solution.py
final answer
benchmark.log
check.log
result.json
"""FP8 e4m3 GEMM using real fp8 tensor-core MMA via Triton.
Layout:
x: fp8_e4m3 (M, K)
weight: fp8_e4m3 (N, K)
weight_scale: fp32 (N,)
y = (x @ weight.T) * weight_scale -> bf16 (M, N)
K dimensions that are not aligned to the tensor-core tile are handled by
padding the operands up to the tile size. The padding values are fp8 zeros,
so they contribute nothing to the result.
"""
import torch
import torch.nn as nn
import torch.nn.functional as F
import triton
import triton.language as tl
OP_TYPE = "gemm"
SUPPORTED_PRECISIONS = ["fp8_e4m3"]
HARDWARE_REQUIRED = ["RTX_PRO_6000", "H100", "B200"]
E4M3_MAX = 448.0
M = 4096
N = 4096
K = 4096
@triton.jit
def fp8_gemm_kernel(
x_ptr,
w_ptr,
s_ptr,
y_ptr,
M,
N,
K,
stride_xm,
stride_xk,
stride_wn,
stride_wk,
stride_ym,
stride_yn,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
GROUP_M: tl.constexpr,
):
"""C = (A @ B.T) * scale. K is assumed a multiple of BLOCK_K."""
pid = tl.program_id(axis=0)
num_pid_m = tl.cdiv(M, BLOCK_M)
num_pid_n = tl.cdiv(N, BLOCK_N)
num_pid_in_group = GROUP_M * num_pid_n
group_id = pid // num_pid_in_group
first_pid_m = group_id * GROUP_M
group_size_m = min(num_pid_m - first_pid_m, GROUP_M)
pid_m = first_pid_m + (pid % group_size_m)
pid_n = (pid % num_pid_in_group) // group_size_m
offs_m = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
offs_n = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
offs_k = tl.arange(0, BLOCK_K)
x_ptrs = x_ptr + (offs_m[:, None] * stride_xm + offs_k[None, :] * stride_xk)
# Load B transposed directly from weight (N, K) row-major into (BLOCK_K, BLOCK_N).
w_ptrs = w_ptr + (offs_k[:, None] * stride_wk + offs_n[None, :] * stride_wn)
acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)
for k0 in range(0, K, BLOCK_K):
a = tl.load(
x_ptrs + k0 * stride_xk,
mask=offs_m[:, None] < M,
other=0.0,
)
b = tl.load(
w_ptrs + k0 * stride_wk,
mask=offs_n[None, :] < N,
other=0.0,
)
acc += tl.dot(a, b)
scale = tl.load(s_ptr + offs_n, mask=offs_n < N, other=0.0)
acc = acc * scale[None, :]
y_ptrs = y_ptr + (offs_m[:, None] * stride_ym + offs_n[None, :] * stride_yn)
tl.store(
y_ptrs,
acc.to(tl.bfloat16),
mask=(offs_m[:, None] < M) & (offs_n[None, :] < N),
)
# Fallback autotuned kernel for shapes outside the hand-tuned set.
@triton.autotune(
configs=[
triton.Config({"BLOCK_M": 128, "BLOCK_N": 256, "BLOCK_K": 128, "GROUP_M": 8}, num_warps=8, num_stages=3),
triton.Config({"BLOCK_M": 256, "BLOCK_N": 128, "BLOCK_K": 128, "GROUP_M": 8}, num_warps=8, num_stages=3),
triton.Config({"BLOCK_M": 128, "BLOCK_N": 128, "BLOCK_K": 128, "GROUP_M": 8}, num_warps=8, num_stages=4),
triton.Config({"BLOCK_M": 64, "BLOCK_N": 256, "BLOCK_K": 128, "GROUP_M": 8}, num_warps=8, num_stages=3),
triton.Config({"BLOCK_M": 64, "BLOCK_N": 128, "BLOCK_K": 128, "GROUP_M": 8}, num_warps=4, num_stages=4),
triton.Config({"BLOCK_M": 32, "BLOCK_N": 128, "BLOCK_K": 128, "GROUP_M": 1}, num_warps=4, num_stages=4),
triton.Config({"BLOCK_M": 16, "BLOCK_N": 128, "BLOCK_K": 128, "GROUP_M": 1}, num_warps=4, num_stages=4),
],
key=["M", "N", "K"],
)
@triton.jit
def fp8_gemm_kernel_autotune(
x_ptr,
w_ptr,
s_ptr,
y_ptr,
M,
N,
K,
stride_xm,
stride_xk,
stride_wn,
stride_wk,
stride_ym,
stride_yn,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
GROUP_M: tl.constexpr,
):
fp8_gemm_kernel(
x_ptr, w_ptr, s_ptr, y_ptr,
M, N, K,
stride_xm, stride_xk, stride_wn, stride_wk, stride_ym, stride_yn,
BLOCK_M, BLOCK_N, BLOCK_K, GROUP_M,
)
class Model(nn.Module):
"""y = ((x @ weight.T) * weight_scale).to(bf16)."""
def __init__(self, M: int, N: int, K: int):
super().__init__()
self.M, self.N, self.K = M, N, K
w = torch.empty(N, K, dtype=torch.bfloat16)
nn.init.normal_(w, std=0.02)
s = (w.float().abs().amax(dim=1, keepdim=True) / E4M3_MAX).clamp(min=1e-12)
w_fp8 = (w.float() / s).to(torch.float8_e4m3fn)
self.register_buffer("weight", w_fp8)
self.register_buffer("weight_scale", s.squeeze(1).to(torch.float32))
def forward(self, x: torch.Tensor) -> torch.Tensor:
M, K = x.shape
N = self.weight.shape[0]
x = x.contiguous()
w = self.weight.contiguous()
s = self.weight_scale.contiguous()
cfg = _pick_config(M, N, K)
if cfg is None:
# Generic path: pad to 128 and autotune.
tile = 128
K_pad = ((K + tile - 1) // tile) * tile
if K_pad != K:
w = F.pad(w, (0, K_pad - K))
x = F.pad(x, (0, K_pad - K))
K = K_pad
_run_autotune_kernel(x, w, s, y := torch.empty((M, N), device=x.device, dtype=torch.bfloat16), M, N, K)
return y
# Hand-tuned path: pad to the config's K tile.
tile = cfg["BLOCK_K"]
K_pad = ((K + tile - 1) // tile) * tile
if K_pad != K:
w = F.pad(w, (0, K_pad - K))
x = F.pad(x, (0, K_pad - K))
K = K_pad
y = torch.empty((M, N), device=x.device, dtype=torch.bfloat16)
_run_manual_kernel(x, w, s, y, M, N, K, cfg)
return y
def _pick_config(M: int, N: int, K: int):
"""Hand-picked configs for the graded shapes."""
if M == 32 and N == 8192 and K == 8192:
return {"BLOCK_M": 16, "BLOCK_N": 128, "BLOCK_K": 128, "GROUP_M": 1, "num_warps": 4, "num_stages": 4}
# Compute-bound square/rectangular shapes (use a 64-wide K tile).
if M >= 4096 and N >= 4096:
return {"BLOCK_M": 128, "BLOCK_N": 256, "BLOCK_K": 64, "GROUP_M": 8, "num_warps": 8, "num_stages": 4}
return None
def _run_manual_kernel(x, w, s, y, M, N, K, cfg):
grid = (triton.cdiv(M, cfg["BLOCK_M"]) * triton.cdiv(N, cfg["BLOCK_N"]),)
fp8_gemm_kernel[grid](
x, w, s, y,
M, N, K,
x.stride(0), x.stride(1),
w.stride(0), w.stride(1),
y.stride(0), y.stride(1),
BLOCK_M=cfg["BLOCK_M"],
BLOCK_N=cfg["BLOCK_N"],
BLOCK_K=cfg["BLOCK_K"],
GROUP_M=cfg["GROUP_M"],
num_warps=cfg["num_warps"],
num_stages=cfg["num_stages"],
)
def _run_autotune_kernel(x, w, s, y, M, N, K):
grid = lambda META: (triton.cdiv(M, META["BLOCK_M"]) * triton.cdiv(N, META["BLOCK_N"]),)
fp8_gemm_kernel_autotune[grid](
x, w, s, y,
M, N, K,
x.stride(0), x.stride(1),
w.stride(0), w.stride(1),
y.stride(0), y.stride(1),
)
def get_inputs():
x = (torch.rand(M, K) * 8 - 4).to(torch.float8_e4m3fn)
return [x]
def get_init_inputs():
return [M, N, K]
Done. The final kernel is in `solution.py`.
What it does:
- Real FP8×FP8 tensor-core MMA via Triton `tl.dot` with `fp8_e4m3fn` inputs and `fp32` accumulation.
- Per-channel `weight_scale` applied in the epilogue before casting to `bf16`.
- K-unaligned shapes (e.g. `K=4127`) are handled by padding `x` and `weight` up to the tile granularity with fp8 zeros, avoiding the slow masked-K tensor-core path.
- Hand-tuned tile configs for the graded shapes, plus an autotuned fallback for other sizes.
`python check.py` passes, and `python benchmark.py` reports:
| shape | ms | TFLOPS | peak fraction |
|-------|----|--------|---------------|
| 4096×4096×4096 | 0.224 | 613 | 0.613 |
| 4096×4096×4127 | 0.281 | 492 | 0.492 |
| 32×8192×8192 | 0.064 | 68 | 0.068 |
| 4096×14336×4096 | 0.713 | 675 | 0.675 |
**Geomean peak fraction: ~0.34–0.35** (well above the 0.1 OK threshold).
warning: `VIRTUAL_ENV=/home/infatoshi/kernelbench.com/benchmarks/hard/.venv` does not match the project environment path `/home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm/repo/.venv` and will be ignored; use `--active` to target the active environment instead
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-15T00:26:37.614962+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-15T00:26:37.826631+00:00 elapsed_s=0.212 ms=0.223904
shape=0 variant=solution tflops=613.830 gbps=299.722 ms=0.224
shape=0 solution_peak_fraction=0.6138
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-15T00:26:38.351750+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-15T00:26:38.368695+00:00 elapsed_s=0.017 ms=0.281360
shape=1 variant=solution tflops=492.178 gbps=239.419 ms=0.281
shape=1 solution_peak_fraction=0.4922
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-15T00:26:40.240480+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-15T00:26:40.246243+00:00 elapsed_s=0.006 ms=0.060496
shape=2 variant=solution tflops=70.996 gbps=1122.311 ms=0.060
shape=2 solution_peak_fraction=0.0710
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-15T00:26:41.931391+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-15T00:26:41.962269+00:00 elapsed_s=0.031 ms=0.713168
shape=3 variant=solution tflops=674.506 gbps=270.537 ms=0.713
shape=3 solution_peak_fraction=0.6745
peak_fraction: 0.3468
RESULT: OK
warning: `VIRTUAL_ENV=/home/infatoshi/kernelbench.com/benchmarks/hard/.venv` does not match the project environment path `/home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm/repo/.venv` and will be ignored; use `--active` to target the active environment instead
warning: Ignoring existing virtual environment linked to non-existent Python interpreter: /home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm/repo/.venv/bin/python3 -> python
Using CPython 3.11.15
Removed virtual environment at: /home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm/repo/.venv
Creating virtual environment at: /home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm/repo/.venv
Building kernelbench-hard @ file:///home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm/repo
Built kernelbench-hard @ file:///home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm/repo
Installed 56 packages in 66ms
PASS
{
"run_id": "20260614_171808_kimi-claude_kimi-k2.7-code_01_fp8_gemm",
"run_group": "",
"problem": "01_fp8_gemm",
"harness": "kimi-claude",
"model": "kimi-k2.7-code",
"reasoning_effort": "",
"started_at": "2026-06-14T17:18:08-06:00",
"harness_finished_at": "2026-06-14T18:26:28-06:00",
"finished_at": "2026-06-14T18:26:42-06:00",
"start_epoch": 1781479088,
"harness_end_epoch": 1781483188,
"end_epoch": 1781483202,
"has_solution": true,
"correct": true,
"failure_reason": "pass",
"retryable_infra_failure": false,
"minimum_useful_output_tokens": 5000,
"peak_fraction": 0.3468,
"template_mutated": false,
"elapsed_seconds": 4100,
"total_elapsed_seconds": 4114,
"check_elapsed_seconds": 8,
"benchmark_elapsed_seconds": 6,
"check_timeout_seconds": 180,
"benchmark_timeout_seconds": 1800,
"check_exit_code": 0,
"benchmark_exit_code": 0,
"harness_exit_code": 0,
"session_complete": true,
"agent_cuda_disabled": false,
"agent_container": true,
"agent_container_image": "nvcr.io/nvidia/tensorrt-llm/release:latest",
"agent_container_network": "bridge",
"gpu_queue_mode": "agent_container_native_profiling_path_wrapper_gpu_lock",
"output_tokens_per_second": 17.02219512195122,
"usage": {"input_tokens": 151563, "output_tokens": 69791, "cache_read_tokens": 5201408, "cache_creation_tokens": 0, "reasoning_tokens": null, "total_cost_usd": 5.103294000000002}
}
timeline (252 events)
system — init
session start cwd=/workspace/problems/01_fp8_gemm model=kimi-k2.7-code permissions=bypassPermissions
assistant
reasoning (776 chars)
We need optimize FP8 GEMM for RTX PRO 6000 Blackwell SM120. Need read reference.py, solution.py (maybe not exists), check.py, benchmark.py. Then design custom kernel. Need run via uv. We can use Triton or CUTLASS. Blackwell SM120 supports WGMMA/mma.sync for FP8. Triton likely has Blackwell support? Maybe current environment torch includes Triton version? Need inspect. If Triton supports tl.dot with fp8 on Blackwell, easiest. But we need K not multiple of 128. Could use block pointers with padding? Triton can handle k loop with K not multiple of block K using tl.load with mask and boundary_check maybe. FP8 dot in Triton needs block sizes multiples of 16? For WGMMA, A must be K multiple of 16? For e4m3, mma instruction maybe 64x8x16? Hmm. Need tune.
Let's read files.
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stdout (2109 chars) — TRUNCATED
1 """FP8 e4m3 GEMM reference (correctness only, NOT the SOTA baseline).
2
3 Genuine fp8 x fp8: BOTH operands are fp8_e4m3. The weight is stored as fp8
4 (normalized into the e4m3 range) together with a per-output-channel scale, the
5 standard scaled-fp8 inference layout. The reference upcasts the fp8 operands to
6 bf16 and matmuls, then applies the per-channel scale — this DEFINES the fp8
7 target. A real fp8 x fp8 MMA kernel matches it (and can exceed the bf16 roofline
8 ceiling of ~0.5); a bf16-upcast kernel also matches but stays capped at ~0.5.
9 """
10 import torch
11 import torch.nn as nn
12
13 OP_TYPE = "gemm"
14 SUPPORTED_PRECISIONS = ["fp8_e4m3"]
15 HARDWARE_REQUIRED = ["RTX_PRO_6000", "H100", "B200"]
16 E4M3_MAX = 448.0
17
18
19 class Model(nn.Module):
20 """y = ((x @ w.T) * weight_scale).to(bf16).
21
22 x: fp8_e4m3 (M, K). w: fp8_e4m3 (N, K) normalized to the e4m3 range.
23 weight_scale: (N,) per-output-channel dequant scale.
24 """
25
26 def __init__(self, M: int, N: int, K: int):
27 super().__init__()
28 self.M, self.N, self.K = M, N, K
29 w = torch.empty(N, K, dtype=torch.bfloat16)
30 nn.init.normal_(w, std=0.02)
31 s = (w.float().abs().amax(dim=1, keepdim=True) / E4M3_MAX).clamp(min=1e-12) # (N,1)
32 w_fp8 = (w.float() / s).to(torch.float8_e4m3fn)
33 self.register_buffer("weight", w_fp8) # (N, K) fp8
34 self.register_buffer("weight_scale", s.squee
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stdout (4575 chars) — TRUNCATED
1 """Correctness runner for FP8 GEMM.
2
3 Runs solution.Model vs reference.Model across all shapes in shapes.py, 3 seeds
4 each, with per-dtype atol/rtol. Also rejects forbidden ops by grep.
5 """
6 import re
7 import sys
8 from pathlib import Path
9
10 import torch
11 import yaml
12
13 # Make the repo's src/ importable
14 REPO_ROOT = Path(__file__).resolve().parents[2]
15 sys.path.insert(0, str(REPO_ROOT))
16
17 from src.eval.correctness import check_correctness # noqa: E402
18 from src.eval.numeric_stress import ( # noqa: E402
19 numeric_stress_cases,
20 numeric_stress_context,
21 tolerance_for_case,
22 )
23
24
25 def main():
26 try:
27 import reference
28 import shapes
29 import solution
30 except Exception as e:
31 print(f"FAIL: import error: {e}")
32 sys.exit(1)
33
34 problem_yaml = Path("problem.yaml")
35 meta = yaml.safe_load(problem_yaml.read_text()) if problem_yaml.exists() else {}
36
37 # --- Forbidden-op check ------------------------------------------------
38 sol_src = Path("solution.py").read_text() if Path("solution.py").exists() else ""
39 for forbidden in meta.get("forbidden", []):
40 pat = re.escape(forbidden)
41 if re.search(pat, sol_src):
42 print(f"FAIL: forbidden op used: {forbidden}")
43 sys.exit(1)
44
45 device = torch.device("cuda:0")
46 tol_override = meta.get("tolerance") or None
47
48 # --- Per-shape correc
... (3075 more chars)
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stdout (5631 chars) — TRUNCATED
1 """Roofline benchmark for FP8 GEMM.
2
3 For each shape: times the agent's solution first. Optional eager, compiled,
4 and SOTA diagnostics are enabled with KBH_BENCHMARK_BASELINES=1. Reports achieved TFLOPS, GB/s, and peak_fraction.
5
6 Output lines the harness picks up:
7 shape=<idx> variant=<name> tflops=<N> gbps=<N> ms=<N>
8 peak_fraction: <N> (geomean over shapes of solution's peak_fraction)
9 """
10 import sys
11 from math import exp, log
12 from pathlib import Path
13
14 import torch
15 import yaml
16
17 REPO_ROOT = Path(__file__).resolve().parents[2]
18 sys.path.insert(0, str(REPO_ROOT))
19
20 from src.eval.roofline import compute_gbps, compute_tflops, peak_fraction # noqa: E402
21 from src.eval.timing import benchmark_baselines_enabled, time_variant # noqa: E402
22 from src.hardware import get as get_hw # noqa: E402
23
24
25 def _eval_formula(expr: str, vars: dict) -> float:
26 # Very small eval: only names from `vars` are valid.
27 return float(eval(expr, {"__builtins__": {}}, vars))
28
29
30 def main():
31 import reference
32 import shapes
33 import solution
34
35 meta = yaml.safe_load(Path("problem.yaml").read_text())
36 hw = get_hw(meta["hardware"][0])
37 peak_tflops = hw.peak_tflops_dense.get(meta["peak_tflops_key"], 0.0)
38 peak_gbps = hw.peak_bandwidth_gb_s
39 regime = meta.get("regime", "compute")
40 flops_formula = meta["flops_formula"]
41 bytes_formula = meta["bytes_formula"]
42 num_perf
... (4131 more chars)
assistant
reasoning (34 chars)
Need read shapes.py, problem.yaml.
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stdout (603 chars)
1 """Canonical shape sweep for FP8 GEMM.
2
3 Mix of:
4 - square aligned (the easy case)
5 - off-alignment K (common real-world failure mode for tile-quantized kernels)
6 - skinny (decode-like, memory-bound)
7 - rectangular (prefill with grouped attention)
8 """
9
10 SHAPES = [
11 {"M": 4096, "N": 4096, "K": 4096}, # square aligned
12 {"M": 4096, "N": 4096, "K": 4127}, # K not multiple of 128 -> forces predicated tails
13 {"M": 32, "N": 8192, "K": 8192}, # skinny M (decode)
14 {"M": 4096, "N": 14336, "K": 4096}, # Llama3 up-proj shape
15 ]
16
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stdout (1249 chars)
1 name: 01_fp8_gemm
2 display_name: "FP8 e4m3 GEMM"
3 precision: fp8_e4m3
4 regime: compute
5
6 # Dense-equivalent FLOPs per invocation. Evaluated per-shape; the benchmark
7 # substitutes M/N/K from each shapes.py entry.
8 flops_formula: "2 * M * N * K"
9
10 # Bytes moved (approximate): fp8 inputs in, bf16 output.
11 bytes_formula: "M*K + K*N + M*N*2"
12
13 hardware: [RTX_PRO_6000]
14 peak_tflops_key: fp8 # index into src/hardware/rtx_pro_6000.py peak_tflops_dense
15 peak_bandwidth_key: dram
16
17 # Per-dtype tolerance override (optional). Defaults are in src/eval/correctness.py.
18 tolerance:
19 bfloat16: 0.2
20 fp8_e4m3fn: 0.2
21
22 # Forbidden ops — using any of these in solution.py fails correctness post-hoc.
23 # torch._scaled_mm is Stanford-style cheating (just call the vendor library).
24 forbidden:
25 - "torch._scaled_mm"
26 - "torch.ops.aten._scaled_mm"
27
28 sota:
29 name: "FlashInfer FP8 GEMM"
30 url: "https://github.com/flashinfer-ai/flashinfer"
31 function: "flashinfer.gemm.fp8_gemm"
32 deps:
33 - "flashinfer>=0.6.8"
34 # Documented H100 throughput for this shape (informational, not graded):
35 reference_throughput_tflops_h100: 550
36
37 num_correct_trials: 3
38 num_perf_trials: 30
39
assistant
reasoning (197 chars)
Need write solution.py with Model, get_inputs, get_init_inputs. Need use fp8 tensor core. Let's inspect environment: torch version, triton version, CUDA. Also device? We can run uv python commands.
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tool
stdout (594 chars)
Using CPython 3.11.15
Creating virtual environment at: /workspace/.venv
Building kernelbench-hard @ file:///workspace
Built kernelbench-hard @ file:///workspace
warning: Failed to hardlink files; falling back to full copy. This may lead to degraded performance.
If the cache and target directories are on different filesystems, hardlinking may not be supported.
If this is intentional, set `export UV_LINK_MODE=copy` or use `--link-mode=copy` to suppress this warning.
Installed 56 packages in 865ms
2.11.0+cu130 13.0 NVIDIA RTX PRO 6000 Blackwell Workstation Edition
tool
stdout (459 chars)
total 44
drwxrwxr-x 2 1002 1002 4096 Jun 14 23:18 .
drwxrwxr-x 3 1002 1002 4096 Jun 14 23:18 ..
-rw-rw-r-- 1 1002 1002 2756 Jun 14 19:26 PROMPT.txt
-rw-rw-r-- 1 1002 1002 5147 Jun 1 21:05 benchmark.py
-rw-rw-r-- 1 1002 1002 4205 Jun 2 01:08 check.py
-rw-rw-r-- 1 1002 1002 1143 Jun 14 19:26 problem.yaml
-rw-rw-r-- 1 1002 1002 1952 Jun 14 19:26 reference.py
-rw-rw-r-- 1 1002 1002 564 Apr 24 06:36 shapes.py
-rw-rw-r-- 1 1002 1002 1725 Apr 24 06:37 sota.py
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reasoning (762 chars)
PyTorch 2.11.0+cu130 (CUDA 13.0), triton 3.6.0. Device RTX PRO 6000 Blackwell. Need FP8 GEMM. Triton 3.6 may support Blackwell? Since CUDA 13.0, architecture sm_100/sm_120? PyTorch 2.11 maybe supports Blackwell. Triton has nvidia backend for Blackwell? Let's check triton availability of tl.dot fp8. We can test simple kernel. Need use UVA? We'll test.
First, can we do torch.matmul with fp8? Not in PyTorch maybe no. _scaled_mm forbidden. But triton tl.dot with fp8 operands on Blackwell should lower to mma.sync.aligned.m64n8k16.row.col.f32.e4m3.e4m3.f32? For sm_120, there is new tcgen05 WGMMA? Let's check. But Triton 3.6 likely supports Hopper wgmma; Blackwell support may be present. Need test.
Let's write a quick test Triton kernel fp8 dot and compare.
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stdout (122 chars)
bf16 dot ok tensor(0., device='cuda:0', dtype=torch.bfloat16)
fp8 dot ok tensor(0., device='cuda:0', dtype=torch.bfloat16)
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reasoning (1877 chars)
Triton FP8 dot works on this device. Great. Need design high-performance FP8 GEMM for Blackwell. Need beat bf16 fallback. Use Triton. Need account for K not multiple of 128. Need per-channel scale at end.
Approach: Implement a Triton matmul kernel similar to standard fp8 matmul, with block sizes tuned for Blackwell. Need handle shapes: (4096,4096,4096), (4096,4096,4127), (32,8192,8192), (4096,14336,4096). We can choose different configs per shape via autotune or manual selection based on M,N,K. The kernel computes C = A @ B.T * scale, where B is (N,K), scale (N,). A x fp8 (M,K). Use fp32 accumulation, scale after reduction.
Performance considerations: For Blackwell SM120, FP8 tensor core throughput high, memory bandwidth 1.8 TB/s. Need large tiles, warp-group cluster? Triton abstracts. For square shapes, use BLOCK_M=128, BLOCK_N=256, BLOCK_K=128 maybe. Need K=4127 -> BLOCK_K=128 leaves tail. Handle tails by masking loads. tl.dot with fp8 requires K block maybe multiple of 16/32? WGMMA k=16 for e4m3? But we can pad with zeros for tail. However if BLOCK_K not dividing K, last iteration load partial. tl.load with mask in K dimension. For fp8 dot, A/B loaded as fp8 block with mask. Should work but maybe tl.dot requires full K tile for fp8? It likely works with masked values zero. Need test.
Potential issue: Triton tl.dot with fp8 requires block sizes multiples of 16? We will choose 128/256 etc. Good.
For skinny M=32, N=8192, K=8192. With BLOCK_M=64 and M=32 -> only one tile row. BLOCK_N maybe 128/256. Need performance; small M is memory-bound. Could use BLOCK_M=32? Triton WGMMA requires M multiple? For WGMMA m=64? Actually Hopper wgmma.mma_async.m64n8k16 uses M grouped in warpgroup. For sm120, maybe WGMMA shapes include m64n8k16, m64n16k16 etc. BLOCK_M must be multiple of 64? But our test with BLOCK=64 worked. Need check smaller. Try BLOCK_M=32.
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stderr (372 chars)
Exit code 1
Traceback (most recent call last):
File "/tmp/test_block.py", line 24, in <module>
run(32,8192,8192,*cfg)
File "/tmp/test_block.py", line 17, in run
a=torch.randn(M,K,device='cuda',dtype=torch.float8_e4m3fn)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
NotImplementedError: "normal_kernel_cuda" not implemented for 'Float8_e4m3fn'
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reasoning (55 chars)
We can create fp8 by casting from bf16. Let's fix test.
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stdout (133 chars)
BM 32 BN 64 BK 64 err 2.0
BM 32 BN 128 BK 64 err 2.0
BM 32 BN 256 BK 64 err 2.0
BM 64 BN 64 BK 64 err 2.0
BM 64 BN 128 BK 128 err 2.0
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reasoning (4530 chars)
Error 2.0 is due to fp8 accumulation vs bf16 reference? It is fine; correctness tolerance loose.
Need tune performance. We need run benchmark.py maybe baseline. Let's first try a simple Triton fp8 matmul kernel and benchmark. Need avoid using torch._scaled_mm. Triton autotune may help. We can use @triton.autotune with configs. However autotune can be slow; acceptable. Need make final solution robust across shapes.
Potential issue: Triton tl.dot on fp8 may generate unsupported shapes for small M, e.g. BLOCK_M=32 works. Good.
Need per-channel scale: kernel can load scale[offs_n] and multiply accumulator before storing as bf16. To reduce memory traffic, apply after all K. Need scale broadcast across M dimension. Could also fuse scale multiply in epilogue. If scale is fp32, multiply acc (fp32) by scale[None,:] then cast bf16.
Memory layout: x fp8 (M,K) row major, weight fp8 (N,K) row major. In GEMM C = x @ W.T. Loading W by rows with K contiguous is natural; each iteration load W block of shape (BLOCK_N, BLOCK_K) row contiguous. For dot, need W transposed to (BLOCK_K, BLOCK_N) for tl.dot. We can load W as (BLOCK_N, BLOCK_K) and pass tl.trans(b). That's what test does. Good.
Need consider K=4127 tail. If we use BLOCK_K=128, K not multiple, mask handles. But tl.dot on fp8 with k dimension not full? The dot loops over whole BLOCK_K. We load zeros for out-of-bounds. Good.
Could use split-K for skinny M? For M=32,N=8192,K=8192, large K and N. If BLOCK_K=128, there are 64 k iterations per tile. With BLOCK_N=128, num tiles N=64, M=1 tile. Total tiles=64. Blackwell has many SMs (e.g. 120). Occupancy maybe low. But each tile heavy. To improve parallelism, can use BLOCK_M=64 or 32; M tile count 1. Better use larger BLOCK_N? If BLOCK_N=256, N tiles=32. Total 32. Could use split-K to increase parallelism and reduce accumulation. For M=32,N=8192,K=8192, M dimension small, we might use BLOCK_M=64 and have 0? Actually M=32. Use group ordering? Better use BLOCK_M=32 to have one row tile. Then to increase parallelism use 2D grid (pid_m maybe 1). We can set BLOCK_N=128 and have 64 tiles. 64 warps/groups. Maybe enough. For decode-style, memory bound; larger K reduces? Actually compute/memory ratio low; performance maybe 200-300 TFLOPS. Need optimize.
For square M=4096, need high utilization. We can choose BLOCK_M=128, BLOCK_N=256, BLOCK_K=128, num_warps=8. Maybe use 2D cluster? Blackwell? Triton supports num_ctas? Not stable. Let's test.
Let's implement a matmul kernel with autotune. However using autotune with fp8 and many configs may take time but okay. Need handle K tail. Let's write a standard kernel.
But we need be careful with Triton fp8 dot and split-K. For now single stage.
Let's first implement solution.py with a basic autotuned fp8 GEMM and see numbers.
Also note check.py uses get_inputs, get_init_inputs at module level. reference.py defines M,N,K at module level. Our solution.py must define same module-level M,N,K and get_inputs/get_init_inputs? It may import shapes and reference? The check imports reference and solution, then sets reference.M etc. It calls solution.Model only. It doesn't call solution.get_inputs. But benchmark imports reference and solution and sets reference.M etc, then uses reference.get_inputs only. So we don't need get_inputs in solution, but safe to include. The prompt says same Model, get_inputs, and get_init_inputs interface as reference.py. We'll include them.
Need Model registers buffers weight and weight_scale. Then forward calls kernel. Also maybe handle case where weight not contiguous.
Let's design kernel. Use tl.dot with allow_tf32? irrelevant fp8.
Need pass dtype_x and dtype_w? Both fp8. We can just treat as fp8.
Potential Triton bug: fp8 tl.dot only supports specific block sizes: A must be (BLOCK_M, BLOCK_K), B must be (BLOCK_K, BLOCK_N). It accepts transposed via tl.trans. We load B as (BLOCK_N, BLOCK_K) and transpose. Good.
Now performance: Blackwell tensor cores for fp8 have shapes? PTX mma.sync.aligned.m64n8k16? Actually for sm100, mma shape e4m3: .m64n8k16 maybe. Triton will tile. BLOCK_M should be multiple of 64 for WGMMA? Our test with BM=32 worked, so Triton can emulate with smaller? But for perf use 64.
Let's implement autotune configs focusing on square and rectangular. Include group_m for better L2. Standard.
Potential issue: K=4127 with BLOCK_K=128 means iterations 33. We should loop with tl.range(0, K, BLOCK_K) and mask loads. Maybe use pointer arithmetic and masking.
Let's create solution.py.
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stdout (139 chars)
File created successfully at: /workspace/problems/01_fp8_gemm/solution.py (file state is current in your context — no need to Read it back)
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reasoning (13 chars)
Run check.py.
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subagent · 19 events · 6 tools
tool
stdout (280 chars)
Command running in background with ID: bgu1ah6o6. Output is being written to: /tmp/claude-1002/-workspace-problems-01-fp8-gemm/fc0b7a6e-4534-4072-813b-e30a8bdaeb17/tasks/bgu1ah6o6.output. You will be notified when it completes. To check interim output, use Read on that file path.
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reasoning (5 chars)
Wait.
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stdout (135 chars)
<retrieval_status>timeout</retrieval_status>
<task_id>bgu1ah6o6</task_id>
<task_type>local_bash</task_type>
<status>running</status>
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reasoning (109 chars)
Check may be compiling autotune configs for all shapes and seeds. Could take a while. Let's read output file.
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stdout (126 chars)
<system-reminder>Warning: the file exists but is shorter than the provided offset (1). The file has 1 lines.</system-reminder>
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reasoning (634 chars)
File exists but maybe empty. The command is still running, likely Triton compiling. We can wait or check process. But to save time, maybe we should avoid autotune in correctness? Autotune compiles all configs for each shape on first call, but 8 configs * 4 shapes = 32 kernels, each may take a few seconds. It may be okay. Let's wait longer. Meanwhile, we can think about performance improvements.
But output file short means maybe the process hasn't flushed. Wait.
We can also test correctness with a quick manual script without autotune. But check.py uses solution.Model; autotune will run. Let's wait maybe 5 min? Use background.
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stdout (4311 chars) — TRUNCATED
<retrieval_status>success</retrieval_status>
<task_id>bgu1ah6o6</task_id>
<task_type>local_bash</task_type>
<status>failed</status>
<exit_code>1</exit_code>
<output>
triton.compiler.errors.UnsupportedLanguageConstruct: at 25:23:
stride_yn,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
GROUP_M: tl.constexpr,
):
pid = tl.program_id(axis=0)
num_pid_n = tl.cdiv(N, BLOCK_N)
num_pid_in_group = GROUP_M * num_pid_n
group_id = pid // num_pid_in_group
first_pid_m = group_id * GROUP_M
group_size_m = min(num_pid_m := tl.cdiv(M, BLOCK_M) - first_pid_m, GROUP_M)
^
unsupported AST node type: NamedExpr
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/workspace/problems/01_fp8_gemm/check.py", line 119, in <module>
main()
File "/workspace/problems/01_fp8_gemm/check.py", line 80, in main
sol_out = sol_model(*inputs)
^^^^^^^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/torch/nn/modules/module.py", line 1779, in _wrapped_call_impl
return self._call_impl(*args, **kwargs)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/torch/nn/modules/module.py", line 1790, in _call_impl
return forward_call(*args, **kwargs)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/workspace/problems/01_fp8_gemm/solution.py", line 153, in forward
_autotuned_fp8
... (2811 more chars)
assistant
reasoning (559 chars)
Triton doesn't support walrus operator in kernel. Need rewrite group_size_m computation without named expression. Fix.
Also autotune wrapper calling inner kernel with all args: We need pass kernel args by name? In Triton, inner function defined with tl.constexpr args; calling it with positional values from outer constexpr may not work? It might work because both are JIT and constants. Let's simplify by merging kernel into autotuned kernel to avoid nested call complexity. Use one function with @triton.autotune. We can keep body.
Let's edit solution.py.
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stdout (5701 chars) — TRUNCATED
1 """FP8 e4m3 GEMM using real fp8 tensor-core MMA via Triton.
2
3 Layout:
4 x: fp8_e4m3 (M, K)
5 weight: fp8_e4m3 (N, K)
6 weight_scale: fp32 (N,)
7 y = (x @ weight.T) * weight_scale -> bf16 (M, N)
8 """
9 import torch
10 import torch.nn as nn
11 import triton
12 import triton.language as tl
13
14 OP_TYPE = "gemm"
15 SUPPORTED_PRECISIONS = ["fp8_e4m3"]
16 HARDWARE_REQUIRED = ["RTX_PRO_6000", "H100", "B200"]
17 E4M3_MAX = 448.0
18
19 M = 4096
20 N = 4096
21 K = 4096
22
23
24 @triton.jit
25 def fp8_gemm_kernel(
26 x_ptr,
27 w_ptr,
28 s_ptr,
29 y_ptr,
30 M,
31 N,
32 K,
33 stride_xm,
34 stride_xk,
35 stride_wn,
36 stride_wk,
37 stride_ym,
38 stride_yn,
39 BLOCK_M: tl.constexpr,
40 BLOCK_N: tl.constexpr,
41 BLOCK_K: tl.constexpr,
42 GROUP_M: tl.constexpr,
43 ):
44 pid = tl.program_id(axis=0)
45 num_pid_n = tl.cdiv(N, BLOCK_N)
46 num_pid_in_group = GROUP_M * num_pid_n
47 group_id = pid // num_pid_in_group
48 first_pid_m = group_id * GROUP_M
49 group_size_m = min(num_pid_m := tl.cdiv(M, BLOCK_M) - first_pid_m, GROUP_M)
50 pid_m = first_pid_m + (pid % group_size_m)
51 pid_n = (pid % num_pid_in_group) // group_size_m
52
53 offs_m = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
54 offs_n = pid_n * BLOCK_N + tl.arange(0, BLOCK_N)
55 offs_k = tl.arange(0, BLOCK_K)
56
57 x_ptrs = x_ptr + (offs_m[:, None] * stride_xm + offs_k[None, :] * stride_xk)
58 w_p
... (4201 more chars)
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reasoning (84 chars)
Rewrite kernel without walrus and maybe without nested call. Let's edit entire file.
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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reasoning (98 chars)
Run check.py again. It will autotune. But autotune may be heavy; let's run in background and wait.
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system — task_started
↳ subagent started
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reasoning (54 chars)
Check passes. Now run benchmark.py to see performance.
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stdout (1309 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T23:33:55.379176+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T23:33:56.887438+00:00 elapsed_s=1.508 ms=0.244448
shape=0 variant=solution tflops=562.242 gbps=274.532 ms=0.244
shape=0 solution_peak_fraction=0.5622
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T23:33:57.421460+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T23:33:58.714975+00:00 elapsed_s=1.294 ms=1.826096
shape=1 variant=solution tflops=75.833 gbps=36.889 ms=1.826
shape=1 solution_peak_fraction=0.0758
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T23:34:00.647844+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T23:34:01.409167+00:00 elapsed_s=0.761 ms=0.068272
shape=2 variant=solution tflops=62.910 gbps=994.482 ms=0.068
shape=2 solution_peak_fraction=0.0629
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T23:34:03.131808+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T23:34:04.067456+00:00 elapsed_s=0.936 ms=0.834320
shape=3 variant=solution tflops=576.561 gbps=231.252 ms=0.834
shape=3 solution_peak_fraction=0.5766
peak_fraction: 0.1983
RESULT: OK
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reasoning (383 chars)
Current performance: square 562 TFLOPS (0.56 peak), K=4127 75 TFLOPS (0.076), skinny 62.9 TFLOPS (0.063), rectangular 576 TFLOPS (0.577). Geomean 0.1983. Need improve. The off-alignment K and skinny M are dragging. Need optimize those.
The square and rectangular are decent but maybe can be higher. Need push up. Let's understand peak TFLOPS value for RTX PRO 6000 in hardware file.
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stdout (1543 chars) — TRUNCATED
1 """RTX PRO 6000 Blackwell Workstation — SM120, consumer-lineage Blackwell.
2
3 Peak tensor-core throughputs are dense-matrix advertised peaks. Actual kernels
4 will see 60-85% of peak on well-tuned code.
5 """
6 from dataclasses import dataclass
7
8
9 @dataclass(frozen=True)
10 class HardwareTarget:
11 name: str
12 sm: str
13 vram_gb: int
14 peak_bandwidth_gb_s: float # DRAM
15 peak_tflops_dense: dict[str, float] # dtype -> TFLOPS
16
17
18 RTX_PRO_6000 = HardwareTarget(
19 name="RTX PRO 6000 Blackwell Workstation",
20 sm="sm_120a",
21 vram_gb=96,
22 peak_bandwidth_gb_s=1800.0,
23 peak_tflops_dense={
24 # Blackwell GB202 dense tensor peaks. Derived from NVIDIA's headline
25 # 4000 fp4-sparse AI TOPS -> fp4 dense 2000 -> fp8 1000 -> bf16 500
26 # (each precision step = 2x; sparse = 2x dense). Verified empirically:
27 # cuBLAS hits fp8 773 / bf16 412 TFLOPS on 4096^3 (~77-82% of these,
28 # normal cuBLAS efficiency). The prior table was ~2.5x too low, which
29 # produced peak_fraction > 1.0 for real fp8 kernels. fp32 is the 125
30 # TFLOPS SIMT figure from the spec sheet.
31 "fp4": 2000.0,
32 "nvfp4": 2000.0,
33 "mxfp4": 2000.0,
34 "fp6": 1000.0,
35 "fp8": 1000.0,
36 "bf16": 500.0,
37 "fp16": 500.0,
38 "tf32": 250.0,
39 "fp32": 125.0, # non-tensor-core SIMT fp32 (spec sheet)
40 "int8": 1000.0,
41
... (43 more chars)
assistant
reasoning (908 chars)
Peak fp8=1000 TFLOPS. We get 562 on square and 576 on rectangular. Could improve to ~700+? Need better configs.
The K=4127 shape: why so slow 75 TFLOPS? Because K not multiple of BLOCK_K=128, maybe Triton generates inefficient predication or uses too few SMs? Also the autotuner likely chose config not good for tail. We need tail-optimized kernel maybe with a smaller K tile for leftover, or use BLOCK_K=64? Actually K=4127, block 128 gives 33 iterations. If each iteration fully masked only last partial, performance should still high. But 75 TFLOPS suggests config with small tiles or memory bound? Need inspect autotune cache which config selected per shape. Triton stores cache in ~/.triton/cache. We can run benchmark with TRITON_PRINT_AUTOTUNING=1 maybe. Or enable debug. Need see chosen config.
Let's run benchmark with env TRITON_PRINT_AUTOTUNING=1? I think triton has env TRITON_PRINT_AUTOTUNING.
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stdout (7972 chars) — TRUNCATED
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T23:34:16.045860+00:00
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 128, BLOCK_N: 256, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 256, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 128, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 64, BLOCK_N: 256, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning failed with out of resource: shared memory, Required: 122880, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 64, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 8, num_warps: 4, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 32, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 1, num_warps: 4, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 32, BLOCK_N: 256, BLOCK_K: 128, GROUP_M: 1, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 64, BLOCK_N: 64, BLOCK_K: 128, GROUP_M: 4, num_warps: 4, num_ctas: 1, num_stages: 4, maxnreg: None
Triton autotuning
... (6472 more chars)
assistant
reasoning (7615 chars)
Autotune choices show K=4127 chose BLOCK_M=128,BLOCK_N=128, num_warps=8, stages=4 -> poor. Maybe because large tile handles tail poorly. Need special-case K not multiple of 128. Could use a kernel that processes K in full blocks and a small tail with masked loads, but large tile already does that. Why poor? Maybe due to K=4127, BLOCK_K=128 -> 32 full blocks and one block of 15. With BLOCK_N=128, each tile's accumulator does many MMAs. Why 75 TFLOPS only? Compare to K=4096 square 0.24 ms, K=4127 1.82 ms (7.5x slower for only 1% more work). This suggests either selected config is bad or Triton generated code with masked loads causing huge slowdown. Maybe a config with smaller stages or BLOCK_K=64 better for tail. Let's test manually for shape1 with different configs (no autotune) to see achievable. We can write benchmark script that calls kernel with specific config. Use time_variant? We can measure with torch.cuda.Event.
But more generally, the K tail issue: Triton dot with masks can be inefficient if K dimension not aligned to BLOCK_K, because it may not be able to use tensor memory/wgmma for masked loads. It might fall back to generic path. Could improve by padding K to multiple of BLOCK_K with zero rows? But weight is fixed buffer; we could allocate x and weight with padded K and run aligned kernel. Since weight is already stored fp8 (N,K). We can pad in forward: create x_padded and w_padded of K' = next multiple of BLOCK_K (or 128), copy data, call aligned kernel. This avoids tail predication and improves perf. Extra memory overhead small. But need ensure correct for K not multiple. We can pad to next multiple of 128. Since scale applied after, padding zeros (fp8 zero? 0.0 maps to fp8 zero) won't affect. We can use torch.nn.functional.pad? For fp8, pad with zeros works? Need check. But copying to padded tensor may cost, but shape1 only once. The benchmark repeats many times, weight fixed; we can pad weight once in Model init or forward? Model __init__ creates weight; we can pad weight to K' and register? But state_dict expects weight shape (N,K) exactly, because reference Model has weight (N,K). If we register a padded buffer, load_state_dict strict will fail shape mismatch. So cannot pad registered weight. We could keep self.weight as original, but in forward create a padded view (copy) each call; cost maybe minor compared to kernel but repeated 30 times. Maybe pad once per forward and cache? Weight is fixed after loading, but shape M,N,K fixed per call; we could pad weight lazily and store in a non-persistent buffer? But strict state dict would load original. We can add attribute _weight_padded not in state_dict. In forward, if K not aligned, copy weight to padded buffer (allocate new each call or reuse cached). Since K fixed, we can create padded buffer once in forward if not exists. For x, we need pad each call (copy M*pad_K). That overhead might be okay. But shape1 K only 4127, pad to 4224? Actually next multiple of 128 is 4224 (128*33), adding 97 columns. Copy weight N*97 ~ 4096*97 ~ 397k bytes, x M*97 ~ 4096*97 ~ 397k. Kernel time would be ~0.24ms maybe. Copy overhead maybe small.
Alternative: Use a kernel specialized for tail with smaller block K (e.g., 64 or 32) for last iterations. But padding is easier and likely faster.
But we need the autotuner not to pick poor config. We can either not autotune K tail shapes, or pad to aligned and autotune on aligned K'.
For skinny M=32,N=8192,K=8192, performance 63.5 TFLOPS. The bytes_formula ~ M*K + K*N + M*N*2 = 32*8192 + 8192*8192 + 32*8192*2 ≈ 0.26 MB + 67.1 MB + 0.5 MB = 67.9 MB. Time at peak BW 1.8TB/s = 0.0377 ms. Our time 0.068 ms -> 1004 GB/s ~ 56% BW. Could improve with larger N tile or split K to improve parallelism? M=32, N=8192, K=8192. Config chosen BM=32,BN=128,BK=128, 4 warps, 4 stages. N tiles=64, M tiles=1, total 64 tiles. 64 warps? Each block 4 warps. 64 blocks. Occupancy limited. Could use BLOCK_N=256 (N tiles=32, blocks=32) but chosen 128. Maybe memory throughput better with larger tile? For M=32, maybe memory-bound, larger tile increases register/shared usage and maybe fewer blocks but each reads more data. Let's test.
For square, 569 TFLOPS (57% peak). Could improve with better configs (e.g., 256x256?). Need push.
We need decide final approach. Maybe use Triton autotune with more configs including larger tiles (but beware shared memory limit 101KB). For fp8 with BLOCK_K=128, BLOCK_M*BLOCK_K + BLOCK_N*BLOCK_K bytes per tile. For 3 stages, shared memory = 3*(BM+BN)*BK bytes. Limit 101376. Example BM=256, BN=128, BK=128: per stage (256+128)*128=49152 bytes; *3=147456 > limit. So 3-stage 256x128 fails. Need 2 stages? But 2 stages maybe lower. Our config 128x256x128, 3 stages: (128+256)*128=49152 per stage; *3=147456 > limit? Wait autotune succeeded for 128x256x128 with 3 stages? In output, it didn't show shared memory failure for that config. Maybe fp8 WGMMA uses descriptor memory not shared? Actually Triton uses shared memory for operands in WGMMA. 128x256 tile: A smem = BM*BK = 128*128 = 16384 bytes, B smem = BN*BK = 256*128 = 32768, total per stage = 49152, *3=147456 > 101376. But it compiled? Wait autotune log shows config evaluated but didn't print failure for it. Maybe Triton uses 2 stages automatically? Or persistent? Actually for Hopper WGMMA, Triton uses descriptors from global memory to tensor memory, not shared. So shared memory not used for operands? Hmm. It compiled. For Blackwell maybe uses tcgen05 MMA with memory operands directly? Anyway.
The config 64x256x128, stages=4 failed due to shared memory. So 256 in N with BM=64 uses more B smem: 64*128+256*128=40960 per stage *4=163840 > limit. The 128x256 stages=3 didn't fail maybe because uses 3*49152=147456 > limit, but maybe didn't fail? It wasn't printed failure. Actually in shape0 log, config BLOCK_M:128,BLOCK_N:256,BLOCK_K:128, num_stages:3 printed no failure. It succeeded. So maybe shared memory accounting different; perhaps Triton reduces stages for Hopper/Blackwell? Hmm. It may not use software pipelining with that much shared? Not sure.
For square, best config is 128x256x128 stages3. Could try 256x256x128 with 2 stages? For M=4096,N=4096, larger tiles could reduce overhead. But need consider K=4096 with BK=128 -> 32 iterations. With 256x256 tile, each block does more compute. Grid = 16x16 =256 blocks. 128x256 grid =32x16=512. Both fine. Larger tile maybe better.
For rectangular M=4096,N=14336,K=4096, 128x256 gives N tiles=56, M tiles=32 -> 1792 blocks. Good.
Let's explore manual tuning. Could use multiple config spaces per shape. But autotune can find best if we provide. We can also implement a fallback for K not aligned.
Potential for better performance: Use TMA/Hopper WGMMA with block-level descriptors? Triton might already do. But our numbers are good but not great.
We can also consider using CUTLASS for fp8 GEMM. That might yield near cuBLAS performance. But building CUTLASS may be more involved. We can use torch.utils.cpp_extension with inline CUDA PTX or CUTLASS headers. However we have PyTorch with CUDA 13.0, Blackwell. CUTLASS 3.8 supports Blackwell? We can clone and use as include path. But solution.py must be self-contained? It can download/clone CUTLASS in forward or build at import. Time is okay. But maybe overkill.
Given time, Triton likely enough. Need improve tail and skinny.
Let's examine tail performance more. We can pad K to multiple of 128. Let's test a quick benchmark: for shape1, pad x and weight to K' and call same kernel with aligned K'. Compare time. We'll use chosen config? Let's write script.
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tool
stdout (792 chars)
masked cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 1.750 tflops 79141.9
aligned cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.209 tflops 661249.4
masked cfg {'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.462 tflops 299882.6
aligned cfg {'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.230 tflops 601691.1
masked cfg {'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 4, 'num_stages': 4} ms 1.575 tflops 87921.4
aligned cfg {'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 4, 'num_stages': 4} ms 0.251 tflops 551566.1
assistant
reasoning (3763 chars)
Massive difference: aligned 0.209 ms vs masked 1.75 ms for 128x256. So padding K is essential. We should pad K to multiple of BLOCK_K and use aligned kernel (mask only M,N). We can choose BLOCK_K fixed 128. Pad to next multiple of 128. Then shape1 becomes aligned K=4224 and time ~0.2ms -> ~750 TFLOPS? Wait tflops computed with original K=4127 but using K_use=4224; actual flops with K_use 4224 is a bit higher. For scoring, benchmark uses original K in flops formula and bytes formula. So tflops computed as 2*M*N*K/time. With time 0.209ms, tflops = 2*4096^3 /0.209e-3 /1e12 = 655? Let's compute: 2*4096^3=137,438,953,472. /0.000209 = 6.576e14 FLOPS = 657 TFLOPS. Our aligned test tflops reported 661 (using original K?). It used K in flops formula original K, yes 661. Great. That will boost shape1 to ~0.66 peak.
Need also pad K for other shapes? They are already multiple of 128. Only shape1. But we can generalize pad if K % BLOCK_K !=0.
Need be careful: We will call kernel with K_padded. The kernel for aligned case still needs mask on M,N only. K loop full blocks. For shapes where K is aligned, no padding. For shape1, allocate padded x and weight. We can pad weight lazily and cache. But must avoid state_dict mismatch. Add non-persistent buffer `_weight_padded` or just compute padded on first forward and store in `self._weight_padded`. Since weight fixed after load, we can create it in forward when needed and reuse. For x, allocate padded each call. Copy cost small.
But we must ensure the kernel's K argument = padded K, not original. The scale unchanged. The output shape M,N unchanged.
However, when K not multiple of 128, padding with zeros in fp8: fp8 zero maps to 0x00 (value 0). Multiplying by weight_scale after dot doesn't affect. Good.
But if we pad weight with zeros, those padded columns contribute 0. Good.
Need also consider x not contiguous? We pad with copy, so contiguous.
Implement in solution.py: compute K_PAD = ((K + BLOCK_K - 1) // BLOCK_K) * BLOCK_K. If K_PAD != K, create x_padded and w_padded. For w_padded, create buffer of (N, K_PAD) and copy weight into first K columns. To reuse, store in a non-persistent attribute `self._weight_padded` keyed by device? Weight will be on cuda after load_state_dict. Model moved to device. We can create `_weight_padded` in forward if not exists or wrong shape. Since weight is registered buffer, its device may change. In forward, check if `hasattr(self,'_weight_padded')` and shape[1]==K_PAD and device matches; else create. But this caching after load_state_dict and .to(device). The first forward after moving will create on device. Fine.
Alternatively, simpler: in forward always pad if needed. Use `torch.nn.functional.pad`? For fp8, does pad work? Need test. But copy assignment is fine.
Need ensure we use K=K_PAD in kernel.
Also need choose kernel config. We can keep autotune. But autotune now will see K padded? Since in forward we pass K_pad to kernel, autotune key is M,N,K_pad? Actually we pass M,N,K_pad as arguments; autotune key includes M,N,K from kwargs? The key list ["M","N","K"] refers to JIT arguments named M,N,K. We pass K_pad as K argument. So autotune key will be (4096,4096,4224). It will compile configs for aligned K=4224, likely selecting 128x256. Good. For other shapes, K aligned.
But the autotune key includes K_pad; for shape0 and shape1 K differs so separate tuning. That's fine.
Potential issue: The autotuner might fail for K_pad=4224 with config requiring too much shared memory, but it will skip. The best config for 128x256 succeeded. Good.
For skinny shape2 (32,8192,8192), we need improve. Padding not relevant. The chosen config gave 63.5 TFLOPS. Maybe we can use larger N tile or split-K. Let's test manual configs for shape2.
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stdout (1109 chars)
cfg {'BLOCK_M': 32, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.019 tflops 220524.6
cfg {'BLOCK_M': 32, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.033 tflops 132011.1
cfg {'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.032 tflops 133351.4
cfg {'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.059 tflops 73071.7
cfg {'BLOCK_M': 32, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.022 tflops 193634.2
cfg {'BLOCK_M': 32, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 4} ms 0.040 tflops 107150.2
cfg {'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.035 tflops 122376.8
cfg {'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 4} ms 0.058 tflops 73910.5
cfg {'BLOCK_M': 16, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.034 tflops 125145.1
assistant
reasoning (1192 chars)
Interesting: skinny shape can get 220 TFLOPS with BM=32,BN=128,BK=128,4 warps,4 stages in manual test (no autotune overhead). Our autotune selected same config but benchmark reported 63.5 TFLOPS. Why huge discrepancy? Possibly because in our solution, the autotune benchmarking of other configs includes very slow ones and then best is selected, but actual time_variant in benchmark.py might not use the autotuned best? It should. Wait manual test used grid = (triton.cdiv(M,BM)*triton.cdiv(N,BN),) = (1*64)=64 blocks. It got 0.019 ms. In solution autotune selected same config, but benchmark gave 0.068 ms. Why? Maybe because of `x.contiguous()` and `w.contiguous()` copies each forward? We call contiguous on inputs and weight; weight is already contiguous. x contiguous copy maybe small (32*8192=256KB). Should not add 0.05 ms. Maybe autotune in solution selected BLOCK_M:32,BLOCK_N:128 but with num_warps=4,num_stages=4 and GROUP_M=1; same. Could be that we use `grid = lambda META: ...` and Triton autotuner wraps; after autotune, subsequent calls use best config. But benchmark time includes kernel launch overhead from Python? time_variant uses torch.profiler? Let's inspect timing.py.
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stdout (4682 chars) — TRUNCATED
1 """Centralized GPU timing for benchmark.py files.
2
3 All problems' benchmark.py should call `time_fn` from here so we have one
4 implementation of warmup, L2 flush, and CUDA event capture to maintain.
5
6 Methodology:
7 - 10 warmup calls absorb Triton autotune (typical ~7 configs) and
8 torch.compile reduce-overhead CUDA-graph capture.
9 - Between each timed call, `_l2_flush()` writes 128 MB to evict L2
10 (Blackwell L2 is 96 MB; we want any prior L2 contents flushed so
11 we measure HBM-load bandwidth, not L2-cached bandwidth).
12 - GPU timing via cuda.Event with synchronize() AFTER record() but
13 BEFORE elapsed_time() — the canonical NVIDIA pattern.
14 - Reported value is the median of `iters` trials, robust to outliers.
15
16 Notes / known biases not addressed here:
17 - torch.compile(mode="reduce-overhead") gets CUDA graphs which eliminate
18 launch overhead. Custom Triton/CUDA kernels do NOT get this treatment.
19 On small shapes where launch overhead matters, this gives compile an
20 artificial advantage. We accept this as the cost of using the agreed
21 "compiled" baseline policy.
22 - cuBLAS / cuDNN allocate workspaces on first call. 10 warmup absorbs.
23 - Median over a fairly small number of trials (default 30) is fine for
24 headline numbers but won't catch bimodal distributions. Use --extra
25 instrumentation if you ever care.
26 """
27 from __future__ import annotations
28
29 import os
30 import re
31
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assistant
reasoning (236 chars)
Each timed call flushes L2, so memory-bound shapes measured without L2 cache. My manual test didn't flush L2, so got faster due to cache. For skinny shape, memory-bound; L2 flush matters. Let's run manual test with L2 flush to simulate.
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tool
stdout (280 chars)
Command running in background with ID: bdzojtnli. Output is being written to: /tmp/claude-1002/-workspace-problems-01-fp8-gemm/fc0b7a6e-4534-4072-813b-e30a8bdaeb17/tasks/bdzojtnli.output. You will be notified when it completes. To check interim output, use Read on that file path.
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reasoning (5 chars)
Wait.
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stdout (1392 chars)
<retrieval_status>success</retrieval_status>
<task_id>bdzojtnli</task_id>
<task_type>local_bash</task_type>
<status>completed</status>
<exit_code>0</exit_code>
<output>
cfg {'BLOCK_M': 32, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.055 tflops 78398.2 gbps 1239.3
cfg {'BLOCK_M': 32, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.061 tflops 70032.7 gbps 1107.1
cfg {'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.055 tflops 77425.9 gbps 1224.0
cfg {'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.079 tflops 54262.3 gbps 857.8
cfg {'BLOCK_M': 32, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.064 tflops 67497.0 gbps 1067.0
cfg {'BLOCK_M': 32, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 4} ms 0.069 tflops 62557.8 gbps 988.9
cfg {'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.072 tflops 59559.7 gbps 941.5
cfg {'BLOCK_M': 16, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.054 tflops 80058.3 gbps 1265.6
cfg {'BLOCK_M': 16, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.057 tflops 75382.0 gbps 1191.6
</output>
assistant
reasoning (639 chars)
With L2 flush, skinny gets ~78-80 TFLOPS (GB/s ~1265). Our benchmark 63.5 maybe due to additional overhead. We can improve by using BM=16? But BM=16 gave 80 TFLOPS. However for correctness, need handle M=32 with BM=16. Also need mask. Triton tl.dot with BM=16 may be less efficient for WGMMA? But works. But need verify. We can include BM=16 config in autotune.
But for square, BM=16 would be terrible. Autotune will choose appropriate.
Need also improve square performance. Let's test square configs with L2 flush maybe. Current 569. Could aim 700+. Let's run a tuning script for square and rectangular with L2 flush and larger configs.
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stdout (3693 chars) — TRUNCATED
--- square 4096^3
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.223 tflops 615280.8
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} failed out of resource: shared memory, Required: 147456, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.224 tflops 614400.6
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 2} ms 0.233 tflops 588956.8
cfg {'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.242 tflops 568643.9
cfg {'BLOCK_M': 256, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 2} ms 8.841 tflops 15545.0
cfg {'BLOCK_M': 256, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} failed out of resource: shared memory, Required: 131072, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.221 tflops 622233.6
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.221 tflops 622188.5
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 4, 'num_warps': 8, 'num_stages': 3} ms 0.223 tflops 615413.0
cfg {'BLOCK_M': 128, 'BLOCK_N
... (2193 more chars)
assistant
reasoning (274 chars)
Our manual test with L2 flush gives square ~615-622 TFLOPS, slightly better than benchmark's 569. Benchmark may include overhead and maybe different config. The 128x256 BK=64 config is best. But for K padded shape1 (4224), need config. Let's test shape1 padded with configs.
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stdout (1154 chars)
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} Kp 4224 ms 0.227 tflops 611354.5
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} failed out of resource: shared memory, Required: 147456, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} Kp 4224 ms 0.227 tflops 610923.0
cfg {'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} Kp 4224 ms 0.244 tflops 567202.7
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} Kp 4160 ms 0.225 tflops 616361.4
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} Kp 4160 ms 0.222 tflops 622613.2
cfg {'BLOCK_M': 64, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 4, 'num_stages': 4} Kp 4224 ms 0.264 tflops 524288.0
cfg {'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} Kp 4224 ms 0.256 tflops 540258.8
assistant
reasoning (7344 chars)
With padding, shape1 can get ~620 TFLOPS. Great. So padding K is the key.
Now we need integrate padding and maybe add better configs to autotune.
However, autotune overhead at correctness and benchmark may be large. But acceptable. Could also manually choose config based on shape to avoid autotune overhead and ensure best. But autotune with good config space should find near best. However benchmark time includes autotune? time_fn does warmup 10; autotune triggered during first call, included in warmup and maybe not timed? Actually time_variant emits variant_start before calling time_fn; time_fn does warmup (10 calls) which triggers autotune; variant_end after time_fn returns. So elapsed_s includes warmup/autotune, but reported ms is median of timed calls only. Good. Scoring uses ms. So autotune not counted.
But we should ensure autotune picks best config under L2 flush conditions? Triton's autotune uses its own do_bench without L2 flush. For compute-bound square, L2 flush matters less. For memory-bound skinny, L2 flush changes ranking? It will rank by no-flush times; best no-flush may still be okay. We can add manual override for shape2.
Alternatively, use triton.Config with pre_hook to flush? Not necessary. We can simply add more configs and rely on autotune. But maybe autotune no-flush picks BM=16, which is best in flush too (80 TFLOPS). In no-flush earlier, BM=16 got 80 vs BM=32 got 78, similar. Good.
Need verify correctness with BM=16 and M=32. Should work.
Potential issue: Our kernel with GROUP_M=8 but for M=32 with BM=16 -> num_pid_m=2. group_size_m = min(2-first_pid_m,8). If group_id 0, first_pid_m=0, group_size_m=2. pid_m = pid%2, pid_n = (pid%num_pid_in_group)//2. num_pid_n=64, num_pid_in_group=512. Works. For GROUP_M=8, grouping fine.
Now, the current solution uses autotune with K as passed. If we pad K, autotune key changes. We need use padded K in kernel. But we also need mask in kernel for M,N; K loop is full. The kernel as written has mask on K too; if K padded, mask always true for K but still includes `k < K` which is fine (all true). For aligned K, we can skip K mask for efficiency? But with K_pad, mask `k < K_pad` always true; Triton may compile same. Could use two kernels: aligned kernel without K mask and tail kernel with K mask. But if we always pad to multiple of BLOCK_K, we can use aligned kernel without K mask, which might be faster. Let's create a kernel variant `fp8_gemm_kernel_aligned` that doesn't mask K. Use it when K padded or already aligned. Actually we can always call aligned version and pad if not aligned. For aligned original, no copy needed, just call. For shape1, pad and call. That avoids K mask.
But what if K is multiple of BLOCK_K for a config but not for another config? Since autotune chooses BLOCK_K per shape, we should pad to chosen BLOCK_K. But we choose config at runtime via autotune; in forward we don't know BLOCK_K before calling kernel. To handle this, we can pad to a fixed BLOCK_K = 128 (the max in configs) before calling kernel. Or we can have a pre-pass: compute K_PAD = ((K + 127)//128)*128. Then all configs have BLOCK_K <= 128, so K_PAD is multiple of 128, but if a config uses BLOCK_K=64, K_PAD also multiple of 64. Good. So pad to multiple of 128 always. Then call kernel; autotune can choose 64 or 128. The kernel's K loop uses full blocks of size BLOCK_K, and K_pad is multiple of BLOCK_K for both. Good.
But if we include configs with BLOCK_K=256? Shared memory maybe too high. Keep max 128.
So solution: always ensure K is multiple of 128 by padding if needed. Use aligned kernel (no K mask). For shapes where K already multiple of 128 (all except shape1), no copy. For shape1, copy. The copy overhead includes in timed calls. But copy of x and weight each call might cost. Could be significant: copy 4096x97 fp8 ~ 397KB each, total ~800KB, at 1.8TB/s = 0.00044 ms, negligible compared to 0.2ms kernel. Good.
But we also need ensure weight_scale shape unaffected.
Could also pad weight once and cache. Let's implement caching for weight_padded. For x, allocate padded each call.
Need choose configs. We can keep autotune configs and add more good ones: BM=16 configs, BK=64 configs. But too many configs increase autotune time. We can use maybe 10 configs. We can also avoid autotune and manually dispatch based on shape for reproducibility. That might be simpler and avoid autotune failures. Since shapes known, we can preselect configs. For square/rect: BM=128, BN=256, BK=128, num_warps=8, stages=3 or BK=64. For shape1 padded: same. For skinny: BM=16, BN=128, BK=128, num_warps=4, stages=4. We can implement a dispatch dict based on (M,N,K) or heuristics. But autotune can adapt if environment differs. The problem says shapes must handle; fixed shapes. Manual dispatch is acceptable and avoids autotune overhead.
But manual selection may not be optimal for other hidden shapes? The prompt says shapes you must handle are those four. But check.py uses shapes.py. So manual mapping to those shapes is fine. However to be safe, use autotune plus padding. Autotune will pick good. But we can also add preselected defaults to avoid poor choices. We can use a small autotune config space that includes good ones.
Let's decide: Keep autotune but with a focused config list. Also pad K to multiple of 128 and use aligned kernel. Need update kernel to use no K mask. But for robustness if K somehow not padded (if a config uses BLOCK_K not dividing K_pad), we can keep K mask? But if K_pad multiple of 128 and BLOCK_K divides 128, it's fine. If we include BLOCK_K=64, divides 128. Good. If we include BLOCK_K=128, fine. So no K mask needed. However if K is 0? Not. We'll keep mask on M,N only.
But wait: The kernel argument K is padded K. For output scaling, no issue. The `stride_xk` for padded x is K_pad. Good.
Now, the autotune key ["M","N","K"] will use padded K for shape1. For shape0/3 K same. For shape2 K=8192. Good.
Potential issue: Triton autotune caches by key; after first shape's autotune, subsequent shapes compile. That's fine.
Let's update solution.py with aligned kernel and padding. Use autotune configs maybe 8 including BM=16. We must ensure all configs compile under shared memory limit. From logs, many fail. Need prune failing configs. We should only include configs that compile for all shapes? Autotune will skip those that fail (out of resource). But for skinny M=32, configs with BM=128 produce only 1 M tile but okay. BM=256 would have M tile 1 (BLOCK_M=256 > M=32) but mask handles; dot with BM=256 and M=32 may waste work (compute 256xN while only 32 rows used), but maybe okay? However dot with fp8 may require M full? It uses mask, other=0; tl.dot on masked block maybe still computes full block, so 8x wasted compute and loads. For skinny, BM=16/32 best.
We need add configs that compile. Based on logs, compiled configs for square: 128x256x128 s3, 256x128x128 s3, 128x128x128 s4, 128x256x64 s4, 256x128x64 s4, 64x128x128 s4, 64x256x128 s3. 64x256x128 s2 compiled but slower. For skinny, BM=16 configs likely compile. Need test.
Let's update solution.py. Need remove GROUP_M reliance that uses num_pid_m etc. Already okay.
One nuance: With padding, `K` passed to kernel is K_pad. But we need not change Model's K. In forward, compute K_pad and pass.
Let's write new solution.py.
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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reasoning (13 chars)
Run check.py.
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stderr (221 chars)
Exit code 1
FAIL: shape 1 {'M': 4096, 'N': 4096, 'K': 4127} seed 42 case small_weight: tolerance exceeded: max_abs_diff=16.5801 max_rel_diff=3.70181e+07 bad=16763441/16777216 worst_idx=(2349, 1017) (atol=0.003, rtol=0.05)
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reasoning (997 chars)
It shows case small_weight with tight tolerance atol=0.003 rtol=0.05? Wait problem.yaml tolerance bfloat16:0.2, but numeric stress case small_weight uses tighter? The numeric stress context maybe scales weights small; the reference dequant scale small. Our padding adds zero columns; dot product should match. But error huge 16.5, meaning something wrong: maybe fp8 padding with zeros doesn't map to fp8 zero? Actually float8_e4m3fn zero is 0x00. torch.zeros(..., dtype=torch.float8_e4m3fn) yields 0? Likely yes. But the huge error suggests maybe we are applying scale incorrectly or using padded K in dot includes padded rows? Wait we padded columns, not rows. For x (M,K) -> x_pad[:, :K] = x, rest zeros. For w (N,K) similarly. Dot uses K_pad, so extra zeros contribute zero. Then multiply scale. Should match reference.
But error only for case small_weight. That case likely modifies weight_scale to small or x small? Need inspect numeric_stress context. Let's read src/eval/numeric_stress.py.
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stdout (7072 chars) — TRUNCATED
1 """Numeric distribution stress cases for correctness checks.
2
3 These cases are not hidden shapes. They rerun the same shape/seed validation
4 under a few scale regimes that catch kernels that only work for the nominal
5 N(0, 1)-ish inputs.
6 """
7 from __future__ import annotations
8
9 import os
10 from collections.abc import Iterator, Mapping, Sequence
11 from contextlib import contextmanager
12 from dataclasses import dataclass, field
13
14 import torch
15
16 ToleranceOverride = Mapping[str, float | Mapping[str, float]]
17
18
19 @dataclass(frozen=True)
20 class NumericStressCase:
21 name: str
22 input_scales: Mapping[int, float] = field(default_factory=dict)
23 state_scales: Mapping[str, float] = field(default_factory=dict)
24 tolerance: ToleranceOverride | None = None
25
26
27 NOMINAL_CASE = NumericStressCase("nominal")
28
29 _SMALL_BF16 = {"bfloat16": {"atol": 1e-4, "rtol": 5e-2}}
30 _MED_BF16 = {"bfloat16": {"atol": 5e-4, "rtol": 5e-2}}
31 _LARGE_BF16 = {"bfloat16": {"atol": 2e-1, "rtol": 5e-2}}
32 _TINY_FP32 = {"float32": {"atol": 1e-7, "rtol": 1e-4}}
33 _LARGE_FP32 = {"float32": {"atol": 1e-1, "rtol": 1e-4}}
34
35 _CASES: dict[str, tuple[NumericStressCase, ...]] = {
36 "01_fp8_gemm": (
37 # fp8 x fp8 has accumulation-order noise vs the bf16-matmul reference that
38 # scales with input magnitude; atols are calibrated to absorb it (measured
39 # fp8-MMA residual x ~1.5 margin) while rtol=5e-2 still catches gross e
... (5572 more chars)
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reasoning (1924 chars)
Numeric stress case small_weight scales weight buffer by 1e-2. That includes our padded weight? The stress context scales `weight` buffer in both models. It modifies `self.weight` (original). It also scales `_weight_padded`? No, `_weight_padded` is not a registered buffer/parameter, named_buffers only includes registered buffers. But we copied original weight into `_weight_padded` in forward. However if weight is scaled after forward? Wait context manager in check.py: for each seed and case, it enters numeric_stress_context before forward. Inside context, it scales states (weight) in ref_model and sol_model. Then yields scaled inputs. Then we call forward. In our forward, we check `_weight_padded` and shape matches (N,K_pad) and device; it exists from previous call with original weight, so we use stale `_weight_padded` (not scaled). So output wrong for small_weight. Need to invalidate `_weight_padded` whenever weight changes. Since weight is a buffer, external code modifies it in place. We can detect by storing a snapshot or just recompute `_weight_padded` each forward if K not aligned. Copy overhead small. Simpler: don't cache weight padded; allocate and copy each time K not aligned. The previous solution cached to avoid copy, but correctness issue. Let's just create padded weight each call. The cost is small.
Alternatively, we can register `_weight_padded` as a non-persistent buffer and update it in forward if shape changes. But scaling stress context won't update it. Could hook state_dict? Simpler to copy each call.
Also need consider that `x_pad` copy each call. Fine.
Let's modify forward to not cache weight padded. Also ensure for K aligned we don't copy.
But wait: The small_weight case also scales the original weight in place. Our forward reads `w = self.weight.contiguous()` which will be scaled. Good. Then if K_pad != K, copy w into new padded tensor. Good.
Let's update solution.
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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reasoning (13 chars)
Run check.py.
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reasoning (32 chars)
Check passes. Now run benchmark.
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stdout (1312 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T23:59:38.311245+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T23:59:39.926019+00:00 elapsed_s=1.615 ms=0.246096
shape=0 variant=solution tflops=558.477 gbps=272.694 ms=0.246
shape=0 solution_peak_fraction=0.5585
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T23:59:40.452666+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T23:59:41.907523+00:00 elapsed_s=1.455 ms=0.307744
shape=1 variant=solution tflops=449.982 gbps=218.892 ms=0.308
shape=1 solution_peak_fraction=0.4500
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T23:59:43.803552+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T23:59:45.122054+00:00 elapsed_s=1.318 ms=0.065840
shape=2 variant=solution tflops=65.233 gbps=1031.216 ms=0.066
shape=2 solution_peak_fraction=0.0652
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T23:59:46.823495+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T23:59:48.408530+00:00 elapsed_s=1.585 ms=0.825984
shape=3 variant=solution tflops=582.380 gbps=233.586 ms=0.826
shape=3 solution_peak_fraction=0.5824
peak_fraction: 0.3126
RESULT: OK
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reasoning (427 chars)
Better geomean 0.3126. Shape1 now 0.45, shape2 0.065, shape0 0.558, shape3 0.582. But shape1 is 0.45 vs manual 0.62. Why slower? Because benchmark includes copy overhead and maybe autotune chose suboptimal config. The autotuner with L2 flush? It doesn't flush, but for compute-bound shape1, time should be ~0.22 ms. It reports 0.308 ms. That's 40% slower. Could be due to autotune selected config? Let's print autotune choices.
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stdout (10026 chars) — TRUNCATED
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T23:59:54.391765+00:00
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 128, BLOCK_N: 256, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 256, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 128, BLOCK_N: 256, BLOCK_K: 64, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 256, BLOCK_N: 128, BLOCK_K: 64, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 128, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 128, BLOCK_N: 128, BLOCK_K: 64, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 64, BLOCK_N: 256, BLOCK_K: 128, GROUP_M: 8, num_warps: 8, num_ctas: 1, num_stages: 3, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 64, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 8, num_warps: 4, num_ctas: 1, num_stages: 4, maxnreg: None
Autotuning kernel fp8_gemm_kernel with config BLOCK_M: 32, BLOCK_N: 128, BLOCK_K: 128, GROUP_M: 1, num_warps: 4, num_ctas: 1, num_stages: 4, maxnreg: None
Autot
... (8526 more chars)
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reasoning (2965 chars)
The autotuner selected 128x256x128 s3 for shape1 (K=4224), but benchmark time 0.303ms vs manual 0.227ms. The difference is due to the copy/pad overhead included in timed call? But our manual test included copy/pad? It did include allocation and copy in each call? The manual test created padded tensors outside loop and reused, so didn't include copy. In solution forward, we allocate and copy w and x each call. That adds time. For shape1, copy x and w ~800KB and allocate; maybe ~0.07 ms? At 1.8TB/s copy 800KB is 0.00044ms, but allocation overhead maybe. Let's measure.
We could avoid copying x each call by using `torch.nn.functional.pad` which may be faster. Or use a preallocated buffer? But x changes each call. We can create x_pad with zeros and copy via slice assignment. That is what we do. `torch.zeros` allocation overhead maybe significant for repeated calls. We can preallocate x_pad and reuse? Since M,K fixed per shape, we can allocate a persistent buffer `self._x_padded` and copy into it. But numeric stress modifies x in place via context manager? It scales input tensor (x) in-place before forward. Our forward receives scaled x. If we preallocate buffer and copy, it's fine. But the buffer shape depends on x shape M; M fixed per model. We can store `self._x_padded` of shape (M, K_pad) and copy x into [:,:K]. But if the input x is overwritten by stress context each time, we copy current values. Good. However if multiple forward calls with different x values, buffer reused. That is fine. But the stress context modifies input tensor before forward, and after context restores original input? Actually context manager yields scaled inputs, then after yield restores state backups (weight) but not inputs. It doesn't restore inputs; they remain scaled? The `yield _scale_inputs(inputs, ...)` returns scaled tensors, and after yield only restores `backups` which are state tensors. So inputs are not restored, but that's per iteration; new seed creates new inputs. So x can vary. Preallocating x_pad and copying is fine.
But to avoid stale padded weight under stress, we must not cache weight. We can preallocate w_pad buffer but copy weight each call; allocation overhead saved. Since K,N fixed, allocate once. However stress context modifies weight in place; our forward reads self.weight, copies into preallocated w_pad first K columns. Good. We can cache the w_pad buffer (zeros) and copy each call. That avoids allocation overhead.
Similarly x_pad buffer can be allocated once. Let's implement self._x_padded and self._weight_padded as non-persistent buffers? We can store as plain attributes. But if we register them as buffers, state_dict strict mismatch. Use plain attributes. Initialize in first forward.
Actually simpler: In forward, allocate padded tensors via `torch.empty` and copy? But allocation overhead maybe 0.07ms? Let's measure.
Let's write a quick script mimicking solution forward with pad each call vs preallocated.
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stdout (66 chars)
alloc_copy ms 0.04891841992503032
prealloc ms 0.043076190049760044
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reasoning (1890 chars)
Padding overhead ~0.044-0.049 ms per call. Kernel time manual 0.227 ms, so total ~0.27-0.28 ms. Benchmark reports 0.303 ms; includes L2 flush overhead? Time_fn records kernel only after L2 flush; but L2 flush writes 128MB before each timed call, maybe adds overhead not in timed event? The event records after flush. But flush affects memory subsystem, may slow subsequent copy and kernel. The manual with flush gave 0.227ms for kernel alone without copy. With copy ~0.27. Benchmark 0.303 includes flush effect + copy. So shape1 ~0.45 peak. Acceptable.
Could we avoid copy by using a kernel that handles unaligned K efficiently without huge slowdown? The masked kernel was 1.75 ms, worse. But maybe a more sophisticated tail kernel that processes full 128-blocks then a separate small tile for the tail could be faster than padding? The huge slowdown likely because Triton couldn't optimize masked K loads. If we write kernel that does loop over full 128-blocks for K//128 iterations, then a final iteration with a smaller BK (e.g., 64,32,16) and appropriate masks, maybe can avoid padding. But more complex. Padding is simpler and gives decent perf.
Could we avoid x copy by reading x with K stride and masking only tail? The weight pad still needed because weight is fixed; we can pad weight once in Model __init__? But state_dict mismatch. Unless we store padded weight under a different name and override load_state_dict? Hmm. The weight buffer must be registered as `weight` for strict load. We could register `weight` as original shape, and in forward use it. But we could pad weight and store in a separate non-persistent tensor. That's what we do. We can preallocate the buffer to avoid allocation overhead. That reduces copy overhead to ~0.022 ms for weight? The 0.044 ms includes both x and w allocation; prealloc both reduces to maybe ~0.005? Let's test preallocated copy only.
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stdout (32 chars)
copy_only ms 0.03986886201892048
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reasoning (2717 chars)
Copy only ~0.04 ms. So preallocation doesn't reduce copy time significantly; allocation overhead small. Padding copy takes ~0.04ms due to memory bandwidth? 800KB at 1.8TB/s = 0.00044ms, but copy via torch.copy maybe much slower due to strided? Wait x[:, :K].copy_(x) copies contiguous block M*K (16.7MB) not 800KB! I mistakenly thought only tail. Actually we copy the entire x (M*K) into padded buffer, because we create zeros and copy full x[:, :K]. That's M*K = 4096*4127 ≈ 16.9M bytes for x, same for weight ~16.9MB, total ~34MB. At 1.8TB/s = 0.019ms, but measured 0.04ms. Reasonable. That's significant relative to kernel 0.2ms. If we could pad only the tail and keep original x pointer for the bulk, we could avoid copying the entire x. We can create x_pad with zeros and copy only tail column(s) and use x for full blocks? But kernel expects contiguous K_pad stride; x and x_pad separate. We could construct x as concatenation of original x and zero tail: `torch.cat([x, torch.zeros(M, K_pad-K, dtype=x.dtype, device=x.device)], dim=1)`. This copies entire x too (cat). To avoid full copy, we can use a kernel that reads x for full blocks from original pointer and tail from padded tail. More complex.
Alternative: Pad weight once and only x tail? But weight full copy is 16.9MB also. Could pad weight in a non-persistent buffer at model init by copying full weight; that's one-time (not per call) if we keep it updated? But stress context modifies weight in place each call, so we'd need to re-copy full weight per call anyway. However weight copy can be done once after state changes? Not possible.
Could we avoid padding x by using a kernel with K mask only for the tail block? The reason masked kernel was slow is because mask on K all blocks. If we loop over full 128-blocks (no mask) for K//128 blocks, then handle last partial block with a masked load of size K%128, maybe the slowdown disappears. We can write a kernel that processes K in two phases: full blocks (unmasked K) and tail block (masked with BLOCK_K_TAIL = K%128). But the tail block size is not compile-time constant; we can use BLOCK_K=128 and in the final iteration load with mask `k < K` (only last block masked). In our original masked kernel, we masked every block. Triton may optimize if only last iteration has mask? The loop still has mask all iterations but condition always true except last; compiler may not know. But we can split loop: for k0 in range(0, K_full, BLOCK_K) unmasked; then if K_tail>0 load masked. This might recover performance. Let's test.
Actually our original solution (before padding) had masked all iterations and was 1.75ms. If we do full blocks unmasked + tail masked, maybe ~0.25ms. Let's test quickly.
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stdout (509 chars)
--- tail 4127
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 3.043 tflops 45511.4
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 1.449 tflops 95560.9
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 1.932 tflops 71681.9
cfg {'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.506 tflops 273700.2
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reasoning (3597 chars)
Tail-aware kernel still slow except 128x128 s4. The masked tail dot inside the same kernel causes severe slowdown for large tiles. Padding remains best.
Can we reduce padding copy cost? Instead of copying full x and weight into padded tensors, we can pad only the tail and use `torch.cat`. But cat also copies full. We could allocate padded weight once and copy full weight each call (same). The cost is inherent to making contiguous K_pad. But perhaps we can use Triton's block pointers with boundary checks for K and still not slow down if we only have a small tail. The huge slowdown suggests Triton currently inefficient for masked fp8 dot. Maybe we can split the problem: compute dot for K_full with unmasked large-tile kernel, and compute tail correction with a small kernel, then add. The large kernel handles K=4096 (full blocks) with high performance. The tail is K=15 columns. The tail correction is x[:,4096:4127] @ w[:,4096:4127].T * scale. We can compute that with a small kernel (or even bf16 upcast) and add to result. This avoids copying full operands and keeps high perf.
Specifically, for K not multiple of 128: K0 = (K // 128) * 128, Kt = K - K0. Compute y0 = x[:, :K0] @ w[:, :K0].T * scale using aligned fp8 kernel. Compute y_tail = x[:, K0:] @ w[:, K0:].T * scale. Add y_tail to y0. Since Kt < 128 (max 127). For shape1 Kt=15. The tail GEMM is very small: M x Kt @ N x Kt.T -> M x N. With Kt=15, this is ~2*M*N*Kt = ~0.5 GFLOPs. We could compute tail in bf16 via torch.matmul or a tiny Triton kernel. Copying tail columns only: x_tail (M, Kt), w_tail (N, Kt) = ~0.25MB + 0.25MB = 0.5MB, much less. Then compute bf16 matmul or fp8 with small K. We need output bf16. We can upcast to bf16 and use torch.matmul. The tail is small enough that using bf16 doesn't affect roofline much. Or use fp8 tl.dot with BLOCK_K=128 and masked loads? Since Kt small, masking overhead minor? But we can just do bf16.
This approach yields y = y0 + y_tail. For fp8 vs reference, the reference computes full K in bf16. Splitting into two fp8 vs bf16 tail may introduce slightly different numeric error, but tolerance is 0.2. For small_weight stress, tail contribution small. Should be fine.
But careful: For shape1, K0=4096, Kt=31? Wait 4127 // 128 = 32 remainder 15? 128*32=4096, Kt=31. Yes Kt=31. Still small. For K not multiple of 128, Kt < 128. Good.
We can implement a separate simple kernel for tail with K small, no tiling in K (iterate over Kt). But copying tail only and using bf16 torch.matmul is simplest.
However, copying tail only still requires slicing w[:, K0:] which returns non-contiguous (N, Kt) with stride K. `contiguous()` copies N*Kt. x[:, K0:].contiguous() copies M*Kt. Total copy ~0.5MB. Then torch.matmul in bf16: x_tail_bf @ w_tail_bf.T -> (M,N). That adds maybe 0.2-0.3 ms? For M=N=4096, K=31, bf16 matmul with cuBLAS may be ~0.1-0.2 ms. Total tail cost ~0.15 ms. Combined with y0 kernel ~0.24 ms = ~0.39 ms, still worse than padding+copy 0.30ms? Actually padding+copy 0.30ms. But tail-only copy reduces memory copy but adds second kernel overhead. Hmm.
Alternative: Use a custom fp8 tail kernel that processes K_tail by iterating over elements or small blocks and accumulating in fp32. But overhead.
The padding approach gives 0.30ms. That's okay. Could improve by padding only tail and using the aligned kernel on padded tensors, but copy full x/w. The cost 0.04ms copy + 0.24ms kernel = 0.28ms; benchmark 0.30ms due to flush. So padding is decent.
Could we improve by using `torch.nn.functional.pad` which may use faster kernels? It likely also copies. Test.
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stdout (73 chars)
pad_with_fn ms 0.048465819854754955
pad_zeros_copy ms 0.04874181991908699
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reasoning (4108 chars)
Similar. So padding overhead unavoidable if full copy.
Could we pad in-place by allocating weight with padded K in Model and adjusting load_state_dict to accept original shape? If we register `weight` as (N,K) original, we cannot change. But we can override `load_state_dict` in Model to reshape weight? However check.py does:
```
sd = ref_model.state_dict()
sol_model.load_state_dict(sd, strict=True)
```
If our Model.load_state_dict receives sd with weight shape (N,K) and our internal weight buffer is (N,K_pad), strict=True will fail because shape mismatch. Could we intercept and copy into padded? We could store the actual param under a different name (e.g., `_weight`) and register `weight` as a non-persistent buffer of shape (N,K) that is not used in forward? But load_state_dict strict checks all parameters/buffers; it would load `weight` into the unused buffer and `_weight` would not be in sd (strict fails). Unless we set _weight as non-persistent and not required? Strict=True requires every key in sd matches module state, and every module parameter/buffer matches a key in sd. `_weight` as persistent buffer would need key in sd; non-persistent doesn't need key? Actually `load_state_dict` with strict=True requires keys in state_dict match exactly the set of parameters and persistent buffers. Non-persistent buffers are not included. So if we register `_weight` as persistent, sd must include it, but reference sd has only weight. If we register `weight` as non-persistent unused buffer shape (N,K), and `_weight` as persistent buffer shape (N,K_pad), then sd has `weight` but not `_weight`, strict fails because `_weight` missing. We could override load_state_dict to map `weight` to `_weight` and ignore the unused? But strict=True checks after hook? We can implement `_load_from_state_dict` to reshape. However simpler to just pad per call.
Alternatively, we can avoid full x copy by using `torch.nn.functional.pad` which copies full x. Not helpful.
Maybe we can use a kernel with split K to reduce padding overhead? No.
Let's focus on improving other shapes and overall geomean. Current geomean 0.3153. We can likely improve square/rect to ~0.65 and skinny to ~0.10. That would push geomean to ~0.45. Need also shape1 ~0.46.
Let's see if we can improve square/rect performance beyond 0.57. Manual L2-flush tests gave 0.62. Benchmark lower due to overhead? For shape0 benchmark 0.246ms vs manual 0.223ms. That's ~10% overhead from L2 flush and Python. Could reduce overhead by using cuda graph? Not allowed easily. But maybe we can improve kernel to run faster, e.g., use larger tile or 2 CTAs cluster? Triton supports num_ctas for Blackwell? Might help. But adding num_ctas=2 might require cluster. Let's test configs with num_ctas=2 for square. Also maxnreg? We can try. But autotune with num_ctas can be tricky.
Could use persistent kernels? Maybe too complex.
Let's investigate cuBLAS fp8 performance via torch._scaled_mm? Forbidden, but we can use it just to measure peak? Not needed.
Maybe Triton's fp8 WGMMA for Blackwell not fully optimized; maybe using CUTLASS would yield higher. But implementing CUTLASS in solution.py may be heavy but possible. Could clone CUTLASS and compile a gemm. However building on the fly may be slow and may require network. But we have network (bridge). Could use `torch.utils.cpp_extension.load_inline` with CUTLASS headers. Need CUTLASS 3.8 supports Blackwell. We can clone into workspace. But the final solution.py would need to compile at import. The grading environment may not allow network? It likely doesn't have CUTLASS installed. We could include CUTLASS as a git submodule? Not in repo. We can download in solution.py via git clone, but scoring environment may not have network. Safer to use Triton.
Could we use inline PTX? That might give max performance but very complex.
Let's first try to tune square/rect with more configs including num_ctas=2, different stages. We can use ncu to inspect occupancy? But maybe trial.
Let's test square configs with num_ctas=2 and num_stages=2/3/4. Use the manual benchmark with L2 flush.
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stdout (2167 chars) — TRUNCATED
<persisted-output>
Output too large (62.7KB). Full output saved to: /home/agent/.claude/projects/-workspace-problems-01-fp8-gemm/fc0b7a6e-4534-4072-813b-e30a8bdaeb17/tool-results/b9541vhsk.txt
Preview (first 2KB):
/tmp/square_tune2.py:23:25: error: failed to legalize operation 'ttg.local_load' that was explicitly marked illegal
acc += tl.dot(a, tl.trans(b))
^
#blocked = #ttg.blocked<{sizePerThread = [1, 16], threadsPerWarp = [4, 8], warpsPerCTA = [8, 1], order = [1, 0], CGALayout = [[1, 0]]}>
#blocked1 = #ttg.blocked<{sizePerThread = [1, 8], threadsPerWarp = [2, 16], warpsPerCTA = [8, 1], order = [1, 0], CGALayout = [[1, 0]]}>
#linear = #ttg.linear<{register = [[0, 1], [0, 2], [0, 16], [0, 32], [0, 64], [32, 0], [64, 0]], lane = [[0, 4], [0, 8], [1, 0], [2, 0], [4, 0]], warp = [[8, 0], [16, 0], [0, 0]], block = [[0, 0]]}>
#mma = #ttg.nvidia_mma<{versionMajor = 2, versionMinor = 0, warpsPerCTA = [2, 4], CGALayout = [[1, 0]], instrShape = [16, 8]}>
#shared = #ttg.swizzled_shared<{vec = 16, perPhase = 1, maxPhase = 8, order = [1, 0], CGALayout = [[1, 0]]}>
#smem = #ttg.shared_memory
module attributes {"ttg.num-ctas" = 2 : i32, "ttg.num-warps" = 8 : i32, ttg.target = "cuda:120", "ttg.threads-per-warp" = 32 : i32} {
tt.func public @gemm_aligned(%arg0: !tt.ptr<f8E4M3FN> {tt.divisibility = 16 : i32}, %arg1: !tt.ptr<f8E4M3FN> {tt.divisibility = 16 : i32}, %arg2: !tt.ptr<f32> {tt.divisibility = 16 : i32}, %arg3: !tt.ptr<bf16> {tt.divisibility = 16 :
... (667 more chars)
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reasoning (97 chars)
Output indicates some configs with num_ctas=2 failed to compile. Need read file to see successes.
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1 /tmp/square_tune2.py:23:25: error: failed to legalize operation 'ttg.local_load' that was explicitly marked illegal
2 acc += tl.dot(a, tl.trans(b))
3 ^
4 #blocked = #ttg.blocked<{sizePerThread = [1, 16], threadsPerWarp = [4, 8], warpsPerCTA = [8, 1], order = [1, 0], CGALayout = [[1, 0]]}>
5 #blocked1 = #ttg.blocked<{sizePerThread = [1, 8], threadsPerWarp = [2, 16], warpsPerCTA = [8, 1], order = [1, 0], CGALayout = [[1, 0]]}>
6 #linear = #ttg.linear<{register = [[0, 1], [0, 2], [0, 16], [0, 32], [0, 64], [32, 0], [64, 0]], lane = [[0, 4], [0, 8], [1, 0], [2, 0], [4, 0]], warp = [[8, 0], [16, 0], [0, 0]], block = [[0, 0]]}>
7 #mma = #ttg.nvidia_mma<{versionMajor = 2, versionMinor = 0, warpsPerCTA = [2, 4], CGALayout = [[1, 0]], instrShape = [16, 8]}>
8 #shared = #ttg.swizzled_shared<{vec = 16, perPhase = 1, maxPhase = 8, order = [1, 0], CGALayout = [[1, 0]]}>
9 #smem = #ttg.shared_memory
10 module attributes {"ttg.num-ctas" = 2 : i32, "ttg.num-warps" = 8 : i32, ttg.target = "cuda:120", "ttg.threads-per-warp" = 32 : i32} {
11 tt.func public @gemm_aligned(%arg0: !tt.ptr<f8E4M3FN> {tt.divisibility = 16 : i32}, %arg1: !tt.ptr<f8E4M3FN> {tt.divisibility = 16 : i32}, %arg2: !tt.ptr<f32> {tt.divisibility = 16 : i32}, %arg3: !tt.ptr<bf16> {tt.divisibility = 16 : i32}, %arg4: i32 {tt.divisibility = 16 : i32}, %arg5: i32 {tt.divisibility = 16 : i32}, %arg6: i32 {tt.divisibility = 16 : i32}, %arg7: i32 {tt.divisibility = 16 : i32}, %arg8: i32 {tt.divisi
... (65440 more chars)
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reasoning (14146 chars)
Great data: manual with flush gives square up to 639 TFLOPS (BK=64, stages=4), rect up to 678 TFLOPS (BK=64, stages=4). The benchmark autotune selected 128x256x128 s3 (615/643). We can improve by adding BK=64 stages=4 config and maybe making it preferred. Our autotune config list includes 128x256 BK=64 stages=4. Why didn't autotune select it? Because autotune does not flush L2, and maybe the BK=64 config measured worse in its quick benchmark? In no-flush earlier square_tune, BK=64 was 622 vs 128 BK 615. But autotune in solution selected 128. Could be due to autotune overhead or random. We can either remove the 128 config or add `enable_filter`? Actually autotune prunes configs by a feature model; maybe 64 config pruned? We can force manual config selection per shape.
Given we know best configs per shape from manual L2-flush tests, we can bypass autotune and dispatch manually. That also reduces compile time. But need ensure correctness for all shapes, including numeric stress. We can write a `forward` that picks config based on (M,N,K) and calls kernel directly (not autotuned). But Triton kernel requires compile-time constants; we can pass them as keyword args. Without autotune, the kernel compiles for chosen config. We can still have a fallback autotuned kernel for other shapes.
Manual mapping:
- square (4096,4096,4096): BM=128, BN=256, BK=64, warps=8, stages=4, GROUP_M=8 (639 TFLOPS) or BK=128 s3 (630). Use BK=64 s4.
- shape1 padded (4096,4096,4224): from shape1_tune, BK=64 s4 was 616, BK=128 s3 was 611. Use BK=64 s4.
- rect (4096,14336,4096): BK=64 s4 was 678, best. Use.
- skinny (32,8192,8192): from flush test, BM=16 BN=128 BK=128 s4 gave 80 TFLOPS (best), BM=32 BN=128 BK=128 s4 78. Use BM=16? But need check correctness for M=32 with BM=16. Should be fine. However dot with BM=16 might be less efficient? It gave best. Use BM=16, BN=128, BK=128, warps=4, stages=4, GROUP_M=1.
But we need also support case where M could be other values? Not required. But fallback autotune covers.
However, if we dispatch manually and call kernel without autotune, the kernel is compiled for that config. Need pass K as padded for shape1. For shape1 original K=4127, we pad to 4224 if using BK=128 or 4160 if using BK=64. But if manual config uses BK=64, K_pad must be multiple of 64. We can pad to next multiple of 64 = 4160. That reduces padding copy (64 extra columns vs 97). Wait 4127 / 64 = 64.48 -> 65*64=4160, tail=33. Copy extra 33 columns only. Total copy M*K ~16.9MB + small. Time maybe similar. But kernel with BK=64 on K=4160 has 65 iterations vs BK=128 on K=4224 has 33 iterations. The BK=64 config might be slower than BK=128? Manual shape1_tune showed BK=64 s4 616 TFLOPS vs BK=128 s3 611. Similar. If we pad to 64, copy less, but kernel maybe slightly slower. We can choose BK=128 and pad to 4224, simpler and tail smaller? Actually tail 97 columns; kernel 33 iterations. Copy overhead dominated by full x/w anyway. Fine.
Alternatively, pad to a multiple of LCM of all configs (128) as before. Good.
For skinny shape, K=8192 aligned, no pad.
Should we still use autotune? If manual dispatch, we can use a non-autotuned kernel. But writing a separate kernel without @autotune but with @triton.jit and passing constants works. However we currently have autotune wrapper. We can define a plain kernel `fp8_gemm_kernel_plain` and call with chosen config. Or we can keep autotune and rely on it for fallback; but if we call kernel directly with config as constexpr, Triton compiles. The autotune wrapper expects grid and uses JIT; we can call the same function but with constants supplied via kwargs; if function decorated with @autotune, calling it directly will still autotune? Actually if function has @autotune, calling it with grid triggers autotune always. To avoid, define a separate non-autotuned kernel.
Let's create two kernels: `fp8_gemm_kernel` (non-autotuned) with body, and `fp8_gemm_kernel_autotune` (autotuned) for fallback. Or keep autotune for general shapes and manual dispatch using the non-autotuned one.
Implementation: In forward, decide if shape matches known case. If yes, set config dict and call plain kernel. Else call autotuned. But plain kernel uses same body as autotuned (without decorator). We can factor body into a function? With Triton JIT, easiest is duplicate code or define a single JIT kernel and call it. We can define `fp8_gemm_kernel` without autotune, and a wrapper function `_run_gemm` that takes a config dict and calls `fp8_gemm_kernel[grid](..., BLOCK_M=cfg['BLOCK_M'], ...)`. For fallback, call autotuned.
But if `fp8_gemm_kernel` is not autotuned, we can call with config. Need still JIT compile per config. For known shapes, compile once.
Let's choose manual configs.
Potential issue: The plain kernel with BM=16, BN=128, BK=128, warps=4, stages=4, GROUP_M=1. Need ensure it compiles. In skinny_flush test, it worked. Good.
For square/rect, configs with BK=64 s4 worked in manual. Need ensure they compile under solution (same body). Yes.
For shape1 padded with config BK=128 s3, 128x256. Good.
But we must ensure that for shape1 padded K=4224, the config's BK=128 divides K_pad. Yes. If we choose BK=64 s4, divides. Let's pick BK=128 s3 for shape1 to avoid extra compile? Actually square also uses BK=64 s4, so same config compiles for both square and rect. If we use BK=64 s4 for shape1, one fewer unique config. Let's test shape1 padded with BK=64 s4 in manual: 616 TFLOPS. With copy overhead, maybe ~0.28 ms -> 491 TFLOPS? Slightly lower than current 455. Could be okay. But BK=128 s3 kernel has 33 iterations vs 65, so maybe faster despite lower TFLOPS. Let's test shape1 with solution using manual BK=128 s3 vs BK=64 s4.
Actually current autotune selected BK=128 s3 and reported 455 peak. Manual shape1 BK=128 s3 gave 611. The difference is copy overhead and flush. If we reduce copy overhead by padding only tail, maybe improve. But full copy unavoidable with this method.
Alternative tail-handling approach could beat padding. Let's revisit tail approach with two-kernel split: y0 from aligned fp8 kernel on K_full (4096) using best config, y_tail from bf16 matmul on tail (31 columns). For shape1, copy only tail columns (x_tail 4096x31 and w_tail 4096x31) ~0.5MB, compute y_tail via bf16 matmul ~? M=N=4096,K=31 bf16 matmul is memory-bound ~0.25 ms? Let's estimate: read x_tail 0.5MB + w_tail 0.5MB + write y 33MB? Wait output y is M*N*2 = 33MB, must be written. The tail matmul reads 1MB and writes 33MB (or accumulates). Time ~0.02ms at 1.8TB/s? Actually 34MB/1.8TB=0.019ms. Plus kernel overhead. Then y0 kernel time ~0.22ms. Total ~0.24ms, similar to square, and no full copy. That would give shape1 ~580 TFLOPS, much better. This might be the best approach!
Need verify correctness: reference computes full K in bf16. We compute y0 = x[:,:4096] @ w[:,:4096].T * scale in fp8. y_tail = x[:,4096:] @ w[:,4096:].T * scale in bf16 (or fp8). Sum. Since scaling is linear, (A+B)*scale = A*scale + B*scale. But y0 already includes scale inside kernel; y_tail we apply scale. Sum = scaled full. Numeric tolerance? fp8 accumulation for main part vs bf16 reference has usual error. Tail in bf16 matches reference tail exactly. The total error relative to reference should be within 0.2. Need check, especially small_weight. Likely fine.
But careful: The per-channel scale in y0 kernel is applied inside fp8 kernel. For y_tail, we need multiply by weight_scale. Use bf16 matmul: x_tail_bf @ w_tail_bf.T * scale. Since scale is fp32, we can cast to bf16 or compute in fp32 then cast. To avoid overflow, use fp32 accumulation: `(x_tail_bf @ w_tail_bf.T).float() * scale`. But torch.matmul bf16 accumulates in fp32 by default? Actually torch.matmul bf16 outputs bf16 with fp32 accumulate? In PyTorch, matmul for bf16 uses fp32 accumulation then casts to bf16. So we can do `(x_tail_bf @ w_tail_bf.T).float() * scale` (scale fp32) -> bf16. Good.
Then add to y0 (bf16). We can add in fp32 and cast: `y = y0.float() + y_tail.float(); y = y.to(bf16)`. But y0 already scaled and cast bf16; addition in fp32 okay. Or `y0.add_(y_tail)`? bf16 add may lose precision but tolerance loose. Better compute y0 + y_tail in fp32 then cast. But that reads/writes y0 again. y0 is 33MB; extra memory. Could instead store y0 in fp32? The kernel outputs bf16. We could modify kernel to output fp32 buffer, but then need cast. Or use `y = y0 + y_tail` in bf16; error small. Let's think.
The tail contribution is small relative to main? For random inputs, tail K=31 vs K=4096 is ~0.75% of magnitude. Error from bf16 addition maybe negligible. Use `y = y0 + y_tail.to(bf16)`? y_tail in bf16. Fine.
Potential issue: For small_weight stress, weight scaled by 1e-2, tail contribution still proportional. Fine.
For large_input stress, x scaled 64, fp8 main accumulation error maybe large but tolerance 12. Tail exact. Sum fine.
For small_input, x scaled 1e-3, tail tiny, fine.
This split approach could also handle any K not multiple of 128 (K_tail < 128) with small overhead. For shapes where K is multiple of 128, just use single fp8 kernel.
But for K not multiple of 128, we need also handle x and weight with K_full = (K // 128)*128. The main fp8 kernel uses x[:, :K_full] and w[:, :K_full]. We can pass sliced tensors to kernel. They are contiguous in memory? x[:, :K_full] is contiguous if x contiguous, with shape (M, K_full) and stride (K, 1). The kernel reads up to K_full. The strides remain K (original), not K_full. In our kernel, we pass `x.stride(1)` = K (full). When loading blocks, the K index ranges 0..K_full-1, stride K. But the memory layout for columns 0..K_full-1 is contiguous, so stride 1. Wait if x shape (M,K) and we slice [:,:K_full], the resulting tensor has stride (K,1), not (K_full,1). The columns are contiguous within each row because K_full < K and rows are length K. The distance between row i and row i+1 is K elements, not K_full. But the kernel uses `stride_xm` = K (original), and `stride_xk` = 1. Loading a tile with k0 + offs_k works because columns are contiguous. The pointer arithmetic for rows uses K, which matches actual layout. The kernel's K argument = K_full, so loops until K_full. Stride_xm = K is fine. We just need pass x_main = x[:, :K_full] (no copy) and w_main = w[:, :K_full] (no copy). That avoids full copy! Great.
But wait: When K not multiple of 128, K_full = K - K_tail. We pass K_full as kernel K. The kernel expects K multiple of BLOCK_K? Yes, K_full is multiple of 128. Good. No padding needed. The kernel loads rows with stride_xm = x.stride(0) = K. That's correct. For w_main stride wn = K, wk=1. Good.
Then tail: x_tail = x[:, K_full:].contiguous() maybe not needed for torch.matmul? torch.matmul handles strided, but for performance maybe contiguous. Copy N*K_tail + M*K_tail small. w_tail similarly. Use bf16 matmul.
For shape1, main kernel runs on K=4096 (same as square), should achieve ~0.22ms. Tail matmul K=31 maybe ~0.02ms. Total ~0.24ms -> ~610 TFLOPS (peak fraction 0.61). Great.
Need ensure the main fp8 kernel uses aligned K = K_full, and no K mask. For shapes with K multiple of 128, K_full=K, no tail.
For skinny shape2, K=8192 multiple of 128, no tail.
For rectangular shape3, K=4096 multiple of 128.
Only shape1 benefits.
Let's implement split-tail. Need handle K_tail = K - K_full. If K_tail == 0, just call main kernel. Else compute y_main and y_tail and add.
We can use a single non-autotuned main kernel for all shapes or manual configs. For tail, use bf16 torch.matmul. The tail matmul must apply scale. We can compute y_tail = (x_tail.to(bf16) @ w_tail.to(bf16).T).float() * scale; then y = y_main + y_tail.to(bf16). Or compute y_tail in bf16 then multiply by scale in bf16? Scale is fp32; cast to bf16 may lose precision but tail small. Better use fp32.
Need ensure dtype conversions. x_tail is fp8. `x_tail.to(torch.bfloat16)` exact. w_tail.to(bf16) exact. torch.matmul outputs bf16 (accumulate fp32). Convert to float, multiply scale, convert to bf16. Then add to y_main bf16. Could do `y = y_main + y_tail_bf16`. If y_main in bf16, addition in fp32? PyTorch bf16 add uses fp32? It may. But result bf16. Fine.
Potential issue: y_main already scaled by per-channel scale in kernel. y_tail also scaled. Sum correct.
Numeric stress small_weight modifies self.weight in place. In forward, w = self.weight; slice w[:, :K_full] and w[:, K_full:] reflect scaled values. Good.
Now, for main kernel, we can use manual configs or autotune. To get best performance, use manual configs per shape. Let's keep autotune as fallback but for the four shapes manually choose. However if we use manual config, we need a plain kernel. Let's define `fp8_gemm_kernel` without autotune. Then in forward, if shape matches known, call with manual config. Else use autotuned fallback.
But Triton JIT kernels can be called with constants as keyword args. We can define:
```
@triton.jit
def fp8_gemm_kernel(..., BLOCK_M, BLOCK_N, BLOCK_K, GROUP_M): ...
```
Then call `fp8_gemm_kernel[grid](..., BLOCK_M=cfg['BLOCK_M'], ...)`? But we also need set num_warps/stages. Those are not kernel arguments; they are Triton launch options. We can pass them in the bracket? Actually Triton JIT allows passing `num_warps`, `num_stages` via kernel[grid](..., num_warps=..., num_stages=...)? I think yes, `JITFunction.run` accepts `num_warps`, `num_stages` as kwargs. But for autotune it sets. For plain call, we can pass `num_warps=cfg['num_warps'], num_stages=cfg['num_stages']` as kwargs. Let's verify. We can test.
Alternatively, we can define separate kernels for each config with hardcoded constants and call them. But many.
Simpler: Use autotune but restrict configs and let it select. However we saw it didn't pick BK=64 for square. We can remove the 128 BK configs for square? But autotune key includes K; for square K=4096, if we include only BK=64 config for that K, autotune picks it. But we need also config for shape1 padded (4224) and skinny. We can use `config_prune_by`? Not.
Maybe best to manually dispatch and avoid autotune uncertainty. Let's test plain call with num_warps/stages.
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reasoning (2462 chars)
Plain call with num_warps/stages works. Error 1.72 due to fp8 vs bf16, fine.
Now implement split-tail with manual configs. Let's decide configs.
Manual configs:
- For M>=4096 and N>=4096 (compute-bound): BM=128, BN=256, BK=64, warps=8, stages=4, GROUP_M=8. This gave square 639, rect 678.
- For skinny M=32,N=8192,K=8192: BM=16, BN=128, BK=128, warps=4, stages=4, GROUP_M=1. Gave 80 TFLOPS (0.08 peak). Could also use BM=32 BN=128 (78), but BM=16 best. Let's use BM=16.
But BM=16 with N=8192 -> N tiles = 64, M tiles = 2 (since M=32). Total blocks 128. Good.
For shape1 main (4096,4096,4096) use compute-bound config. Tail bf16 matmul.
Potential issue: For shape1, we compute y_main with K_full=4096. The main kernel uses x_main = x[:, :4096], w_main = w[:, :4096]. Stride_xm = K=4127, stride_xk=1. The kernel loops K=4096. Works. But the kernel `offs_k = tl.arange(0, BLOCK_K)` and pointer `x_ptrs = x_ptr + offs_m*stride_xm + offs_k*stride_xk`. With k0 increasing by BLOCK_K up to 4096, loads columns 0..4095. Since row stride is 4127, fine. The memory is contiguous within each block. Good.
Tail: x_tail = x[:, 4096:] shape (4096,31). We can use `x[:, 4096:].to(torch.bfloat16)`. torch.matmul handles non-contiguous? It may create contiguous internally. We can call `.contiguous()` to be safe; copy small. Actually x_tail has shape (4096,31) with stride (4127,1). torch.matmul may handle. But for performance, contiguous copy 0.25MB. Fine.
Compute y_tail = (x_tail_bf @ w_tail_bf.T).float() * s[None,:] -> bf16.
Then y = y_main + y_tail. y_main is bf16. y_tail bf16. Use `y = y_main + y_tail`. This will compute in bf16? Actually PyTorch promotes to common dtype bf16. Fine.
But we can add in fp32: `y = (y_main.float() + y_tail.float()).to(torch.bfloat16)`. This adds memory traffic (read y_main 33MB, write 33MB) ~0.04ms. Acceptable. Maybe `y_main.add_(y_tail)` uses in-place bf16 add but less memory. Tolerance okay. Let's use in-place add to avoid extra allocation: `y_main.add_(y_tail); return y_main`. But y_main is output of kernel, we can modify it. `add_` in bf16 might be fine. For safety with scale, tail exact. Use `y_main.add_(y_tail)`. But PyTorch in-place add may promote? It will compute in fp32 then cast? Actually `torch.add` with bf16 inputs uses bf16 kernel? Not sure. The tolerance is loose. Use fp32 addition then cast.
Let's implement and test correctness/benchmark.
Need restructure solution.py. Let's write new solution.py.
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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reasoning (13 chars)
Run check.py.
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reasoning (28 chars)
Check passes. Now benchmark.
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stdout (1310 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-15T00:14:53.822174+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-15T00:14:54.034352+00:00 elapsed_s=0.212 ms=0.225568
shape=0 variant=solution tflops=609.302 gbps=297.511 ms=0.226
shape=0 solution_peak_fraction=0.6093
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-15T00:14:54.552777+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-15T00:14:54.722956+00:00 elapsed_s=0.170 ms=2.387776
shape=1 variant=solution tflops=57.995 gbps=28.212 ms=2.388
shape=1 solution_peak_fraction=0.0580
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-15T00:14:56.556072+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-15T00:14:56.561878+00:00 elapsed_s=0.006 ms=0.061984
shape=2 variant=solution tflops=69.292 gbps=1095.368 ms=0.062
shape=2 solution_peak_fraction=0.0693
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-15T00:14:58.230747+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-15T00:14:58.262085+00:00 elapsed_s=0.031 ms=0.718496
shape=3 variant=solution tflops=669.505 gbps=268.530 ms=0.718
shape=3 solution_peak_fraction=0.6695
peak_fraction: 0.2012
RESULT: OK
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reasoning (2199 chars)
Interesting: shape0 improved to 0.609, shape3 to 0.6695, shape2 to 0.0693. But shape1 regressed to 2.388 ms (58 TFLOPS)! Why? The tail bf16 matmul is unexpectedly slow? Wait M=N=4096, K_tail=31. torch.matmul bf16 should be fast. Why 2.388ms? Maybe because x[:, K_full:] is not contiguous and torch.matmul chooses a slow path? Or because the tail matmul is using the default cuda context and we didn't synchronize? But benchmark times median of events. The event for tail matmul includes y computation and y add. Hmm.
Actually shape1 time 2.388ms is huge. Something wrong: maybe the main kernel with K_full=4096 and config BK=64 s4, but K_full=4096, BK=64 fine. It should be ~0.22ms. Then tail bf16 matmul maybe 2ms? That seems wrong. Could be because we compute y_main on x[:,:4096] with original stride_xm=K=4127. The kernel passed x[:, :K_full] and w[:, :K_full]. But in `_run_kernel`, we pass x.stride(0)=K=4127. The kernel loads with `stride_xm`. For shape1, M=4096, N=4096, K_full=4096. The grid is based on BLOCK_M/N. But the kernel uses K_full=4096 as K. Should be fine. Then tail: `x[:, K_full:]` shape (4096,31). But we call `.to(torch.bfloat16)` which creates a contiguous copy? `.to` on a slice may allocate contiguous. Then matmul. Should be fast.
Why 2.388ms? Maybe because of the fallback autotune? Wait `_pick_config` for shape1: M=4096,N=4096,K_full=4096 returns compute-bound config (since M,N>=4096). Good.
But maybe `_run_kernel` for shape1 uses `cfg` with `autotune` false and calls plain kernel. But the plain kernel's `num_stages=4` and `BLOCK_K=64` compiled with K=4096, M=4096,N=4096 should be fast. Maybe the issue is that x[:, :K_full] is not contiguous? It's a slice, but as argued it's valid. But Triton's `x` is non-contiguous in the M dimension (stride 4127 vs 4096). The kernel uses `x.stride(0)=K=4127` and `x.stride(1)=1`. That's correct. But maybe Triton assumes `stride_xm` divisible? It uses divisibility. Should be fine.
Could the tail matmul be slow because `w[:, K_full:]` has shape (4096,31) and torch.matmul with such skinny K might pick a slow algorithm? Actually M=N=4096, K=31. cuBLAS may not optimize and take ~2ms? Let's test tail matmul standalone.
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stdout (34 chars)
tail matmul ms 0.10680000111460686
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reasoning (9294 chars)
Tail matmul alone 0.107ms. Main kernel should be 0.22ms. Total expected ~0.33ms. But benchmark reports 2.388ms. Something else. Maybe the main kernel for shape1 is slow because K_full=4096 but `x[:, :K_full]` is not contiguous in a way that Triton cannot use tensor memory? Wait stride_xm = K = 4127, which is not a multiple of 16? 4127 not divisible by 16. Triton async copy may require alignment. The divisibility hint for stride_xm might be 1, causing unaligned slow loads. For shape0/3, K is 4096 divisible by 16/128, enabling vectorized loads. For shape1, K=4127 => stride_xm=4127 not divisible by 16, so Triton uses scalar loads, causing huge slowdown. That's likely the issue.
We need ensure the main operand slices are contiguous or at least aligned. If we pass x[:, :K_full] with stride K=4127, the row stride is odd. Triton may not vectorize. We could make x_main contiguous by copying into a tensor of shape (M, K_full) with stride K_full. That copy is M*K_full ~16.7MB, cost ~0.01ms, but then kernel fast. Similarly w_main. But then total copy ~33MB + tail, and we are back to padding approach but with smaller K? Actually copying full K_main is similar to padding but K_main=4096 vs pad=4224. But the row stride becomes K_main=4096 (aligned). The kernel will be fast. The tail matmul 0.1ms. Total maybe 0.22+0.01+0.1 = 0.33ms, peak fraction ~0.42. Slightly better than previous padding 0.45? Wait previous padding gave 0.45. Hmm.
But we can do better: Instead of copying full x_main, we can use `as_strided` to view x as (M, K_full) with stride (K_full, 1)? But the data layout of x is row-major with row length K. We cannot view it as stride K_full without copying. So copy needed.
Alternatively, we can permute x in memory? The input x is fp8 (M,K). For shape1, K=4127. We could transpose? Not helpful.
Could we pad x to K_pad (multiple of 128) and use the padded K as K argument, but the row stride would be K_pad (aligned). The copy cost M*K_pad + N*K_pad ~34MB, kernel fast. Time ~0.22 + 0.02 = 0.24ms -> 0.6 peak. This is the padding approach (which gave 0.45 in benchmark). Why padding approach gave 0.45? Because it included copy and flush. Wait padding solution earlier gave shape1 0.45. Why did our split-tail with copy full main give maybe 0.33? Actually if we copy main to contiguous, kernel fast, plus tail. But copy main is almost same as padding copy. The difference is tail bf16 0.1ms vs padded kernel does extra zero columns. Maybe padding approach with K_pad=4224 uses BK=128 (33 iterations) and includes zero columns (97 extra) but no extra kernel call overhead. It got 0.30ms -> 0.45 peak. Split with copy main + tail might be ~0.33ms -> 0.42 peak, similar. The split-tail extra matmul call overhead maybe high.
The key issue is row stride alignment for shape1. The best approach is to copy x and w to aligned K_pad (or K_main) before kernel. The padding approach already did that and gave 0.45. But our manual config might improve over autotune. Earlier padding with autotune selected BK=128 s3 and got 0.30ms. If we use manual BK=64 s4 on padded K=4224 or 4160, maybe 0.28ms -> 0.48. Could try.
But the real win is reducing copy cost. Is there a way to avoid copying x entirely? We can make x contiguous with K_pad only once per forward. Copy cost is unavoidable if K not aligned. But maybe we can use Triton's block pointers that handle non-multiple-of-16 row stride by using vectorized loads within each row? The row stride doesn't affect contiguous column loads; the issue is async copy global to local may require row stride aligned to 16 bytes? fp8 elements 1 byte; 16 bytes = 16 elements. Row stride 4127 is not multiple of 16, but the starting column for each block may not be 16-byte aligned across rows? Actually each row starts at offset i*4127 bytes. For i=1, offset 4127 bytes, not aligned to 16. Triton's cp.async global->shared needs 16-byte alignment per thread. If row start not 16-byte aligned, it cannot vectorize loads across rows. That causes scalar loads. Copying x to aligned K_pad fixes alignment. So copy is needed for efficient vectorized loads.
Could we instead transpose x to (K,M) and use K-leading layout? That would make columns contiguous but rows strided by M. The GEMM x @ w.T with x (M,K) row-major is natural. If x is transposed, we could compute y = (w @ x.T).T? But weight scale per N complicates. Not worth.
Thus for K not multiple of 128, copying to aligned buffer seems necessary for full speed. Padding approach is best.
But we can improve padding approach by using best manual config and minimizing padding. For shape1 K=4127, pad to 4160 (multiple of 64) if using BK=64 config. Copy 33 extra columns per row (total extra 33*4096*2 ~ 270KB) vs 97 extra for 4224. The kernel with BK=64 on K=4160 has 65 iterations. The autotune earlier for padded shape1: BK=64 s4 0.225ms (616 TFLOPS). With copy overhead, benchmark maybe 0.28ms -> 494 TFLOPS (0.494 peak). That's better than current 0.45. Let's test by reverting to padding with manual config.
Alternatively, pad to 4224 and use BK=128 s3: kernel 0.227ms, copy extra 97 columns -> maybe 0.30ms (455 peak). The 64 padding seems slightly better.
But the split-tail with copy main to K_full=4096 and tail bf16 might be even better because no wasted compute. Let's estimate: copy main x/w to contiguous (M,4096) and (N,4096) = 33MB -> ~0.02ms. Kernel K=4096 BK=64 s4 -> 0.22ms. Tail bf16 0.11ms. Total ~0.35ms -> 0.40 peak. Worse than padding 0.45? Hmm because tail matmul adds 0.11ms and copy main adds 0.02. Padding to 4160: copy ~33.5MB -> 0.02ms, kernel ~0.225ms, no tail. Total ~0.245ms -> 565 TFLOPS (0.565 peak). Wait why did earlier padding benchmark show 0.30ms/455 peak? Because autotune selected BK=128 s3 and maybe copy overhead larger. Let's test padding to 4160 with BK=64 s4 in solution.
Actually earlier pad_test for shape1 with BK=64 s4 reported 0.225ms tflops 616 (without flush and copy included? It included copy in each call? The script allocated padded tensors before loop and reused, so copy not included). It then called kernel. The copy time 0.04ms. So total ~0.265ms -> tflops = 2*4096^3/0.265e-3/1e12 = 523 TFLOPS. That matches 0.45-0.5. Good.
We can include the copy in timed call. To get 0.565, need copy faster. Maybe copy with `torch.nn.functional.pad` is faster? It was similar. Hmm.
Let's directly measure solution with padding to 4160 and manual BK=64 s4, including copy and flush. But maybe we can optimize copy by using `torch.empty` + `copy_` for x and w, which we measured ~0.04ms. That's ~15% overhead. Total ~0.265ms. Peak fraction ~0.52. Better than current 0.45.
Wait earlier padding solution with autotune got 0.30ms (455 peak). The difference: manual BK=64 s4 kernel ~0.215ms vs autotune BK=128 s3 ~0.227ms; plus copy 0.04ms; plus flush effect. So manual could yield ~0.26ms -> ~0.5 peak.
Let's implement padding approach again with manual config. But need avoid numeric stress caching issue. We'll not cache weight padded; copy each call. However, we can make copy more efficient by padding only to next multiple of max BLOCK_K in manual configs. If we use BK=64 config, pad to multiple of 64. But our manual config for square/rect uses BK=64. For shape1, pad to multiple of 64. For skinny, no pad. For shape0/3, K already multiple of 64.
But what about fallback autotune configs with BK=128? If shape not in manual set and K not multiple of 128, fallback would pad? We can keep general pad to _TILE_K=128. For manual shape1, we can pad to multiple of 64 and use BK=64 config. But if K not multiple of 64? K%64 could be up to 63. We can pad to multiple of 64. The kernel with BK=64 will work. For shapes with K not multiple of 64, fallback? We can use general pad to 128 and autotune.
Simplify: For all shapes, if K % 64 != 0, pad to next multiple of 64? But our manual square config uses BK=64, so we need K multiple of 64. For shape0/3 K=4096 (multiple of 64). For shape1 K=4127 -> pad to 4160 (multiple of 64). For skinny K=8192 (multiple of 128). Good. So set tile = 64 and pad if needed. But if we include BK=128 config in fallback, K_pad multiple of 64 also multiple of 128? Not necessarily; 4160 is multiple of 64 but not 128 (4160/128=32.5). So fallback BK=128 would fail. But fallback is for unknown shapes; we can pad to multiple of 128 in fallback. Let's separate.
For manual known shapes, use pad to 64 and BK=64 config. For fallback, pad to 128 and use autotune.
Alternatively, always pad to multiple of 128 for K not aligned, and use BK=128 config for shape1. But manual BK=64 config gives slightly better on square/rect. For shape1, BK=128 pad to 4224 might be similar to BK=64 pad to 4160. Let's compare actual benchmark.
Test two padding approaches in solution. But to avoid too much iteration, let's implement padding to 64 for shape1 with BK=64 manual config, and run benchmark.
Actually the split-tail approach failed because x_main stride unaligned. But if we copy x_main/w_main to contiguous buffers, it would work and avoid wasted compute. But copy cost same as padding to K_full. Since K_full=4096 vs pad=4160, copy saves 64 columns per row (~0.5MB total) but tail matmul adds 0.1ms. Padding to 4160 likely wins.
Let's test padding to 64 manually in a script with flush and copy.
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stdout (290 chars)
Korig 4127 Kpad 4160 cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.276 tflops 501416.3
Korig 4127 Kpad 4224 cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.287 tflops 482815.3
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reasoning (2070 chars)
Padding to 4160 with BK=64 gives 0.276ms -> 501 TFLOPS (0.501 peak). Better than previous 0.45. Good.
Now shape0 and shape3 with manual BK=64 s4 got 0.609 and 0.669. Good. Shape2 0.069.
Geomean would be exp((ln0.609+ln0.501+ln0.069+ln0.669)/4). Let's compute: ln0.609=-0.496, ln0.501=-0.691, ln0.069=-2.674, ln0.669=-0.402. Sum=-4.263, /4=-1.066, exp=0.344. So geomean ~0.344. Better than 0.315.
Can we improve skinny further? 0.069 is low. The memory-bound peak fraction uses bandwidth? Wait regime compute, so peak_fraction based on TFLOPS/1000. Skinny 69 TFLOPS -> 0.069. But for memory-bound shape, compute roofline not appropriate. The benchmark uses compute regime regardless. So to improve score, need increase TFLOPS for skinny. It's memory-bound; bytes_moved ~67.9MB. At 1.8TB/s, min time 0.0377ms -> 180 TFLOPS (0.18 peak). We achieve 0.062ms -> 69 TFLOPS. Could improve by using larger N tile or split K? Let's test more configs for skinny with flush, maybe use BN=256 with BM=16, or use split-K to increase parallelism and reduce output writes. But output is small (M*N*2=0.5MB). The bottleneck is reading weight (N*K=67MB) and x (0.25MB). Larger N tile reads same weight but maybe better memory coalescing? Let's explore.
We can also use a vectorized load kernel that uses TMA? Triton might not.
Let's test skinny configs with manual non-autotune, including BM=8? Triton maybe. Also BLOCK_N=512? But shared memory? For BM=16, BN=512, BK=128, B smem=512*128=64KB, A=2KB, total per stage ~66KB*4=264KB > limit. Stages=2 maybe. Could test.
But the fundamental memory bandwidth maybe limiting. Let's measure achievable memory bandwidth for reading weight. The weight is fp8 (N,K) row-major. Reading it in blocks of (BN,BK). For N=8192,K=8192, reading 67MB with L2 flush. Our kernel time 0.062ms -> 67MB/0.062ms = 1080 GB/s. Peak 1800. Could improve to ~1300 GB/s -> time 0.052ms -> 83 TFLOPS (0.083). Let's try to push.
Maybe using larger BN and fewer stages to reduce shared memory and increase occupancy. BM=16, BN=256, BK=128, warps=8, stages=2? Test.
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stdout (1209 chars)
cfg {'BLOCK_M': 16, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.054 tflops 79114.5 gbps 1250.7
cfg {'BLOCK_M': 16, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.057 tflops 75915.0 gbps 1200.1
cfg {'BLOCK_M': 16, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 2} ms 0.087 tflops 49645.9 gbps 784.8
cfg {'BLOCK_M': 16, 'BLOCK_N': 512, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 2} ms 0.104 tflops 41272.4 gbps 652.4
cfg {'BLOCK_M': 32, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.055 tflops 78743.2 gbps 1244.8
cfg {'BLOCK_M': 32, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.061 tflops 70846.0 gbps 1119.9
cfg {'BLOCK_M': 8, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 3} ms 0.055 tflops 78627.8 gbps 1243.0
cfg {'BLOCK_M': 16, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 4, 'num_stages': 4} ms 0.062 tflops 69669.2 gbps 1101.3
cfg {'BLOCK_M': 16, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 1, 'num_warps': 8, 'num_stages': 4} ms 0.065 tflops 66280.4 gbps 1047.8
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reasoning (3242 chars)
Skinny best ~0.054ms -> 79 TFLOPS (0.079 peak), up from 0.069. Use BM=16, BN=128, BK=128, warps=4, stages=4. Good.
Now square/rect: maybe we can push further with other configs. Our manual BK=64 s4 gave 0.609 and 0.669. The manual test with L2 flush gave square 639, rect 678. Benchmark lower due to flush. Could try num_ctas=2 on square? Some failed. The 128x256 BK=128 s3 gave 630 square, 677 rect (similar). BK=64 s4 gave 639 square, 678 rect. So manual is near best.
Can we reduce L2 flush overhead? No. But maybe using CUDA graphs could reduce launch overhead and improve small shapes? For square, launch overhead negligible. For skinny, launch overhead maybe significant (0.054ms). Could use CUDA graph to amortize. But benchmark's time_variant does not use graphs. We could wrap our kernel in a CUDA graph inside Model.forward? For skinny, launch overhead might be large fraction. But graphs require fixed tensors; inputs change each call. We can use graph with static weight but input x changes; not possible with static graph unless we update input pointer? Not trivial.
Could use `torch.compile`? Not for Triton custom kernel? It would trace Python, not lower kernel. Might add overhead. Skip.
Let's implement padding to 64 for K not multiple of 64, manual configs, and test. Need adjust `_pick_config` and `_run_kernel`. For shape1, K=4127, pad to 4160 and use BK=64 config. For shape0/3, no pad. For skinny, no pad.
But we need to ensure the kernel body uses K padded. We'll create padded x/w if needed. For shape1, copy. For K multiple of 64, no copy.
Need ensure numeric stress: copy weight each call from scaled self.weight. Good.
Let's rewrite solution.py accordingly. Also we can remove the split-tail code.
One detail: The padding to 64 means for shapes where K%64!=0 but K%128==0 (e.g., K=192), no pad. For K not multiple of 64, pad to multiple of 64. But our manual configs use BK=64. For fallback, if K not multiple of 128, we might pad to 128 and use autotune with BK=128 configs. Let's keep fallback as autotune with padding to 128 (or maybe 64). For simplicity, in fallback, pad to next multiple of 128 and call autotuned kernel. The autotuned kernel configs include BK=128 and BK=64; if K_pad multiple of 128, both work.
For manual known shapes, we can still use a manual config and pad to multiple of config's BLOCK_K. In `_run_kernel`, we can pass K as padded and x/w padded.
Implementation plan:
- `_TILE_K = 64` for manual configs.
- In forward: compute `K_pad = ((K + _TILE_K - 1) // _TILE_K) * _TILE_K` if K not multiple of _TILE_K? Actually for manual shapes, if K%64!=0, pad to 64. But for shape0/3 K multiple of 64, no pad. For shape1, pad to 4160.
- For fallback, we can pad to _TILE_K_FALLBACK=128.
- But `_run_kernel` needs to know K to pass. We'll pad x/w before calling `_run_kernel` if needed.
Simpler: In forward, determine config. If cfg is manual (known shape), set tile = cfg['BLOCK_K'] (64). Pad K to multiple of tile if needed. Then call kernel. If config is None (fallback), pad to 128 and call autotune.
But if shape is known but K already multiple of 64, no pad. For shape1, pad to 64.
Let's code.
Also, for shape2 (M=32), K=8192 multiple of 64, no pad.
Let's write solution.py.
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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reasoning (13 chars)
Run check.py.
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reasoning (14 chars)
Run benchmark.
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stdout (1312 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-15T00:20:11.235340+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-15T00:20:11.451874+00:00 elapsed_s=0.217 ms=0.225552
shape=0 variant=solution tflops=609.345 gbps=297.532 ms=0.226
shape=0 solution_peak_fraction=0.6093
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-15T00:20:11.974512+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-15T00:20:11.991824+00:00 elapsed_s=0.017 ms=0.283312
shape=1 variant=solution tflops=488.787 gbps=237.769 ms=0.283
shape=1 solution_peak_fraction=0.4888
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-15T00:20:13.835312+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-15T00:20:13.841105+00:00 elapsed_s=0.006 ms=0.060656
shape=2 variant=solution tflops=70.809 gbps=1119.350 ms=0.061
shape=2 solution_peak_fraction=0.0708
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-15T00:20:15.512078+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-15T00:20:15.543236+00:00 elapsed_s=0.031 ms=0.718416
shape=3 variant=solution tflops=669.579 gbps=268.560 ms=0.718
shape=3 solution_peak_fraction=0.6696
peak_fraction: 0.3447
RESULT: OK
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reasoning (1122 chars)
Geomean 0.3447. Good improvement. Shape1 0.489, shape0 0.609, shape3 0.670, shape2 0.071.
Can we improve shape1 further? The pad64 bench gave 0.276ms -> 0.55 peak, but benchmark gives 0.283ms -> 0.489. Difference due to flush? The pad64 bench included flush and copy inside event. It got 0.276ms. Why solution 0.283ms? Maybe overhead of zero tensors allocation and copy in Python vs script. Could try using `torch.empty` instead of `torch.zeros` for padded buffers and copy full x/w into them? Wait zeros vs empty+copy entire buffer? We currently allocate zeros and copy [:, :K]. That's same as pad64_bench. Slight difference maybe due to `w.contiguous()` etc. Not big.
Could use `torch.nn.functional.pad` which might use a fused padding kernel? It was similar but maybe slightly faster? Let's test in solution by replacing with F.pad. But for fp8, F.pad works? Earlier test showed 0.048 vs 0.048. Similar.
Could avoid copying x by using `torch.nn.functional.pad(x, (0, K_pad-K))` and same for w. It's a single kernel that copies and pads zeros, maybe slightly faster than zeros+copy. Let's test in a script with flush.
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stderr (404 chars)
Exit code 1
Traceback (most recent call last):
File "/tmp/pad_fn_bench.py", line 72, in <module>
bench(zeros_copy)
File "/tmp/pad_fn_bench.py", line 44, in bench
xp,wp = pad_fn(x,w,Korig,Kpad)
^^^^^^^^^^^^^^^^^^^^^^
File "/tmp/pad_fn_bench.py", line 63, in zeros_copy
xp=torch.zeros(M,Kpad,device='cuda',dtype=x.dtype)
^
NameError: name 'M' is not defined
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reasoning (14 chars)
Fix M,N scope.
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stdout (67 chars)
zeros_copy ms 0.277 tflops 499564.0
fn_pad ms 0.276 tflops 501358.2
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reasoning (385 chars)
Same. So shape1 ~0.49 peak. Good.
Can we improve square/rect further? Let's try more configs with manual tuning including num_stages=5? But shared memory limit. Maybe use BLOCK_N=512 with stages=2? Let's test. Also try BM=128, BN=256, BK=128 s3 vs BK=64 s4. Already have. Try BM=128, BN=256, BK=128, num_warps=8, num_stages=4 failed smem. Try BM=64, BN=256, BK=64 s4? Let's test more.
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stdout (2752 chars) — TRUNCATED
--- square
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.214 tflops 641854.2
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.216 tflops 635538.2
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.216 tflops 635303.2
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 4, 'num_warps': 8, 'num_stages': 3} ms 0.218 tflops 630453.9
cfg {'BLOCK_M': 128, 'BLOCK_N': 512, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 2} ms 0.938 tflops 146563.4
cfg {'BLOCK_M': 128, 'BLOCK_N': 512, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 2} ms 8.572 tflops 16033.8
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.215 tflops 638229.8
cfg {'BLOCK_M': 256, 'BLOCK_N': 128, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.218 tflops 629161.0
cfg {'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.255 tflops 539840.0
cfg {'BLOCK_M': 64, 'BLOCK_N': 256, 'BLOCK_K': 128, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 3} ms 0.244 tflops 564125.2
cfg {'BLOCK_M': 128, 'BLOCK_N': 128, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.230 tflops 597436.0
--- rect
cfg {'BLOCK_M': 128, 'BLOCK_N': 256, 'BLOCK_K': 64, 'GROUP_M': 8, 'num_warps': 8, 'num_stages': 4} ms 0.705 tflops
... (1252 more chars)
assistant
reasoning (10707 chars)
The current config is near optimal. Square 0.214ms manual -> benchmark 0.226. Rect 0.705ms -> benchmark 0.718. Good.
Can we reduce benchmark overhead? The difference is ~5% due to L2 flush. Not much.
What about using `enable_filter` to use TMA? Not.
Could we use split-K for rectangular shape to improve? N=14336, M=4096, K=4096. The grid is 32x56=1792 blocks with BM=128,BN=256. That's plenty. No need.
Could we improve square by using BLOCK_N=256, BLOCK_M=128, BK=64 s4. Already best. Good.
Now, can we improve shape1 by using a config with larger BLOCK_N to amortize padding copy? For shape1 padded K=4160, N=4096. With BN=256, N tiles=16. With BN=512 failed. BN=128 would be 32 tiles. Not. BK=64 s4 is best.
Could we pad to K=4160 but use BLOCK_K=128? Not dividing. So BK=64 is needed. But BK=64 means 65 iterations; maybe slower than BK=128 with K=4224. Compare manual: BK=64 K=4160 0.214? Wait pad64_bench gave 0.276. BK=128 K=4224 pad_test earlier gave 0.287. Similar. Use BK=64 for less padding.
One idea: For shape1, instead of padding to 4160, pad to 4224 and use BK=128 s3. The wasted compute 97 columns but fewer iterations. We measured 0.287 vs 0.276. Slightly worse. So BK=64 pad to 4160 is better.
What if we pad to 4096+128=4224 and use BK=128 s3 but avoid copying full x by using a kernel that handles a small tail? We tried and failed due to masked dot. But if we pad only weight to 4224 and x to 4224? That's full copy. Not better.
Could we use a different layout for weight: store as (N, K_pad) in a non-persistent buffer, but copy only once? Not valid under stress.
Let's consider using CUTLASS for potentially better performance on all shapes. But time and complexity. Maybe Triton is sufficient. The geomean 0.3447. The threshold for OK is 0.1. We are well above. But can we push higher? The user wants optimize; more is better. Let's see if we can get square to ~0.7 and rect to ~0.75 and skinny to ~0.1, shape1 to ~0.5 -> geomean ~0.45.
Potential bottleneck for square/rect is Triton's fp8 MMA not fully exploiting Blackwell. The manual kernel uses MMAv2? The PTX shows `ttg.nvidia_mma<{versionMajor = 2, ...}>` which is Ampere-era mma.sync, not Hopper WGMMA or Blackwell tcgen05. Wait the target is cuda:120 (sm120), but it uses nvidia_mma version 2? That might be suboptimal. Triton 3.6 may not yet use Blackwell-specific WGMMA for fp8? It might use mma.sync which has lower throughput. That's why we only get 60-70% peak. To get higher, we may need to use PTX `tcgen05.mma` or CUTLASS with Blackwell support.
The problem explicitly mentions "Blackwell SM120 ... real fp8 x fp8 tensor-core MMA". It suggests maybe Triton's current support is okay but not optimal. The user says we can use inline PTX (mma.sync ... e4m3) or CUTLASS. Maybe Triton uses mma.sync, which is not the Blackwell tensor core. We should consider writing inline PTX using `tcgen05.mma` or using CUTLASS.
But is Triton using mma.sync version 2 for sm120? The IR shows `#ttg.nvidia_mma<{versionMajor = 2, versionMinor = 0, ... instrShape = [16, 8]}>`. For fp8, the actual PTX may lower to `mma.sync.aligned.m64n8k16.row.col.f32.e4m3.e4m3.f32` which is Hopper? Actually the `nvidia_mma` version 2 is a generic representation; the backend may emit different PTX. But it might not use WGMMA. The performance we get (~60% peak) is decent but maybe can be improved.
Let's inspect generated PTX for our kernel to see instructions. But maybe too deep.
Alternative: Use `torch._scaled_mm`? Forbidden. But we can use cuBLAS via `torch.mm`? `torch.mm` with fp8 inputs? Not supported. Could call `torch.backends.cuda.matmul.allow_fp16_reduced_precision_reduction`? No.
Could use CUTLASS 3.8 with Blackwell fp8 gemm. Building it via `torch.utils.cpp_extension.load_inline` may be possible if CUTLASS headers available. We can clone CUTLASS. But network may not be reliable in scoring. However the container has network (bridge). The scoring environment may not have internet. The prompt says "Anything you're uncertain about, look up PTX docs, clone CUTLASS or other reference repos". So network is allowed during development, but final solution should not depend on external clones at runtime? Actually it can, if we clone in solution.py; but if scoring has no network, it fails. Safer to not rely on network.
Could we embed CUTLASS in solution.py? Too large.
Inline PTX for tcgen05.mma is complex but possible. We can write a CUDA C++ kernel with inline PTX for Blackwell. Need know the instruction format. Blackwell tcgen05 MMA for e4m3: `tcgen05.mma.sync.aligned.m64n8k16.row.col.f32.e4m3.e4m3.f32`? Actually Hopper H100 has `wgmma.mma_async` with shapes m64n8k16 for e4m3. Blackwell SM100/SM120 has `tcgen05.mma` (tensor core generation 5). The PTX instructions: `tcgen05.mma.sync.aligned.shape.row.col.f32.e4m3.e4m3.f32` where shape maybe `.m64n8k16`, `.m64n16k16`, etc. Also supports grouped GEMM? But writing a full GEMM kernel in PTX is a lot.
Maybe we can use `cutlass` Python interface? Not installed. FlashInfer SOTA not installed.
Given time constraints, Triton solution at 0.345 geomean may be acceptable. But the user emphasized pushing numbers up. Let's see if we can improve Triton further by enabling TMA or other options. Triton 3.6 may support `num_ctas` cluster; some configs failed. Could try `maxnreg`. Not likely.
Maybe the issue is that Triton uses `mma.sync` instead of `wgmma` because our kernel uses 8 warps not warp-group (4 warps). For WGMMA, need 4-warps per warp group and use `num_warps=4`? Actually Hopper WGMMA is triggered by warpgroup; Triton uses warpgroup MMA when `num_warps` is multiple of 4 and block sizes appropriate. Our configs use 8 warps (2 warpgroups). The IR shows nvidia_mma version 2, not WGMMA. Why? Maybe because we load from global into shared then dot; Triton uses mma.sync on shared memory for Ampere/Hopper? But for Hopper, it should use WGMMA. The IR shows `ttg.local_load` from shared to dot_op, then `tt.dot`, which is classic mma.sync path. The async_copy global_to_local also. Triton 3.6 on Blackwell may still use this path. To use WGMMA, maybe need `num_warps=4` and block sizes like 64x256? But our manual config uses 8 warps.
Let's try a config with num_warps=4, BM=64, BN=256, BK=128, stages=4 for square. In earlier square_tune, 64x256x128 s3 gave 0.252, slower. So not.
Maybe the backend for sm120 doesn't have WGMMA in Triton yet, so mma.sync is the only path. Then 60-70% peak is good.
Let's see if using `tl.dot` with `inputPrecision='tf32'` matters? It shows `inputPrecision = tf32` in IR for fp8 dot? That is for mma.sync? Actually for fp8, inputPrecision irrelevant. Not.
Could we use 2 CTAs cluster for better L2? Some configs failed to compile. Maybe Triton 3.6 not stable for clusters on sm120.
Given time, I think 0.345 is solid. But let's see if we can squeeze skinny by using a different config in solution. Our manual config BM=16 BN=128 gave 0.061ms benchmark, but manual flush gave 0.054ms. Why solution 0.061 vs manual 0.054? Maybe due to `.contiguous()` on x/w (small) and y allocation. Not much. Could use `num_warps=4` as is.
Maybe we can avoid `x.contiguous()` and `w.contiguous()` in forward; they are already contiguous. But `.contiguous()` call is cheap. Remove? Not necessary.
Could we fuse scale load? Already.
Could we use a custom kernel for skinny that reads weight in a more cache-friendly way? Since M=32, weight is 8192x8192 fp8 = 64MB. Each output element uses K=8192 weight values. With BN=128, each block reads 128*8192=1MB of weight. There are 64 N blocks, total 64MB. The L2 flush means each block's weight not cached, so total weight read 64MB. Time 0.061ms -> bandwidth 64MB/0.061ms=1050 GB/s. Peak 1800. To reach peak, time 0.036ms. Is that possible? Maybe not due to small M causing underutilization and overhead. With more blocks (BM=8, BN=128 gives 256 N blocks? M tiles=4, N tiles=64 -> 256 blocks). Manual BM=8 gave 0.055ms (slightly better than BM=16). But benchmark 0.061? We can try BM=8 manual config for skinny. However BM=8 might have correctness? tl.dot with BM=8 should work. Let's test with check. But using BM=8 means each block computes only 8 rows, more blocks, maybe better occupancy. Manual flush gave 0.055ms vs BM=16 0.054ms, similar. Benchmark might be similar.
Could use BN=64 and more blocks? Manual BM=16 BN=128 best.
What about using a kernel that doesn't use shared memory pipeline (num_stages=1) for skinny to reduce overhead? Manual with stages=2 was slower. So stages=4 best.
Maybe we can use `num_warps=2`? Not.
I think current is near best for Triton.
Let's run `check.py` one more time after any changes. Already passes.
Potential issue: The fallback path uses autotune with `key=["M","N","K"]`. For unknown shapes, it pads K to 128 and calls autotune. Good.
Potential issue: The `y := torch.empty(...)` walrus inside if cfg is None uses Python 3.8+? We have 3.11. Fine. But maybe readability.
Potential issue: In forward, we compute `N = self.weight.shape[0]`; weight is fp8 (N,K). Good.
Potential issue: Numeric stress large_input scales x by 64. x is fp8. Scaling by 64 may saturate many values to E4M3 max (448). The reference does the same scaling on the input tensor before forward. Our forward receives scaled x. The kernel uses fp8 values. Good.
Potential issue: Numeric stress small_weight scales weight by 1e-2. We copy scaled weight into padded buffer. Good.
Potential issue: The check uses `strict=True` state_dict load. Our Model registers `weight` and `weight_scale` same as reference. Good.
Potential issue: The `get_inputs` uses module-level M,N,K = 4096. Not used by check/benchmark, but okay.
Potential issue: framework label regex for solution.py: It checks for `import triton`, `@triton.jit`, `tl.dot`. Our solution has these. Good.
Let's consider if using `torch.nn.functional.pad` with fp8 is supported and exact zero. We tested. Good.
One more optimization: For shape1, instead of allocating two zero tensors each call, we could use `torch.empty` and copy full buffer (including uninitialized tail) then copy x/w into start. But the tail values would be garbage, affecting dot. Need zeros. Could use `torch.empty` + `zero_()` then copy. That's two kernels (zero + copy) vs `torch.zeros` (one kernel). `torch.zeros` likely uses a single fill kernel. Fine.
Could use `torch.nn.functional.pad` which is a single kernel that copies and fills zeros. Might be marginally faster. Let's switch to F.pad to simplify. But our earlier measurements same. Let's keep zeros+copy for clarity? F.pad is simpler. However `F.pad` with fp8 may not be optimized but works. Use `torch.nn.functional.pad`. Let's test check with F.pad.
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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reasoning (24 chars)
Run check and benchmark.
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stdout (1317 chars)
PASS
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-15T00:22:53.733408+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-15T00:22:53.948345+00:00 elapsed_s=0.215 ms=0.224224
shape=0 variant=solution tflops=612.954 gbps=299.294 ms=0.224
shape=0 solution_peak_fraction=0.6130
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-15T00:22:54.472123+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-15T00:22:54.489205+00:00 elapsed_s=0.017 ms=0.281520
shape=1 variant=solution tflops=491.898 gbps=239.283 ms=0.282
shape=1 solution_peak_fraction=0.4919
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-15T00:22:56.339287+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-15T00:22:56.345042+00:00 elapsed_s=0.006 ms=0.060480
shape=2 variant=solution tflops=71.015 gbps=1122.607 ms=0.060
shape=2 solution_peak_fraction=0.0710
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-15T00:22:58.023310+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-15T00:22:58.054655+00:00 elapsed_s=0.031 ms=0.714816
shape=3 variant=solution tflops=672.951 gbps=269.913 ms=0.715
shape=3 solution_peak_fraction=0.6730
peak_fraction: 0.3465
RESULT: OK
assistant
reasoning (1959 chars)
Slightly better: geomean 0.3465. F.pad seems marginally better. Good.
Can we improve shape1 by padding to 64 with F.pad? It's doing that. Good.
Could we improve shape1 by using K_pad=4096+64=4160 and BK=64 config. Already.
What about using K_pad=4160 with a config optimized for K=4160? Maybe BM=256? Since K is not huge (4160), more M tiles? M=4096, BM=256 -> 16 M tiles; BN=128 -> 32 N tiles; total 512 blocks. Try? Manual square_tune2 showed 256x128x64 s4 638 similar. Not better.
Could we avoid padding x for shape1 by making x contiguous with K_pad? F.pad does that. Good.
Now, maybe we can improve square/rect by using a config with `num_warps=4` and larger blocks? But not.
Let's see if using `BLOCK_M=256, BLOCK_N=128, BK=64 s4` yields similar square (0.215) but maybe better rect? Rect 0.714 vs 0.705. Current BN=256 is best for rect.
Could we use `BLOCK_M=128, BLOCK_N=256, BK=64 s4` for all compute-bound. Good.
Could we add `num_stages=5`? Shared memory for 128x256x64: per stage A=128*64=8KB, B=256*64=16KB -> 24KB; *5=120KB > 101KB. Fail. `num_stages=4` uses 96KB, fits. Good.
Now, maybe we can improve skinny by using `BLOCK_M=8, BN=128, BK=128, warps=4, stages=4`. Manual flush gave 0.055ms vs BM=16 0.054ms. Benchmark might be similar or slightly worse due to more blocks. BM=16 is fine. Could try BM=8 in solution? But check correctness? Should pass. Let's not risk.
Potential improvement: Use `tl.dot` with `max_num_imprecise_acc`? Not.
Could we use `inputPrecision='ieee'`? Not for fp8.
Let's run ncu or nsys to see if kernel is memory or compute bound. Not necessary.
Let's check if the problem's `framework.txt` label uses 'triton'. Good.
Now, ensure solution.py doesn't contain forbidden strings? Forbidden ops are torch._scaled_mm and torch.ops.aten._scaled_mm. We don't. But the framework regex for ptx includes `mma.sync`; our source doesn't contain that string. Good.
Let's read final solution.py to ensure no issues.
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stdout (7727 chars) — TRUNCATED
1 """FP8 e4m3 GEMM using real fp8 tensor-core MMA via Triton.
2
3 Layout:
4 x: fp8_e4m3 (M, K)
5 weight: fp8_e4m3 (N, K)
6 weight_scale: fp32 (N,)
7 y = (x @ weight.T) * weight_scale -> bf16 (M, N)
8
9 K dimensions that are not aligned to the tensor-core tile are handled by
10 padding the operands up to the tile size. The padding values are fp8 zeros,
11 so they contribute nothing to the result.
12 """
13 import torch
14 import torch.nn as nn
15 import torch.nn.functional as F
16 import triton
17 import triton.language as tl
18
19 OP_TYPE = "gemm"
20 SUPPORTED_PRECISIONS = ["fp8_e4m3"]
21 HARDWARE_REQUIRED = ["RTX_PRO_6000", "H100", "B200"]
22 E4M3_MAX = 448.0
23
24 M = 4096
25 N = 4096
26 K = 4096
27
28
29 @triton.jit
30 def fp8_gemm_kernel(
31 x_ptr,
32 w_ptr,
33 s_ptr,
34 y_ptr,
35 M,
36 N,
37 K,
38 stride_xm,
39 stride_xk,
40 stride_wn,
41 stride_wk,
42 stride_ym,
43 stride_yn,
44 BLOCK_M: tl.constexpr,
45 BLOCK_N: tl.constexpr,
46 BLOCK_K: tl.constexpr,
47 GROUP_M: tl.constexpr,
48 ):
49 """C = (A @ B.T) * scale. K is assumed a multiple of BLOCK_K."""
50 pid = tl.program_id(axis=0)
51 num_pid_m = tl.cdiv(M, BLOCK_M)
52 num_pid_n = tl.cdiv(N, BLOCK_N)
53 num_pid_in_group = GROUP_M * num_pid_n
54 group_id = pid // num_pid_in_group
55 first_pid_m = group_id * GROUP_M
56 group_size_m = min(num_pid_m - first_pid_m, GROUP_M)
57 pid_m = first_pid_m +
... (6227 more chars)
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reasoning (3239 chars)
Looks good. One concern: The fallback path uses `y := torch.empty(...)` inside the function call argument. That's fine but maybe less readable. It creates y before calling autotune. Good.
Potential issue: For fallback path, after padding, we pass K_pad to autotune key. Good.
Potential issue: `_pick_config` for M>=4096,N>=4096 returns compute-bound config for any K, including K not multiple of 64. It will pad to BLOCK_K=64. But if K is e.g. 33, padding to 64, the main kernel computes a 4096x4096 GEMM with K=64, which is tiny; still okay. But for very small K, this config may not be optimal. But fallback covers shapes not in this heuristic? Actually any M,N>=4096 will use this config. For K small, padding to 64 and using large tiles might be okay. For K not multiple of 64, F.pad works. Good.
Potential issue: For M>=4096,N>=4096 but K very large and not multiple, padding to 64 may require large copy. But not relevant.
Potential issue: For shape1, M=4096,N=4096,K=4127, the heuristic M>=4096,N>=4096 triggers, uses BK=64 config, pads to 4160. Good.
Potential issue: For shape2, M=32,N=8192,K=8192, specific config. Good.
Now, let's see if we can get a bit more from shape1 by choosing a different config when K not aligned. For shape1, after padding to 4160, the config is same as square but K=4160. Could a config with BN=128 be better? Manual shape1_tune tested configs and BK=64 256x128 gave 622, 128x256 gave 616. Our current 128x256 BK=64 gave 616. The solution benchmark shows 491 (with flush+overhead). The manual pad64_bench gave 501. So solution overhead ~10%. Not much.
Could we reduce overhead by preallocating y before padding? We already allocate y after padding. The event includes y allocation (small). Could allocate y before padding to exclude from timing? But benchmark times `fn(*inputs)` which includes everything in forward. We cannot exclude Python overhead. But we can reduce by not calling `.contiguous()` if already contiguous. Use `x = x if x.is_contiguous() else x.contiguous()`. Similarly w. But `.contiguous()` on contiguous tensor returns same tensor quickly. Not significant.
For shape1, F.pad dominates overhead. Not much.
Could we avoid F.pad for shape1 by using a custom fp8 kernel with a separate tail path that is efficient? The masked tail dot inside same kernel was slow. But perhaps we can write a kernel that uses `tl.dot` on full K blocks and a separate small `tl.dot` for tail with `BLOCK_K=32` or 16 and small masks. The earlier tail_kernel had tail dot with BLOCK_K=128 masked only tail; it was slow for large tiles. But maybe because the tail dot inside the kernel still uses full BLOCK_K=128 and the compiler cannot optimize. If we make the tail loop with `BLOCK_K=32` and iterate over tail elements, maybe faster. But tail is only 31 elements; a small kernel could do it. However the overhead of a second kernel and the copy of tail columns may be similar to padding.
What about using `tl.dot` with `inputPrecision='tf32'`? Irrelevant.
I think current solution is good.
Let's run a final check and benchmark to confirm stable. Also maybe run with baseline to see comparison? Baseline opt-in. Not needed.
Let's run check.py and benchmark.py again to ensure no flakiness.
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stdout (1317 chars)
PASS
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-15T00:23:33.599555+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-15T00:23:33.813171+00:00 elapsed_s=0.214 ms=0.222992
shape=0 variant=solution tflops=616.340 gbps=300.947 ms=0.223
shape=0 solution_peak_fraction=0.6163
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-15T00:23:34.325643+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-15T00:23:34.342609+00:00 elapsed_s=0.017 ms=0.281824
shape=1 variant=solution tflops=491.367 gbps=239.024 ms=0.282
shape=1 solution_peak_fraction=0.4914
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-15T00:23:36.197439+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-15T00:23:36.203176+00:00 elapsed_s=0.006 ms=0.060176
shape=2 variant=solution tflops=71.373 gbps=1128.279 ms=0.060
shape=2 solution_peak_fraction=0.0714
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-15T00:23:37.880755+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-15T00:23:37.911721+00:00 elapsed_s=0.031 ms=0.714080
shape=3 variant=solution tflops=673.645 gbps=270.191 ms=0.714
shape=3 solution_peak_fraction=0.6736
peak_fraction: 0.3474
RESULT: OK
assistant
reasoning (1769 chars)
Stable geomean ~0.347. Good.
Could we try to use Triton 3.6 new feature `tl.dot` with `num_warps=8` and `num_stages=4` already. Maybe we can try enabling `TRITON_F32_DEFAULT`? Not.
Let's see if using `BLOCK_M=128, BLOCK_N=256, BLOCK_K=64` for square/rect can be improved by `GROUP_M=4`? Manual square_tune2 showed GROUP_M=4 128x256x128 s3 630 vs GROUP_M=8 635; not. For BK=64 not tested. But not big.
Could use `BLOCK_M=128, BLOCK_N=256, BLOCK_K=64, num_stages=4, num_warps=8` is best.
One more idea: For square shape, the output y is 33MB. The benchmark bytes_formula includes output write. Our kernel writes bf16 y. For compute-bound, not limiting.
Let's consider whether using `fp8_gemm_kernel_autotune` fallback inside `_run_autotune_kernel` recompiles every forward? No, Triton caches by key. For manual, also cached. Good.
Potential issue: The autotune fallback path uses the same `fp8_gemm_kernel` body but the autotune wrapper adds overhead on first call. Not relevant.
Let's verify that `framework.txt` is written as 'triton'. It should.
Could we add a comment header? Not needed.
Now, the user asked to "Take as long as you need to actually push the number up." We have a decent result. But maybe we should attempt a quick experiment with a Blackwell-specific PTX kernel? That could push to 0.5+ geomean. But it's complex and risky. Let's consider if it's worth it.
We have time. Could we use `torch.utils.cpp_extension.load_inline` to compile a simple CUTLASS-like kernel? The challenge is writing a high-performance GEMM. Triton already gives 60-70% peak. Writing PTX from scratch likely not better than Triton for square, but maybe better for skinny? Not.
Could we use the `cutlass` library if installed? Let's check if cutlass python available.
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stdout (131 chars)
Traceback (most recent call last):
File "<string>", line 1, in <module>
ModuleNotFoundError: No module named 'cutlass'
no cutlass
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reasoning (560 chars)
No cutlass python. Could clone CUTLASS and compile a kernel via cpp_extension. But building at runtime in solution.py may take minutes. The benchmark does warmup and times median; compile time not counted. But check.py would wait for compile. It could be okay. However if network absent in scoring, clone fails.
Could we include CUTLASS headers in solution.py as inline strings? Too large.
Could we use `torch._scaled_mm` just to measure peak? It's forbidden in solution, but we can test in a scratch script to see cuBLAS peak. Let's do that to know ceiling.
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stderr (1595 chars) — TRUNCATED
Exit code 1
Traceback (most recent call last):
File "/tmp/cublas_peak.py", line 8, in <module>
y=torch._scaled_mm(x,w.T,out_dtype=torch.bfloat16,scale_a=torch.tensor(1.0,device='cuda'),scale_b=s)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
RuntimeError: Invalid scaling configuration.
- For TensorWise scaling, a and b should be float8, scales should be float and singletons.
- For RowWise scaling, a and b should be float8, scales should be float, scale_a should be (4096, 1) and scale_b should be (1, 4096), and both should be contiguous.
- For BlockWise 1x128 scaling, a and b should be float8, scales should be float, scale_a should be (4096, 32) and scale_b should be (32, 4096), and both should be outer-dim-major.
- For BlockWise 128x128 scaling, a and b should be float8, scales should be float, scale_a should be (32, 32) and scale_b should be (32, 32), and both should be near-inner-dim-major (with 16-byte aligned strides).
- For Blockwise 1x32 scaling, a and b should be float8, scales should be float8_e8m0fnu, scale_a should have 524288 elements and scale_b should have 524288 elements, and both should be contiguous.
- For Blockwise 1x16 scaling, a and b should be float4 (packed 2x), scales should be float8_e4m3fn, scale_a should have 2097152 elements and scale_b should have 2097152 elements, and both should be contiguous.
Got a.dtype()=Float8_e4m3fn, scale_a.dtype()=Float, scale_a.size()=[], scale_a.stride()=[],
... (95 more chars)
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reasoning (207 chars)
_scaled_mm requires scale_b shape (1,N) for rowwise. We can test with scale_b = s[None,:]. But _scaled_mm does C = (A @ B) * scale_a * scale_b. We need scale_a=1, scale_b rowwise. Let's test to measure peak.
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stderr (1604 chars) — TRUNCATED
Exit code 1
Traceback (most recent call last):
File "/tmp/cublas_peak.py", line 8, in <module>
y=torch._scaled_mm(x,w.T,out_dtype=torch.bfloat16,scale_a=torch.tensor(1.0,device='cuda'),scale_b=s)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
RuntimeError: Invalid scaling configuration.
- For TensorWise scaling, a and b should be float8, scales should be float and singletons.
- For RowWise scaling, a and b should be float8, scales should be float, scale_a should be (4096, 1) and scale_b should be (1, 4096), and both should be contiguous.
- For BlockWise 1x128 scaling, a and b should be float8, scales should be float, scale_a should be (4096, 32) and scale_b should be (32, 4096), and both should be outer-dim-major.
- For BlockWise 128x128 scaling, a and b should be float8, scales should be float, scale_a should be (32, 32) and scale_b should be (32, 32), and both should be near-inner-dim-major (with 16-byte aligned strides).
- For Blockwise 1x32 scaling, a and b should be float8, scales should be float8_e8m0fnu, scale_a should have 524288 elements and scale_b should have 524288 elements, and both should be contiguous.
- For Blockwise 1x16 scaling, a and b should be float4 (packed 2x), scales should be float8_e4m3fn, scale_a should have 2097152 elements and scale_b should have 2097152 elements, and both should be contiguous.
Got a.dtype()=Float8_e4m3fn, scale_a.dtype()=Float, scale_a.size()=[], scale_a.stride()=[],
... (104 more chars)
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reasoning (256 chars)
Need scale_b contiguous? It says scale_b should be (1,4096) and contiguous. Our s[None,:] has stride (4096,1), contiguous. But scale_a is scalar; rowwise requires scale_a shape (M,1). Let's set scale_a = torch.ones(M,1). Also need scale_a float. Let's try.
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stdout (57 chars)
cuBLAS fp8 ms 0.19979199767112732 tflops 687910.201980336
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reasoning (1743 chars)
cuBLAS fp8 for square achieves 687 TFLOPS (0.688 peak). Our Triton 0.616 peak (0.616). So we are within ~10% of cuBLAS. Good. For rect, cuBLAS maybe similar. So Triton is decent.
Could we get closer to cuBLAS by using a different config? Manual square best 641 vs cuBLAS 687. Maybe cuBLAS uses a better algorithm. But we are close.
Let's measure cuBLAS for rect and skinny? Not necessary. But it shows ceiling.
Given that, I think Triton solution is good. We could try to use `torch._scaled_mm`? Forbidden. But our performance is near cuBLAS, likely acceptable.
Could we improve square by using `BLOCK_M=128, BLOCK_N=256, BLOCK_K=64, num_stages=4` got manual 641 vs cuBLAS 687. The difference maybe due to not using row-wise scale as efficiently? We load scale in epilogue. cuBLAS fuses. Not big.
One thing: In our kernel, we use `tl.dot(a, tl.trans(b))`. This transposes B in shared memory. For performance, maybe it's better to load B as (BLOCK_K, BLOCK_N) transposed? We load W block as (BLOCK_N, BLOCK_K) row-major and transpose. That's fine.
Could we avoid the `tl.trans` by loading W with pointer offsets that treat it as (BLOCK_K, BLOCK_N)? Since W is (N,K) row-major, the block W[offs_n, offs_k] is rows N, columns K. To get a (BLOCK_K, BLOCK_N) matrix for dot, we need W.T[offs_k, offs_n] = W[offs_n, offs_k] but with K as leading dimension. We can create pointer `w_ptrs_T = w_ptr + offs_k[:,None]*stride_wk + offs_n[None,:]*stride_wn` and load shape (BLOCK_K, BLOCK_N). That avoids `tl.trans`. Does it improve? Maybe. Let's test.
Modify kernel: load b_T directly as (BLOCK_K, BLOCK_N) using `offs_k[:,None]` and `offs_n[None,:]`. Then `acc += tl.dot(a, b_T)`. This might change layout and performance. Let's test in a script.
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stdout (222 chars)
gemm_trans ms 0.213 tflops 644212.9
gemm_no_trans ms 0.214 tflops 641998.1
gemm_trans ms 0.702 tflops 684862.3
gemm_no_trans ms 0.704 tflops 683647.6
gemm_trans ms 0.055 tflops 78124.4
gemm_no_trans ms 0.055 tflops 78604.8
assistant
reasoning (779 chars)
No-transpose B load is slightly better for skinny, similar for square/rect. The difference is minor. We can keep current `tl.trans` for clarity. Actually no-transpose avoids a transpose instruction. Could adopt it for slight gain on skinny. But current solution uses `tl.trans`. Changing to no-transpose might improve skinny from 0.0714 to maybe 0.072? Minor. Let's consider updating kernel to avoid `tl.trans`. It also changes the mask: loading b_T as (BLOCK_K, BLOCK_N) mask on N across columns: `mask=offs_n[None, :] < N`. This is fine. Let's update kernel to no-transpose; it's a simple change and may give tiny improvement. Need also update autotune wrapper? It calls same body.
Let's modify `fp8_gemm_kernel` to load B_T directly and dot without trans. Ensure correctness.
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stdout (149 chars)
The file /workspace/problems/01_fp8_gemm/solution.py has been updated successfully. (file state is current in your context — no need to Read it back)
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reasoning (24 chars)
Run check and benchmark.
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stdout (1317 chars)
PASS
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-15T00:25:28.539124+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-15T00:25:28.764571+00:00 elapsed_s=0.225 ms=0.223008
shape=0 variant=solution tflops=616.296 gbps=300.926 ms=0.223
shape=0 solution_peak_fraction=0.6163
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-15T00:25:29.306210+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-15T00:25:29.323419+00:00 elapsed_s=0.017 ms=0.281824
shape=1 variant=solution tflops=491.367 gbps=239.024 ms=0.282
shape=1 solution_peak_fraction=0.4914
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-15T00:25:31.228562+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-15T00:25:31.234362+00:00 elapsed_s=0.006 ms=0.060400
shape=2 variant=solution tflops=71.109 gbps=1124.094 ms=0.060
shape=2 solution_peak_fraction=0.0711
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-15T00:25:32.918256+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-15T00:25:32.949217+00:00 elapsed_s=0.031 ms=0.713600
shape=3 variant=solution tflops=674.098 gbps=270.373 ms=0.714
shape=3 solution_peak_fraction=0.6741
peak_fraction: 0.3471
RESULT: OK
assistant
reasoning (2375 chars)
Geomean 0.3471, similar. Good.
Could we improve shape2 by using no-transpose config BM=16,BN=128? It is. Fine.
Let's consider if we can improve shape1 by padding to 64 and using a config with BN=256 but maybe BK=64 s3? We use s4. Let's test shape1 with F.pad and config s3 vs s4 in solution? Not needed.
I think we have a solid solution. The geomean 0.347 is far above OK threshold. We can present final.
But before final, let's ensure there are no leftover scratch files that could interfere? The user said scratch files okay. Only solution.py matters.
Let's also consider if `torch.nn.functional.pad` with fp8 has any issue with `F.pad` on non-contiguous? We call x.contiguous() first. Good.
Potential issue: The autotune fallback path uses `F.pad(w, (0, K_pad-K))`. `F.pad` expects tuple (left,right) for last dim. Good.
Potential issue: For the manual path, if K_pad != K, we pad w and x. But then `w` and `x` are new tensors; `w` not registered, fine.
Potential issue: The manual config for compute-bound shapes uses `BLOCK_K=64`. If K is multiple of 64 but not 128 (e.g., K=192), no pad. The kernel loops K/64 times. Good. If K not multiple of 64, pads to multiple of 64.
Potential issue: For very small K (e.g., K=64) and M,N large, the compute-bound config may be okay. For K=32, pad to 64, loop once. Works.
Potential issue: The `GROUP_M=8` for manual config with M=4096, BLOCK_M=128 => 32 M tiles. Grouping 8 means 4 groups. Fine. For smaller M, e.g., M=4096 still. If M=8192, 64 tiles, 8 groups. Fine.
Potential issue: For skinny config GROUP_M=1. Good.
Now, we should maybe add a brief comment about hand-tuned configs.
Let's also run `python check.py` once more to be safe after all edits. Already did.
Final answer: report performance numbers and that check passes.
But the user might expect just the final solution, not a long explanation. We can summarize: implemented real fp8 tensor-core GEMM in Triton, K-padding for unaligned K, hand-tuned tile configs, passes check, geomean 0.347.
Let's also mention scratch files left in /tmp and workspace? We can say scratch files are in /tmp and current directory unchanged except solution.py. The user said can make mess; final answer in solution.py.
Check if any scratch files in current dir? We only wrote solution.py. Good.
Let's read final solution.py one more time to ensure no syntax issues.
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stdout (7808 chars) — TRUNCATED
1 """FP8 e4m3 GEMM using real fp8 tensor-core MMA via Triton.
2
3 Layout:
4 x: fp8_e4m3 (M, K)
5 weight: fp8_e4m3 (N, K)
6 weight_scale: fp32 (N,)
7 y = (x @ weight.T) * weight_scale -> bf16 (M, N)
8
9 K dimensions that are not aligned to the tensor-core tile are handled by
10 padding the operands up to the tile size. The padding values are fp8 zeros,
11 so they contribute nothing to the result.
12 """
13 import torch
14 import torch.nn as nn
15 import torch.nn.functional as F
16 import triton
17 import triton.language as tl
18
19 OP_TYPE = "gemm"
20 SUPPORTED_PRECISIONS = ["fp8_e4m3"]
21 HARDWARE_REQUIRED = ["RTX_PRO_6000", "H100", "B200"]
22 E4M3_MAX = 448.0
23
24 M = 4096
25 N = 4096
26 K = 4096
27
28
29 @triton.jit
30 def fp8_gemm_kernel(
31 x_ptr,
32 w_ptr,
33 s_ptr,
34 y_ptr,
35 M,
36 N,
37 K,
38 stride_xm,
39 stride_xk,
40 stride_wn,
41 stride_wk,
42 stride_ym,
43 stride_yn,
44 BLOCK_M: tl.constexpr,
45 BLOCK_N: tl.constexpr,
46 BLOCK_K: tl.constexpr,
47 GROUP_M: tl.constexpr,
48 ):
49 """C = (A @ B.T) * scale. K is assumed a multiple of BLOCK_K."""
50 pid = tl.program_id(axis=0)
51 num_pid_m = tl.cdiv(M, BLOCK_M)
52 num_pid_n = tl.cdiv(N, BLOCK_N)
53 num_pid_in_group = GROUP_M * num_pid_n
54 group_id = pid // num_pid_in_group
55 first_pid_m = group_id * GROUP_M
56 group_size_m = min(num_pid_m - first_pid_m, GROUP_M)
57 pid_m = first_pid_m +
... (6308 more chars)
assistant
reasoning (1148 chars)
Looks good.
One more thought: The autotune fallback path also uses `fp8_gemm_kernel` body with no-transpose B load. The autotune configs include `BLOCK_K=128`. For K padded to 128, works. Good.
Now, maybe we can improve the fallback path for shape2 if it didn't match manual? It does.
Potential issue: `_run_autotune_kernel` uses `y := torch.empty(...)` inside argument. If autotune compiles multiple configs, it creates y once and passes same y to all; that's fine. But the autotune `do_bench` will call kernel multiple times writing to y; no issue.
Potential issue: The autotune wrapper `fp8_gemm_kernel_autotune` calls inner `fp8_gemm_kernel` with positional args including constexprs. This works as earlier. But note Triton may compile the inner function separately? The wrapper's body is small. It compiled earlier.
We should ensure no memory leak from autotune cache. Not relevant.
Now final answer. Mention the achieved geomean and per-shape peak fractions. Also mention check.py passes.
Before final, maybe run check.py and benchmark.py one more time to get final numbers. Already have 0.3471.
Let's run a clean benchmark to report.
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stdout (1317 chars)
PASS
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-15T00:26:03.863394+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-15T00:26:04.074925+00:00 elapsed_s=0.212 ms=0.224192
shape=0 variant=solution tflops=613.041 gbps=299.337 ms=0.224
shape=0 solution_peak_fraction=0.6130
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-15T00:26:04.587754+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-15T00:26:04.604718+00:00 elapsed_s=0.017 ms=0.281296
shape=1 variant=solution tflops=492.290 gbps=239.473 ms=0.281
shape=1 solution_peak_fraction=0.4923
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-15T00:26:06.452641+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-15T00:26:06.458618+00:00 elapsed_s=0.006 ms=0.063584
shape=2 variant=solution tflops=67.548 gbps=1067.805 ms=0.064
shape=2 solution_peak_fraction=0.0675
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-15T00:26:08.125997+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-15T00:26:08.156892+00:00 elapsed_s=0.031 ms=0.712512
shape=3 variant=solution tflops=675.127 gbps=270.786 ms=0.713
shape=3 solution_peak_fraction=0.6751
peak_fraction: 0.3425
RESULT: OK
assistant
reasoning (3273 chars)
Slight variance: shape2 0.0675 this run vs 0.071 earlier. Geomean 0.3425. Still good. Variation due to timing.
Maybe we should pick a skinny config that is more stable. BM=32 BN=128 gave similar. But fine.
The geomean fluctuates around 0.34-0.35. Acceptable.
Could we improve stability/performance of skinny by using BM=32, BN=128? Earlier manual flush: BM=32 BN=128 0.055ms tflops 78.7. BM=16 0.054ms 79.1. Similar. BM=16 has more blocks (128 vs 64) and gave slightly better peak in some runs. The benchmark run got 0.064ms this time (slower). Maybe due to timing noise. Let's not change.
I think final answer ready.
One more idea: Could we use a persistent stream/ CUDA graph for skinny to reduce launch overhead? Since inputs change, not straightforward. But we could create a graph that replays the kernel with the same input pointers but we can update the input pointer using graph capture with `torch.cuda.make_graphed_callables`? That would copy data into a static buffer inside graph? Actually we can graph the entire forward including copies from input to static buffer. But the input x changes each call; we can copy x into a static tensor inside the graph using `x_static.copy_(x)` and then run kernel. The graph records the copy and kernel. Then each call replays graph. This could reduce launch overhead for small shapes. But for square, not needed. For skinny, launch overhead might be significant. However, implementing CUDA graphs in solution.py is complex and may not interact well with varying shapes. The benchmark calls the model fresh for each shape with same input shape; within shape, input is same shape but values change. We could capture graph on first forward. But `torch.cuda.make_graphed_callables` expects a callable and warmup. It can graph a Module forward. It copies inputs into static buffers inside graph. Then subsequent calls with new inputs update the static buffers via recorded copies. This is possible. But it may not be allowed? The benchmark calls `sol_model(*inputs)`; if we graph, it returns static output tensor, which is fine. However, autotune would happen before graph capture. This could improve skinny.
But time is limited. Also, the benchmark uses L2 flush before each call; the graph replay includes copy from input to static buffer, then kernel. The copy reads input from memory (not cached), so L2 flush effect remains. The kernel launch overhead reduction could help skinny. But graph capture has overhead and memory. Could give maybe 10-20% improvement on skinny, raising geomean slightly.
Let's estimate: skinny time 0.064ms. If launch overhead is ~0.01ms, graph could reduce to 0.054ms -> 79 TFLOPS (0.079). Geomean would increase to ~0.36. Not huge. Given complexity, skip.
We can consider adding `torch.compile` to Model.forward? It would compile Python, not kernel. Might reduce overhead. But Triton kernel launch inside compiled function may still be same. Could try `torch.compile` on Model? The benchmark doesn't compile solution. We could use `@torch.compile` on forward? It may add overhead first call. Not worth.
Given time and solid result, finalize.
One final check: Does solution.py use any forbidden strings? It uses `F.pad`, no `_scaled_mm`. Good.
Let's produce final response summarizing.
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Done. The final kernel is in `solution.py`.
What it does:
- Real FP8×FP8 tensor-core MMA via Triton `tl.dot` with `fp8_e4m3fn` inputs and `fp32` accumulation.
- Per-channel `weight_scale` applied in the epilogue before casting to `bf16`.
- K-unaligned shapes (e.g. `K=4127`) are handled by padding `x` and `weight` up to the tile granularity with fp8 zeros, avoiding the slow masked-K tensor-core path.
- Hand-tuned tile configs for the graded shapes, plus an autotuned fallback for other sizes.
`python check.py` passes, and `python benchmark.py` reports:
| shape | ms | TFLOPS | peak fraction |
|-------|----|--------|---------------|
| 4096×4096×4096 | 0.224 | 613 | 0.613 |
| 4096×4096×4127 | 0.281 | 492 | 0.492 |
| 32×8192×8192 | 0.064 | 68 | 0.068 |
| 4096×14336×4096 | 0.713 | 675 | 0.675 |
**Geomean peak fraction: ~0.34–0.35** (well above the 0.1 OK threshold).
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