KernelBench hard · H100
W4A16 GEMM LongCat 2.0
12.2%geomean peak fraction across shapes
manually audited: clean
harnesslongcat-claudeagent session1h 29mtotal wall1h 29mcheck23sbenchmark5soutput tokens115,085cost$9.66gpu-lock wait0sgpu-lock held28sregimememory
Per-shape vs governing ceilingeach shape graded against whichever binds — bf16 compute or HBM bandwidth
1×12288×40960.087 ms15.1%0.31 TB/s · 15% of 2.0 TB/s HBM · also 1 TFLOPS (0% of compute)
32×12288×40960.082 ms16.7%0.34 TB/s · 17% of 2.0 TB/s HBM · also 39 TFLOPS (5% of compute)
256×12288×40960.209 ms8.2%123 TFLOPS · 16% of 756 TF bf16 peak · also 0.17 TB/s (8% of HBM)
1×4096×40960.064 ms6.9%0.14 TB/s · 7% of 2.0 TB/s HBM · also 1 TFLOPS (0% of compute)
16×14336×40960.083 ms18.7%0.38 TB/s · 19% of 2.0 TB/s HBM · also 23 TFLOPS (3% of compute)
compute-bound memory-bound · bar + right column = official fraction of the ceiling (the geomean input)
geomean(15.1% · 16.7% · 8.2% · 6.9% · 18.7%) = 12.2%
Kernel source (redacted)
from __future__ import annotations
import math
import torch
import torch.nn as nn
import triton
import triton.language as tl
OP_TYPE = "gemm_w4a16"
SUPPORTED_PRECISIONS = ["int4_bf16"]
HARDWARE_REQUIRED = ["RTX_PRO_6000", "H100", "B200"]
GROUP_SIZE = 128
@triton.jit
def _w4a16_gemm(
xe_ptr, xo_ptr, wq_ptr, s_ptr, z_ptr, out_ptr,
M, N, K,
sxe, sN_w, sN_s,
s_out_m, s_out_n,
HALF: tl.constexpr, N_GROUPS: tl.constexpr,
TM: tl.constexpr, TN: tl.constexpr,
):
pid_m = tl.program_id(0)
pid_n = tl.program_id(1)
m0 = pid_m * TM
n0 = pid_n * TN
ms = m0 + tl.arange(0, TM)
ns = n0 + tl.arange(0, TN)
m_mask = ms < M
n_mask = ns < N
acc = tl.zeros((TM, TN), dtype=tl.float32)
for g in range(N_GROUPS):
sg = tl.load(s_ptr + g * sN_s + ns, mask=n_mask, other=0.0)
zg = tl.load(z_ptr + g * sN_s + ns, mask=n_mask, other=0.0)
k0 = g * HALF
tk = tl.arange(0, HALF)
w_bytes = tl.load(wq_ptr + (k0 + tk[:, None]) * sN_w + ns[None, :],
mask=n_mask[None, :], other=0)
ev = (w_bytes & 0x0F).to(tl.bfloat16)
od = ((w_bytes.to(tl.uint8) >> 4) & 0x0F).to(tl.bfloat16)
we = (ev - zg) * sg
wo = (od - zg) * sg
k_idx = k0 + tk[None, :]
rxe = tl.load(xe_ptr + ms[:, None] * sxe + k_idx,
mask=m_mask[:, None], other=0.0)
rxo = tl.load(xo_ptr + ms[:, None] * sxe + k_idx,
mask=m_mask[:, None], other=0.0)
acc += tl.dot(rxe, we)
acc += tl.dot(rxo, wo)
tl.store(out_ptr + ms[:, None] * s_out_m + ns[None, :],
acc.to(tl.bfloat16), mask=m_mask[:, None] & n_mask[None, :])
# Per-(M,N) best tile configuration from sweep.
_TILE = {
(1, 4096): (8, 32),
(1, 12288): (1, 64),
(16, 14336): (16, 64),
(32, 12288): (32, 64),
(256, 12288): (64, 64),
}
def _pick_tile(M: int, N: int):
return _TILE.get((M, N), (64, 64))
@torch.no_grad()
def w4a16_gemm_reuse(x, w_q, scales, zeros, xe, xo, out):
M, K = x.shape
N = w_q.shape[1]
TM, TN = _pick_tile(M, N)
xe[:, :] = x[:, 0::2]
xo[:, :] = x[:, 1::2]
HALF = GROUP_SIZE // 2
N_GROUPS = K // GROUP_SIZE
grid = (math.ceil(M / TM), math.ceil(N / TN))
_w4a16_gemm[grid](
xe, xo, w_q, scales, zeros, out,
M, N, K,
xe.stride(0), w_q.stride(0), scales.stride(0),
out.stride(0), out.stride(1),
HALF=HALF, N_GROUPS=N_GROUPS, TM=TM, TN=TN,
)
return out
class Model(nn.Module):
def __init__(self, M: int, N: int, K: int, group_size: int = GROUP_SIZE):
super().__init__()
assert K % group_size == 0
assert K % 2 == 0
self.M, self.N, self.K = M, N, K
self.group_size = group_size
n_groups = K // group_size
torch.manual_seed(0xC0DE ^ (M * 1315423911 + N * 2654435761 + K))
w_full = torch.randn(K, N, dtype=torch.float32) * 0.02
w_g = w_full.view(n_groups, group_size, N)
w_min = w_g.min(dim=1, keepdim=True).values
w_max = w_g.max(dim=1, keepdim=True).values
scales = (w_max - w_min).clamp_min(1e-8) / 15.0
zeros_g = (-w_min / scales).round().clamp(0, 15)
w_q = ((w_g / scales) + zeros_g).round().clamp(0, 15).to(torch.uint8).view(K, N)
scales_2d = scales.squeeze(1).to(torch.bfloat16)
zeros_2d = zeros_g.squeeze(1).to(torch.bfloat16)
Kh = K // 2
lo = w_q[0::2].to(torch.uint8) & 0xF
hi = w_q[1::2].to(torch.uint8) & 0xF
w_packed = (lo | (hi << 4)).contiguous()
self.register_buffer("w_q", w_packed)
self.register_buffer("scales", scales_2d)
self.register_buffer("zeros", zeros_2d)
dev = torch.device('cuda')
self._buf_xe = torch.empty(M, Kh, dtype=torch.bfloat16, device=dev)
self._buf_xo = torch.empty(M, Kh, dtype=torch.bfloat16, device=dev)
self._buf_out = torch.empty(M, N, dtype=torch.bfloat16, device=dev)
def forward(self, x: torch.Tensor) -> torch.Tensor:
return w4a16_gemm_reuse(x, self.w_q, self.scales, self.zeros,
self._buf_xe, self._buf_xo, self._buf_out)
M = 1
N = 12288
K = 4096
def get_inputs():
x = torch.randn(M, K, dtype=torch.bfloat16)
return [x]
def get_init_inputs():
return [M, N, K]
20260708_012529_longcat-claude_LongCat-2.0_07_w4a16_gemm