solution.py
final answer
benchmark.log
check.log
result.json
"""FP8 e4m3 GEMM — Triton kernel using fp8 tensor cores on Blackwell SM120.
Model interface: same as reference.py — holds `weight` (fp8_e4m3, N×K) and
`weight_scale` (float32, N). Forward: y = ((x @ w.T) * weight_scale).to(bf16).
Uses a 2D grid launch and dynamically pads K to a multiple of BLOCK_K so every
inner-loop iteration loads full, unmasked tiles (avoiding the Triton tail
slowdown on fp8 masked loads).
"""
import torch
import torch.nn as nn
import triton
import triton.language as tl
E4M3_MAX = 448.0
# ---------------------------------------------------------------------------
# Triton kernel — 2D grid (M-blocks × N-blocks)
# ---------------------------------------------------------------------------
@triton.jit
def _fp8_gemm_kernel(
a_ptr, # fp8 activation (M, K_padded)
b_ptr, # fp8 weight (N, K_padded) — read transposed as (K, N)
c_ptr, # bf16 output (M, N)
scale_ptr, # float32 scale (N,)
M,
N,
K_padded, # Padded K (multiple of BLOCK_K)
stride_am,
stride_ak,
stride_bn,
stride_bk,
stride_cm,
stride_cn,
BLOCK_M: tl.constexpr,
BLOCK_N: tl.constexpr,
BLOCK_K: tl.constexpr,
):
pid_m = tl.program_id(0)
pid_n = tl.program_id(1)
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)
a_ptrs = a_ptr + offs_m[:, None] * stride_am + offs_k[None, :] * stride_ak
b_ptrs = b_ptr + offs_n[None, :] * stride_bn + offs_k[:, None] * stride_bk
acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)
# K_padded is a multiple of BLOCK_K — every iteration loads a full tile.
for k in range(0, K_padded, BLOCK_K):
a = tl.load(a_ptrs)
b = tl.load(b_ptrs)
acc = tl.dot(a, b, acc)
a_ptrs += BLOCK_K * stride_ak
b_ptrs += BLOCK_K * stride_bk
# Apply per-channel dequant scale
scale = tl.load(scale_ptr + offs_n, mask=offs_n < N, other=1.0)
acc = acc * scale[None, :]
# Store with edge masks
c_ptrs = c_ptr + offs_m[:, None] * stride_cm + offs_n[None, :] * stride_cn
tl.store(c_ptrs, acc.to(tl.bfloat16),
mask=(offs_m[:, None] < M) & (offs_n[None, :] < N))
# ---------------------------------------------------------------------------
# Padding helpers
# ---------------------------------------------------------------------------
def _pad_tensor(t: torch.Tensor, K_padded: int) -> torch.Tensor:
"""Pad the last dimension of an fp8 tensor to *K_padded* with zeros."""
K = t.shape[1]
if K == K_padded:
return t
padded = torch.zeros(t.shape[0], K_padded, dtype=t.dtype, device=t.device)
padded[:, :K].copy_(t)
return padded
# ---------------------------------------------------------------------------
# Kernel dispatch
# ---------------------------------------------------------------------------
def _run_kernel(
x: torch.Tensor,
weight: torch.Tensor,
weight_scale: torch.Tensor,
out: torch.Tensor,
):
M, K = x.shape
N = weight.shape[0]
# Choose tile sizes.
# - Skinny M (≤64): narrower M, wider K to amortise memory latency.
# - All other shapes: balanced tile that fits 3-stage pipelining in
# 128 KB of shared memory.
if M <= 64:
BLOCK_M, BLOCK_N, BLOCK_K = 64, 128, 256
else:
BLOCK_M, BLOCK_N, BLOCK_K = 128, 128, 64
# Pad K so every inner-loop iteration loads a full tile.
K_padded = ((K + BLOCK_K - 1) // BLOCK_K) * BLOCK_K
x_padded = _pad_tensor(x, K_padded)
w_padded = _pad_tensor(weight, K_padded)
grid = (triton.cdiv(M, BLOCK_M), triton.cdiv(N, BLOCK_N))
_fp8_gemm_kernel[grid](
x_padded, w_padded, out, weight_scale,
M, N, K_padded,
x_padded.stride(0), x_padded.stride(1),
w_padded.stride(0), w_padded.stride(1),
out.stride(0), out.stride(1),
BLOCK_M=BLOCK_M,
BLOCK_N=BLOCK_N,
BLOCK_K=BLOCK_K,
)
# ---------------------------------------------------------------------------
# Model
# ---------------------------------------------------------------------------
class Model(nn.Module):
"""FP8 GEMM: y = (x @ w.T) * weight_scale → 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]
out = torch.empty(M, N, dtype=torch.bfloat16, device=x.device)
_run_kernel(x, self.weight, self.weight_scale, out)
return out
# ---------------------------------------------------------------------------
# Entry points — identical to reference
# ---------------------------------------------------------------------------
M = 4096
N = 4096
K = 4096
def get_inputs():
x = (torch.rand(M, K) * 8 - 4).to(torch.float8_e4m3fn)
return [x]
def get_init_inputs():
return [M, N, K]
The solution is complete. Here's a summary of what was done:
## Solution: FP8 GEMM for RTX PRO 6000 (Blackwell SM120)
**Approach**: Triton kernel with 2D grid launch, using genuine fp8 tensor-core `tl.dot` operations.
### Key Design Decisions
1. **Real fp8×fp8 tensor cores**: Uses `tl.dot(a, b, acc)` with fp8_e4m3 inputs accumulating in fp32 — this maps to `mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32` PTX on Blackwell SM120. No upcasting to bf16.
2. **K-dimension padding**: The fp8 MMA instruction requires K to be a multiple of 32 for peak throughput. Triton generates slow fallback code when masked fp8 loads have K tails that aren't 32-aligned. The solution pads input tensors to multiples of BLOCK_K (64/128) with fp8 zeros so every inner-loop iteration loads a full, unmasked tile.
3. **Shape-adaptive tile sizes**:
- Large shapes (M > 64): `128×128×64` — fits 3-stage software pipelining in 128KB shared memory
- Skinny M (M ≤ 64): `64×128×256` — amortizes memory latency with wider K tiles
### Performance
| Shape | Dimensions | TFLOPS | Peak Fraction | Notes |
|-------|-----------|--------|---------------|-------|
| 0 | 4096×4096×4096 | 597 | 59.7% | Square aligned |
| 1 | 4096×4096×4127 | 483 | 48.3% | K=4127, padded to 4160 |
| 2 | 32×8192×8192 | 69.5 / 1098 GB/s | 61% BW | Decode-style, memory-bound |
| 3 | 4096×14336×4096 | 652 | 65.2% | Llama3 up-proj |
**Geometric mean peak fraction: 0.338** — well above the 0.1 threshold, and ~2× the bf16-upcast ceiling (~500 TFLOPS peak for bf16 vs 1000 for fp8).
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_163128_deepseek-claude_deepseek-v4-pro_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=2026-06-14T23:07:09.184495+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T23:07:09.395404+00:00 elapsed_s=0.211 ms=0.228336
shape=0 variant=solution tflops=601.915 gbps=293.904 ms=0.228
shape=0 solution_peak_fraction=0.6019
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T23:07:09.913712+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T23:07:09.930960+00:00 elapsed_s=0.017 ms=0.286432
shape=1 variant=solution tflops=483.463 gbps=235.179 ms=0.286
shape=1 solution_peak_fraction=0.4835
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T23:07:11.791252+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T23:07:11.797100+00:00 elapsed_s=0.006 ms=0.061456
shape=2 variant=solution tflops=69.887 gbps=1104.779 ms=0.061
shape=2 solution_peak_fraction=0.0699
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T23:07:13.486865+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T23:07:13.518758+00:00 elapsed_s=0.032 ms=0.735328
shape=3 variant=solution tflops=654.179 gbps=262.384 ms=0.735
shape=3 solution_peak_fraction=0.6542
peak_fraction: 0.3396
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_163128_deepseek-claude_deepseek-v4-pro_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_163128_deepseek-claude_deepseek-v4-pro_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_163128_deepseek-claude_deepseek-v4-pro_01_fp8_gemm/repo/.venv
Creating virtual environment at: /home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_163128_deepseek-claude_deepseek-v4-pro_01_fp8_gemm/repo/.venv
Building kernelbench-hard @ file:///home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_163128_deepseek-claude_deepseek-v4-pro_01_fp8_gemm/repo
Built kernelbench-hard @ file:///home/infatoshi/kernelbench.com/benchmarks/hard/outputs/runs/20260614_163128_deepseek-claude_deepseek-v4-pro_01_fp8_gemm/repo
Installed 56 packages in 80ms
PASS
{
"run_id": "20260614_163128_deepseek-claude_deepseek-v4-pro_01_fp8_gemm",
"run_group": "",
"problem": "01_fp8_gemm",
"harness": "deepseek-claude",
"model": "deepseek-v4-pro",
"reasoning_effort": "",
"started_at": "2026-06-14T16:31:28-06:00",
"harness_finished_at": "2026-06-14T17:06:59-06:00",
"finished_at": "2026-06-14T17:07:13-06:00",
"start_epoch": 1781476288,
"harness_end_epoch": 1781478419,
"end_epoch": 1781478433,
"has_solution": true,
"correct": true,
"failure_reason": "pass",
"retryable_infra_failure": false,
"minimum_useful_output_tokens": 5000,
"peak_fraction": 0.3396,
"template_mutated": false,
"elapsed_seconds": 2131,
"total_elapsed_seconds": 2145,
"check_elapsed_seconds": 9,
"benchmark_elapsed_seconds": 5,
"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": null,
"usage": {"input_tokens": null, "output_tokens": null, "cache_read_tokens": null, "cache_creation_tokens": null, "reasoning_tokens": null, "total_cost_usd": null}
}
timeline (269 events)
system — init
session start cwd=/workspace/problems/01_fp8_gemm model=deepseek-v4-pro permissions=bypassPermissions
assistant
reasoning (486 chars)
Let me start by understanding the problem:
1. We need to implement an FP8 GEMM (fp8_e4m3 x fp8_e4m3) with tensor cores
2. The reference implementation is in `reference.py`
3. Our solution goes in `solution.py`
4. We need to match the interface: `Model`, `get_inputs`, `get_init_inputs`
5. The kernel must use real fp8 tensor-core MMA operations
6. We need to handle various shapes including non-multiples of 128
Let me first read the reference implementation and understand the setup.
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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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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)
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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)
assistant
reasoning (144 chars)
Let me read the shapes file and problem.yaml to understand all requirements, and also check what hardware specs and peak TFLOPS we're targeting.
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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
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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 (76 chars)
PROMPT.txt
benchmark.py
check.py
problem.yaml
reference.py
shapes.py
sota.py
assistant
reasoning (745 chars)
Let me understand the environment better. I need to check what's available — CUDA version, Triton, CUTLASS, hardware specs, etc.
The key requirements:
1. Real fp8 x fp8 tensor-core MMA (fp8 inputs, fp32 accumulate)
2. Per-channel scale dequant
3. Handle shapes: (4096,4096,4096), (4096,4096,4127), (32,8192,8192), (4096,14336,4096)
4. Must match reference within 0.2 abs/rel tolerance
5. Must use solution.py with Model, get_inputs, get_init_inputs interface
6. No torch._scaled_mm or torch.ops.aten._scaled_mm
For Blackwell (SM120), I should use:
- PTX `mma.sync` with `.e4m3` for fp8 tensor core operations
- Or Triton with `tl.dot` on fp8
- Or CUTLASS 3.x with `cutlass::arch::Sm120`
Let me check what's available in the environment first.
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Sun Jun 14 22:31:38 2026
+-----------------------------------------------------------------------------------------+
| NVIDIA-SMI 610.43.02 KMD Version: 610.43.02 CUDA UMD Version: 13.3 |
+-----------------------------------------+------------------------+----------------------+
| GPU Name Persistence-M | Bus-Id Disp.A | Volatile Uncorr. ECC |
| Fan Temp Perf Pwr:Usage/Cap | Memory-Usage | GPU-Util Compute M. |
| | | MIG M. |
|=========================================+========================+======================|
| 0 NVIDIA RTX PRO 6000 Blac... On | 00000000:01:00.0 Off | Off |
| 44% 59C P8 15W / 600W | 40649MiB / 97887MiB | 0% Default |
| | | N/A |
+-----------------------------------------+------------------------+----------------------+
+-----------------------------------------------------------------------------------------+
| Processes: |
| GPU GI CI PID Type Process name GPU Memory |
| ID ID Usage |
|======================================================================================
... (188 more chars)
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1 """SOTA reference for FP8 GEMM: flashinfer.gemm.fp8_gemm.
2
3 If flashinfer is not installed or the SM120 path isn't supported, this falls
4 back to torch._scaled_mm which is the cuBLAS FP8 path. The benchmark treats
5 whichever succeeds as the SOTA reference line.
6
7 Agents are FORBIDDEN from using torch._scaled_mm in their solution (see
8 problem.yaml.forbidden). This file is only for the benchmark's reference line.
9 """
10 from __future__ import annotations
11
12 import torch
13
14
15 def _try_flashinfer(x: torch.Tensor, w: torch.Tensor) -> torch.Tensor | None:
16 try:
17 import flashinfer # noqa: F401
18 # Note: flashinfer's FP8 GEMM API surface may differ; adapt if needed.
19 # Placeholder call — replace with the actual flashinfer entry point
20 # once validated on SM120.
21 return None
22 except ImportError:
23 return None
24
25
26 def _scaled_mm(x: torch.Tensor, w: torch.Tensor) -> torch.Tensor:
27 # torch._scaled_mm wants per-tensor scales. Use unit scales for the reference.
28 scale_a = torch.tensor(1.0, device=x.device)
29 scale_b = torch.tensor(1.0, device=x.device)
30 out = torch._scaled_mm(
31 x,
32 w.T,
33 scale_a=scale_a,
34 scale_b=scale_b,
35 out_dtype=torch.bfloat16,
36 )
37 return out if not isinstance(out, tuple) else out[0]
38
39
40 def sota_forward(x: torch.Tensor, w: torch.Tensor) -> torch.Tensor:
41 """Best-available
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stdout (243 chars)
2.8.0a0+5228986c39.nv25.06
12.9
_CudaDeviceProperties(name='NVIDIA RTX PRO 6000 Blackwell Workstation Edition', major=12, minor=0, total_memory=97288MB, multi_processor_count=188, uuid=d594fb7a-abcb-bad5-1fc4-675b478a47df, L2_cache_size=128MB)
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reasoning (2737 chars)
Okay, so we have:
- NVIDIA RTX PRO 6000 Blackwell (SM120, compute capability 12.0)
- CUDA 12.9
- PyTorch 2.8.0a0 (nightly, NVIDIA build)
- 188 SMs, 97GB VRAM, 128MB L2 cache
SM120 (Blackwell) supports:
- `mma.sync.aligned.m16n8k32` for fp8 (e4m3) tensor core operations
- The key PTX instruction for fp8 on Blackwell is `mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32`
Wait, let me think about SM120 more carefully. Blackwell (SM100/SM120) supports:
- FP8 MMA: `mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32` — this does A (fp8) × B (fp8) → accumulate in f32
- Shape is M=16, N=8, K=32 per warp. This is a warp-level instruction.
- On Blackwell, each warp executes one MMA instruction per cycle.
For the RTX PRO 6000:
- 188 SMs
- Each SM has 4 warp schedulers (or more?)
- FP8 peak: need to compute
Let me compute the theoretical peak. On Blackwell:
- Each SM has a certain number of tensor core throughput
- For SM120 (RTX PRO 6000), FP8 peak TFLOPS should be around 1000+ TFLOPS
Let me think about the approach. I have several options:
1. **PTX inline assembly** (`asm volatile` with `mma.sync`) — gives full control
2. **Triton** — `tl.dot` supports fp8 on Blackwell
3. **CUTLASS 3.x** — the canonical library
Let me first check what's available and try the simplest approach first. Given the complexity, let me try a Triton-based approach since it's easier to iterate on.
Actually, wait — let me check if Triton is installed and supports fp8 dot on Blackwell.
Actually, the key challenge is:
- The weight is (N, K) fp8, stored as is
- The activation x is (M, K) fp8, passed in
- We need: y = (x @ w.T) * weight_scale
In fp8 tensor core, the MMA instruction does: D = A * B + C, where A and B are fp8, C and D are fp32.
So the computation is:
1. Load fp8 tiles from x (M, K) and w (N, K)
2. Perform mma: partial_sum += fp8_mma(tile_x, tile_w^T)
3. Multiply by weight_scale
For maximum performance on Blackwell, I should aim for:
- 128-byte aligned global loads (for fp8, that's 128 elements)
- Use of TMA (Tensor Memory Access) if possible
- Efficient shared memory usage
- Handle tail cases (K not multiple of tile size)
Let me think about what approach to use. Let me try Triton first since it's easier to iterate quickly, and if performance isn't good enough, I'll switch to raw PTX/CUDA.
Actually, let me think about this more carefully. For maximum performance:
- Blackwell tensor cores do m16n8k32 per warp instruction
- Each warp in a warpgroup (4 warps) can execute together
- For better occupancy, we want to tile across M and N dimensions
Let me check what Triton supports for fp8.
Actually, let me start by checking what's available in the environment — Triton version, CUTLASS availability, etc.
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stdout (574 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 879ms
Triton: N/A
triton: 3.6.0
triton.language: True
tool
stderr (181 chars)
Exit code 1
Traceback (most recent call last):
File "<string>", line 6, in <module>
NotImplementedError: "normal_kernel_cuda" not implemented for 'Float8_e4m3fn'
fp8 support: True
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reasoning (65 chars)
Let me check Triton's fp8 dot support on this version and system.
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stdout (1953 chars) — TRUNCATED
float8 types: ['PropagateNan', 'TRITON_MAX_TENSOR_NUMEL', '__all__', '__builtins__', '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__path__', '__spec__', 'abs', 'add', 'advance', 'arange', 'argmax', 'argmin', 'associative_scan', 'assume', 'atomic_add', 'atomic_and', 'atomic_cas', 'atomic_max', 'atomic_min', 'atomic_or', 'atomic_xchg', 'atomic_xor', 'bfloat16', 'bitonic_merge', 'block_type', 'broadcast', 'broadcast_to', 'cast', 'cat', 'cdiv', 'ceil', 'clamp', 'condition', 'const', 'constexpr', 'constexpr_type', 'core', 'cos', 'cumprod', 'cumsum', 'debug_barrier', 'device_assert', 'device_print', 'div_rn', 'dot', 'dot_scaled', 'dtype', 'erf', 'exp', 'exp2', 'expand_dims', 'extra', 'fdiv', 'flip', 'float16', 'float32', 'float64', 'float8e4b15', 'float8e4b8', 'float8e4nv', 'float8e5', 'float8e5b16', 'floor', 'fma', 'full', 'gather', 'histogram', 'inline_asm_elementwise', 'int1', 'int16', 'int32', 'int64', 'int8', 'interleave', 'join', 'load', 'load_tensor_descriptor', 'log', 'log2', 'make_block_ptr', 'make_tensor_descriptor', 'map_elementwise', 'math', 'max', 'max_constancy', 'max_contiguous', 'maximum', 'min', 'minimum', 'mul', 'multiple_of', 'num_programs', 'pair_uniform_to_normal', 'permute', 'philox', 'philox_impl', 'pi32_t', 'pointer_type', 'program_id', 'rand', 'rand4x', 'randint', 'randint4x', 'randn', 'randn4x', 'random', 'range', 'ravel', 'reduce', 'reduce_or', 'reshape', 'rsqrt', 'sigmoid', 'sin', 'slice', 'softmax', 'sort', 'split', 'sq
... (453 more chars)
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stderr (1481 chars)
Exit code 1
Traceback (most recent call last):
File "/workspace/.venv/lib/python3.11/site-packages/triton/runtime/jit.py", line 461, in __init__
self.raw_src, self.starting_line_number = inspect.getsourcelines(fn)
^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/uv-cache/python/cpython-3.11.15-linux-x86_64-gnu/lib/python3.11/inspect.py", line 1240, in getsourcelines
lines, lnum = findsource(object)
^^^^^^^^^^^^^^^^^^
File "/uv-cache/python/cpython-3.11.15-linux-x86_64-gnu/lib/python3.11/inspect.py", line 1077, in findsource
raise OSError('could not get source code')
OSError: could not get source code
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "<string>", line 7, in <module>
File "/workspace/.venv/lib/python3.11/site-packages/triton/runtime/jit.py", line 935, in jit
return decorator(fn)
^^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/triton/runtime/jit.py", line 923, in decorator
return JITFunction(
^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/triton/runtime/jit.py", line 756, in __init__
super().__init__(fn)
File "/workspace/.venv/lib/python3.11/site-packages/triton/runtime/jit.py", line 463, in __init__
raise ValueError("@jit functions should be defined in a Python file") from e
ValueError: @jit functions should be defined in a Python file
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reasoning (2678 chars)
Good, Triton is available (3.6.0). Let me note the fp8 types:
- `float8e4m15` and `float8e4b8` — these are likely different fp8 formats. `float8e4b8` is probably for `float8_e4m3fn` (8-bit with 4 exponent bits, 3 mantissa bits).
- `float8e5` and `float8e5b16` — these are `float8_e5m2` variants.
So in Triton, I should use `tl.float8e4b8` for fp8_e4m3fn.
Now let me plan the solution. I'll use a Triton kernel with:
1. Split the M, N dimensions across programs/thread blocks
2. Each block loads a tile of x (fp8, M×K) and w (fp8, N×K)
3. Performs dot product accumulation with `tl.dot` in fp8
4. Applies the per-channel scale
Let me first write a solution.py and test it. Let me also check what `tl.dot` supports for these types on Blackwell.
Let me think about the approach more carefully.
For the Triton kernel:
- Block size: BM × BN tile, with BK reduction dimension
- Load fp8 tiles from global memory
- Use `tl.dot` with fp8 inputs
- Accumulate in fp32
- Apply weight_scale at the end
For Blackwell SM120 with `mma.sync.aligned.m16n8k32`, the hardware MMA shape is M=16, N=8, K=32. Triton will handle the mapping.
Key considerations:
1. Global memory access pattern: coalesced loads (128-bit or 32-byte aligned)
2. Shared memory: use it for staging
3. Tile sizes: pick BM, BN, BK that are multiples of MMA shapes (M=16, N=8, K=32) for good utilization
4. For the tail K (e.g., K=4127 which is not multiple of 128), need to handle it properly with predication
Let me write a first pass at the solution.
Actually, let me first think about tile sizes. For Blackwell:
- Each SM has 128KB L1/shared memory
- We want good occupancy
- MMA tile: m16n8k32
Common tile choices:
- BM=128, BN=128, BK=128 — good for large matrices
- BM=64, BN=64, BK=128 — more occupancy
For the core loop:
```python
for k in range(0, K, BK):
a = tl.load(a_ptrs, mask=..., other=0.0)
b = tl.load(b_ptrs, mask=..., other=0.0)
acc = tl.dot(a, b, acc)
```
Wait, for fp8 dot, I need to be careful. `tl.dot` with fp8 on Blackwell should work with `tl.float8e4b8` type. Let me check the Triton docs/conventions.
In Triton 3.x:
- `tl.float8e4b8` is the 8-bit float with 4 exponent bits (not the NV variant)
- `tl.float8e4nv` is the NVIDIA variant
Actually, in PyTorch, `torch.float8_e4m3fn` is the standard format. Let me check what Triton maps this to.
Let me just write the kernel and test it. The key issue will be getting the types right for `tl.dot`.
Let me start with a working solution and iterate.
Here's my plan:
1. Write a Triton kernel for fp8 GEMM
2. Handle the weight_scale multiplication
3. Test with check.py
4. Profile and optimize
Let me write the first version.
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stdout (89 chars)
fp8_e4m3fn: torch.float8_e4m3fn itemsize: 1
tl.float8e4b8: fp8e4b8
tl.float8e4nv: fp8e4nv
tool
stdout (1778 chars) — TRUNCATED
Help on function dot in module triton.language.core:
dot(input, other, acc=None, input_precision=None, allow_tf32=None, max_num_imprecise_acc=None, out_dtype=triton.language.float32, _semantic=None)
Returns the matrix product of two blocks.
The two blocks must both be two-dimensional or three-dimensional and have compatible inner dimensions.
For three-dimensional blocks, `tl.dot` performs the batched matrix product,
where the first dimension of each block represents the batch dimension.
:param input: The first tensor to be multiplied.
:type input: 2D or 3D tensor of scalar-type in {:code:`int8`, :code:`float8_e5m2`, :code:`float16`, :code:`bfloat16`, :code:`float32`}
:param other: The second tensor to be multiplied.
:type other: 2D or 3D tensor of scalar-type in {:code:`int8`, :code:`float8_e5m2`, :code:`float16`, :code:`bfloat16`, :code:`float32`}
:param acc: The accumulator tensor. If not None, the result is added to this tensor.
:type acc: 2D or 3D tensor of scalar-type in {:code:`float16`, :code:`float32`, :code:`int32`}
:param input_precision: How to exercise the Tensor Cores for f32 x f32. If
the device does not have Tensor Cores or the inputs are not of dtype f32,
this option is ignored. For devices that do have tensor cores, the
default precision is tf32.
:type input_precision: string. Available options for nvidia: :code:`"tf32"`, :code:`"tf32x3"`, :code:`"ieee"`. Default: :code:`"tf32"`. Ava
... (278 more chars)
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reasoning (842 chars)
Interesting — `tl.dot` documentation says input types are `int8, float8_e5m2, float16, bfloat16, float32`. It mentions `float8_e5m2` but NOT `float8_e4m3`. Wait, let me re-read: "scalar-type in {:code:`int8`, :code:`float8_e5m2`, :code:`float16`, :code:`bfloat16`, :code:`float32`}".
Hmm, this suggests that Triton's `tl.dot` may only support `float8_e5m2` directly and not `float8_e4m3`. But Blackwell hardware supports e4m3. Let me check more carefully.
Actually, wait. Let me check the Triton version more carefully. Triton 3.6.0 should support fp8_e4m3 on Blackwell. Let me look at what types are actually accepted.
Also, `float8_e5m2` in Triton terminology might be the general fp8 family name, and it might accept both e5m2 and e4m3. Or maybe I'm reading the old docs and Triton 3.6 has broader support.
Let me test it empirically.
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stdout (32 chars)
max diff: 48.53716278076172
FAIL
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reasoning (3221 chars)
OK, that was bf16 x bf16 so it should have worked. Let me check — the issue is the w is (N, K) and I'm using w in the dot. The dot computes x @ w^T implicitly. But wait, I'm loading b from w with (offs_k, offs_n) mapping to (K, N), and then doing `tl.dot(a, b, acc)`.
Actually, `tl.dot` computes C = A @ B where A is (M, K) and B is (K, N). If `a` is (BLOCK_M, BLOCK_K) from x (M, K) and `b` is (BLOCK_K, BLOCK_N) from w.T, that would be x @ w.T. But w is stored as (N, K), so w.T would be (K, N). My loading is wrong — I'm loading w as if it's (K, N) but it's actually (N, K). Let me fix: I should load b from w as w[k, n] which is stride_bk = w.stride(0) (the outer stride, N dimension) and stride_bn = w.stride(1) (the inner stride, K dimension).
Wait no, w is (N, K), so:
- To get w[n, k]: offset = n * stride(0) + k * stride(1) = n * K + k * 1
- For b, I want (K, N) = w.T, so b[k, n] = w[n, k]
- So b_ptrs should go: offs_k[:, None] * w.stride(1) + offs_n[None, :] * w.stride(0)
But I had `b_ptrs = b_ptr + offs_k[:, None] * stride_bk + offs_n[None, :] * stride_bn` where stride_bk = w.stride(0) and stride_bn = w.stride(1). That means:
- b[k, n] = b_ptr + k * w.stride(0) + n * w.stride(1) = w[k, n]
But w is (N, K), so w.stride(0) = K and w.stride(1) = 1. So:
- b[k, n] = w[k, n] — but w has N rows and K cols, so accessing row k (up to K) when K might be larger than N...
Actually wait, for this test case M=256, N=128, K=64. w.stride(0) = 64, w.stride(1) = 1. So b[k, n] = w_ptr + k * 64 + n. For k < 64 and n < 128, this accesses valid memory but in a weird layout. It's loading w transposed effectively.
Hmm, the error is large. Let me think about this more carefully.
For `tl.dot(a, b, acc)`:
- a has shape (BLOCK_M, BLOCK_K) — rows vary in M, cols vary in K
- b has shape (BLOCK_K, BLOCK_N) — rows vary in K, cols vary in N
- Result: (BLOCK_M, BLOCK_N) where result[m, n] = sum_k a[m, k] * b[k, n]
So `b[k, n]` should be `weight[n, k]` (the weight at row n, column k).
- weight[n, k] = w_ptr + n * w.stride(0) + k * w.stride(1)
In my code, for b:
- b_ptrs = b_ptr + offs_k[:, None] * stride_bk + offs_n[None, :] * stride_bn
- With stride_bk = w.stride(0) and stride_bn = w.stride(1)
- This gives b[k, n] = w_ptr + k * w.stride(0) + n * w.stride(1)
But we need b[k, n] = w_ptr + n * w.stride(0) + k * w.stride(1) = weight[n, k].
So the strides are swapped! I need:
- b_ptrs = b_ptr + offs_n[None, :] * stride_bn_as_n + offs_k[:, None] * stride_bk_as_k
Where stride for the N dimension should be w.stride(0) and stride for the K dimension should be w.stride(1).
So: b_ptrs = b_ptr + offs_n[None, :] * w_stride_0 + offs_k[:, None] * w_stride_1
But actually, I can just pass w.T (contiguous) as the b matrix. Then b is (K, N) and I can load it directly. That's cleaner.
Actually wait, for the fp8 case I can't transpose in fp8 directly. But I can pass the strides correctly. Let me just fix the bug and test with bf16 first, then move to fp8.
Let me also reconsider: I should just use `w.T.contiguous()` for the b input since the kernel needs b to be (K, N) layout for the dot product. Actually, for fp8 that would require copying. Better to just use the correct strides.
Let me fix and retest.
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stdout (33 chars)
max diff: 3.814697265625e-06
PASS
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reasoning (125 chars)
Good, the bf16 kernel works. Now let me test with fp8 inputs. The key question is whether `tl.dot` supports `fp8e4b8` inputs.
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stdout (56 chars)
max diff: 0.015625
mean diff: 0.0005804875981993973
PASS
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reasoning (2346 chars)
The fp8 Triton kernel works correctly! The max diff is 0.015625 which is well within the 0.2 tolerance. Now I need to:
1. Write a proper `solution.py` with the kernel
2. Optimize tile sizes for the RTX PRO 6000
3. Handle all the required shapes (including K=4127, M=32)
4. Profile and iterate
Let me think about the tile sizes. For Blackwell (SM120):
- `mma.sync.aligned.m16n8k32` for fp8 — the hardware MMA tile is M=16, N=8, K=32
- Each warp has 32 threads, so 16×8 = 128 elements produced per MMA across 32 threads
- For optimal performance, we want the Triton block to be a multiple of these MMA dims
Good tile sizes for fp8 on Blackwell:
- BLOCK_M: multiple of 16 (e.g., 64, 128, 256)
- BLOCK_N: multiple of 8 (e.g., 64, 128, 256)
- BLOCK_K: multiple of 32 (e.g., 64, 128, 256)
For large matrices (M=4096, N=4096, K=4096):
- We want to maximize throughput
- Larger tiles = more compute per load, but lower occupancy
- A good starting point: BLOCK_M=128, BLOCK_N=128, BLOCK_K=128
Wait, but Triton maps block sizes to MMA instructions. Let me think about what tile sizes are supported.
For the `mma.sync.aligned.m16n8k32` instruction, each MMA produces a 16×8 tile with K=32. Multiple MMAs can be combined by the compiler.
For a block of 128×128 with K=128:
- M direction: ceil(128/16) = 8 warps ("M-major" warp distribution or mixed)
- N direction: ceil(128/8) = 16 warps
- Total: 8 * 16 = 128 warps... that's way too many for one block. We need to reconsider.
Actually, Triton handles this by scheduling across threads (warps) within a block. Each thread block has a certain number of warps (e.g., 4-16 warps). Each warp can issue one MMA per cycle.
Let me think about this differently. A typical Triton block size might be:
- BLOCK_M=64, BLOCK_N=64: this produces 64×64 = 4096 elements
- With 4 warps per block (128 threads), each warp handles multiple MMAs
- Number of MMAs: ceil(64/16) * ceil(64/8) = 4 * 8 = 32 MMAs per block per K-tile
Actually, I think Triton uses warp-specialization for MMA. Let me just pick reasonable tile sizes and iterate based on profiling.
For now, let me write a complete solution.py and test it. Key considerations:
1. Handle all shapes
2. Correct model interface (register `weight` as fp8, `weight_scale` as float32 buffers)
3. Apply per-channel scale
4. Output bf16
Let me write the solution.
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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 (37 chars)
Let me test this with check.py first.
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reasoning (82 chars)
The correctness check passes. Now let me run the benchmark to see the performance.
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stdout (1310 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T22:35:03.821135+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T22:35:04.032049+00:00 elapsed_s=0.211 ms=0.234944
shape=0 variant=solution tflops=584.986 gbps=285.638 ms=0.235
shape=0 solution_peak_fraction=0.5850
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T22:35:04.557751+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T22:35:06.143727+00:00 elapsed_s=1.586 ms=39.503168
shape=1 variant=solution tflops=3.506 gbps=1.705 ms=39.503
shape=1 solution_peak_fraction=0.0035
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T22:35:08.009902+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T22:35:08.015538+00:00 elapsed_s=0.006 ms=0.088128
shape=2 variant=solution tflops=48.736 gbps=770.417 ms=0.088
shape=2 solution_peak_fraction=0.0487
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T22:35:09.689636+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T22:35:09.722763+00:00 elapsed_s=0.033 ms=0.754528
shape=3 variant=solution tflops=637.533 gbps=255.707 ms=0.755
shape=3 solution_peak_fraction=0.6375
peak_fraction: 0.0893
RESULT: LOW
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reasoning (4620 chars)
Let me analyze the results:
1. **Shape 0 (4096×4096×4096)**: 584.99 TFLOPS, 0.585 peak fraction — pretty good for first try
2. **Shape 1 (4096×4096×4127)**: 3.506 TFLOPS — TERRIBLE! Something is very wrong
3. **Shape 2 (32×8192×8192)**: 48.736 TFLOPS, 770 GB/s — memory-bound, 0.049 peak fraction
4. **Shape 3 (4096×14336×4096)**: 637.53 TFLOPS, 0.638 peak fraction — good
Shape 1 is clearly broken - 39.5ms for a matrix that's almost the same size as shape 0 (which takes 0.235ms). Something is causing a massive slowdown for the K=4127 case.
Let me think about what's happening. K=4127 is not a multiple of 128. My BLOCK_K=128 means:
- 4127 / 128 = 32 remainder 31
- So I have 33 iterations with 32 full tiles and 1 tail tile of K=31
Wait, 0.235ms for shape 0 but 39.5ms for shape 1? That's 168x slower! This suggests something pathological. Let me check if there's a triton autotuning compilation issue, or maybe the kernel is being recompiled for this shape.
Actually, the 39.5ms might include compilation time. The benchmark might only run a few iterations and the first call includes JIT compilation. But shape 0 was fast... Let me look at the benchmark more carefully.
Actually, looking at the benchmark output more carefully:
- Shape 0: elapsed_s=0.211, ms=0.235 — total time was 0.211s which includes warmup, then the timed portion was 0.235ms
- Shape 1: elapsed_s=1.586, ms=39.503 — the TIMED portion is 39.5ms!
So the kernel itself is taking 39.5ms for shape 1! That's way too slow for a 4096×4096×4127 GEMM. Something is very wrong.
Could it be that the kernel is falling back to a software path when K is not a multiple of 128? That seems unlikely with Triton.
Let me think about what's different between shape 0 and shape 1:
- Shape 0: K=4096, which is 32 * 128 (exact multiple)
- Shape 1: K=4127, which is 32 * 128 + 31
The difference is the tail tile of 31 elements. Could the masked load cause a dramatic slowdown? That seems unlikely.
Wait, actually, I bet the issue is that Triton is recompiling the kernel for shape 1 (with a different grid), and the compilation time is being included in the measurement. Let me check the benchmark code...
Looking at benchmark.py line 81-87:
```python
ms_sol = time_variant(
sol_model, inputs, ...,
iters=num_perf_trials,
)
```
With 30 trials, the first call might include compilation but subsequent calls should be fast. Let me check `time_variant` to understand what it does.
Actually wait, re-reading the output:
```
shape=1 variant=solution tflops=3.506 gbps=1.705 ms=39.503
```
39.5ms for a 4096×4096×4127 GEMM — that's roughly 2 * 4096 * 4096 * 4127 / 0.0395 = 3.5 TFLOPS. This is terrible.
Hmm, maybe the issue is with the triton kernel being recompiled for each shape and the benchmark includes compilation time. Let me check `time_variant`.
Actually, let me look at this differently. The `elapsed_s=1.586` for shape 1 is the total elapsed time, and `ms=39.503` is the per-trial time. If there were 30 trials and total time was 1.586s, that's about 53ms per trial including overheads. But 39.5ms for the computed time... that doesn't add up.
Actually wait: `elapsed_s=1.586` seconds total, and `ms=39.503` — if ms is per iteration, then 30 * 39.5ms = 1185ms for the trials alone, plus warmup/overhead bringing it to 1586ms. That seems consistent.
So the kernel IS taking 39.5ms per call for shape 1. Let me investigate why.
One possibility: for K=4127 with BLOCK_K=128, the tail iteration has only 31 elements. The `tl.dot` with masked loads might be causing issues — perhaps the dot requires a full tile and the mask causes it to fall back?
Actually, I think the issue might be different. Let me re-read the kernel... hmm, I see the problem. My `k_mask` handling:
```python
a_mask = offs_k[None, :] < k_remaining
```
But `offs_k` shape is `(BLOCK_K,)`. So `offs_k[None, :]` is `(1, BLOCK_K)`. And `a_ptrs` is `(BLOCK_M, BLOCK_K)`. So `a_mask` is `(1, BLOCK_K)` and should broadcast correctly against `a_ptrs` shape `(BLOCK_M, BLOCK_K)`.
For loading, this should be fine. The issue might be that when K is not divisible by BLOCK_K, triton recompiles with different parameters.
Actually, wait. Let me reconsider. The benchmark calls `time_variant` which probably does a warmup then times the calls. If the kernel doesn't change between shapes 0 and 1 (same block sizes), then there should be no recompilation. But maybe the grid is different, and that triggers something.
Let me look at the actual time_variant function to understand the timing.
Actually, let me just profile the kernel for shape 1 to see what's happening.
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Let me investigate the shape 1 (K=4127) performance issue.
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stdout (63 chars)
Average time: 39.693 ms
Reference (bf16) average time: 0.905 ms
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reasoning (3519 chars)
OK so the kernel really is taking 39.7ms for shape 1 (K=4127), while the bf16 reference takes only 0.9ms. Something is catastrophically wrong.
Let me think about what could cause this. The main difference is K=4127 vs K=4096. With BLOCK_K=128:
- K=4096: 32 iterations, all full
- K=4127: 33 iterations, 32 full + 1 tail of 31
The tail iteration has a load with mask `offs_k[None, :] < 31`. This should be fine...
Wait, could it be that Triton is triggering autotuning for the tail case? Or could there be an issue with the fp8 dot instruction requiring aligned K dimensions?
Actually, I bet the problem is that `tl.dot` with fp8 inputs requires the input to be a specific shape that's a multiple of the MMA instruction's K dimension. The MMA instruction `mma.sync.aligned.m16n8k32` requires K to be a multiple of 32. With BLOCK_K=128 and a tail of 31, the dot input would be (BLOCK_M, 31) x (31, BLOCK_N) — but the MMA can only handle K multiples of 32. Triton might be falling back to a software emulation path for the tail!
This would explain the massive slowdown: if every thread block is doing a software emulation for the tail iteration (K=31), that would be extremely slow.
The fix would be to ensure that the tail K dimension is padded to a multiple of 32 (the MMA K dimension). We need to load only valid elements but compute with a full tile.
Let me think about how to handle this:
1. When K is not evenly divisible by BLOCK_K, the last iteration has fewer than BLOCK_K elements
2. For fp8 MMA, we need K to be a multiple of 32
3. Solution: pad the K dimension to ensure the tail is still a multiple of 32, and only load valid elements (other=0.0 handles the padding)
But wait, in my kernel I load with `other=0.0` for masked elements, which should be fine. The issue is that `tl.dot` might not handle the case where the input dimensions aren't multiples of the MMA size.
Let me test this theory by using BLOCK_K values that are multiples of 32.
Actually, BLOCK_K=128 is already a multiple of 32. The issue is that on the tail iteration, the loaded tile has shape (BLOCK_M, k_remaining) where k_remaining=31, which is NOT a multiple of 32. The `tl.dot` with fp8 likely requires the inner dimension to be a multiple of the MMA's K=32.
So the solution is: on the tail iteration, we still load BLOCK_K elements (padding with 0 where out of bounds), and do the full dot product. This way the dot always sees a K dimension that's a multiple of 32.
Wait, that's what I'm already doing with `other=0.0` in the load... but the mask only allows `k_remaining` elements to be loaded. The dot product should still work because the other elements are 0.0.
Hmm, maybe the issue is different. Let me check if Triton is using a different code path for the masked dot.
Actually, let me try a different approach: always load a full tile of BLOCK_K elements (with padding via `other=0.0`), even on the last iteration. But I'm already doing that with mask and other...
Oh wait, I see. The issue might be more subtle. The `tl.dot` with fp8 might need the K dimension of the dot input to be exactly a compile-time constant. Let me check.
Actually, in my kernel, `a` and `b` are loaded with masks. When k_remaining < BLOCK_K, the shape of `a` is still `(BLOCK_M, BLOCK_K)` — the mask just determines which elements are loaded from memory vs set to `other`. So the tensor shapes should still be compile-time constants.
Let me take a different approach — let me verify my hypothesis by testing with different K values.
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stdout (189 chars)
K= 4096: 0.030 ms, 283.3 TFLOPS
K= 4127: 2.335 ms, 3.7 TFLOPS
K= 4080: 0.033 ms, 262.6 TFLOPS
K= 4064: 0.030 ms, 282.0 TFLOPS
K= 4032: 0.030 ms, 281.5 TFLOPS
K= 3968: 0.029 ms, 284.9 TFLOPS
assistant
reasoning (469 chars)
Interesting! The issue is specifically K=4127 which is `32*128 + 31` — a tail of 31 elements. K=4080 = 32*128 - 16 = 31*128 + 112, which is also not a multiple of 128.
Wait: K=4080 = 31 * 128 + 112. That has a tail of 112 which works fine.
K=4127 = 32 * 128 + 31. That has a tail of 31 which is broken.
Hmm wait, my calculation is: 4127 / 128 = 32 remainder 31. So the tail is 31 elements. This is the case that breaks.
Let me test more values to find the threshold:
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stdout (299 chars)
K= 4096 (tail= 0): 0.0303 ms
K= 4127 (tail= 31): 2.3366 ms
K= 4128 (tail= 32): 0.0311 ms
K= 4095 (tail=127): 2.2660 ms
K= 4094 (tail=126): 2.2675 ms
K= 4093 (tail=125): 2.2668 ms
K= 4065 (tail= 97): 2.2659 ms
K= 4064 (tail= 96): 0.0302 ms
K= 4033 (tail= 65): 2.2683 ms
K= 4032 (tail= 64): 0.0300 ms
assistant
reasoning (4216 chars)
Now I see the pattern clearly: when the tail is not a multiple of 32, the performance tanks (from 0.03ms to 2.27ms — about 75x slower). When the tail is a multiple of 32, it's fast.
This confirms my theory: the fp8 MMA instruction `mma.sync.aligned.m16n8k32` requires K to be a multiple of 32. When the tail K is not a multiple of 32, Triton falls back to a software path.
But wait — the MMA tile is `m16n8k32`, so the K-dimension of the dot product needs to be a multiple of 32. When I use BLOCK_K=128 and the tail is 31, the last iteration has K_remaining=31 which is not a multiple of 32.
The solution: on the tail iteration, still load BLOCK_K elements (with valid elements loaded normally and out-of-bounds elements set to 0 via mask), but ensure the K dimension presented to tl.dot is a multiple of 32.
One approach: change BLOCK_K to be a multiple of the MMA K tile (32), and always do full-tile loads. When we're on the tail, we load only the valid elements and pad with zeros. This is already what's happening with the mask and `other=0.0`. The issue is that Triton's dot implementation doesn't handle the reduced K dimension well.
Actually, looking at this again — the `tl.load` with mask and `other=0.0` should give us a full (BLOCK_M, BLOCK_K) tensor, with the tail elements being 0.0. So the dot product should still be `(BLOCK_M, BLOCK_K) @ (BLOCK_K, BLOCK_N)` = `(BLOCK_M, BLOCK_N)`. This should be fine in theory, but Triton might not be handling it correctly for fp8.
Let me try a different approach: manually handle the K dimension padding. Instead of loading with a mask, I'll pre-compute the valid range and clip the K loop bound to the actual K, handling the tail separately.
Actually, wait — let me re-think. Maybe the issue is that the mask causes the loaded tensor to have a non-compile-time-constant shape in the Triton IR. Let me try a different approach:
Instead of using a mask on the K dimension, I'll:
1. Load the full BLOCK_K tile unconditionally (no mask on K)
2. Handle the out-of-bounds by computing a separate pointer that's always valid
Or better yet, let me use `tl.make_block_ptr` with boundary checks, which handles this natively.
Actually, a simpler approach: compute the number of full tiles and handle the tail differently. For the tail, load a full tile but use the remainder to construct the properly masked tile.
Actually, the simplest fix: set K to be a multiple of BLOCK_K and BLOCK_K to be a multiple of 32. But K is a runtime value for the kernel shape. Wait — what if I round up K to the next multiple of some tile size for the loop bound?
Hmm, another approach is to use `K_ROUNDED = ((K + BLOCK_K - 1) // BLOCK_K) * BLOCK_K` for the loop bound, but still only load valid elements. But this won't work because the out-of-bounds access would be to invalid memory.
OK, the real solution: I need to ensure the K dimension of the `tl.dot` always has a shape that's a multiple of 32. The way to do this is:
1. Change the main loop to iterate over `K_padded = ((K + 31) // 32) * 32`, i.e., pad K to a multiple of 32.
2. On the last iteration, load a full BLOCK_K tile but with `other=0.0` for out-of-bounds elements.
Wait, that's exactly what I'm doing! The issue is that `tl.dot` with fp8 can't handle the tail when K is not a multiple of the MMA instruction's K dimension (32).
Let me try a completely different approach: instead of varying the K dimension on each iteration, always use the full BLOCK_K (which is a multiple of 32), and handle the out-of-bounds by [clamping the memory access](https://triton-lang.org/).
Actually, the problem might be more subtle. Let me look at what Triton generates. When `k_remaining < BLOCK_K`, the loaded tensor still has shape `(BLOCK_M, BLOCK_K)` because of the mask + other=0.0. But the dot product might be generating code that checks whether the K dimension is a full multiple of the MMA instruction's K, and if not, falling back.
Let me try another approach: use `tl.make_block_ptr` with boundary checks. Block pointers handle out-of-bounds access gracefully on Blackwell hardware.
Actually, let me try a much simpler approach: just pad the K loop by rounding K up to a multiple of 32 for the loop bound.
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stdout (94 chars)
K= 4096: 0.0303 ms
K= 4127: 2.4087 ms
K= 4095: 2.3361 ms
K= 4065: 2.3351 ms
K= 4033: 2.3355 ms
assistant
reasoning (1634 chars)
The padded K loop didn't help. The issue is deeper — it's specifically about the `tl.dot` call with fp8 not handling the tail K dimension. Let me inspect the generated code more carefully.
The problem is likely that the fp8 `tl.dot` is being compiled to use `mma.sync.aligned` PTX instructions, and these require the K dimension to be a multiple of 32. When the tail K iteration has `a` of shape `(BLOCK_M, BLOCK_K)` where BLOCK_K=128 (which IS a multiple of 32), the dot should still be `(128, 128) @ (128, 128)` = `(128, 128)`. But even though the mask causes some elements to be 0, the K dimension of the tensor is still 128...
Wait, but maybe the problem isn't the shape — maybe it's that the loaded fp8 values for the masked elements get a specific NaN or inf pattern that causes issues in the MMA. Or maybe Triton's compiler can't prove the K dimension alignment at compile time when there's a mask.
Let me try a completely different approach: don't use a mask on the K dimension at all. Instead, for the last tile, align the pointers to the last valid BLOCK_K segment and load the full tile, with the understanding that some elements will be garbage (but they should be zeroed out). Actually no, that would read invalid memory.
Better approach: use block pointers (`tl.make_block_ptr`) which handle boundary conditions natively on Blackwell hardware.
Actually, let me try yet another approach. What if I use `tl.dot` with `input_precision`? Or maybe the issue is that for fp8, Triton generates different code when the inputs have mask predicates.
Let me try using block pointers which natively handle boundary conditions.
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stdout (94 chars)
K= 4096: 0.0345 ms
K= 4127: 0.1319 ms
K= 4095: 0.1280 ms
K= 4065: 0.1283 ms
K= 4033: 0.1287 ms
assistant
reasoning (1779 chars)
Much better! The block pointer approach runs at 0.13ms for tail cases vs 0.035ms for the aligned case. That's about 3.8x slower, but 18x faster than the 2.3ms we were getting before. The 3.8x slowdown for the tail is likely due to the boundary checking overhead in the block pointers.
But 0.13ms is still much better than the previous approach. Let me check the performance for the actual shape (M=4096, N=4096, K=4127):
For M=4096, N=4096:
- M=1024: 0.13ms
- Scaling factor: (4096/1024)^2 = 16x more blocks
- Expected: ~2.08ms — that's still 5x better than the 39ms from before!
Wait, but the boundary_check applied to the block pointer is done per-load, and with block pointers the hardware handles it. The 3.8x slowdown might be because block pointers with boundary checking disable some optimization. Let me check if there's a way to avoid boundary checking for the K dimension specifically.
Actually, the slowdown might be from `tl.trans` which transposes the b matrix. Let me restructure to avoid the transpose.
Actually, for the fp8 case, I can just load b as `(BLOCK_K, BLOCK_N)` directly using the right strides in the block pointer, rather than loading as `(BLOCK_N, BLOCK_K)` and transposing.
Let me restructure:
- a_bp: (M, K) view, block shape (BLOCK_M, BLOCK_K) → loads (BLOCK_M, BLOCK_K)
- b_bp: Create a view of b as if it were (K, N), i.e., reinterpret the strides.
For b stored as (N, K), I want to load a (BLOCK_K, BLOCK_N) block from a logical (K, N) view. The block pointer needs:
- shape=(K, N)
- strides=(stride_bk, stride_bn) — where stride_bk = w.stride(1) = 1, stride_bn = w.stride(0) = K
- offsets=(k, pid_n * BLOCK_N)
- block_shape=(BLOCK_K, BLOCK_N)
This would give me b as (BLOCK_K, BLOCK_N) directly, no transpose needed.
Let me try this.
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stdout (189 chars)
K= 4096: 0.0344 ms, max_diff=8.000000
K= 4127: 0.1473 ms, max_diff=8.000000
K= 4095: 0.1418 ms, max_diff=8.000000
K= 4065: 0.1437 ms, max_diff=8.000000
K= 4033: 0.1444 ms, max_diff=8.000000
assistant
reasoning (6823 chars)
The max_diff of 8.0 is a problem — there's a correctness issue. The issue is that `tl.load(a_bp, boundary_check=(0, 1), padding_option='zero')` on fp8 data is producing zeros for out-of-bounds, but the zeros in fp8_e4m3 representation are actual 0.0 values. But I'm seeing errors of 8.0 which suggests the boundary check isn't working correctly, or there's a shape mismatch with the b matrix.
Wait, the issue might be with how I defined the b block pointer. b is stored as (N, K) in memory. I create a block pointer with shape=(K, N) and strides=(stride_bk, stride_bn). But:
- stride_bk = w.stride(1) = 1 (the inner dimension of w)
- stride_bn = w.stride(0) = K (the outer dimension of w)
So for the block pointer with shape=(K, N) and strides=(1, K):
- element [k, n] = base + k * 1 + n * K
But w[n, k] = base + n * K + k * 1. So:
- block_ptr[k, n] = base + k + n * K = w[n, k] ✓
That looks correct. But there might be an order issue. When I do `tl.advance(b_bp, (BLOCK_K, 0))`, I advance in the K dimension (first dimension). This should be: offsets become (BLOCK_K, pid_n * BLOCK_N). So the next block loads [k+BLOCK_K, n] = w[n, k+BLOCK_K]. But actually, I advance the K dimension so it should be: base + (k + BLOCK_K) * 1 + n * K = base + k + BLOCK_K + n*K = w[n, k+BLOCK_K]. That's correct for moving along the K dimension.
Hmm, the max_diff=8.0 suggests some elements are completely wrong. Let me debug the correctness.
Actually wait, it might be that `padding_option='zero'` produces literal bit-pattern zeros in fp8, which is 0.0. But the issue of diff=8.0 suggests something structurally wrong, not just a padding issue.
Let me try a simpler approach — avoid block pointers and go back to pointer arithmetic, but handle the tail by preloading into shared memory or by restructuring the K loop.
Actually, let me take a step back. The problem is specifically with fp8 dot product tails. Let me consider an alternative: pad the input matrices to be multiples of the BLOCK_K, then run the kernel. This wastes some computation but avoids the tail issue entirely.
Or better: pad K to a multiple of 32 (the MMA K dimension), since that's the true atomic unit. The padding adds at most 31 elements to K, which is negligible for large matrices.
Let me try this approach: pad K to a multiple of 32 by appending zero columns to both x and w.
Wait, but the user provides x and w is stored in the model. I can't easily pad the stored weight. Let me think differently.
What if I use a block pointer but with better boundary handling? Or what if I avoid boundary_check altogether and handle it with explicit masking in the load?
Actually, rethinking: the original kernel with masked loads was CORRECT (it passed check.py), but it was SLOW for non-multiple-of-32 K values. The block pointer approach was FASTER but INCORRECT.
Let me try another approach: use the block pointer for the fast path, but only use `boundary_check=(1,)` (check only the M/N boundaries, not K), and handle the K boundary differently.
The issue is: when K is not a multiple of 32, the fp8 MMA instruction can't handle it. So I need to ensure the K dimension presented to `tl.dot` is always a multiple of 32.
One approach: handle the tail K separately. Divide the K loop into:
1. Full BLOCK_K tiles for k = 0 to K - (K % min_tile)
2. One tail tile where I load only valid elements but pad to a multiple of some smaller granularity
But the fundamental issue is that `tl.dot` with fp8 can't handle K dimensions that aren't multiples of 32.
What if I use a different approach entirely? Let me use a CUDA kernel written with `torch.utils.cpp_extension.load_inline`. This gives me full control over the PTX and I can handle the tail explicitly.
Actually, let me try one more thing with Triton. What if I use `tl.dot_scaled` instead of `tl.dot`?
Or, let me try restructuring so that the K loop always uses full tiles, and the masking on the K dimension is done AFTER the dot product. For the tail iteration, I compute the dot product with a full tile (some elements are from out-of-bounds memory), and then fix up the result.
Actually wait — that's not possible because we can't read out-of-bounds memory safely.
OK here's another idea: what if I create a "safe" area in memory for the tail? I could allocate a padded version of x and w with extra zero columns. But this has overhead.
Let me try yet another approach: detect if K is not a multiple of 32, and if so, use a different kernel or different BLOCK_K that makes the tail a multiple of 32.
Actually, the simplest fix: choose BLOCK_K values based on K. For K=4127, I could use BLOCK_K=32 so every iteration is a multiple of 32. But that would be very inefficient.
Or: use BLOCK_K that divides K evenly or makes the remainder a multiple of 32. For K=4127:
- 4127 = 128 * 32 + 31 — tail of 31
- 4127 = 96 * 42 + 95 — doesn't help
- 4127 = 64 * 64 + 31 — tail of 31
- 4127 = 32 * 128 + 31 — tail of 31
So no matter what BLOCK_K I use, the remainder of K % 32 is always 31 (since 4127 = 128*32 + 31). The tail will always have a K dimension that's not a multiple of 32.
This means the ONLY way to handle this is to either:
1. Pad the data to a multiple of 32
2. Handle the tail explicitly in a way that's compatible with the MMA instruction
For approach 1: I can pad the number of K loop iterations to a multiple of 32 (i.e., add one more iteration that processes only the remaining elements and pads to 32). The issue is reading out-of-bounds memory.
One clean solution: for the last iteration, instead of loading the full BLOCK_K tile, load only `((k_remaining + 31) // 32) * 32` elements (round up to multiple of 32). This requires adjusting the pointer arithmetic.
Actually, wait. Let me re-examine the original code. In the original `_fp8_gemm_kernel`, I use:
```python
a = tl.load(a_ptrs, mask=offs_k[None, :] < k_remaining, other=0.0)
```
This loads a tensor of shape `(BLOCK_M, BLOCK_K)` with `other=0.0` for masked elements. Then:
```python
acc = tl.dot(a, b, acc)
```
The dot computes `(BLOCK_M, BLOCK_K) @ (BLOCK_K, BLOCK_N)` = `(BLOCK_M, BLOCK_N)`. But when k_remaining < BLOCK_K, the effective K dimension is reduced. The fp8 MMA `mma.sync.aligned.m16n8k32` requires K to be a multiple of 32.
My theory is that Triton's codegen for fp8 dot can handle this BUT it generates slow code when K is not a guaranteed multiple of 32. Triton might guard each MMA with a conditional, or it might use a different instruction sequence.
Let me look at what Triton actually generates. Let me dump the PTX for both the aligned and misaligned cases.
Actually, let me try a completely different approach. What if I use `torch.utils.cpp_extension.load_inline` to write a CUDA kernel with inline PTX? This would give me full control over the MMA instructions and tail handling.
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stderr (275 chars)
Exit code 1
Compiled successfully for aligned case
Traceback (most recent call last):
File "/tmp/debug_ptx.py", line 50, in <module>
print("Cache:", test_aligned.cache)
^^^^^^^^^^^^^^^^^^
AttributeError: 'JITFunction' object has no attribute 'cache'
assistant
reasoning (3308 chars)
Let me try a different approach to inspect the PTX. Or, more importantly, let me focus on solving the problem rather than debugging the Triton internals.
The key insight is: fp8 `tl.dot` is slow when K is not a multiple of 32. The solution is to ensure the K dimension is always a multiple of 32.
My approach: for the tail, load a rounded-up number of K elements (to the next multiple of 32) with zero-padding, and compute the dot product with that. This requires reading out-of-bounds memory, which I can avoid by clamping the K pointers to the last valid position for out-of-bounds elements.
But actually, a simpler approach: just ensure BLOCK_K itself is always a multiple of 32, and when K is not divisible by BLOCK_K, for the last iteration, load the full BLOCK_K but from the LAST valid position (backing up the pointer to fit within bounds).
Wait, that's still problematic. Let me think about this differently.
Idea: On the last K iteration, instead of using the normal BLOCK_K stride, adjust the pointers to read from the LAST BLOCK_K elements of the row (which overlap with some already-processed elements), then zero out the elements that have already been processed. This avoids out-of-bounds reads and gives us a full tile for the MMA.
But "zeroing out" already-processed elements in a tile requires a mask on the load, which brings us back to the same problem.
Let me try a different strategy entirely: use shared memory to accumulate across the K dimension. Load fp8 tiles into shared memory, then have warps cooperatively compute the MMA using shared memory tiles. This way, I can control exactly how the tail is handled.
Actually, I realize the problem might be simpler than I think. Let me look at what `tl.dot_scaled` does — maybe it handles fp8 differently.
Wait, I just realized: maybe I should try `tl.dot` with the block pointer approach but without boundary_check on K, and instead handle K-boundary by modifying the base pointer.
Here's a cleaner approach:
1. For all but the last iteration, use block pointers without boundary checks (fast path)
2. For the last iteration, if K is not divisible by BLOCK_K, use a separate codepath with a smaller K tile that IS a multiple of 32
But Triton doesn't support dynamic K tile sizes within a kernel...
Let me try yet another approach. What if I check at the Python level whether K is a multiple of 32, and if not, pad the inputs?
```python
K_pad = ((K + 31) // 32) * 32
if K_pad != K:
x_padded = torch.nn.functional.pad(x, (0, K_pad - K))
w_padded = torch.nn.functional.pad(weight, (0, K_pad - K))
else:
x_padded = x
w_padded = weight
```
This adds at most 31 elements to K, which for K=4096 is <1% overhead. The kernel then runs on the padded data. But I need to make sure the padding values are zero.
Wait, there's an issue: `torch.nn.functional.pad` on fp8 tensors — does it work? Let me check.
Actually, for the weight, padding would require modifying the stored buffer, which is registered as a buffer. I could pad it in the forward pass. But this adds overhead.
Let me try a completely different approach: use `torch.utils.cpp_extension.load_inline` to write a CUDA kernel with inline PTX. This gives me full control.
Actually, let me first try the padding approach since it's simple and should work.
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stdout (411 chars)
K= 4096 (padded to 4096): 0.2033 ms, 675.9 TFLOPS, max_diff=4.000000
K= 4127 (padded to 4224): 0.2082 ms, 665.0 TFLOPS, max_diff=4.000000
K= 4095 (padded to 4096): 0.2025 ms, 678.5 TFLOPS, max_diff=4.000000
K= 4065 (padded to 4096): 0.2024 ms, 673.9 TFLOPS, max_diff=4.000000
K= 4033 (padded to 4096): 0.2020 ms, 670.1 TFLOPS, max_diff=4.000000
K= 32 (padded to 128): 0.0171 ms, 62.6 TFLOPS, max_diff=0.500000
assistant
reasoning (4372 chars)
The padding approach works — but there's a max_diff of 4.0 for large matrices! That's a correctness issue. This is likely because the kernel uses NO masks on M and N dimensions — wait, it does have masks on the store and on the scale load. But actually, the issue might be with the padding: for K=4127, I pad to 4224, but the last 97 columns of weight contain garbage data (since the original weight only has 4127 columns). When I pad with zeros, those columns should be all zeros, and the dot product should be correct.
Wait, for K=4096, which is already a multiple of 128 and NOT padded, I still get max_diff=4.0. So the problem isn't with padding — it's with the kernel itself! Let me check.
Actually, 4096 is not padded and still gets diff=4.0. This kernel differs from the original working kernel in that it has NO masks on the loads. But K=4096 is exactly divisible by BLOCK_K=128, so the loads should be in-bounds. Yet the kernel produces wrong results.
Hmm, let me compare with the original working kernel more carefully. The original used masked loads even for the aligned case:
```python
a = tl.load(a_ptrs, mask=offs_k[None, :] < k_remaining, other=0.0)
```
where k_remaining = K - k. When K is divisible by BLOCK_K, k_remaining >= BLOCK_K for all k < K, so the mask is all True. So the load is effectively unmasked.
But wait, maybe there's a shape issue. Let me check if K_pad is being passed correctly. For K=4096 (no padding), K_pad = 4096, and the loop runs for k=0, 128, 256, ..., 3968 = 32 iterations, all full. This should be fine.
Actually, wait. I'm passing K_pad as the K parameter to the kernel, but the kernel uses it as the loop bound: `for k in range(0, K, BLOCK_K)`. If K_pad = 4096, this runs for k in [0, 128, ..., 3968] — that's 32 iterations, each processing a full tile. Each tile accesses rows 0 to K_pad. Since K_pad = K = 4096, all accesses are in bounds. This should be correct.
But there's a max_diff of 4.0? Let me add a correctness check against the reference.
Actually, wait — for K=4096 unpadded, the diff is 4.0 which is wrong. But my original kernel with masked loads was correct (passed check.py). The difference is: original used masked loads, this version uses unmasked loads.
But for an exactly divisible K, masked vs unmasked loads should produce the same result (since the mask is always True). Unless there's something else going on.
Let me compare the two kernels more carefully. In the original kernel:
```python
for k in range(0, K, BLOCK_K):
k_remaining = K - k
a_mask = offs_k[None, :] < k_remaining
a = tl.load(a_ptrs, mask=a_mask, other=0.0)
```
vs the new kernel:
```python
for k in range(0, K, BLOCK_K):
a = tl.load(a_ptrs)
```
For K=4096, BLOCK_K=128, k=0: k_remaining=4096, mask is all True. These should be equivalent.
UNLESS there's an issue with strides or tensor shapes. Let me add explicit debugging.
Hmm, actually let me just go back to a simpler investigation. The diff of 4.0 for K=4096 (which was working before with the masked kernel) means something is different about this kernel. Let me re-check.
Oh wait, I think the issue might be with the grid size or pid computation. Let me check if the new kernel handles the M and N boundary conditions correctly. The store has:
```python
tl.store(c_ptrs, acc.to(tl.bfloat16), mask=(offs_m[:, None] < M) & (offs_n[None, :] < N))
```
For M=4096, N=4096, BLOCK_M=128, BLOCK_N=128, the last blocks in each dimension have offs_m from 4096-128=3968 to 4095 — all within bounds. All blocks should be entirely in bounds.
Actually, I think I may have introduced a bug when I changed the kernel. Let me compare with the original very carefully...
OH WAIT. I see it. The original kernel uses `scale_ptr + offs_n` with `mask=offs_n < N`. The new kernel does the same. But the original has `offs_k` with `mask=offs_k[None, :] < k_remaining`.
Actually, I think the diff of 4.0 might be a red herring — let me verify by running a proper check with the reference implementation.
Actually, you know what, let me not get sidetracked by the correctness of this specific kernel. Let me go back to the approach that works (the original masked kernel), and solve the performance problem by using a different technique. Let me try the dual-kernel approach: one kernel for well-aligned K, and a different handling for misaligned K using padding.
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stdout (249 chars)
K= 4096 masked_diff=4.000000 padded_diff=4.000000
K= 4127 masked_diff=4.000000 padded_diff=4.000000
K= 4095 masked_diff=4.000000 padded_diff=4.000000
K= 4065 masked_diff=4.000000 padded_diff=4.000000
K= 4033 masked_diff=4.000000 padded_diff=4.000000
assistant
reasoning (3279 chars)
Both kernels are giving max_diff=4.0 which means there's a bug in my reference computation or the kernel. Let me debug. The reference computation I wrote:
```python
ref = (x_orig.float().to(torch.bfloat16) @ wf_orig.float().to(torch.bfloat16).T)
ref = (ref.float() * ws[None, :]).to(torch.bfloat16)
```
Wait, `x_orig.float().to(torch.bfloat16)` — this is casting `float8 -> float32 -> bfloat16`. But the actual data values might be different. Let me think...
In the reference Model:
```python
x_bf = x.to(torch.bfloat16) # fp8 -> bf16 directly
w_bf = self.weight.to(torch.bfloat16) # fp8 -> bf16 directly
y = (x_bf @ w_bf.T).float()
y = y * self.weight_scale[None, :]
return y.to(torch.bfloat16)
```
So it's `x.to(torch.bfloat16) @ weight.to(torch.bfloat16).T * scale`. This is what I should compute as reference. But I wrote `x_orig.float().to(torch.bfloat16)` which is fp8->f32->bf16 vs fp8->bf16. These should be the same conversion since fp8->bf16 is exact (bf16 has larger range and precision than fp8_e4m3).
Actually wait, `x_orig.float()` converts fp8 to float32, then `.to(torch.bfloat16)` converts to bf16. Since fp8_e4m3 has 4 exponent bits and 3 mantissa bits, and bf16 has 8 exponent bits and 7 mantissa bits, the conversion from fp8 to bf16 is exact (bf16 can represent all fp8_e4m3 values exactly). So the double conversion should be fine.
But the diff is 4.0 which is very large. Let me check with the actual reference model.
Actually, let me just run the kernel from solution.py directly and compare with the reference model. Maybe the problem is in my test code, not the kernel.
Actually wait, let me re-read the original kernel that passed check.py. I know check.py passed. Let me reproduce the exact conditions.
Hmm, let me look at the data more carefully. The max_diff of 4.0 with K=4096 is suspicious. Let me add numpy-level debugging.
Actually, let me just check a simpler case. M=256, N=256, K=256 to see if the kernel works at all.
Wait, actually, I know the kernel works because check.py passed. Let me check if there's something wrong with my test. Let me just re-run the actual check.py and then run benchmark.py again.
Actually wait, I modified solution.py but never re-ran check.py after my changes. Let me check what's in solution.py now vs what passed earlier.
Let me just go back to basics. The first version of solution.py passed check.py and had reasonable performance for shape 0. Let me focus on fixing the K tail issue. Let me try a completely different approach: use a CUDA kernel.
Actually, let me try one more thing with Triton. What if instead of using a masked load, I use `tl.load` without a mask and set `other=0.0`, but with `boundary_check` disabled? No wait, that doesn't make sense — out of bounds loads would fault.
Hmm, let me try using `tl.inline_asm_elementwise` or a completly different approach.
Wait, actually, let me try using a special technique: use `K_padded` as the loop bound, and for the last iteration, load from the actual data (which has been padded with zeros). This way, all dot products see a full tile size.
But I already tried this and got diff=4.0. There must be a bug in my test.
Let me just go back to the solution.py that passed check.py and modify it to use padding for non-aligned K.
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Let me go back to a clean approach. First, verify the current solution still passes check.py, then fix the tail K issue.
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stdout (5232 chars) — TRUNCATED
1 """FP8 e4m3 GEMM — Triton kernel using fp8 tensor cores (mma.sync ... e4m3).
2
3 Model interface: same as reference.py — holds `weight` (fp8_e4m3, N×K) and
4 `weight_scale` (float32, N). Forward: y = ((x @ w.T) * weight_scale).to(bf16)
5 """
6
7 import torch
8 import torch.nn as nn
9 import triton
10 import triton.language as tl
11
12 E4M3_MAX = 448.0
13
14
15 # ---------------------------------------------------------------------------
16 # Triton kernel
17 # ---------------------------------------------------------------------------
18
19 @triton.jit
20 def _fp8_gemm_kernel(
21 a_ptr, # fp8 activation (M, K)
22 b_ptr, # fp8 weight (N, K) — read transposed as (K, N)
23 c_ptr, # bf16 output (M, N)
24 scale_ptr, # float32 scale (N,)
25 M,
26 N,
27 K,
28 stride_am,
29 stride_ak, # a strides
30 stride_bn,
31 stride_bk, # b strides (b[k,n] = b_ptr + n*stride_bn + k*stride_bk)
32 stride_cm,
33 stride_cn, # c strides
34 # Block sizes — autotuned
35 BLOCK_M: tl.constexpr,
36 BLOCK_N: tl.constexpr,
37 BLOCK_K: tl.constexpr,
38 GROUP_M: tl.constexpr,
39 ):
40 # Program id — use swizzling for better L2 reuse
41 pid = tl.program_id(0)
42 num_pid_m = tl.cdiv(M, BLOCK_M)
43 num_pid_n = tl.cdiv(N, BLOCK_N)
44 num_pid_in_group = GROUP_M * num_pid_n
45 group_id = pid // num_pid_in_group
46 first_pid_m = group_id * GROUP_M
47
... (3732 more chars)
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reasoning (59 chars)
Let me check if the current solution.py passes correctness.
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reasoning (5290 chars)
Good, the current solution passes correctness. The problem is specifically performance for non-multiple-of-32 K values. Let me think about the best approach.
The core issue: `tl.dot(a, b, acc)` with fp8 inputs generates PTX `mma.sync.aligned.m16n8k32` instructions that require K to be a multiple of 32. When the loaded tile has K elements that aren't a multiple of 32 (because k_remaining < BLOCK_K and k_remaining % 32 != 0), Triton generates slow fallback code.
My plan:
1. Detect when K is not a multiple of 32
2. Pad the inputs to the next multiple of 32 (or BLOCK_K)
3. Use a kernel that assumes aligned access (no K masks)
4. The kernel still needs M and N masks for edge blocks
Let me implement this cleanly. For padding fp8 tensors, I'll need to convert to float32, pad, and convert back to fp8.
Actually wait, there's a problem with this approach. The weight is a registered buffer, so I need to pad it in the forward pass. But this creates a new tensor each time, which adds overhead. However, the padding overhead is O(N * pad_width) which is much smaller than the GEMM itself. For K=4096, padding to 4096 (no change) would cost zero. For K=4127, padding to 4224 adds 97 columns, which is about 2.4% overhead — negligible.
But converting fp8 → float32 → pad → fp8 requires two conversions. Let me think of a better way.
Actually, for the weight, I can pre-pad it in `__init__`! Since the weight is (N, K), I can store it as (N, K_padded) with the extra columns being zero. The weight_scale stays the same. Then the forward pass just passes the padded weight to the kernel.
For x, I need to pad it in the forward pass. But x is fp8, and `torch.nn.functional.pad` doesn't support fp8. I can use:
```python
if K_padded > K:
x_pad = torch.zeros(M, K_padded - K, dtype=torch.float8_e4m3fn, device=x.device)
x = torch.cat([x, x_pad], dim=1)
```
This way, x is padded with fp8 zeros (which have bit pattern 0x00 = 0.0 in fp8_e4m3). Concatenation should be fast (it's just allocating a new tensor and copying).
Actually, `torch.cat` for fp8 might not work. Let me check.
Hmm, let me think about a completely different approach. Instead of padding, what if I modify the kernel to handle the tail correctly?
Here's an idea: for the last K iteration, instead of loading BLOCK_K elements with a mask, I load fewer elements that exactly round up to a multiple of 32. For example, if k_remaining = 31, I load 32 elements (the last 32, which includes 1 element of overlap with the previous iteration, but that's OK since the overlapping element is zeroed by subtraction or handled differently).
Wait, that still requires out-of-bounds access. Unless I back up the pointer so that the loaded tile ends exactly at K.
For K=4127, BLOCK_K=128:
- Iterations: k = 0, 128, 256, ..., 3968, 4096
- At k=3968: k_remaining = 4127 - 3968 = 159
- But 159 > 128, so this is a full tile. We load elements 3968 to 4095.
- At k=4096: k_remaining = 4127 - 4096 = 31
- We need to load 32 elements (round up to multiple of 32).
- Option: load from K-32 = 4095 to 4127. But that's elements 4095 to 4126 = 32 elements. Element 4095 was already processed in the previous iteration!
- This creates double-counting!
So backing up the pointer doesn't work. We'd need a more sophisticated approach.
What if I just round up the tail size to a multiple of 32 and handle it as a special case? For k_remaining < BLOCK_K:
- Let k_tail = ((k_remaining + 31) // 32) * 32
- Load k_tail elements (padding out-of-bounds with zeros)
- The shape is (BLOCK_M, k_tail) and (k_tail, BLOCK_N) — both have K dim that's a multiple of 32
- But the tile shapes are not compile-time constants!
OK, I think the padding approach is the most practical. Let me implement it properly.
For fp8 tensor padding, let me try:
```python
x_padded = torch.nn.functional.pad(x.float(), (0, pad), value=0.0).to(torch.float8_e4m3fn)
```
This converts fp8→f32, pads with zeros (f32), converts back to fp8. The overhead should be minimal for large matrices.
For weight, I'll pre-pad in __init__.
Actually, an even simpler approach: allocate x as already padded. Since I create x in get_inputs(), this is straightforward. But for the forward pass, x comes from the user.
Let me just implement the padding in the forward pass. It's a one-time conversion that adds negligible overhead for large matrices.
Here's the refined plan:
1. In `__init__`: compute `K_padded = ((K + 127) // 128) * 128`, store weight as (N, K_padded) with zero-padded columns
2. In `forward`: pad x to K_padded if needed
3. Use an unmasked kernel (no K masks) for maximum speed
4. The kernel still needs M and N edge masks
Let me implement this.
Actually, wait. Let me think about whether this is really the best approach. What if I just switch to a CUDA kernel with inline PTX? This would give me full control over:
- Memory coalescing
- Shared memory usage
- MMA instruction scheduling
- Tail K handling (I can zero-pad in shared memory)
Let me try the CUDA approach since it gives me more control. But first, let me try the simpler Triton+padding approach since it's faster to implement and iterate.
Let me try the padding approach properly this time. The key fix is to ensure the reference computation in my test matches the reference Model.
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tool
stdout (280 chars)
Command running in background with ID: b9bn646if. Output is being written to: /tmp/claude-1002/-workspace-problems-01-fp8-gemm/7885f009-0e25-41c7-955d-04515b48ff29/tasks/b9bn646if.output. You will be notified when it completes. To check interim output, use Read on that file path.
assistant
reasoning (1152 chars)
That's running in background. Let me check the output while I plan ahead.
Actually, let me think about what approach to take. I have several options:
1. **Triton with padding**: Pad K to multiple of BLOCK_K (128) and use an unmasked kernel. Simple but requires data conversion.
2. **Triton with block pointers**: The block pointer approach was faster (0.13ms vs 2.3ms for 1024x1024) but had a 3.8x slowdown for tail cases. Maybe I can use block pointers WITHOUT boundary_check on K for the fast path and only enable it when needed.
3. **CUDA C++ with inline PTX**: Full control. Write a kernel that does:
- Load fp8 tiles into shared memory
- Use `mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32` PTX
- Handle tail K by zero-padding in shared memory
- Apply per-channel scale
- Store bf16 output
4. **Mixed approach**: For the main loop, use aligned loads and MMA. For the tail, use a different strategy.
Let me go with option 3 (CUDA inline PTX) since it gives the most control and I can be sure about the performance. But it's more complex to implement.
Actually, let me first check the result of the padded kernel approach.
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stdout (280 chars)
Command running in background with ID: b7saq1sct. Output is being written to: /tmp/claude-1002/-workspace-problems-01-fp8-gemm/7885f009-0e25-41c7-955d-04515b48ff29/tasks/b7saq1sct.output. You will be notified when it completes. To check interim output, use Read on that file path.
assistant
reasoning (7121 chars)
Let me wait for the background task and meanwhile start working on a CUDA-based approach. The CUDA approach with inline PTX will give me maximum control and performance. Let me design it.
For a Blackwell (SM120) CUDA kernel with fp8 MMA:
1. **MMA instruction**: `mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32`
- Each warp processes a 16×8×32 tile
- Threads in a warp provide fragments of A (fp8) and B (fp8) and accumulate D (f32)
2. **Thread block design**:
- Use a warp group of 4 warps (128 threads) to produce a larger output tile
- Tile shape: let's say 128×128 output, with BK=128 inner dimension
- Distribute output elements across warps
3. **Memory hierarchy**:
- Global → shared memory (coalesced loads of fp8)
- Shared → registers (for MMA fragments)
- MMA in registers
4. **Tail handling**:
- Pad shared memory with zeros for out-of-bounds elements
- This ensures MMA always sees valid, aligned data
Actually, let me think about this more carefully. For the `mma.sync.aligned.m16n8k32` instruction:
Each thread in a warp contributes specific elements of A and B matrices. The register layout for MMA fragments is well-defined in the PTX ISA.
For A (fp8, m16n8k32, row-major):
- Each thread holds 4 elements of A (since K=32 across 32 threads... wait, that's not quite right for the new MMA)
Actually, I need to look up the exact PTX instruction format for Blackwell. The `mma.sync.aligned.m16n8k32` on SM120 uses a specific register layout. Let me look this up.
Actually, for the CUDA inline PTX approach, I need to understand the MMA fragment layout. On Blackwell, the MMA instruction for fp8 is:
```
mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32
```
This computes D = A * B + C where:
- A is m16×k32 (fp8 e4m3, row-major)
- B is k32×n8 (fp8 e4m3, col-major)
- C and D are m16×n8 (f32)
Wait, but my data is row-major for both. The weight is (N, K) and needs to be transposed to (K, N). For the MMA, I need:
- A as (M, K) row-major → reshape into 16×32 tiles
- B as (K, N) → but for MMA, B should be (K, N) column-major, which is the same as (N, K) row-major
Hmm, the standard MMA layout is:
- A: row-major (m16 × k32)
- B: column-major (k32 × n8)
For my case:
- x is (M, K) row-major → A fragments are row-major ✓
- w is (N, K) row-major → This is the transpose of what we need. w[n,k] = B_effective[k,n] in row-major form. But MMA expects B in column-major (k, n). So w stored as (N, K) row-major IS (K, N) column-major. Actually wait, that's not right either.
Let me think again. w.shape = (N, K), w.row_major. w[n, k] is at offset n*K + k.
For the GEMM, I need to compute x[M, K] @ w.T[K, N]. The second operand is w.T which is (K, N).
In the MMA: A is (16, 32) row-major from x, B is (32, 8) from w.T.
If w is stored as (N, K) row-major:
- w.T[k, n] = w[n, k] (where element is at n*K + k)
- For B as (K, N) column-major: B[k, n] is at offset k*N + n (if column-major, the first dimension K varies fastest)
- Actually wait, column-major means B[k, n] is at k + n*K_c where K_c is the leading dimension.
Hmm, this is getting complex. Let me think about it differently.
For the MMA instruction `.row.col`:
- A matrix: row-major. Each row of A is in contiguous memory.
- B matrix: column-major. Each column of B is in contiguous memory.
For my case:
- A comes from x[M, K]. Each row of x is contiguous in memory. ✓ (row-major)
- B comes from w.T[K, N] or equivalently from w[N, K] viewed as (K, N).
- For column-major B[k, n], we need each column n to be contiguous.
- B's column n is w[:, n] which is the n-th row of w (since w is N×K).
- w[n, :] is contiguous in memory (it's a row of w). ✓
So B is naturally column-major when w is stored row-major. Specifically:
- B[k, n] = w[n, k] — element at w_ptr + n*K + k
- In column-major layout, B column n is at address w_ptr + n*K with stride 1 between elements. This means B[k, n] = w_ptr + n*K + k. ✓
So the data layout naturally matches the MMA requirements:
- A (x): row-major with leading dimension K
- B (w): column-major with leading dimension N (i.e., column stride is K)
Wait, for B in column-major: columns are contiguous in memory. Column n starts at w_ptr + n*K and has elements w[n, 0], w[n, 1], ..., w[n, K-1]. This IS column-major because the first dimension (K) varies fastest.
So the layout matches perfectly. x is row-major and w is effectively column-major for the transposed operation.
OK, so the plan for the CUDA kernel:
```cuda
// Each thread block processes a 128x128 output tile
// With 4 warps (128 threads total)
// Each warp does mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32
// Shared memory:
// - A_tile: [128][128] fp8
// - B_tile: [128][128] fp8
// Each warp: produces 16x8 outputs per MMA
// Warp (warp_m, warp_n): handles rows [warp_m*16, (warp_m+1)*16) and cols [warp_n*8, (warp_n+1)*8)
// With 128x128 tile: 8 warps in M direction, 16 warps in N direction → 128 warps — too many for 128 threads!
// Better approach: each warp handles MULTIPLE MMAs sequentially
// With 4 warps per block:
// - Warp 0: rows [0,16), cols [0,8) then [0,16), [8,16) then [0,16), [16,24) ...
// Each warp covers many 16x8 tiles
// Actually, the standard Triton approach is to have each warp handle multiple MMA tiles.
// Let me think about what tile sizes give good performance.
// For 128x128 output tile with 4 warps (128 threads):
// Each warp handles 128*128/4 = 4096 elements / 128 elements_per_mma = 32 MMA operations per K tile
// With BK=128: total 4096 MMAs per block, 128 per warp
// Actually on Blackwell each SM has 128KB shared memory and 4 warp schedulers.
// A typical block uses 256 or 512 threads (8 or 16 warps).
```
Hmm, this is getting complex. Let me think about the simplest approach that works.
Actually, for the PTX approach, the key challenge is getting the register fragment layout right for the MMA instruction. Each thread in a warp contributes specific elements of the A and B matrices. The layout is specified in the PTX ISA documentation.
Let me just use the Triton approach with padding and accept the small overhead. Let me check my background task first.
Actually, let me try a completely different approach. What if instead of padding, I adjust BLOCK_K dynamically so that it always divides K with a remainder that's a multiple of 32?
For K=4127:
- 4127 = 32 * 128 + 31
- 4127 = 33 * 125 + 2 → tail of 2, not multiple of 32
- 4127 = 34 * 121 + 13 → tail of 13
- 4127 = 64 * 64 + 31 → NO, still 31
The problem is 4127 ≡ 31 (mod 32). Any K that's ≡ 31 mod 32 will have a tail that's not a multiple of 32, regardless of BLOCK_K, as long as BLOCK_K ≡ 0 (mod 32).
So the only way with Triton is to either:
1. Pad the data
2. Handle the tail differently (but Triton doesn't support this cleanly)
3. Use a different framework (CUDA/PTX)
Let me go with option 1: pad the data. I'll pre-pad the weight in __init__ and pad x in forward. The overhead is minimal.
For fp8 padding, I need to be careful:
- fp8 zero is 0x00 in memory
- I can create a zero fp8 tensor and concatenate
Let me check if torch.cat supports fp8.
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stderr (315 chars)
Exit code 1
Traceback (most recent call last):
File "/tmp/test_fp8_pad.py", line 4, in <module>
x = torch.randn(4, 100, dtype=torch.float8_e4m3fn, device='cuda')
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
NotImplementedError: "normal_kernel_cuda" not implemented for 'Float8_e4m3fn'
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reasoning (73 chars)
Let me get that background task output and also fix the fp8 padding test.
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stdout (466 chars)
<retrieval_status>success</retrieval_status>
<task_id>b9bn646if</task_id>
<task_type>local_bash</task_type>
<status>completed</status>
<exit_code>0</exit_code>
<output>
K= 4096 (padded=4096): max_diff=4.000000
K= 4127 (padded=4224): max_diff=4.000000
K= 4095 (padded=4096): max_diff=4.000000
K= 256 (padded=256): max_diff=1.000000
K= 128 (padded=128): max_diff=0.500000
K= 64 (padded=128): max_diff=0.500000
K= 32 (padded=128): max_diff=0.250000
</output>
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reasoning (2491 chars)
OK, the background task completed. The padded kernel approach has correctness issues (max_diff up to 4.0 even for K=4096 aligned case). There's something fundamentally wrong with the "no mask" kernel, even for perfectly aligned data. Let me debug this.
Wait, when K=4096 (perfectly aligned), the kernel loads WITHOUT mask and should be identical to the masked version. But I get diff=4.0. There must be a bug.
Let me check: for K=4096, BLOCK_K=128, the loop runs 32 iterations. Each iteration loads a full 128-element tile. Since K=4096, all loads are in bounds. The dot products are full (128, 128) @ (128, 128). This should be identical to the masked version.
But the masked version passes check.py with the EXACT SAME K=4096 test case. Let me check what's different...
Hmm, wait. Let me re-check the original solution.py. The original `_fp8_gemm_kernel` uses MASKED loads but that should be equivalent for aligned K...
Oh wait, I see the difference! In the original kernel, the load is:
```python
a = tl.load(a_ptrs, mask=offs_k[None, :] < k_remaining, other=0.0)
```
And in the unmasked kernel:
```python
a = tl.load(a_ptrs)
```
The `other=0.0` in the masked load is a float32 zero. For fp8 data, this might cause a different conversion than loading a literal fp8 zero. But for in-bounds elements (all elements when K is aligned), the mask is all true, so `other` is never used. The two should be equivalent.
UNLESS... there's a compiler optimization difference. Let me check by actually comparing the two approaches with K=4096 on the same data.
Actually, let me just check the original solution.py more carefully. The solution that passes check.py IS the one in solution.py right now. Let me verify this by re-running check.py.
Wait, I already verified that check.py passes with the current solution.py. So the original masked kernel works correctly. The issue must be with my unmasked kernel test.
Let me look at the unmasked kernel more carefully:
```python
for k in range(0, K, BLOCK_K):
a = tl.load(a_ptrs) # no mask — K is aligned
b = tl.load(b_ptrs)
acc = tl.dot(a, b, acc)
a_ptrs += BLOCK_K * stride_ak
b_ptrs += BLOCK_K * stride_bk
```
For K=4096, BLOCK_K=128, this runs for k in [0, 128, 256, ..., 3968] — 32 iterations. All loads are fully in bounds. After each load, we advance by 128 in the K dimension. The computation should be identical to the masked version.
Let me create a minimal test that compares the two kernels on the same data.
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tool
stdout (280 chars)
Command running in background with ID: b8zhxma17. Output is being written to: /tmp/claude-1002/-workspace-problems-01-fp8-gemm/7885f009-0e25-41c7-955d-04515b48ff29/tasks/b8zhxma17.output. You will be notified when it completes. To check interim output, use Read on that file path.
assistant
reasoning (4367 chars)
Let me wait for that background task. Meanwhile, let me think about the alternative approach using a CUDA kernel with inline PTX.
Actually, let me look at this from a different angle. Maybe I should write a CUDA kernel using `torch.utils.cpp_extension.load_inline`. This gives me:
1. Full control over shared memory
2. Direct PTX MMA instructions
3. Proper tail handling via shared memory zero-padding
4. No Triton quirks
Let me start drafting the CUDA kernel. For Blackwell SM120 with fp8 MMA:
The key PTX instruction is:
```
mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32 {%d0, %d1, %d2, %d3}, {%a0, %a1, %a2, %a3}, {%b0, %b1}, {%d0, %d1, %d2, %d3};
```
Wait, I need to check the exact register counts. The fragment sizes:
- A matrix (m16×k32, e4m3): Each element is 1 byte. 16×32 = 512 bytes / 32 threads = 16 bytes = 4 x 32-bit registers per thread. So 4 registers for A.
- B matrix (k32×n8, e4m3): 32×8 = 256 bytes / 32 threads = 8 bytes = 2 x 32-bit registers per thread. So 2 registers for B.
- C/D matrix (m16×n8, f32): 16×8 = 128 elements × 4 bytes = 512 bytes / 32 threads = 16 bytes = 4 x 32-bit registers per thread. So 4 registers for C/D.
So the MMA instruction is:
```ptx
mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32
{d0, d1, d2, d3}, // 4 f32 accumulators
{a0, a1, a2, a3}, // 4 x 32-bit holding 16 fp8 values
{b0, b1}, // 2 x 32-bit holding 8 fp8 values
{d0, d1, d2, d3}; // same accumulators for C
```
Each `a0` register holds 4 fp8 values packed into 32 bits.
Each `b0` register holds 4 fp8 values packed into 32 bits.
The mapping of threads to matrix elements follows a specific pattern. Let me think about how to load data into the right registers.
For A (16×32, row-major):
- Thread t (in 0..31) contributes specific elements
- For Blackwell, the mapping for `.row` layout: thread t contributes elements from row (t/4) and column (t%4)*8 + group within group of 8
Actually, the exact layout is quite complex and specified in the PTX ISA. Let me look at CUTLASS or other references for the correct register blocking.
Actually, I know that for `mma.sync.aligned.m16n8k32`, the thread-to-element mapping for A uses the identity permutation (row-major), and for B uses column-major. The specific mapping within a warp is:
For A (row-major m16×k32, fp8):
- Lan e t: t contributes to rows in groups
- Each thread provides 4 fp8 values
- The mapping groups threads into 4 groups of 8
For B (col-major k32×n8, fp8):
- Each thread provides 2 fp8 values
- Threads are mapped across the K and N dimensions
This is getting complex. Let me look for a simpler approach...
Actually, let me try a different Triton technique. What if I use a dynamic BLOCK_K that adjusts to make the tail always a multiple of 32?
For any K, I can pick BLOCK_K such that K % BLOCK_K is a multiple of 32. If K ≡ 31 (mod 32), then I need BLOCK_K ≡ 31 (mod 32) or BLOCK_K that divides K-31 evenly... wait, that's the wrong approach.
Actually, the issue is: when k_remaining < BLOCK_K, the loaded tensor still has K-dim = BLOCK_K, but only k_remaining elements are valid. The dot product still uses the full BLOCK_K dimension. When k_remaining is not a multiple of 32, the MMA instruction can't handle it efficiently.
Wait, am I wrong about this? Let me re-examine. The `tl.dot(a, b, acc)` takes:
- a: shape (BLOCK_M, BLOCK_K) — this always has K-dim = BLOCK_K (compile-time constant)
- b: shape (BLOCK_K, BLOCK_N) — same
The mask only affects which elements are loaded from memory vs filled with `other`. The tensor shapes are always the full block sizes. So the dot product always computes a full (BLOCK_M, BLOCK_K) @ (BLOCK_K, BLOCK_N) product. The question is: does Triton generate efficient MMA code when the loads are masked?
Maybe the issue is that the masked load produces different IR that causes Triton to avoid the MMA path. Let me check by looking at the generated PTX/SASS for both cases.
Actually, let me try a workaround: for the tail, don't use a mask at all. Instead, rely on the fact that we can read beyond K-1 safely in Triton (with `other` padding), but adjust the approach to avoid the performance cliff.
Actually, here's a key insight: what if I use `tl.make_block_ptr` with `boundary_check=(0,)` (only check M/N boundaries, not K)? This might produce efficient code for the K dimension.
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stdout (611 chars)
<retrieval_status>success</retrieval_status>
<task_id>b8zhxma17</task_id>
<task_type>local_bash</task_type>
<status>completed</status>
<exit_code>0</exit_code>
<output>
masked vs ref: 1.000000
unmasked vs ref: 1.000000
masked vs unmasked: 0.000000
y1 sample: tensor([-19.7500, 42.5000, 39.7500, 11.0000, -5.4062], device='cuda:0',
dtype=torch.bfloat16)
y2 sample: tensor([-19.7500, 42.5000, 39.7500, 11.0000, -5.4062], device='cuda:0',
dtype=torch.bfloat16)
ref sample: tensor([-19.7500, 42.5000, 40.0000, 11.0625, -5.4062], device='cuda:0',
dtype=torch.bfloat16)
</output>
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reasoning (4087 chars)
Interesting! The masked and unmasked kernels produce identical results (diff=0.0), but both differ from the reference by about 1.0. The difference is small (about 0.25 for individual elements based on the samples). But the max diff is 1.0.
Wait, max_diff=1.0 and the reference tolerance for bf16 is 0.2. So both kernels fail correctness with this test! But the solution passed check.py...
The difference must be in how the reference is computed. In my test:
```python
ref = (x.to(torch.bfloat16) @ wf.to(torch.bfloat16).T).float() * ws[None, :]
ref = ref.to(torch.bfloat16)
```
But in the reference model:
```python
x_bf = x.to(torch.bfloat16)
w_bf = self.weight.to(torch.bfloat16)
y = (x_bf @ w_bf.T).float()
y = y * self.weight_scale[None, :]
return y.to(torch.bfloat16)
```
These look the same to me. But maybe `torch.bfloat16` operations use different precision internally? In PyTorch, bf16 @ bf16 is computed in fp32 or bf16 depending on the hardware and settings.
Actually, the difference might be because `x.to(torch.bfloat16)` is converting fp8→bf16 directly vs my test which should also do that. Let me check...
Hmm, actually, looking at the sample output:
```
y1 sample: [-19.7500, 42.5000, 39.7500, 11.0000, -5.4062]
ref sample: [-19.7500, 42.5000, 40.0000, 11.0625, -5.4062]
```
The difference for the 3rd element is 0.25 and for the 4th is 0.0625. These are small but the max across all elements is 1.0.
Now let me think: check.py uses tolerance of 0.2 for bf16. The max diff of 1.0 should fail! Let me re-run check.py to make sure...
Actually, I already ran check.py and it passed! Let me verify again. Maybe the circumstances are different. check.py uses numeric_stress_cases and different seeds. Let me check if the specific combination I'm testing triggers a failure that check.py doesn't catch.
Actually, let me look at this differently. The tolerance is 0.2 but check.py might use relative OR absolute tolerance. Let me check the correctness checking code.
Hmm, for now, let me focus on the performance issue. The correctness check passes with the current solution.py (masked kernel). The issue is performance for shape 1 (K=4127).
Let me try a completely different approach. Since Triton's fp8 dot has performance issues with non-multiple-of-32 K, let me try using CUDA C++ with inline PTX via `torch.utils.cpp_extension.load_inline`.
Actually, let me first try one more Triton approach: what if I pad K in the FORWARD PASS to a multiple of 32 (not BLOCK_K, but just 32)?
Wait, that's what I already tried with padding. The issue is that the "unmasked" kernel doesn't produce correct results even for aligned K (max_diff=1.0).
But the MASKED kernel DOES pass check.py. So let me focus on making the masked kernel fast for K=4127.
The problem: when k_remaining < BLOCK_K and k_remaining % 32 != 0, the masked fp8 load followed by tl.dot is slow.
One idea: pad the data to make K a multiple of BLOCK_K, but continue using the MASKED kernel (which is correct). The masked kernel will then always have full tiles (k_remaining >= BLOCK_K for all iterations), and the tail won't be a problem.
For K=4127 with BLOCK_K=128:
- Pad to K=4224 (next multiple of 128)
- The loop runs for k in [0, 128, 256, ..., 4096] — 33 iterations
- At k=4096: k_remaining = 4224 - 4096 = 128 — full tile!
- All loads are fully in-bounds (since data is padded with zeros)
This approach combines the correctness of the masked kernel with the performance of aligned access. Let me implement this.
For padding fp8 tensors, I'll convert to float32, pad with zeros, and convert back to fp8_e4m3fn. The overhead is: M*K + N*K float32 conversions + memory allocation. For large matrices, this should be small relative to the GEMM itself.
Actually wait, there's a simpler way. Since `torch.float8_e4m3fn` stores 0.0 as the bit pattern 0x00, I can just:
1. Allocate a new fp8 tensor of shape (M, K_padded) or (N, K_padded)
2. Copy the original data into the first K columns
3. The rest is automatically zero (since torch.zeros for fp8 should produce 0x00)
Let me try this approach.
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stdout (242 chars)
Original: torch.Size([4, 100]) torch.float8_e4m3fn
Last column of original: tensor([-0.0625, 0.5000, 0.3750, 0.5625], device='cuda:0')
First padded column: tensor([0., 0., 0., 0.], device='cuda:0')
Is zero? True
Max diff after padding: 0.0
assistant
reasoning (3403 chars)
Now I have a clean padding approach: allocate a zero-initialized fp8 tensor (torch.zeros creates bit pattern 0x00 which is fp8 zero) and copy the original data. The padding is zero-cost for aligned dimensions.
Now let me redesign the solution:
1. Pre-pad the weight in `__init__`: store weight as (N, K_padded) where K_padded is the next multiple of 128
2. In `forward`: pad x to K_padded, run the (already correct) kernel
3. The kernel will always process full tiles (since K_padded is a multiple of 128)
Let me also compute: what's the overhead of padding? For K=4127, K_padded=4224, which is only 2.3% more elements. For the FLOPs calculation, I'll use the original K, keeping the "useful" FLOPs accurate. The actual kernel does 2.3% more work, but this is fine since the kernel was previously 168x slower for this shape.
Wait, there's a subtlety: the benchmark.py computes flops based on shape["K"], not K_padded. So I get credit for the original FLOPs, and the actual work is only slightly higher. This is fine — the overhead is negligible.
Actually, let me reconsider. What if I pad to a multiple of 32 (the MMA K dimension) instead of a multiple of 128 (BLOCK_K)? The tail would then be a multiple of 32 which should avoid the performance cliff.
With K_padded aligned to 32:
- K=4127 → K_padded=4128 (1 extra element)
- The last iteration: k=4096, k_remaining=32 → which is a multiple of 32!
This is much better because the padding overhead is only 1 element for K=4127 instead of 97. But will the masked kernel be fast when k_remaining=32? Let me test.
Actually, the key question: is the performance cliff at 32 (MMA K dimension) or at 128 (BLOCK_K)?
From my earlier experiments:
- K=4127 (tail=31): slow (2.34ms)
- K=4128 (tail=32): fast (0.03ms)
- K=4095 (tail=127): slow (2.27ms)
- K=4096 (tail=0): fast
Wait, K=4095 has tail=127 with BLOCK_K=128. 127 % 32 ≠ 0. But 127 > 32, so it's not a single-iteration issue.
Hmm, but K=4095: the loop runs for k in [0, 128, 256, ..., 3968, 4096]. At k=3968: k_remaining = 127. The loaded tile has shape (BLOCK_M, 128) but only the first 127 K elements are valid. The dot product is computed with the full 128 elements. The 128th element is 0 (from `other=0.0`).
The MMA instruction for fp8: `mma.sync.aligned.m16n8k32`. This works on tiles of K=32. With K=128, the MMA processes 4 sub-tiles of K=32 each. For the last sub-tile, all elements have K values that are past the valid range... wait, no. For k_remaining=127:
- Sub-tile 0: K indices 0-31, all valid (31 < 127) ✓
- Sub-tile 1: K indices 32-63, all valid ✓
- Sub-tile 2: K indices 64-95, all valid ✓
- Sub-tile 3: K indices 96-127, only indices 96-126 valid, index 127 is padded
So only the very last element in the last sub-tile is padded. But it's still ONE element in a sub-tile that has a partial mask. The MMA instruction itself processes the full K=32 tile, but the data for the padded elements is zero. This should be fine functionally... but maybe the *compiler* can't prove this and generates slow code.
The issue might be that Triton's codegen sees the mask and doesn't optimize the MMA instruction for the last sub-tile. It might insert conditionals around each MMA or use a completely different code path.
OK, let me just go with the padding approach and test. I'll pad to a multiple of 32 (minimal padding), and use the same kernel that already passes 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)
assistant
reasoning (3982 chars)
Wait, I need to be careful. The kernel now loads WITHOUT masks on K (since K_padded is a multiple of BLOCK_K=128). But the check.py tests whether the Model matches the reference. The reference model uses the ORIGINAL K (not padded). Since my model pads weight to K_padded, the state_dict will have a weight of shape (N, K_padded) instead of (N, K). This will fail the strict state_dict check!
Let me re-read the check code:
```python
sd = ref_model.state_dict()
try:
sol_model.load_state_dict(sd, strict=True)
except RuntimeError as e:
print(f"FAIL: state_dict mismatch at shape {shape_idx} ({shape}): {e}")
sys.exit(1)
```
This requires `strict=True` which means the state_dict keys and shapes must match exactly. If I pad the weight, the solution's weight will have shape (N, K_padded) while the reference's weight has shape (N, K). This will fail!
So I need to either:
1. Not pad the weight in __init__, but pad it in forward (adds overhead but preserves the state_dict)
2. Override `load_state_dict` to handle the shape mismatch
3. Store the original weight and pad it in forward
Option 1 is simplest. I'll store the weight with original shape (N, K) and pad it in forward. The overhead is minimal: converting fp8→fp8 only involves an allocation and copy, which is O(N*K) and much smaller than the O(M*N*K) GEMM.
But wait, if I pad x and weight every forward call, I'm doing two allocations and copies. For large matrices this is still negligible (1-2% overhead), but for small ones like M=32 it might be more significant.
Actually, let me think about this differently. What if I keep the original weight shape but use the kernel with masking?
The original kernel was correct but slow for K=4127. The issue was specifically that when k_remaining = 31 (not a multiple of 32), the dot product is slow.
What if I handle the tail specially? For the K loop, process all full BLOCK_K tiles with unmasked loads (fast path), and handle the last tile separately only when it's not a full tile.
But in Triton, the loop bound K is a runtime variable, and within the loop body, I can't change the code path based on the iteration.
Actually, I can! I can write the loop to process all full tiles:
```python
for k in range(0, K - K % BLOCK_K, BLOCK_K):
a = tl.load(a_ptrs) # full tile, no mask
b = tl.load(b_ptrs)
acc = tl.dot(a, b, acc)
```
And then handle the remainder separately:
```python
if K % BLOCK_K != 0:
k = K - K % BLOCK_K
k_remaining = K - k
# Only load valid elements, pad with zeros
...
```
But this still has the performance cliff on the tail!
OK, let me think about option 1 more carefully. I'll store the weight at its original shape (N, K) to match the reference state_dict, then pad it in the forward pass. The forward pass will:
1. Pad x to K_aligned (if needed)
2. Pad weight to K_aligned (if needed)
3. Run the kernel
4. Return output
The padding overhead for fp8 is:
- x padding: allocate (M, K_aligned) fp8 tensor + copy M*K bytes — about 16MB for M=4096, K=4096, which is ~9us at 1.8TB/s
- weight padding: allocate (N, K_aligned) fp8 tensor + copy N*K bytes
This is indeed negligible compared to the GEMM itself.
Let me update the solution.
Actually wait, there's another option. What if I use BLOCK_K that's variable, not constexpr? In Triton, you can autotune BLOCK_K. What if I set BLOCK_K to a value that makes the tail always a multiple of 32?
For K=4127:
- If BLOCK_K=4127, there's just one iteration, k_remaining=4127 which is NOT a multiple of 32
- If BLOCK_K=128, there are 33 iterations, tail=31
- If BLOCK_K=64, there are ceil(4127/64)=65 iterations, tail=4127-64*64=31
The tail is always = K % BLOCK_K, and K % 32 = 4127 % 32 = 31. So the tail will always have K_tail ≡ 31 (mod 32) = not a multiple of 32.
So the only clean solution is padding. Let me implement it properly, either in __init__ or in forward.
Since `load_state_dict(strict=True)` requires matching shapes, I'll pad in forward.
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Now I realize the state_dict check requires matching shapes. Let me fix this — pad in forward, not in `__init__`.
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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)
assistant
reasoning (81 chars)
Now let me run check.py to verify correctness, then benchmark.py for performance.
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stderr (103 chars)
Exit code 1
FAIL: shape 1 {'M': 4096, 'N': 4096, 'K': 4127} seed 42 case nominal: solution contains NaN
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reasoning (2077 chars)
NaN in the output? That's unexpected. The kernel should be producing valid results. Let me think about what could cause NaN.
With the padded kernel:
- `_pad_tensor` creates a zero-initialized fp8 tensor (bit pattern 0x00 = 0.0 in fp8_e4m3)
- Copies the original data into the first K columns
- The kernel then loads full tiles with no masks
Could the padded area cause NaN? The fp8 zero (0x00) represents 0.0 in float8_e4m3fn format. When loaded into the MMA, it should contribute 0.0 to the accumulation. The dot product should be well-behaved.
Wait, but I'm comparing the padded kernel result against the reference. The reference uses the unpadded (original K) data. My kernel uses padded data. The padded columns should contribute zero, so the result should be identical (within numerical precision) to the unpadded case.
But NaN suggests something else is wrong. Maybe there's an issue with the padding or memory access.
Let me debug this. The issue is with shape 1 (M=4096, N=4096, K=4127). Let me test this specific shape.
Actually, wait — K=4127 padded to K_ALIGN=32 means K_padded=4128. Then BLOCK_K=128, and K_padded/128 = 32.25. So the loop runs for k in [0, 128, 256, ..., 3968, 4096]. At k=4096: k_remaining = 32.
But the kernel doesn't use k_remaining at all! It loads a full 128-element tile from x_padded and w_padded, even though only elements 4096..4127 (32 elements) are valid and elements 4128..4223 are out of bounds!
The issue is: K_padded=4128 is NOT a multiple of BLOCK_K=128. So on the last iteration, we load elements 4096..4223, but elements 4128..4223 are beyond K_padded=4128! This is an out-of-bounds memory access!
I need to ensure K_padded is a multiple of BOTH K_ALIGN (32) AND BLOCK_K (128), or use a different approach.
Let me fix: K_padded should be a multiple of BLOCK_K, not just K_ALIGN. BLOCK_K=128 is already a multiple of 32, so this is fine.
K_padded = ((K + BLOCK_K - 1) // BLOCK_K) * BLOCK_K
For K=4127: K_padded = ((4127 + 127) // 128) * 128 = 33 * 128 = 4224
This ensures the kernel always loads full, in-bounds tiles.
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The issue is that K_padded must be a multiple of BLOCK_K (128), not just K_ALIGN (32). The last iteration loads a full BLOCK_K tile, so K_padded must be evenly divisible by BLOCK_K.
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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)
assistant
reasoning (291 chars)
Wait, but I also need to update the comment about padding. Let me also update the docstring and the `_pad_tensor` usage to be consistent. Actually, the logic is already correct — `K_padded = ((K + K_ALIGN - 1) // K_ALIGN) * K_ALIGN` will now use 128 as the alignment. Let me re-run check.py.
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reasoning (41 chars)
Correctness passes. Now let me benchmark.
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stdout (1311 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T22:51:46.061895+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T22:51:46.278076+00:00 elapsed_s=0.216 ms=0.237728
shape=0 variant=solution tflops=578.135 gbps=282.293 ms=0.238
shape=0 solution_peak_fraction=0.5781
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T22:51:46.809803+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T22:51:46.827751+00:00 elapsed_s=0.018 ms=0.302128
shape=1 variant=solution tflops=458.346 gbps=222.961 ms=0.302
shape=1 solution_peak_fraction=0.4583
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T22:51:48.727461+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T22:51:48.733116+00:00 elapsed_s=0.006 ms=0.088064
shape=2 variant=solution tflops=48.771 gbps=770.977 ms=0.088
shape=2 solution_peak_fraction=0.0488
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T22:51:50.444092+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T22:51:50.477084+00:00 elapsed_s=0.033 ms=0.764656
shape=3 variant=solution tflops=629.089 gbps=252.320 ms=0.765
shape=3 solution_peak_fraction=0.6291
peak_fraction: 0.3003
RESULT: OK
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reasoning (1166 chars)
The results improved significantly:
- Shape 0 (4096×4096×4096): 578 TFLOPS, 0.578 peak fraction — same as before
- Shape 1 (4096×4096×4127): 458 TFLOPS, 0.458 peak fraction — HUGE improvement from 3.5 TFLOPS!
- Shape 2 (32×8192×8192): 48.8 TFLOPS, 770 GB/s — memory-bound
- Shape 3 (4096×14336×4096): 629 TFLOPS, 0.629 peak fraction — good
Geometric mean peak fraction: 0.3003 (up from 0.0893). Now RESULT: OK (was LOW).
The padding overhead for shape 1: padding from 4127 to 4224 adds 2.3% extra work. The TFLOPS calculation uses the original K=4127, so the "useful" TFLOPS is slightly lower than what the hardware actually computes. But 458 TFLOPS is still very good.
Now I need to figure out what the peak TFLOPS is. The report says 1000 TFLOPS peak for fp8. Let me check.
Actually, let me check: shape 0 achieves 578/1000 = 0.578. That's decent but could be better. The peak is probably around 1000 TFLOPS for fp8 on the RTX PRO 6000.
Let me push further — can I improve the kernel performance? Let me try:
1. Larger tile sizes
2. Multi-wave approach
3. Better occupancy
Actually, let me first look at what the peak TFLOPS actually is for fp8 on this GPU.
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Good progress! Shape 1 is now fast. Let me now optimize further. Let me check the peak and see what the top solutions achieve.
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stdout (274 chars)
Hardware: RTX_PRO_6000
Peak TFLOPS keys: {'fp4': 2000.0, 'nvfp4': 2000.0, 'mxfp4': 2000.0, 'fp6': 1000.0, 'fp8': 1000.0, 'bf16': 500.0, 'fp16': 500.0, 'tf32': 250.0, 'fp32': 125.0, 'int8': 1000.0, 'int4': 2000.0}
fp8 peak: 1000.0
bf16 peak: 500.0
Peak bandwidth: 1800.0 GB/s
assistant
reasoning (4889 chars)
So the fp8 peak is 1000 TFLOPS. My current results:
- Shape 0: 578 TFLOPS (57.8% of peak)
- Shape 1: 458 TFLOPS (45.8% of peak)
- Shape 2: 48.8 TFLOPS (memory-bound, 770 GB/s)
- Shape 3: 629 TFLOPS (62.9% of peak)
Geometric mean peak fraction: 0.300
For the memory-bound shape 2 (M=32, N=8192, K=8192):
- Bytes: 32*8192 + 8192*8192 + 32*8192*2 = 262,144 + 67,108,864 + 524,288 ≈ 67.9 MB
- FLOPs: 2 * 32 * 8192 * 8192 = 4.29 GFLOPs
- Peak bandwidth: 1800 GB/s
- At 770 GB/s, we're at 42.8% of peak bandwidth
For shape 0 (M=N=K=4096):
- FLOPs: 2 * 4096^3 = 137.4 GFLOPs
- Bytes: 4096^2 + 4096^2 + 4096^2 * 2 = 67.1 MB
I can do better. Let me try:
1. Use larger tile sizes for better compute utilization
2. Try 2D grid launch (separate program_id for M and N)
3. Maybe try autotuning
4. Optimize the padding to be cached/memoized
5. Try different BLOCK_M, BLOCK_N, BLOCK_K combinations
Actually, the current kernel uses BLOCK_M=128, BLOCK_N=128, BLOCK_K=128. On Blackwell with m16n8k32 MMA:
- Each block produces 128×128 = 16384 output elements
- Each MMA produces 16×8 = 128 output elements
- So each block needs 16384/128 = 128 MMAs per K-tile
- With 4 warps (128 threads), each warp does 32 MMAs per K-tile
- For BK=128: K=128/32 = 4 sub-steps per MMA tile = 4*32 = 128 MMA instructions per warp per K iteration
Actually, the number of warps per block is determined by Triton based on the tile size. Let me think about what block size gives good occupancy.
On Blackwell SM120, each SM has:
- 128KB shared memory
- 4 warp schedulers
- 65536 registers (64K x 32-bit)
For the kernel, each block uses:
- Shared memory: not explicitly used (Triton may use some for the MMA)
- Registers: each thread holds accumulator registers, pointer values, etc.
Let me try some larger tile sizes and profile. Let me also consider a 2D grid launch for better occupancy on skinny shapes.
Actually, for better performance, I should also try:
1. Using `tl.dot` with `max_num_imprecise_acc` parameter
2. Using larger BLOCK_M and BLOCK_N (e.g., 256×128 or 128×256)
Let me try a few things:
- BLOCK_M=256, BLOCK_N=128, BLOCK_K=128
- BLOCK_M=128, BLOCK_N=256, BLOCK_K=128
- BLOCK_M=128, BLOCK_N=128, BLOCK_K=256
And also try different GROUP_M values.
Actually, one big thing: the current kernel uses a 1D grid. This means each block handles a specific (pid_m, pid_n) pair. For M=32 (skinny), there are very few blocks in the M dimension, leading to low occupancy. Let me check the current grid size for each shape.
For shape 2 (M=32, N=8192):
- num_pid_m = ceil(32/128) = 1
- num_pid_n = ceil(8192/128) = 64
- Total blocks: 1 * 64 = 64 blocks
- With 188 SMs, occupancy is 64/188 = 34% — not great but not terrible
For shape 0 (M=N=K=4096):
- num_pid_m = 32, num_pid_n = 32
- Total blocks: 32 * 32 = 1024 blocks
- With 188 SMs, this is 5.4 waves — good occupancy
Let me try some optimizations:
1. First, let me try BLOCK_M=64 and BLOCK_N=256 for the skinny M case. With BLOCK_M=64:
- num_pid_m = ceil(32/64) = 1 (still just 1)
- num_pid_n = ceil(8192/256) = 32
- Total: 32 blocks
That's worse! Let me try BLOCK_M=32:
- num_pid_m = 1
Hmm, with M=32, we can't get more than 1 block in the M direction regardless.
For the skinny case, the real optimization would be to increase BLOCK_K to amortize the memory cost better. With BLOCK_K=256, each load brings in 256 elements per thread per iteration.
Let me focus on improving the large-matrix cases first (shapes 0, 1, 3) and then address the skinny case.
For large matrices, the key optimization levers are:
1. Tile sizes that maximize compute intensity
2. Occupancy (enough blocks to keep SMs busy)
3. Reducing instruction overhead
Let me try autotuning with Triton's autotune decorator. Actually, let me first try some manual tuning.
Actually, one important thing: the current kernel uses `tl.load` without any `mask` on K, which means no boundary checking for K. But it still uses masks for M and N in the store. The store mask is free because it's just predication on the store instruction.
Let me try a tuned version with different block sizes. I'll use Triton's autotuner.
Actually, let me start by measuring the current kernel's performance more carefully to understand where time is spent. Let me use ncu (NVIDIA Nsight Compute) for a quick profile.
Actually, profiling might take too long. Let me instead try some known-good configurations:
- For Blackwell, larger tiles (256) often work better because of the larger register file and shared memory
- BLOCK_K=128 is decent but 256 might give better compute intensity
Let me also try making BLOCK_K=256 to see if that helps.
And one more important thing: I should ensure the K_padded is actually a multiple of whatever BLOCK_K I use. Since I'm currently using BLOCK_K=128 and K_ALIGN=128, this is already aligned.
Let me try a few different configurations.
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stdout (65 chars)
Task #1 created successfully: Optimize GEMM kernel for all shapes
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reasoning (421 chars)
Let me set up autotuning. Triton has an `@triton.autotune` decorator that allows trying different configurations. But since the kernel function signature depends on constexpr values for the block sizes, the autotuner will recompile for each config.
Let me set up autotuning for the block sizes and see what works best.
Actually, let me try a simpler approach first: manually test a few configurations and pick the best.
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reasoning (133 chars)
Let me manually test different tile sizes for each shape and pick the best config. I should test a handful of promising combinations.
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stdout (2701 chars) — TRUNCATED
Shape BM BN BK ms TFLOPS
--------------------------------------------------
Sq 128 128 128 0.2073 663.0
Sq 128 128 256 ERROR: out of resource: shared memory, Required: 131072, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
Sq 128 256 128 6.7459 20.4
Sq 256 128 128 6.6413 20.7
Sq 256 256 128 ERROR: out of resource: shared memory, Required: 131072, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
Sq 64 256 128 0.2220 619.1
Sq 256 64 128 0.2239 613.9
Sq 64 128 256 0.2414 569.3
Sq 128 64 256 0.2412 569.9
BEST: (128, 128, 128) -> 663.0 TFLOPS
Tail 128 128 128 0.2125 651.5
Tail 128 128 256 ERROR: out of resource: shared memory, Required: 131072, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
Tail 128 256 128 6.9473 19.9
Tail 256 128 128 6.8155 20.3
Tail 256 256 128 ERROR: out of resource: shared memory, Required: 131072, Hardware limit: 101376. Reducing block sizes or `num_stages` may help.
Tail 64 256 128 0.2284 606.3
Tail 256 64 128 0.2378 582.3
Tail 64 128 256 0.2595 533.6
Tail 128 64 256 0.2613 529.9
BEST: (128, 128, 128) -> 651.5 TFLOPS
Skinny 128 128 128 0.0574 74.9
Skinny 128 128 256 ERROR: out of resource: shared mem
... (1201 more chars)
assistant
reasoning (4293 chars)
Interesting results:
1. The large tile configs (128×256, 256×128, 256×256) are VERY slow (1.7-20 TFLOPS). This is likely because they exceed the shared memory or register budget for the default Triton compilation without explicit shared memory usage. But our kernel doesn't EXPLICITLY use shared memory — Triton might be adding software pipelining stages. The "num_stages" default might cause shared memory allocation for prefetch buffers.
2. BLOCK_K=256 with smaller M/N tiles causes shared memory errors: "Required: 131072, Hardware limit: 101376". This is because Triton allocates shared memory for multi-stage pipelining. For BLOCK_K=256, each prefetch buffer is (BLOCK_M * BLOCK_K + BLOCK_N * BLOCK_K) bytes of fp8, and with `num_stages` defaulting to something like 3-5, this adds up.
3. The best configs:
- Square/Rect: (128, 128, 128) → ~650-663 TFLOPS
- Tail: (128, 128, 128) → ~651 TFLOPS
- Skinny: (64, 128, 256) → ~137 TFLOPS (much better than 75 TFLOPS with BLOCK_K=128)
For the skinny case, BLOCK_K=256 helps because:
- M=32 is very small, so there are few blocks
- Larger K reduces the number of iterations, reducing loop overhead
- The memory access pattern is better amortized
But BLOCK_K=256 for large matrices causes shared memory overflow. So I need different configurations for different shapes.
Let me think about how to implement this. I could:
1. Use autotuning to pick the best config for each shape
2. Use heuristics based on M, N, K
3. Use different kernel specializations
Triton's `@triton.autotune` decorator can handle this. Let me set up autotuning with a set of configs that avoid the shared memory issues.
Actually, for the large shapes, the issue with BLOCK_K=256 + BLOCK_M=128 is that Triton allocates 2*128*256 = 65536 bytes per stage for the fp8 buffers. With `num_stages=3` (default), that's 196608 bytes, which exceeds 101376 bytes (99KB available? No, 128KB total, but some is reserved).
Actually wait, let me re-examine. The shared memory error says "Required: 131072, Hardware limit: 101376". 131072 = 128KB. But the hardware limit is 101376 = 99KB? That's odd — Blackwell has 128KB shared memory per SM.
Hmm, 101376 = 99 * 1024. Maybe there's some configuration that limits shared memory. Or maybe the limit is per-block and there's some overhead.
In any case, BLOCK_K=128 is the safe maximum for the large shapes.
For the skinny case (M=32), I can use BLOCK_K=256 with BLOCK_M=64 (smaller M) to stay within budget: 64*256 + 128*256 = 49152 bytes per stage, with num_stages=3 = 147456 bytes — still too much... Wait, B uses BLOCK_N not BLOCK_M. So it's: BLOCK_M*BLOCK_K + BLOCK_N*BLOCK_K = 64*256 + 128*256 = 49152 bytes. With num_stages=3, that's 147456 bytes > 99KB. But the test showed it works... maybe Triton uses only 2 stages for this config?
Actually, let me check: 64*256=16384, 128*256=32768. Total per stage: 49152 bytes. 128KB - 49152*2 = 128KB - 96KB = 32KB remaining for other shared memory. So num_stages=2 works, num_stages=3 doesn't.
For the (128, 128, 256) config: 128*256+128*256 = 65536 per stage. 65536*2 = 131072 = 128KB. That's exactly the shared memory limit. But the error says hardware limit is 101376 = 99KB. So even num_stages=2 doesn't work.
Hmm, I think there might be a way to set `num_stages` in Triton's autotuner to control this. Or I can use `@triton.autotune` with `num_stages` as a tuning parameter.
Actually, let me try setting `num_stages=2` explicitly in the kernel to fit within shared memory for larger tiles.
Wait, `num_stages` is a parameter of `@triton.autotune`, not the kernel itself. Let me set up autotuning properly.
For now, let me use a pragmatic approach:
1. For the skinny case (M <= 64): use (64, 128, 256)
2. For all other cases: use (128, 128, 128)
Let me also see if I can get BLOCK_K=256 working with the large shapes by reducing num_stages or by using other techniques.
Actually, let me try one more thing: use a 2D grid instead of 1D with swizzling. This might improve occupancy for some shapes.
Let me also try using different pipelining configurations with Triton's autotuner.
Actually, the simplest and most effective thing right now: use shape-specific tile sizes. Let me update the kernel to use different configurations based on the problem dimensions.
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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 (45 chars)
Let me verify correctness and then benchmark.
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stdout (1312 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T22:54:05.147620+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T22:54:05.356983+00:00 elapsed_s=0.209 ms=0.237072
shape=0 variant=solution tflops=579.735 gbps=283.074 ms=0.237
shape=0 solution_peak_fraction=0.5797
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T22:54:05.885626+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T22:54:05.903423+00:00 elapsed_s=0.018 ms=0.302224
shape=1 variant=solution tflops=458.200 gbps=222.890 ms=0.302
shape=1 solution_peak_fraction=0.4582
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T22:54:07.772817+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T22:54:07.778731+00:00 elapsed_s=0.006 ms=0.062928
shape=2 variant=solution tflops=68.252 gbps=1078.936 ms=0.063
shape=2 solution_peak_fraction=0.0683
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T22:54:09.474584+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T22:54:09.507631+00:00 elapsed_s=0.033 ms=0.765104
shape=3 variant=solution tflops=628.720 gbps=252.172 ms=0.765
shape=3 solution_peak_fraction=0.6287
peak_fraction: 0.3267
RESULT: OK
assistant
reasoning (2277 chars)
Results improved:
- Shape 0: 580 TFLOPS (same)
- Shape 1: 458 TFLOPS (same)
- Shape 2: 68.3 TFLOPS, 1079 GB/s — improved from 49 TFLOPS! The BLOCK_K=256 for skinny M is helping significantly.
- Shape 3: 629 TFLOPS (same)
Geometric mean peak fraction: 0.327 (up from 0.300).
Let me push further. Let me try to improve the large-matrix cases. The current bottleneck for shapes 0/1/3 might be:
1. Shared memory bandwidth
2. Occupancy
3. Padding overhead
Let me try a different approach for large matrices. Let me check if using BLOCK_K=128 with num_stages control helps fit larger tiles.
Actually, let me try reducing num_stages to fit BLOCK_K=256 for all shapes. I can use the `num_stages` parameter in Triton's autotuner or as a config parameter.
Actually, one thing I notice: the current kernel doesn't use any explicit shared memory allocation. The `tl.load` directly from global memory. Triton might be adding software pipelining automatically based on heuristics. On Blackwell with TMA (Tensor Memory Access) support, the compiler might use different strategies.
Let me try using `@triton.autotune` to find the best config per shape. This way Triton can also tune `num_stages` and `num_warps`.
But actually, Triton's autotuner requires a list of configs, and the kernel must be written to accept `BLOCK_M`, `BLOCK_N`, `BLOCK_K` as constexpr values (which my kernel already does). Let me set it up.
Actually, let me try something simpler first. Let me check if using explicit shared memory prefetching improves performance. But that requires significant kernel restructuring.
Let me instead focus on the padding overhead. For shapes 0 and 3, K=4096 is already a multiple of 128, so no padding is needed. For shape 1, K=4127 pads to 4224, adding 2.3% overhead. This seems acceptable.
What about occupancy? For shape 0 (4096×4096), with 128×128 tiles, we have 32×32=1024 blocks. With 188 SMs, that's 5.4 waves. Good occupancy.
Let me try one more thing: use explicit `num_stages` and `num_warps` in the kernel invocation to see if different pipelining helps.
Actually, Triton's JIT compiler automatically chooses num_warps and num_stages. I can influence this with `@triton.autotune`.
Let me set up a proper autotuning approach with configs that are known to work.
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stdout (400 chars)
Sq: best config = BM=128 BN=128 BK=128 num_stages=3 num_warps=4
Timing: 0.2207 ms, 622.8 TFLOPS
Tail: best config = BM=128 BN=128 BK=128 num_stages=3 num_warps=4
Timing: 0.2325 ms, 595.5 TFLOPS
Skinny: best config = BM=64 BN=64 BK=256 num_stages=2 num_warps=4
Timing: 0.0338 ms, 127.1 TFLOPS
Rect: best config = BM=128 BN=128 BK=128 num_stages=3 num_warps=4
Timing: 0.8678 ms, 554.3 TFLOPS
assistant
reasoning (2940 chars)
The autotuner selected (128, 128, 128) with num_stages=3, num_warps=4 for all large shapes, and (64, 64, 256) with num_stages=2, num_warps=4 for the skinny case. But the timing results are slightly different from the benchmark — likely because of differences in how timing is done (benchmark.py uses `time_variant` with different methodology).
Also interesting: for the skinny case, the autotuner picked (64, 64, 256) but my manual test showed (64, 128, 256) was faster. The autotuner only tests the configs I give it — for skinny, it tried several but maybe (64, 128, 256) wasn't in the config list.
Let me update the solution to use the best configs. For the skinny case, I'll keep (64, 128, 256) which from my manual test was 137 TFLOPS. For large cases, (128, 128, 128) with num_stages=3, num_warps=4 is consistently best.
But wait — I can't set num_stages and num_warps in the kernel invocation directly without the autotuner. Let me check if there's a way to pass these as launch parameters...
Actually, `num_stages` and `num_warps` are compilation parameters that can be passed to the kernel at compile time. In Triton 3.x, there are `@triton.jit` preprocessor options or I can use `@triton.autotune`.
Let me think about whether I should use autotuning in the final solution. The autotuner adds a one-time cost (it tests each config once) but caches the result. Subsequent calls use the cached best config. This means the first call is slower but subsequent calls are fast. The benchmark.py runs 30 trials and uses `time_variant` which handles warmup, so the autotuning overhead should be amortized.
However, `time_variant` might not account for the first-call autotuning overhead properly. Let me check how it works.
Actually, looking at the benchmark more carefully, the `time_variant` function likely does warmup iterations before timing. If the warmup includes the autotuning, the timed iterations should use the cached best config.
But there's a risk: autotuning has HIGH variance on the first few runs. Some configs might cause OOM or shared memory errors. Let me stick with the manual approach for now and focus on performance.
Let me go back to the manually-tuned approach but try one more thing: using `num_stages` and `num_warps` parameters. In Triton 3.x, I can specify these as kernel compile-time hints.
Actually, looking at the benchmark results:
- Shape 0: 580 TFLOPS (0.58 peak) — good
- Shape 3: 629 TFLOPS (0.63 peak) — great
- Shape 1: 458 TFLOPS (0.46 peak) — OK but lower due to padding overhead and slightly larger K
- Shape 2: 68 TFLOPS / 1079 GB/s — memory bandwidth bound
For shape 1, the lower performance might be from the padding overhead (allocating + copying fp8 data). Let me check if I can avoid the padding by using a different kernel for the tail.
Actually, let me try a hybrid kernel: process full tiles without masks (fast), and handle the tail with masks only for the tail iteration.
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stdout (280 chars)
Command running in background with ID: bm8tnvjd6. Output is being written to: /tmp/claude-1002/-workspace-problems-01-fp8-gemm/7885f009-0e25-41c7-955d-04515b48ff29/tasks/bm8tnvjd6.output. You will be notified when it completes. To check interim output, use Read on that file path.
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reasoning (2259 chars)
Let me wait for that and continue thinking about other optimizations.
While that runs, let me think about what else I can do:
1. The current kernel uses direct global memory loads for fp8 data. Triton's compiler may or may not insert prefetching into shared memory. By default, Triton generates a software-pipelined loop with `num_stages` stages of prefetch buffers in shared memory. The `num_stages` parameter controls this.
2. For 128×128×128 tiles with fp8 data:
- Per stage: (128*128 + 128*128) = 32768 bytes of fp8 data
- With num_stages=3: 3 * 32768 = 98304 bytes ≈ 96KB
- Blackwell has 128KB shared memory, so num_stages=3 fits (barely)
- num_stages=4 would be 128KB which might or might not fit (there's overhead)
3. The autotuner preferred num_stages=3 for large shapes, which makes sense — more pipelining hides global memory latency better.
4. For the skinny case with (64, 128, 256):
- Per stage: 64*256 + 128*256 = 49152 bytes
- num_stages=2: 98304 bytes ≈ 96KB — fits
- num_stages=3: 147456 bytes ≈ 144KB — exceeds
5. The throughput numbers are decent but not spectacular. Let me think about what could push it higher.
Wait, let me look at the peak fraction numbers again. The geomean is 0.327. That means across all shapes, the weighted performance is 32.7% of peak. For reference, the bf16 reference would be capped at 500/1000 = 0.5 peak fraction (since bf16 peak is half of fp8 peak). My fp8 kernel should theoretically reach up to 1000 TFLOPS but in practice, 60-70% of peak is common for well-tuned GEMMs.
Let me see if I can push the large shapes higher. Some ideas:
- Use 2D grid (one program axis for M, one for N) instead of 1D swizzled grid
- Try `tl.dot_scaled`
- Use cooperative groups / warpgroup MMA
Actually, let me check if the current 1D grid is causing load imbalance. For shapes like 4096×14336 (rectangular), the N dimension is much larger than M. With GROUP_M=8 swizzling, the blocks might not be distributed optimally.
Let me also check if there's a simple way to use the new Blackwell-specific features.
Actually, I think I should try a 2D grid launch. Instead of a 1D grid with swizzle, use program_id(0) for M and program_id(1) for N. This gives the hardware scheduler more flexibility.
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stdout (135 chars)
<retrieval_status>timeout</retrieval_status>
<task_id>bm8tnvjd6</task_id>
<task_type>local_bash</task_type>
<status>running</status>
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reasoning (72 chars)
The task is still running, let me wait a bit longer or check the output.
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stdout (373 chars)
<retrieval_status>success</retrieval_status>
<task_id>bm8tnvjd6</task_id>
<task_type>local_bash</task_type>
<status>completed</status>
<exit_code>0</exit_code>
<output>
K= 4096: 0.0321 ms, max_diff=8.000000
K= 4127: 2.0838 ms, max_diff=8.000000
K= 4095: 2.0190 ms, max_diff=8.000000
K= 4065: 2.0209 ms, max_diff=8.000000
K= 4033: 2.0200 ms, max_diff=8.000000
</output>
assistant
reasoning (3053 chars)
The hybrid kernel still has the same issue: it's slow for tails and has a large max_diff of 8.0 (correctness issue). The correctness issue is present even for perfectly aligned K=4096 (diff=8.0), which suggests a more fundamental bug in this kernel variant.
Wait, the diff for K=4096 (aligned) is also 8.0. That means the kernel is broken even for aligned data. Compare with the padded approach which passes check.py...
The issue is likely with the condition `if k_remaining > 0:` which is a runtime conditional. For K=4096 (perfectly aligned), k_remaining = 0, so the tail branch is skipped, and only the full-tile loop runs. But the result is still wrong (diff=8.0), so there's a bug in the full-tile loop too.
Hmm, actually the loop `for _ in range(0, NUM_FULL_TILES):` — `NUM_FULL_TILES = K // BLOCK_K`. For K=4096, BLOCK_K=128, NUM_FULL_TILES = 32. This should run 32 times, just like the working kernel's `for k in range(0, K, BLOCK_K)`. These should be equivalent...
Wait, the difference: the working kernel uses `for k in range(0, K_padded, BLOCK_K)` where `K_padded` is a triton JIT parameter. The hybrid uses `NUM_FULL_TILES = K // BLOCK_K` where K is runtime and BLOCK_K is constexpr. These should both compile to similar loops.
But the correctness issue persists even for aligned data. This means there's a fundamental difference in how the kernel is compiled. Let me check if the issue is with how Triton compiles the conditional loop vs unconditional loop.
Actually, I'm going in circles. Let me step back and focus on what WORKS: the padded approach with BLOCK_M=128, BLOCK_N=128, BLOCK_K=128 for large shapes and (64, 128, 256) for skinny. This passes correctness and gets decent performance.
Let me now try to improve the large-shape performance. The current 580-630 TFLOPS is 58-63% of the 1000 TFLOPS peak. For a first-cut kernel, this is reasonable. But let me see if I can squeeze more out.
Key optimization ideas:
1. Use a 2D grid launch (separate program_id for M and N) — this might improve scheduling
2. Try different block sizes for the rectangular shape (4096×14336)
3. Add `tl.multiple_of` hints for the compiler
4. Use `tl.max_contiguous` or other optimizations
Actually, let me try using a 2D grid and see if it helps. The current 1D swizzled grid requires computing pid_m and pid_n from a 1D index, which adds a few integer ops. A 2D grid is cleaner.
Let me also try `multiple_of` hints for strides, which help the compiler generate better addressing modes.
And let me try the square shape 4096×4096 with a larger tile to see if BLOCK_M=256, BLOCK_N=128, BLOCK_K=64 works (reducing BK to fit in shared memory).
Wait, actually, let me look at this from a different angle. What if I use `tl.dot_scaled`? This is a new Triton feature that directly supports fp8 scaled dot products.
Actually, I think the most impactful optimization would be to use the 2D grid, plus some `multiple_of` hints. Let me also try `BLOCK_M=256, BLOCK_N=128, BLOCK_K=64` which reduces the K tile size but increases the output tile size.
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Let me try a 2D grid kernel with compiler hints for better performance.
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stdout (400 chars)
2D Grid — M=4096, N=4096, K=4096
BM BN BK ms TFLOPS diff
128 128 128 0.2093 656.7 2.000000
128 128 64 0.2051 670.2 4.000000
256 128 64 0.8322 165.1 1.000000
128 256 64 0.8267 166.2 2.000000
64 256 128 0.2242 613.1 4.000000
256 64 128 0.2274 604.3 2.000000
256 256 64 11.3731 12.1 4.000000
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reasoning (3468 chars)
The 2D grid with (128, 128, 64) gives 670 TFLOPS vs 657 TFLOPS for (128, 128, 128). That's a small improvement. But the diff is 4.0 which is a correctness issue — these all seem to have correctness issues compared to the reference (which is the bf16 reference from reference.py).
Wait, the correctness issues are all quite large (1-4). But the kernel that passes check.py uses padded data and the EXACT SAME logic. What's different?
Actually, I think my reference computation in the test might be wrong. Let me use the actual reference model. But more importantly, let me verify with check.py which uses the REAL reference model.
Let me take the 2D grid kernel with (128, 128, 64) and integrate it into solution.py, then run check.py. If check.py passes, the correctness is fine and the issue was in my manual reference computation.
Actually, the diff in my test is large because my reference uses `(x[:, :K].to(torch.bfloat16) @ w[:, :K].to(torch.bfloat16).T)` without the weight_scale multiplication. Or with wrong scale. Let me not worry about my test's reference — I trust check.py.
Let me go ahead and update solution.py to use the 2D grid kernel. But also, I notice that (128, 128, 64) gives 670 TFLOPS, which is better than 580 with the 1D swizzled grid (128, 128, 128).
Wait, but the benchmark says 580, not 657. The difference is because:
1. Benchmark measures differently (time_variant with warmup/trials)
2. My manual test uses `torch.ones` for scale instead of the actual scale
Let me just update to use the 2D grid with (128, 128, 64) for large shapes and see what the actual benchmark shows.
Actually, wait. BLOCK_K=64 means the inner loop runs twice as many iterations (K_padded/BLOCK_K = 64 vs 32 iterations). Each iteration does a smaller dot product. Could this be faster because:
- Less shared memory per stage: 128*64 + 128*64 = 16384 bytes
- More stages can fit: up to 6 stages (128KB/16384 ≈ 8 stages)
- Better pipelining of global loads
Or could it be faster because of how the dot product maps to MMA instructions? Each dot is (128, 64) @ (64, 128), which requires ceil(128/16)*ceil(128/8)*ceil(64/32) = 8*16*2 = 256 MMA instructions per K iteration. vs (128, 128) @ (128, 128): ceil(128/16)*ceil(128/8)*ceil(128/32) = 8*16*4 = 512 MMAs. Half the MMAs per iteration but twice the iterations — same total.
Hmm, the total work is the same. But the shared memory usage is lower, allowing more pipelining. This might be the key.
Let me also try BLOCK_K=32:
- Per stage: 128*32 + 128*32 = 8192 bytes
- Very low shared memory usage, more stages possible
- Each dot: (128, 32) @ (32, 128) = 8*16*1 = 128 MMAs per iteration
- 4096/32 = 128 iterations
- Total: 128*128 = 16384 MMAs vs before: 32*512 = 16384 MMAs — same
But more iterations means more loop overhead and more address updates.
Let me integrate the best configs into solution.py and run the benchmark.
Actually, let me reconsider. The difference between my manual test (657 TFLOPS) and the benchmark (580 TFLOPS) is significant. Let me look at what the benchmark does differently:
- benchmark.py uses `time_variant` from the framework
- It creates the actual model with correct weight_scale
- It uses the correct problem shapes
The difference might be from weight_scale multiplication in the kernel (which I'm testing with `torch.ones`).
Let me just update the kernel and re-benchmark. The key change: 2D grid with (128, 128, 64) for large shapes, (64, 128, 256) for skinny.
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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)
assistant
reasoning (1226 chars)
Wait, BLOCK_K=64 might not be a multiple of 32. Let me check: 64 is a multiple of 32 (64 = 2*32). So that's fine for the MMA instruction.
But I should also make sure K_ALIGN is a multiple of BLOCK_K. Currently I use `K_padded = ((K + BLOCK_K - 1) // BLOCK_K) * BLOCK_K` which ensures K_padded is a multiple of BLOCK_K.
For the large case: BLOCK_K=64, K=4096, K_padded=4096 (already aligned).
For tail case: K=4127, K_padded=((4127+63)//64)*64 = (4190//64)*64 = 65*64 = 4160? Wait: 4190/64 = 65.46875, floor = 65, 65*64 = 4160. But 4160 is NOT a multiple of 128. Does that matter?
Actually, the only requirement is that K_padded is a multiple of BLOCK_K (64). Since 4160 = 65*64, that's fine. Each inner loop iteration loads exactly 64 K elements. The last iteration loads elements 4096..4159 (indices 0-based), which is 64 elements from x_padded. Since x_padded has 4160 columns, this is in bounds.
But wait, I need to double check: 4127 rounded up to next multiple of 64: 4127 = 64*64 + 31, so K_padded = 65*64 = 4160. The last 33 elements (4160-4127=33) are padding. The kernel loop runs: k = 0, 64, 128, ..., 4096 = 65 iterations. At k=4096, k+K=4160 which is valid. Good.
Let me verify correctness and then benchmark.
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reasoning (34 chars)
Correctness passes. Now benchmark.
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stdout (1312 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T23:04:25.358109+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T23:04:25.566972+00:00 elapsed_s=0.209 ms=0.230640
shape=0 variant=solution tflops=595.902 gbps=290.968 ms=0.231
shape=0 solution_peak_fraction=0.5959
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T23:04:26.091212+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T23:04:26.108439+00:00 elapsed_s=0.017 ms=0.288864
shape=1 variant=solution tflops=479.392 gbps=233.199 ms=0.289
shape=1 solution_peak_fraction=0.4794
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T23:04:27.988195+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T23:04:27.994108+00:00 elapsed_s=0.006 ms=0.061648
shape=2 variant=solution tflops=69.669 gbps=1101.338 ms=0.062
shape=2 solution_peak_fraction=0.0697
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T23:04:29.699371+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T23:04:29.731714+00:00 elapsed_s=0.032 ms=0.745840
shape=3 variant=solution tflops=644.959 gbps=258.685 ms=0.746
shape=3 solution_peak_fraction=0.6450
peak_fraction: 0.3366
RESULT: OK
assistant
reasoning (3445 chars)
Results:
- Shape 0: 596 TFLOPS (0.596) — improved from 580
- Shape 1: 479 TFLOPS (0.479) — improved from 458
- Shape 2: 69.7 TFLOPS / 1101 GB/s (0.070) — slightly improved
- Shape 3: 645 TFLOPS (0.645) — improved from 629
Geometric mean: 0.337 — up from 0.327.
That's a nice improvement from the 2D grid and BLOCK_K=64. Let me try one more thing: test BLOCK_K=32 for the large shapes to see if even smaller K tiles help.
Actually wait, let me think about the roofline. For fp8 on Blackwell, the peak is 1000 TFLOPS. The current 595-645 TFLOPS for the large compute-bound shapes is 60-65% of peak.
For a GEMM kernel, getting 60-65% of theoretical peak is decent but could be better. Usually, well-tuned GEMMs reach 70-85% of peak. Let me think about what's limiting us.
Possible bottlenecks:
1. Global memory bandwidth: we're reading fp8 data at M*K + N*K = 2*4096*4096 = 33.6 MB of fp8 data per GEMM, and writing M*N*2 = 33.6 MB of bf16 data. Total: 67 MB. At 1800 GB/s, this takes 37μs. Our kernel takes 230μs, so we're compute-bound (not memory-bound).
2. L2 cache misses: The fp8 data doesn't fit in L2 (128 MB). For 4096×4096, each row is 4KB. But we access data in a strided pattern.
3. Shared memory bandwidth: For each 128×64 tile, we load 8KB of A and 8KB of B from global to shared (via prefetch). Then we read from shared for the MMA. At 128 bytes/cycle/SM shared memory bandwidth...
Actually, let me think about the computational intensity. Each block does:
- 128*128*64 = 1,048,576 multiply-accumulates per K iteration
- With K=4096, BLOCK_K=64: 64 iterations → 67,108,864 MACs per block
- Each MAC is 2 FLOPs → 134.2 MFLOPs per block
- Data loaded per block: 128*4096 (fp8 from x) + 128*4096 (fp8 from w) = 1 MB
- Data stored per block: 128*128*2 = 32 KB
- Compute intensity: 134.2 MFLOPs / 1.032 MB ≈ 130 FLOPs/byte
At 1000 TFLOPS and 1800 GB/s, the roofline break-even is 1000/1.8 = 556 FLOPs/byte. Our compute intensity of 130 is below this, meaning we're possibly bandwidth-limited! But wait, that's per-block. The global bandwidth is shared across all blocks.
Actually, the right way to think about it: each element is reused sqrt(.) times. For the A matrix: each element of x is used N/BLOCK_N times (across N-dimension blocks). For 4096/128 = 32 blocks in N, each x element is reused 32 times. For w: each element is reused M/BLOCK_M = 32 times.
From L2 cache perspective: the working set is 2*4096*4096 = 33.6 MB of fp8 data, which should mostly fit in L2 (128 MB). So L2 hit rate should be good.
From shared memory: each block loads 128*4096 bytes of each matrix, but this is spread across 64 iterations with 3-stage pipelining. The shared memory acts as a prefetch buffer.
The performance might be limited by:
1. Instruction throughput (MMA instruction dispatch rate)
2. Register pressure
3. Occupancy
Let me check occupancy. For the (128, 128, 64) config:
- Grid: 32×32 = 1024 blocks (for 4096×4096)
- Each block uses 4 warps (128 threads)?
- 188 SMs: each SM gets ~5.4 blocks
- If each block uses 128 threads = 4 warps, each SM has ~22 warps
- Each SM has 4 warp schedulers → ~5.5 warps per scheduler
- This is decent occupancy
Let me try increasing the tile sizes to use more warps per block.
Actually, let me try one more thing: BLOCK_K=32. This would give:
- Per stage: 128*32 + 128*32 = 8KB
- num_stages could be higher (e.g., 4-8)
- More iterations (128 vs 64) but better pipelining
Let me test it.
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stdout (95 chars)
BK= 32: 0.2472 ms, 556.1 TFLOPS
BK= 64: 0.2011 ms, 683.3 TFLOPS
BK=128: 0.2054 ms, 669.0 TFLOPS
assistant
reasoning (813 chars)
BLOCK_K=64 gives the best results (683 TFLOPS in my test). BLOCK_K=32 is slower (556 TFLOPS) — too many iterations. BLOCK_K=128 is slightly slower than 64 (669 vs 683).
Actually, these numbers are from my manual test. The benchmark showed 596 TFLOPS for the same config. The difference is because my test uses `torch.ones` for scale and doesn't use the reference model's scale computation. But the relative ranking should be similar.
Let me now try some additional optimizations:
1. Try different M/N tile combinations with BLOCK_K=64
2. Try the skinny case with different configs
3. Maybe try `tl.multiple_of` hints
Actually, let me first check: for BLOCK_K=64 and BLOCK_M=256, BLOCK_N=128:
- Per stage: 256*64 + 128*64 = 24576 bytes
- num_stages=3: 72KB — fits
- num_stages=4: 96KB — fits
Let me test this.
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tool
stdout (367 chars)
BM=128 BN=128 BK= 64: 0.2007 ms, 684.7 TFLOPS
BM=256 BN=128 BK= 64: 0.8249 ms, 166.6 TFLOPS
BM=128 BN=256 BK= 64: 0.8190 ms, 167.8 TFLOPS
BM=256 BN=256 BK= 64: 11.3537 ms, 12.1 TFLOPS
BM=256 BN=128 BK= 32: 0.7489 ms, 183.5 TFLOPS
BM=128 BN=256 BK= 32: 0.7299 ms, 188.3 TFLOPS
BM= 64 BN=256 BK= 64: 0.2137 ms, 643.3 TFLOPS
BM=256 BN= 64 BK= 64: 0.2150 ms, 639.2 TFLOPS
assistant
reasoning (2719 chars)
Interesting! (128, 128, 64) is clearly the best at 685 TFLOPS. Any config with BM=256 or BN=256 is much slower (160-180 TFLOPS). This suggests that 256-wide tiles exceed some resource limit.
Why would 256-wide tiles be slow?
- 256 threads per block = 8 warps
- For 256×128 output with 4 warps: each warp handles 256*128/4 = 8192/128 = 64 MMA operations — equivalent
- But each warp handles tiles that span 256 in M dimension, needing ceil(256/16)=16 MMA tiles in M per warp
Actually, the issue might be that Triton can't efficiently decompose a 256-wide tile with 4 warps. 256/16 = 16 MMA tiles in M, 128/8 = 16 MMA tiles in N. Total: 256 MMA tiles per K-iteration. With 4 warps, each warp does 64 MMAs. But the warp can only work on one MMA at a time, and the register pressure from holding 64*4 f32 accumulator values per warp might be too high.
Actually, 256×128 = 32768 elements. With 4 warps and 32 threads each: 32768/128 = 256 elements per thread = 256 f32 registers. That's way too many for a single thread! The accumulator for a 256×128 tile requires each thread to hold 256 f32 values, which is 1024 bytes = way beyond register budget.
So for 256-wide tiles, Triton must be tiling the output differently, possibly using shared memory for the accumulator, which is slow.
The (128, 128, 64) config: 128×128 = 16384 elements, 16384/128 = 128 elements per thread = 128 f32 registers per thread = 512 bytes. This is still a lot but more reasonable. Each thread holds 128 f32 accumulators, which fits in the register file (each SM has 65536 registers = 256KB, spread across warps).
So (128, 128, 64) seems to be the sweet spot. Let me also check the skinny case more carefully.
For M=32, N=8192, K=8192:
- (64, 128, 256): blocks = ceil(32/64)*ceil(8192/128) = 1*64 = 64 blocks
- (32, 128, 256): blocks = 1*64 = 64 blocks
- (64, 256, 128): blocks = 1*32 = 32 blocks
With fewer blocks, occupancy might suffer. But the skinny M case is memory-bound anyway.
Let me try a few more configs for the skinny case.
Actually, I think the current solution is decent. Let me keep (128, 128, 64) for large shapes and (64, 128, 256) for skinny. Let me run the final benchmark and check the results.
Wait, actually let me try one more thing: for the rectangular shape (4096×14336), the N dimension is very large. Maybe I should use a different BN for that case. With BN=128 and N=14336, we get 112 blocks in N (14336/128 = 112). Let me try BN=256:
- Blocks in N: ceil(14336/256) = 56
- (128, 256, 64) was slow (168 TFLOPS), but maybe (128, 256, 32) would be different...
No, I already tested (128, 256, 64) and it was slow. The issue is the 256-N dimension, not the BK.
Let me go with the current config and finalize.
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The current (128,128,64) for large shapes and (64,128,256) for skinny is already at the sweet spot. Let me finalize and run the benchmark.
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tool
stdout (1312 chars)
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T23:05:19.008049+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T23:05:19.216382+00:00 elapsed_s=0.208 ms=0.230304
shape=0 variant=solution tflops=596.772 gbps=291.393 ms=0.230
shape=0 solution_peak_fraction=0.5968
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T23:05:19.740298+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T23:05:19.757547+00:00 elapsed_s=0.017 ms=0.287712
shape=1 variant=solution tflops=481.312 gbps=234.133 ms=0.288
shape=1 solution_peak_fraction=0.4813
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T23:05:21.628105+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T23:05:21.634015+00:00 elapsed_s=0.006 ms=0.062000
shape=2 variant=solution tflops=69.274 gbps=1095.085 ms=0.062
shape=2 solution_peak_fraction=0.0693
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T23:05:23.329914+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T23:05:23.362082+00:00 elapsed_s=0.032 ms=0.741216
shape=3 variant=solution tflops=648.983 gbps=260.299 ms=0.741
shape=3 solution_peak_fraction=0.6490
peak_fraction: 0.3371
RESULT: OK
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reasoning (1904 chars)
The results are stable. Geomean peak fraction is 0.337.
Let me think about whether there's more headroom. The current 597-649 TFLOPS for large compute-bound shapes represents about 60-65% of the fp8 peak (1000 TFLOPS). For well-tuned GEMM, 70-80% is achievable.
What might be limiting performance:
1. No explicit shared memory management — Triton's automatic pipelining might not be optimal for fp8
2. No warp-level optimizations
3. The padding overhead for K=4127 is about 2.3%
Let me try one more thing: a CUDA kernel with inline PTX. This would give me full control over:
- Shared memory prefetching
- MMA instruction scheduling
- Register allocation
- Tail handling without padding
But this is complex. Let me estimate: writing a full CUDA kernel with inline PTX could take significant time, and the benefit might be 10-20% more TFLOPS. Let me try a simpler optimization first: using `tl.dot` with `max_num_imprecise_acc` flag to allow more aggressive hardware optimizations.
Actually, let me try something else. In Triton 3.x, there's `@triton.autotune` that can also tune `num_warps` and `num_stages`. Let me try autotuning with more configs for the large shapes.
Also, I wonder if adding `tl.multiple_of` hints would help the compiler generate better code. These hints tell the compiler that certain pointers are aligned or dimensions are multiples of certain values, allowing it to use more efficient addressing modes.
Let me try:
1. Adding `tl.multiple_of` hints for stride_ak and stride_bk (which are 1 for contiguous fp8 tensors)
2. Adding `tl.max_contiguous` for the fp8 loads
Actually, `stride_ak = 1` and `stride_bk = 1` for contiguous fp8 tensors. The compiler should already know this from the constexpr strides... but wait, the strides are passed as runtime arguments to the kernel. Using `tl.multiple_of` would hint the compiler about alignment.
Let me try this optimization.
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stderr (3121 chars) — TRUNCATED
Exit code 1
Traceback (most recent call last):
File "/workspace/.venv/lib/python3.11/site-packages/triton/language/core.py", line 43, in wrapper
return fn(*args, **kwargs)
^^^^^^^^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/triton/language/core.py", line 2911, in multiple_of
return _semantic.multiple_of(input, values)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/triton/language/semantic.py", line 1806, in multiple_of
if max(1, len(x.shape)) != len(values):
^^^^^^^
AttributeError: 'constexpr' object has no attribute 'shape'
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/tmp/test_hints.py", line 46, in <module>
for _ in range(5): gemm_hints[g](x,w,y,ws,M,N,Kp,x.stride(0),x.stride(1),w.stride(0),w.stride(1),y.stride(0),y.stride(1),BLOCK_M=128,BLOCK_N=128,BLOCK_K=64)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/triton/runtime/jit.py", line 370, in <lambda>
return lambda *args, **kwargs: self.run(grid=grid, warmup=False, *args, **kwargs)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/workspace/.venv/lib/python3.11/site-packages/triton/runtime/jit.py", line 720, in run
... (1621 more chars)
assistant
reasoning (4422 chars)
`tl.multiple_of` doesn't work with constexpr values (which `stride_ak` etc. become when captured in the kernel closure). Let me skip this optimization and focus on what works.
Let me think about what else I can do. The current performance is:
- Shape 0: 597 TFLOPS (59.7% of peak)
- Shape 1: 481 TFLOPS (48.1%) — limited by padding overhead
- Shape 2: 69 TFLOPS / 1095 GB/s (60.8% of peak bandwidth)
- Shape 3: 649 TFLOPS (64.9%)
Geomean: 33.7%
For shape 1 (K=4127), the padding from 4127 to 4160 adds 33 columns (0.8%). But from 4127 to 4224=33*128 would be 97 columns (2.3%). Since I use BLOCK_K=64, K_padded=4160, which is only 0.8% overhead. The 481 TFLOPS is lower because of the extra 33 columns of zero-padding work the kernel has to do.
Wait, 479 TFLOPS for K=4127 — but the benchmark uses the original K=4127 for FLOPs calculation. The kernel actually processes K_padded=4160 elements. So the kernel does 4160/4127 = 1.008x more work. The "true" TFLOPS (including padding work) would be 479 * 1.008 = 483 TFLOPS. Still quite a bit lower than 597 TFLOPS for K=4096.
The 20% lower performance for the tail case might be due to compiling different grid sizes or some other issue. Actually, let me check: for K=4096, K_padded=4096, grid=(32, 32). For K=4127, BLOCK_K=64, K_padded=4160, grid=(32, 32). Same grid! So it's not a grid issue.
Hmm, the inner loop does 4096/64=64 iterations for K=4096, and 4160/64=65 iterations for K_padded=4160. That's 1 extra iteration. Each iteration does 128*128*64 MACs = 1,048,576 MACs. One extra iteration adds 1/64 = 1.56% overhead. So the "useful" TFLOPS should be very close. But 481 vs 597 is a 19.4% difference!
Let me think about this... 4127 is not a "nice" number for memory alignment. The last column being at index 4126 means some loads might cross cache line boundaries or be less optimal. But with K_padded=4160, all loads are aligned within the padded tensor.
Wait, maybe the issue is that the kernel is being recompiled with a different K_padded value (4160 vs 4096). This triggers a recompilation which might use different optimizations.
Actually, looking at the benchmark output more carefully:
```
shape=1 variant=solution tflops=481.312 gbps=234.133 ms=0.288
shape=0 variant=solution tflops=596.772 gbps=291.393 ms=0.230
```
The difference in ms is 0.288 vs 0.230 — about 25% slower. With 65 iterations vs 64, that's 1.56% more iterations. The extra time can't be explained by iterations alone.
Maybe the kernel is being compiled differently for K_padded=4160. Or maybe there's a shared memory allocation difference.
Let me check if the compilation is different for different K_padded values. In Triton, the kernel is compiled for specific parameter values (including K_padded as a runtime argument). The compiler might generate different code for different K_padded values because the loop bound is different.
Actually, `K_padded` is a runtime argument, so the compiler should generate generic code that works for any K_padded value. The loop bound is variable. So recompilation shouldn't be an issue.
Hmm, let me just accept the current performance and move on. 481 TFLOPS for shape 1 is still very good and much better than the original 3.5 TFLOPS.
Actually, let me try one thing: for the tail shape, maybe I should use a smaller BLOCK_K to reduce padding. With BLOCK_K=32 and K=4127, K_padded=4128 (just 1 element of padding), and the grid is the same. Let me test this.
Wait, but BLOCK_K=32 was slower in my tests (556 TFLOPS vs 684 for BLOCK_K=64). So the trade-off might not be worth it.
Actually let me try BLOCK_K=128 for the tail shape. With K=4127, K_padded=4224, that's 97 extra elements (2.3% overhead). The benchmark would report the same "useful" TFLOPS for the aligned case. Let me test.
Hmm, actually, I already tested BLOCK_K=128 and got 479 TFLOPS (similar to BLOCK_K=64's 481). The issue isn't the BLOCK_K value — it's some other factor.
Let me just accept the current results and finalize the solution. The geomean peak fraction of 0.337 is solid.
Actually wait, one more idea. What about using Triton's `@triton.autotune` with a proper warmup that caches the best config? This would add a bit of first-call overhead but might find better configs for each shape. And the results would be cached for subsequent calls.
Let me try adding autotuning with a carefully chosen set of configs that avoid the shared memory issues.
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Let me try autotuning for potentially better per-shape performance.
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stderr (247 chars)
Exit code 1
Traceback (most recent call last):
File "/tmp/test_autotune2.py", line 69, in <module>
if gemm_autotuned.best_config is not None:
^^^^^^^^^^^^^^^^^^^^^^^^^^
AttributeError: 'Autotuner' object has no attribute 'best_config'
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reasoning (454 chars)
The autotuner API might be different in Triton 3.6. Let me not waste time on autotuning and just finalize the solution. The current performance is solid and I should verify everything is correct before submitting.
Let me do a final check:
1. correctness.py passes
2. benchmark.py passes with RESULT: OK
3. The kernel uses real fp8 tensor core operations
Let me also verify that the check.py and benchmark.py work correctly with the current solution.py.
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stdout (1321 chars)
PASS
---
benchmark_event event=variant_start shape=0 variant=solution ts=2026-06-14T23:06:18.993754+00:00
benchmark_event event=variant_end shape=0 variant=solution ts=2026-06-14T23:06:19.207016+00:00 elapsed_s=0.213 ms=0.230128
shape=0 variant=solution tflops=597.228 gbps=291.615 ms=0.230
shape=0 solution_peak_fraction=0.5972
benchmark_event event=variant_start shape=1 variant=solution ts=2026-06-14T23:06:19.726890+00:00
benchmark_event event=variant_end shape=1 variant=solution ts=2026-06-14T23:06:19.744001+00:00 elapsed_s=0.017 ms=0.286752
shape=1 variant=solution tflops=482.923 gbps=234.917 ms=0.287
shape=1 solution_peak_fraction=0.4829
benchmark_event event=variant_start shape=2 variant=solution ts=2026-06-14T23:06:21.612006+00:00
benchmark_event event=variant_end shape=2 variant=solution ts=2026-06-14T23:06:21.617914+00:00 elapsed_s=0.006 ms=0.061824
shape=2 variant=solution tflops=69.471 gbps=1098.203 ms=0.062
shape=2 solution_peak_fraction=0.0695
benchmark_event event=variant_start shape=3 variant=solution ts=2026-06-14T23:06:23.303393+00:00
benchmark_event event=variant_end shape=3 variant=solution ts=2026-06-14T23:06:23.335413+00:00 elapsed_s=0.032 ms=0.738304
shape=3 variant=solution tflops=651.542 gbps=261.326 ms=0.738
shape=3 solution_peak_fraction=0.6515
peak_fraction: 0.3380
RESULT: OK
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reasoning (1548 chars)
Results are stable:
- Shape 0: 597 TFLOPS (59.7% of fp8 peak)
- Shape 1: 483 TFLOPS (48.3%)
- Shape 2: 69.5 TFLOPS / 1098 GB/s (61% of peak bandwidth)
- Shape 3: 652 TFLOPS (65.2%)
Geomean peak fraction: 0.338, RESULT: OK.
The solution is working correctly. Let me verify the framework label gets detected properly:
Check the patterns in check.py:
```python
("triton", r"import\s+triton\b|@triton\.jit|\btl\.dot\b"),
```
My solution uses `import triton`, `@triton.jit`, and `tl.dot` — so it should be labeled as "triton". Good.
Let me do one final review of solution.py to make sure everything is clean.
Actually, let me try one more optimization: for the rectangular shape (M=4096, N=14336), the N dimension is 3.5x larger than M. Maybe I should use an asymmetric tile (wider in N) to reduce the number of blocks in the N direction. But from my tests, BN=256 was very slow (168 TFLOPS). So (128, 128, 64) is optimal.
Wait, actually, let me think about why BN=256 is slow. The issue is that the accumulator for a 128×256 block requires 128*256 = 32768 f32 values. With 4 warps, each thread holds 32768/128 = 256 f32 values = 1KB of registers. This exceeds the register budget per thread (typically 255 registers for NVIDIA GPUs). Triton might spill to shared memory, which is slow.
For (128, 128), each thread holds 128 f32 values = 512 bytes = 128 registers. This fits within the 255-register limit.
So the tile size is register-limited. (128, 128) is the sweet spot.
Let me verify the solution is clean and mark the task as complete.
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Final results are solid. Let me verify the framework label and clean up.
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reasoning (1972 chars)
The framework is detected as "triton". Let me finalize by reading the final solution.py and making sure everything is clean.
Let me also think about whether there are any last-minute improvements I can make. The current performance is:
- Large compute-bound shapes (0, 1, 3): 483-652 TFLOPS
- Skinny memory-bound shape (2): 69.5 TFLOPS / 1098 GB/s
One more idea: for the tail shape (K=4127), I could avoid the padding entirely by using a different kernel strategy. Instead of padding, I could process full tiles without masks and then handle the tail separately. But my earlier attempt at this failed because of Triton's code generation for the tail.
Actually, I have one more idea: since the issue is specifically with `tl.dot` for fp8 when K is not a multiple of 32, what if I pad ONLY to a multiple of 32 instead of a multiple of BLOCK_K (64)?
K=4127 padded to 32: K_padded=4128. Then K_padded=4128 with BLOCK_K=64:
- 4128 / 64 = 64.5 → ceil = 65 iterations
- Last iteration: k=64*64=4096, k_remaining=4128-4096=32
- Load mask: offs_k < 32 (only the first 32 elements)
- But the loaded tensor is (128, 64), and the dot is (128, 64) @ (64, 128)
- The last 32 elements of the K dimension are from out-of-bounds memory... wait, they're padded with 0 (other=0.0 from the mask)
But this would still have the slow tail issue! Because tl.dot with a mask and other=0.0 on fp8 data is what's slow.
Unless... I handle the tail DIFFERENTLY. What if instead of using a mask with `other=0.0`, I load a FULL tile that ends exactly at K_padded? For K=4127, K_padded=4128, BLOCK_K=64:
- 4128 / 64 = 64.5 — NOT evenly divisible!
- I need K_padded to be a multiple of BLOCK_K
So K_padded must be a multiple of BLOCK_K. With BLOCK_K=64, K_padded=4160 (65*64). With BLOCK_K=128, K_padded=4224 (33*128).
The current solution uses BLOCK_K=64 and K_padded=4160, which adds 33 elements of padding (0.8%). This is very reasonable.
I think the current solution is good. Let me finalize.
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stdout (5928 chars) — TRUNCATED
1 """FP8 e4m3 GEMM — Triton kernel using fp8 tensor cores on Blackwell SM120.
2
3 Model interface: same as reference.py — holds `weight` (fp8_e4m3, N×K) and
4 `weight_scale` (float32, N). Forward: y = ((x @ w.T) * weight_scale).to(bf16).
5
6 Uses a 2D grid launch and dynamically pads K to a multiple of BLOCK_K so every
7 inner-loop iteration loads full, unmasked tiles (avoiding the Triton tail
8 slowdown on fp8 masked loads).
9 """
10
11 import torch
12 import torch.nn as nn
13 import triton
14 import triton.language as tl
15
16 E4M3_MAX = 448.0
17
18
19 # ---------------------------------------------------------------------------
20 # Triton kernel — 2D grid (M-blocks × N-blocks)
21 # ---------------------------------------------------------------------------
22
23 @triton.jit
24 def _fp8_gemm_kernel(
25 a_ptr, # fp8 activation (M, K_padded)
26 b_ptr, # fp8 weight (N, K_padded) — read transposed as (K, N)
27 c_ptr, # bf16 output (M, N)
28 scale_ptr, # float32 scale (N,)
29 M,
30 N,
31 K_padded, # Padded K (multiple of BLOCK_K)
32 stride_am,
33 stride_ak,
34 stride_bn,
35 stride_bk,
36 stride_cm,
37 stride_cn,
38 BLOCK_M: tl.constexpr,
39 BLOCK_N: tl.constexpr,
40 BLOCK_K: tl.constexpr,
41 ):
42 pid_m = tl.program_id(0)
43 pid_n = tl.program_id(1)
44
45 offs_m = pid_m * BLOCK_M + tl.arange(0, BLOCK_M)
46 offs_n = pid_n * BLOCK_N + tl.arange
... (4428 more chars)
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reasoning (858 chars)
The solution looks clean. Let me verify one more time by running check.py and confirming the framework label.
Actually, I realize the solution is working and correct. Let me mark the task as complete and provide a summary.
Wait, one thing I should double-check: the solution needs to use exactly the same `get_inputs` and `get_init_inputs` as the reference. Let me verify this is the case.
From reference.py:
```python
def get_inputs():
x = (torch.rand(M, K) * 8 - 4).to(torch.float8_e4m3fn)
return [x]
def get_init_inputs():
return [M, N, K]
```
My solution has identical implementations. Good.
The Model.__init__ creates the same `weight` (fp8_e4m3) and `weight_scale` (float32) buffers as reference.py. The initialization uses the same random seed logic (normal_ with std=0.02).
Everything looks correct. Let me do a final verification.
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reasoning (63 chars)
The solution is complete and working. Let me provide a summary.
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The solution is complete. Here's a summary of what was done:
## Solution: FP8 GEMM for RTX PRO 6000 (Blackwell SM120)
**Approach**: Triton kernel with 2D grid launch, using genuine fp8 tensor-core `tl.dot` operations.
### Key Design Decisions
1. **Real fp8×fp8 tensor cores**: Uses `tl.dot(a, b, acc)` with fp8_e4m3 inputs accumulating in fp32 — this maps to `mma.sync.aligned.m16n8k32.row.col.f32.e4m3.e4m3.f32` PTX on Blackwell SM120. No upcasting to bf16.
2. **K-dimension padding**: The fp8 MMA instruction requires K to be a multiple of 32 for peak throughput. Triton generates slow fallback code when masked fp8 loads have K tails that aren't 32-aligned. The solution pads input tensors to multiples of BLOCK_K (64/128) with fp8 zeros so every inner-loop iteration loads a full, unmasked tile.
3. **Shape-adaptive tile sizes**:
- Large shapes (M > 64): `128×128×64` — fits 3-stage software pipelining in 128KB shared memory
- Skinny M (M ≤ 64): `64×128×256` — amortizes memory latency with wider K tiles
### Performance
| Shape | Dimensions | TFLOPS | Peak Fraction | Notes |
|-------|-----------|--------|---------------|-------|
| 0 | 4096×4096×4096 | 597 | 59.7% | Square aligned |
| 1 | 4096×4096×4127 | 483 | 48.3% | K=4127, padded to 4160 |
| 2 | 32×8192×8192 | 69.5 / 1098 GB/s | 61% BW | Decode-style, memory-bound |
| 3 | 4096×14336×4096 | 652 | 65.2% | Llama3 up-proj |
**Geometric mean peak fraction: 0.338** — well above the 0.1 threshold, and ~2× the bf16-upcast ceiling (~500 TFLOPS peak for bf16 vs 1000 for fp8).
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