feat: SM-constraint-GEMM by triton persistent kernel (#982)

Add SM-constraint GEMM operation by triton persistent kernel to support
Nanoflow infra-device parallelism.

Checklist:
- [x] functional test passed
- [x] benchmark 
- [x] SM usage by nsys profile
- [ ] (optional for this PR) tune: get best config for gemm 

**Benchmark results**:

https://docs.google.com/document/d/189f1VdZ36B-iJTYlC2LDgWGDSWKCiZI6PTfg-ltjXv4/edit?usp=sharing

**Nsys Results**
>             When num_sm = 1:
>               gemm_kernel_persistent
>               Begins: 3.89591s
>               Ends: 3.89592s (+5.248 μs)
>               grid:  <<<1, 1, 1>>>
>               block: <<<128, 1, 1>>>
>             
>             When num_sm = 32:
>               gemm_kernel_persistent
>               Begins: 3.91269s
>               Ends: 3.92016s (+7.466 ms)
>               grid:  <<<32, 1, 1>>>
>               block: <<<128, 1, 1>>>
>             
>             When num_sm = 64:
>               gemm_kernel_persistent
>               Begins: 3.59851s
>               Ends: 3.60234s (+3.829 ms)
>               grid:  <<<64, 1, 1>>>
>               block: <<<128, 1, 1>>>
>               Launch Type: Regular
>             
>             When num_sm = 128:
>               gemm_kernel_persistent
>               Begins: 3.17387s
>               Ends: 3.17586s (+1.992 ms)
>               grid:  <<<128, 1, 1>>>
>               block: <<<128, 1, 1>>>
>             
>             When num_sm = 133:
>               gemm_kernel_persistent
>               Begins: 3.51542s
>               Ends: 3.5173s (+1.879 ms)
>               grid:  <<<132, 1, 1>>>
>               block: <<<128, 1, 1>>>

Related issues:
#591 
#675

Author: yyihuang

benchmarks/bench_persistent_gemm.py

@@ -0,0 +1,76 @@
+import pytest
+import torch
+import triton
+from triton.testing import do_bench
+
+import flashinfer
+import flashinfer.triton
+
+
+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 bench_gemm_persistent(num_sms, dtype, M, N, K, reps=1000, warmup_reps=10000):
+    ms = do_bench(
+        lambda: flashinfer.triton.sm_constraint_gemm.gemm_persistent(
+            a=torch.randn((M, K), device="cuda", dtype=torch.float16).to(dtype),
+            b=torch.randn((N, K), device="cuda", dtype=torch.float16).to(dtype),
+            alpha=1.0,
+            beta=0.0,
+            num_sms=num_sms,
+        ),
+        warmup=warmup_reps,
+        rep=reps,
+    )
+
+    # matmul: 2 * M * N * K
+    # scale and add: 3 * M * N
+    flops = (2 * M * N * K + 3 * M * N) / ms / 1e9
+    print(
+        f"GEMM Persistent | num_sms: {num_sms}, M: {M}, N: {N}, K: {K}, {dtype}: {flops:.3f} TFLOPs/s"
+    )
+
+
+def bench_gemm_descriptor_persistent(
+    num_sms, dtype, M, N, K, reps=1000, warmup_reps=10000
+):
+    if dtype == torch.float32:
+        return
+    ms = do_bench(
+        lambda: flashinfer.triton.sm_constraint_gemm.gemm_descriptor_persistent(
+            a=torch.randn((M, K), device="cuda", dtype=torch.float16).to(dtype),
+            b=torch.randn((N, K), device="cuda", dtype=torch.float16).to(dtype),
+            alpha=1.0,
+            beta=0.0,
+            num_sms=num_sms,
+        ),
+        warmup=warmup_reps,
+        rep=reps,
+    )
+
+    # matmul: 2 * M * N * K
+    # scale and add: 3 * M * N
+    flops = (2 * M * N * K + 3 * M * N) / ms / 1e9
+    print(
+        f"GEMM Descriptor | num_sms: {num_sms}, M: {M}, N: {N}, K: {K}, {dtype}: {flops:.3f} TFLOPs/s"
+    )
+
+
+if __name__ == "__main__":
+    assert supports_tma()
+
+    for M, N, K in [(4096, 4096, 4096), (8192, 8192, 8192)]:
+        for dtype in [
+            torch.float8_e4m3fn,
+            torch.float16,
+            torch.bfloat16,
+            torch.float32,
+        ]:
+            for num_sms in [1, 16, 32, 64, 128, 132, 133, 256]:
+                bench_gemm_persistent(num_sms, dtype, M, N, K)
+                bench_gemm_descriptor_persistent(num_sms, dtype, M, N, K)

flashinfer/triton/__init__.py

@@ -1 +1,2 @@
 from . import cascade  # noqa: F401
+from . import sm_constraint_gemm  # noqa: F401

flashinfer/triton/kernels/sm_constraint_gemm.py

@@ -0,0 +1,290 @@
+import triton  # type: ignore[import]
+import triton.language as tl  # type: ignore[import]
+
+
+def matmul_get_configs():
+    return [
+        triton.Config(
+            {
+                "BLOCK_SIZE_M": BM,
+                "BLOCK_SIZE_N": BN,
+                "BLOCK_SIZE_K": BK,
+                "GROUP_SIZE_M": 8,
+            },
+            num_stages=s,
+            num_warps=w,
+        )
+        for BM in [128]
+        for BN in [128]
+        for BK in [64]
+        for s in ([3])
+        for w in [4]
+    ]
+
+
+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}"] = 2.0 * M * N * K
+    ret["bytes"] = bytes_per_elem * (M * K + N * K + M * N)
+    return ret
+
+
+@triton.jit
+def _compute_pid(tile_id, num_pid_in_group, num_pid_m, GROUP_SIZE_M, 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
+    return pid_m, pid_n
+
+
+@triton.autotune(
+    configs=matmul_get_configs(),
+    key=["M", "N", "K"],
+)
+@triton.jit(launch_metadata=_matmul_launch_metadata)
+def gemm_kernel_persistent(
+    a_ptr,
+    b_ptr,
+    c_ptr,
+    M,
+    N,
+    K,
+    stride_am,
+    stride_ak,
+    stride_bk,
+    stride_bn,
+    stride_cm,
+    stride_cn,
+    alpha,
+    beta,
+    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
+
+    # NOTE: There is currently a bug in blackwell pipelining that means it can't handle a value being
+    # used in both the prologue and epilogue, so we duplicate the counters as a work-around.
+    tile_id_c = start_pid - NUM_SMS
+
+    offs_k_for_mask = tl.arange(0, BLOCK_SIZE_K)
+    num_pid_in_group = GROUP_SIZE_M * num_pid_n
+
+    for tile_id in tl.range(start_pid, num_tiles, NUM_SMS, flatten=True):
+        pid_m, pid_n = _compute_pid(
+            tile_id, num_pid_in_group, num_pid_m, GROUP_SIZE_M, NUM_SMS
+        )
+        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)
+
+        accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+        for ki in range(k_tiles):
+            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)
+
+        tile_id_c += NUM_SMS
+        pid_m, pid_n = _compute_pid(
+            tile_id_c, num_pid_in_group, num_pid_m, GROUP_SIZE_M, NUM_SMS
+        )
+        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)
+        c = accumulator.to(c_ptr.dtype.element_ty)
+
+        c = tl.fma(c, alpha, beta * tl.load(c_ptrs, mask=c_mask))
+        tl.store(c_ptrs, c, mask=c_mask)
+
+
+@triton.jit(launch_metadata=_matmul_launch_metadata)
+def gemm_kernel_descriptor_persistent(
+    a_ptr,
+    b_ptr,
+    c_ptr,  #
+    M,
+    N,
+    K,  #
+    alpha,
+    beta,
+    BLOCK_SIZE_M: tl.constexpr,  #
+    BLOCK_SIZE_N: tl.constexpr,  #
+    BLOCK_SIZE_K: tl.constexpr,  #
+    GROUP_SIZE_M: tl.constexpr,  #
+    EPILOGUE_SUBTILE: tl.constexpr,  #
+    NUM_SMS: tl.constexpr,
+):  #
+    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.make_tensor_descriptor(
+        a_ptr,
+        shape=[M, K],
+        strides=[K, 1],
+        block_shape=[BLOCK_SIZE_M, BLOCK_SIZE_K],
+    )
+    b_desc = tl.make_tensor_descriptor(
+        b_ptr,
+        shape=[N, K],
+        strides=[K, 1],
+        block_shape=[BLOCK_SIZE_N, BLOCK_SIZE_K],
+    )
+    c_desc = tl.make_tensor_descriptor(
+        c_ptr,
+        shape=[M, N],
+        strides=[N, 1],
+        block_shape=[
+            BLOCK_SIZE_M,
+            BLOCK_SIZE_N if not EPILOGUE_SUBTILE else BLOCK_SIZE_N // 2,
+        ],
+    )
+
+    # tile_id_c is used in the epilogue to break the dependency between
+    # the prologue and the epilogue
+    tile_id_c = start_pid - NUM_SMS
+    num_pid_in_group = GROUP_SIZE_M * num_pid_n
+
+    for tile_id in tl.range(start_pid, num_tiles, NUM_SMS, flatten=True):
+        pid_m, pid_n = _compute_pid(
+            tile_id, num_pid_in_group, num_pid_m, GROUP_SIZE_M, NUM_SMS
+        )
+        offs_am = pid_m * BLOCK_SIZE_M
+        offs_bn = pid_n * BLOCK_SIZE_N
+
+        accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+        for ki in range(k_tiles):
+            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)
+
+        tile_id_c += NUM_SMS
+        pid_m, pid_n = _compute_pid(
+            tile_id_c, num_pid_in_group, num_pid_m, GROUP_SIZE_M, NUM_SMS
+        )
+        offs_cm = pid_m * BLOCK_SIZE_M
+        offs_cn = pid_n * BLOCK_SIZE_N
+
+        if EPILOGUE_SUBTILE:
+            acc = tl.reshape(accumulator, (BLOCK_SIZE_M, 2, BLOCK_SIZE_N // 2))
+            acc = tl.permute(acc, (0, 2, 1))
+            acc0, acc1 = tl.split(acc)
+            acc0 = tl.fma(acc0, alpha, beta * c_desc.load([offs_cm, offs_cn]))
+            acc1 = tl.fma(
+                acc1, alpha, beta * c_desc.load([offs_cm, offs_cn + BLOCK_SIZE_N // 2])
+            )
+            c0 = acc0.to(dtype)
+            c_desc.store([offs_cm, offs_cn], c0)
+            c1 = acc1.to(dtype)
+            c_desc.store([offs_cm, offs_cn + BLOCK_SIZE_N // 2], c1)
+        else:
+            accumulator = tl.fma(
+                accumulator, alpha, beta * c_desc.load([offs_cm, offs_cn])
+            )
+            c = accumulator.to(dtype)
+            c_desc.store([offs_cm, offs_cn], c)
+
+
+# only for testing
+@triton.autotune(
+    configs=matmul_get_configs(),
+    key=["M", "N", "K"],
+)
+@triton.jit(launch_metadata=_matmul_launch_metadata)
+def gemm_kernel(
+    a_ptr,
+    b_ptr,
+    c_ptr,  #
+    M,
+    N,
+    K,  #
+    stride_am,
+    stride_ak,  #
+    stride_bk,
+    stride_bn,  #
+    stride_cm,
+    stride_cn,  #
+    alpha,
+    beta,
+    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
+
+    c = accumulator.to(c_ptr.dtype.element_ty)
+
+    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)
+    c = tl.fma(c, alpha, beta * tl.load(c_ptrs, mask=c_mask))
+    tl.store(c_ptrs, c, mask=c_mask)