange(0, BLOCK_SIZE_N)
            offs_am = tl.where(offs_am < M, offs_am, 0)
            offs_bn = tl.where(offs_bn < N, offs_bn, 0)
            offs_am = tl.max_contiguous(tl.multiple_of(offs_am, BLOCK_SIZE_M), BLOCK_SIZE_M)
            offs_bn = tl.max_contiguous(tl.multiple_of(offs_bn, BLOCK_SIZE_N), BLOCK_SIZE_N)
        offs_k = ki * BLOCK_SIZE_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)

        a = tl.load(a_ptrs, mask=offs_k_for_mask[None, :] < K - ki * BLOCK_SIZE_K, other=0.0)
        b = tl.load(b_ptrs, mask=offs_k_for_mask[:, None] < K - ki * BLOCK_SIZE_K, other=0.0)
        accumulator = tl.dot(a, b, accumulator)

        if ki == k_tiles - 1:
            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)
            if (c_ptr.dtype.element_ty == tl.float8e4nv):
                c = accumulator.to(tl.float8e4nv)
            else:
                c = accumulator.to(tl.float16)
            tl.store(c_ptrs, c, mask=c_mask)
            accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)


def matmul_persistent(a, b):
    configs = {
        torch.float8_e4m3fn: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 128, "GROUP_SIZE_M": 8, "num_stages": 4,
            "num_warps": 8
        }, torch.float16: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64, "GROUP_SIZE_M": 8, "num_stages": 3,
            "num_warps": 8
        }
    }
    # Check constraints.
    assert a.shape[1] == b.shape[0], "Incompatible dimensions"
    assert a.dtype == b.dtype, "Incompatible dtypes"
    NUM_SMS = torch.cuda.get_device_properties("cuda").multi_processor_count
    M, K = a.shape
    K, N = b.shape
    dtype = a.dtype
    # Allocates output.
    c = torch.empty((M, N), device=a.device, dtype=dtype)
    # 1D launch kernel where each block gets its own program.
    grid = lambda META: (min(NUM_SMS, triton.cdiv(M, META["BLOCK_SIZE_M"]) * triton.cdiv(N, META["BLOCK_SIZE_N"])), )
    matmul_kernel_persistent[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),  #
        BLOCK_SIZE_M=configs[dtype]["BLOCK_SIZE_M"],  #
        BLOCK_SIZE_N=configs[dtype]["BLOCK_SIZE_N"],  #
        BLOCK_SIZE_K=configs[dtype]["BLOCK_SIZE_K"],  #
        GROUP_SIZE_M=configs[dtype]["GROUP_SIZE_M"],  #
        NUM_SMS=NUM_SMS,  #
        num_stages=configs[dtype]["num_stages"],  #
        num_warps=configs[dtype]["num_warps"],  #
    )
    return c


@triton.jit(launch_metadata=_matmul_launch_metadata)
def matmul_kernel_tma_persistent(a_desc_ptr, b_desc_ptr, c_desc_ptr,  #
                                 M, N, K,  #
                                 BLOCK_SIZE_M: tl.constexpr,  #
                                 BLOCK_SIZE_N: tl.constexpr,  #
                                 BLOCK_SIZE_K: tl.constexpr,  #
                                 GROUP_SIZE_M: tl.constexpr,  #
                                 FP8_OUTPUT: tl.constexpr,  #
                                 NUM_SMS: tl.constexpr):  #
    dtype = tl.float8e4nv if FP8_OUTPUT else tl.float16
    start_pid = tl.program_id(axis=0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    k_tiles = tl.cdiv(K, BLOCK_SIZE_K)
    num_tiles = num_pid_m * num_pid_n

    tiles_per_SM = num_tiles // NUM_SMS
    if start_pid < num_tiles % NUM_SMS:
        tiles_per_SM += 1

    tile_id = start_pid - NUM_SMS
    ki = -1

    pid_m = 0
    pid_n = 0
    offs_am = 0
    offs_bn = 0

    num_pid_in_group = GROUP_SIZE_M * num_pid_n

    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)

    for _ in range(0, k_tiles * tiles_per_SM):
        ki = tl.where(ki == k_tiles - 1, 0, ki + 1)
        if ki == 0:
            tile_id += NUM_SMS
            group_id = tile_id // 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 + (tile_id % group_size_m)
            pid_n = (tile_id % num_pid_in_group) // group_size_m

            offs_am = pid_m * BLOCK_SIZE_M
            offs_bn = pid_n * BLOCK_SIZE_N

        offs_k = ki * BLOCK_SIZE_K

        a = tl._experimental_descriptor_load(a_desc_ptr, [offs_am, offs_k], [BLOCK_SIZE_M, BLOCK_SIZE_K], dtype)
        b = tl._experimental_descriptor_load(b_desc_ptr, [offs_bn, offs_k], [BLOCK_SIZE_N, BLOCK_SIZE_K], dtype)
        accumulator = tl.dot(a, b.T, accumulator)

        if ki == k_tiles - 1:
            c = accumulator.to(dtype)

            tl._experimental_descriptor_store(c_desc_ptr, c, [offs_am, offs_bn])
            accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)


def matmul_tma_persistent(a, b):
    # Autotuner does not work with TMA. Use manual config.
    configs = {
        torch.float8_e4m3fn: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 128, "GROUP_SIZE_M": 8, "num_stages": 4,
            "num_warps": 8
        }, torch.float16: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64, "GROUP_SIZE_M": 8, "num_stages": 3,
            "num_warps": 8
        }
    }

    # Check constraints.
    assert a.shape[1] == b.shape[1], "Incompatible dimensions"  # b is transposed
    assert a.dtype == b.dtype, "Incompatible dtypes"

    M, K = a.shape
    N, K = b.shape
    dtype = a.dtype

    c = torch.empty((M, N), device=a.device, dtype=dtype)
    desc_a = triton.tools.experimental_descriptor.create_2d_tma_descriptor(a.data_ptr(), M, K,
                                                                           configs[dtype]["BLOCK_SIZE_M"],
                                                                           configs[dtype]["BLOCK_SIZE_K"],
                                                                           a.element_size())
    desc_b = triton.tools.experimental_descriptor.create_2d_tma_descriptor(b.data_ptr(), N, K,
                                                                           configs[dtype]["BLOCK_SIZE_N"],
                                                                           configs[dtype]["BLOCK_SIZE_K"],
                                                                           b.element_size())
    desc_c = triton.tools.experimental_descriptor.create_2d_tma_descriptor(c.data_ptr(), M, N,
                                                                           configs[dtype]["BLOCK_SIZE_M"],
                                                                           configs[dtype]["BLOCK_SIZE_N"],
                                                                           c.element_size())
    NUM_SMS = torch.cuda.get_device_properties("cuda").multi_processor_count

    grid = lambda META: (min(NUM_SMS, triton.cdiv(M, META["BLOCK_SIZE_M"]) * triton.cdiv(N, META["BLOCK_SIZE_N"])), )
    matmul_kernel_tma_persistent[grid](
        desc_a, desc_b, desc_c,  #
        M, N, K,  #
        BLOCK_SIZE_M=configs[dtype]["BLOCK_SIZE_M"],  #
        BLOCK_SIZE_N=configs[dtype]["BLOCK_SIZE_N"],  #
        BLOCK_SIZE_K=configs[dtype]["BLOCK_SIZE_K"],  #
        GROUP_SIZE_M=configs[dtype]["GROUP_SIZE_M"],  #
        FP8_OUTPUT=dtype == torch.float8_e4m3fn,  #
        NUM_SMS=NUM_SMS,  #
        num_stages=configs[dtype]["num_stages"],  #
        num_warps=configs[dtype]["num_warps"],  #
    )
    return c


@triton.jit(launch_metadata=_matmul_launch_metadata)
def matmul_kernel_descriptor_persistent(a_ptr, b_ptr, c_ptr,  #
                                        M, N, K,  #
                                        BLOCK_SIZE_M: tl.constexpr,  #
                                        BLOCK_SIZE_N: tl.constexpr,  #
                                        BLOCK_SIZE_K: tl.constexpr,  #
                                        GROUP_SIZE_M: tl.constexpr,  #
                                        NUM_SMS: tl.constexpr):  #
    # Matmul using TMA and device-side descriptor creation
    dtype = c_ptr.dtype.element_ty
    start_pid = tl.program_id(axis=0)
    num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)
    num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
    k_tiles = tl.cdiv(K, BLOCK_SIZE_K)
    num_tiles = num_pid_m * num_pid_n

    a_desc = tl._experimental_make_tensor_descriptor(
        a_ptr,
        shape=[M, K],
        strides=[K, 1],
        block_shape=[BLOCK_SIZE_M, BLOCK_SIZE_K],
    )
    b_desc = tl._experimental_make_tensor_descriptor(
        b_ptr,
        shape=[N, K],
        strides=[K, 1],
        block_shape=[BLOCK_SIZE_N, BLOCK_SIZE_K],
    )
    c_desc = tl._experimental_make_tensor_descriptor(
        c_ptr,
        shape=[M, N],
        strides=[N, 1],
        block_shape=[BLOCK_SIZE_M, BLOCK_SIZE_N],
    )

    tiles_per_SM = num_tiles // NUM_SMS
    if start_pid < num_tiles % NUM_SMS:
        tiles_per_SM += 1

    tile_id = start_pid - NUM_SMS
    ki = -1

    pid_m = 0
    pid_n = 0
    offs_am = 0
    offs_bn = 0

    num_pid_in_group = GROUP_SIZE_M * num_pid_n

    accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)

    for _ in range(0, k_tiles * tiles_per_SM):
        ki = tl.where(ki == k_tiles - 1, 0, ki + 1)
        if ki == 0:

            tile_id += NUM_SMS
            group_id = tile_id // 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 + (tile_id % group_size_m)
            pid_n = (tile_id % num_pid_in_group) // group_size_m

            offs_am = pid_m * BLOCK_SIZE_M
            offs_bn = pid_n * BLOCK_SIZE_N

        offs_k = ki * BLOCK_SIZE_K

        a = a_desc.load([offs_am, offs_k])
        b = b_desc.load([offs_bn, offs_k])
        accumulator = tl.dot(a, b.T, accumulator)

        if ki == k_tiles - 1:
            c = accumulator.to(dtype)

            c_desc.store([offs_am, offs_bn], c)

            accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)


def matmul_descriptor_persistent(a, b):
    configs = {
        torch.float8_e4m3fn: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 128, "GROUP_SIZE_M": 8, "num_stages": 4,
            "num_warps": 8
        }, torch.float16: {
            "BLOCK_SIZE_M": 128, "BLOCK_SIZE_N": 256, "BLOCK_SIZE_K": 64, "GROUP_SIZE_M": 8, "num_stages": 3,
            "num_warps": 8
        }
    }

    # Check constraints.
    assert a.shape[1] == b.shape[1], "Incompatible dimensions"  # b is transposed
    assert a.dtype == b.dtype, "Incompatible dtypes"

    M, K = a.shape
    N, K = b.shape
    dtype = a.dtype

    c = torch.empty((M, N), device=a.device, dtype=dtype)
    NUM_SMS = torch.cuda.get_device_properties("cuda").multi_processor_count

    # TMA descriptors require a global memory allocation
    def alloc_fn(size: int, alignment: int, stream: Optional[int]):
        return torch.empty(size, device="cuda", dtype=torch.int8)

    triton.set_allocator(alloc_fn)

    grid = lambda META: (min(NUM_SMS, triton.cdiv(M, META["BLOCK_SIZE_M"]) * triton.cdiv(N, META["BLOCK_SIZE_N"])), )
    matmul_kernel_descriptor_persistent[grid](
        a, b, c,  #
        M, N, K,  #
        BLOCK_SIZE_M=configs[dtype]["BLOCK_SIZE_M"],  #
        BLOCK_SIZE_N=configs[dtype]["BLOCK_SIZE_N"],  #
        BLOCK_SIZE_K=configs[dtype]["BLOCK_SIZE_K"],  #
        GROUP_SIZE_M=configs[dtype]["GROUP_SIZE_M"],  #
        NUM_SMS=NUM_SMS,  #
        num_stages=configs[dtype]["num_stages"],  #
        num_warps=configs[dtype]["num_warps"],  #
    )
    return c


def cublas_matmul(a, b):
    # Check constraints.
    assert a.shape[1] == b.shape[1], "Incompatible dimensions"  # b is transposed
    M, K = a.shape
    N, K = b.shape
    dtype = a.dtype
    c = torch.empty((M, N), device=a.device, dtype=dtype)
    bytes_per_elem = a.element_size()
    flops_str = f"flops{bytes_per_elem * 8}"
    with proton.scope(f"cublas [M={M}, N={N}, K={K}]",
                      {"bytes": bytes_per_elem * (M * K + N * K + M * N), flops_str: 2. * M * N * K}):
        cublas.matmul(a, b, c)
    return c


def torch_matmul(a, b):
    M, K = a.shape
    N, K = b.shape
    bytes_per_elem = a.element_size()
    flops_str = f"flops{bytes_per_elem * 8}"
    with proton.scope(f"torch [M={M}, N={N}, K={K}]",
                      {"bytes": bytes_per_elem * (M * K + N * K + M * N), flops_str: 2. * M * N * K}):
        c = torch.matmul(a, b.T)
    return c


@contextmanager
def proton_context():
    proton.activate(0)
    try:
        yield
    finally:
        proton.deactivate(0)


def bench_fn(reps, warmup_reps, fn, *args):
    for _ in range(warmup_reps):
        fn(*args)
    with proton_context():
        for _ in range(reps):
            fn(*args)


def bench(K, dtype, reps=1000, warmup_reps=10000):
    M = 8192
    N = 8192
    a = torch.randn((M, K), device="cuda", dtype=torch.float16).to(dtype)
    b = torch.randn((K, N), device="cuda", dtype=torch.float16).to(dtype)

    b = b.T.contiguous()

    if cublas is not None:
        bench_fn(reps, warmup_reps, cublas_matmul, a, b)
    if dtype == torch.float16:
        bench_fn(reps, warmup_reps, torch_matmul, a, b)
    bench_fn(reps, warmup_reps, matmul, a, b.T)
    bench_fn(reps, warmup_reps, matmul_persistent, a, b.T)
    if supports_tma():
        bench_fn(reps, warmup_reps, matmul_tma_persistent, a, b)
        bench_fn(reps, warmup_reps, matmul_descriptor_persistent, a, b)


def validate(M, N, K, dtype):
    a = torch.randn((M, K), device="cuda", dtype=torch.float16).to(dtype)
    b = torch.randn((K, N), device="cuda", dtype=torch.float16).to(dtype)
    b = b.T.contiguous()

    torch_result = torch_matmul(a, b) if dtype == torch.float16 else None
    cublas_result = cublas_matmul(a, b) if cublas is not None else None
    naive_result = matmul(a, b.T)
    persistent_result = matmul_persistent(a, b.T)
    tma_persistent_result = matmul_tma_persistent(a, b) if supports_tma() else None
    descriptor_persistent_result = matmul_descriptor_persistent(a, b) if supports_tma() else None

    if torch_result is not None:
        naive_vs_torch = "✅" if torch.allclose(naive_result.to(torch.float16), torch_result.to(torch.float16),
                                               atol=1.0) else "❌"
    if cublas_result is not None:
        naive_vs_cublas = "✅" if torch.allclose(naive_result.to(torch.float16), cublas_result.to(torch.float16),
                                                atol=1.0) else "❌"
    naive_vs_persistent = "✅" if torch.allclose(naive_result.to(torch.float16), persistent_result.to(torch.float16),
                                                atol=1.0) else "❌"
    if tma_persistent_result is not None:
        naive_vs_tma_persistent = "✅" if torch.allclose(cublas_result.to(torch.float16),
                                                        tma_persistent_result.to(torch.float16), atol=1.0) else "❌"
    if descriptor_persistent_result is not None:
        naive_vs_descriptor_persistent = "✅" if torch.allclose(cublas_result.to(
            torch.float16), descriptor_persistent_result.to(torch.float16), atol=1.0) else "❌"
    print(f"M={M}, N={N}, K={K} verification naive vs: ", end="")
    if torch_result is not None:
        print(f"torch: {naive_vs_torch} ", end="")
    if cublas_result is not None:
        print(f"cublas: {naive_vs_cublas} ", end="")
    print(f"persistent: {naive_vs_persistent} ", end="")
    if tma_persistent_result is not None:
        print(f"TMA persistent: {naive_vs_tma_persistent} ", end="")
    if descriptor_persistent_result is not None:
        print(f"Tensor descriptor persistent: {naive_vs_descriptor_persistent} ", end="")
    print()


def show_profile(precision, profile_name):
    import triton.profiler.viewer as proton_viewer
    metrics = ["time/ms"]
    if precision == 'fp8':
        metrics = ["tflop8/s"] + metrics
    elif precision == 'fp16':
        metrics = ["tflop16/s"] + metrics
    file_name = f"{profile_name}.hatchet"
    proton_viewer.parse(metrics, file_name, depth=100)


if __name__ == "__main__":
    parser = argparse.ArgumentParser()
    parser.add_argument("-K", type=int, required=False, default=512)
    parser.add_argument("--K_range", type=int, nargs=2)
    parser.add_argument("--K_step", type=int, default=512)
    parser.add_argument("--prec", type=str, choices=["fp8", "fp16"], default="fp16")
    args = parser.parse_args()

    if args.prec == 'fp8' and (not hasattr(torch, "float8_e4m3fn") or not is_cuda()):
        print("This example requires CUDA with fp8 support.")
        exit(1)

    dtype = torch.float8_e4m3fn if args.prec == 'fp8' else torch.float16

    if args.K and args.K_range is None:
        args.K_range = [args.K, args.K]
        args.K_step = 1  # doesn't matter as long as it's not 0

    torch.manual_seed(0)

    validate(32, 32, 32, dtype)
    validate(8192, 8192, 512, dtype)

    proton.start("matmul", hook="triton")
    for K in range(args.K_range[0], args.K_range[1] + 1, args.K_step):
        bench(K, dtype)
    proton.finalize()
    show_profile(args.prec, "matmul")

Total running time of the script: (0 minutes 19.373 seconds)

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