{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/reference.py"
}

{
  "raw": "{\"path\": \"/home/infatoshi/cuda/KernelBench-Hard/problems/03"
}

{
  "raw": "{\"path\": \"/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/benchmark.py"
}

{
  "raw": "{\"path\": \"/home/infatoshi/cuda/Kernel"
}

{
  "raw": "{\"path\": \"/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/problem.yaml"
}

{
  "raw": "{\"path\": \"/home/infatos"
}

{
  "raw": "{\"path\": \"/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/PROMPT.txt"
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard && python -c \"import torch; print(torch.__version__); print(torch.cuda.get_device_name()); print(torch.cuda.get_device_capability())\""
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard && python -c \"import triton; print(triton.__version__)\""
}

{
  "command": "python -c \"import triton.language as tl; print(dir(tl))\" | tr ',' '\\n' | grep -i dot"
}

{
  "raw": "{\"command\": \""
}

{
  "command": "find /home -path \"*/vllm/*\" -name \"*.py\" 2>/dev/null | head -20"
}

{
  "path": "/home/infatoshi/PufferLib/.venv/lib/python3.12/site-packages/jax/experimental/pallas/ops/gpu/paged_attention.py"
}

{
  "raw": "{\"command\": \"find /home -"
}

{
  "command": "find /home/infatoshi/.cache/uv -path \"*/vllm*\" -name \"*.py\" 2>/dev/null | head -50"
}

{
  "path": "/home/infatoshi/.cache/uv/.tmpR4nmo3/vllm/attention/ops/paged_attn.py"
}

{
  "raw": "{\"command\": \"find /home -"
}

{
  "path": "/home/infatoshi/.cache/uv/.tmpR4nmo3/vllm/attention/ops/triton_decode_attention.py"
}

{
  "command": "python -c \"import torch; print(torch.cuda.get_device_properties(0))\""
}

{
  "command": "find /home -name \"decode_attention.py\" 2>/dev/null | head -10"
}

{
  "command": "find /home -name \"*decode*attention*.py\" 2>/dev/null | head -10"
}

{
  "path": "/home/infatoshi/qwen3.6-dense/.venv-sglang/lib/python3.12/site-packages/sglang/srt/layers/attention/triton_ops/decode_attention.py"
}

{
  "todos": [
    {
      "title": "Write initial Triton paged attention decode kernel for packed KV layout",
      "status": "in_progress"
    },
    {
      "title": "Test correctness with check.py",
      "status": "pending"
    },
    {
      "title": "Profile and optimize performance",
      "status": "pending"
    },
    {
      "title": "Iterate until peak_fraction target is met",
      "status": "pending"
    }
  ]
}

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "content": "<13438 chars \u2014 see diff>"
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python check.py 2>&1",
  "timeout": 120
}

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "edit": {
    "old": "            # Load full page: (PAGE_SIZE, 2*HEAD_DIM)\n            page_data = tl.load(\n                page_base + offs_token_in_page[:, None] * stride_kv1 + offs_dim[None, :],\n                mask=token_mask[:, None],\n                other=0.0,\n            )\n\n            # Extract K and V\n            k = page_data[:, :HEAD_DIM]  # (PAGE_SIZE, HEAD_DIM)\n            v = page_data[:, HEAD_DIM:]  # (PAGE_SIZE, HEAD_DIM)",
    "new": "            # Load K and V separately (

... (493 more chars)

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python check.py 2>&1",
  "timeout": 120
}

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "edit": [
    {
      "old": "@triton.jit\ndef _fwd_kernel_stage1(\n    Q,\n    KV_Cache,\n    block_table,\n    seq_lens,\n    sm_scale,\n    Mid_O,\n    Mid_LSE,\n    stride_qb,\n    stride_qh,\n    stride_bt0,\n    stride_bt1,\n    stride_kv0,\n    stride_kv1,\n    stride_kv2,\n    stride_kv3,\n    stride_mid_ob,\n    stride_mid_oh,\n    stride_mid_os,\n    kv_group_num: tl.constexpr,\n    q_head_num: tl.constexpr,\n    BLOCK_DMODEL: tl.constexpr,\n    BLOCK_DV: tl.constexpr,\n    BLOCK_H: tl.cons

... (10153 more chars)

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python check.py 2>&1",
  "timeout": 120
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python benchmark.py 2>&1",
  "timeout": 180
}

{
  "command": "<1249 chars \u2014 see below>"
}

cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && cat > /tmp/test_perf.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")

for shape_idx, shape in enumerate(shapes.SHAPES):
    apply_shape(shape)
    init_args = reference.get_init_inputs()
    ref_model = reference.Model(*init_args).to(device).eval()
    sol_model = solution.Model(*init_args).to(device).eval()
    
    torch.manual_seed(42)
    inputs = [t.to(device) for t in reference.get_inputs()]
    
    # Warmup
    for _ in range(5):
        sol_model(*inputs)
    torch.cuda.synchronize()
    
    # Time it
    import time
    start = time.perf_counter()
    for _ in range(30):
        sol_model(*inputs)
    torch.cuda.synchronize()
    elapsed = (time.perf_counter() - start) / 30 * 1000
    
    print(f"shape={shape_idx} {shape} ms={elapsed:.3f}")
EOF
uv run python /tmp/test_perf.py

{
  "command": "find /home/infatoshi/cuda/KernelBench-Hard -name \"timing.py\" | xargs cat"
}

{
  "command": "python -c \"import triton.language as tl; print([x for x in dir(tl) if 'cat' in x or 'join' in x or 'concat' in x or 'stack' in x])\""
}

{
  "command": "python -c \"import triton.language as tl; help(tl.cat)\""
}

{
  "command": "<930 chars \u2014 see below>"
}

cat > /tmp/test_blockh.py << 'EOF'
import torch
import triton
import triton.language as tl

@triton.jit
def test_kernel(Q, K, Out, BLOCK_H: tl.constexpr, BLOCK_D: tl.constexpr, BLOCK_N: tl.constexpr):
    offs_h = tl.arange(0, BLOCK_H)
    offs_d = tl.arange(0, BLOCK_D)
    q = tl.load(Q + offs_h[:, None] * BLOCK_D + offs_d[None, :])
    k = tl.load(K + offs_d[:, None] * BLOCK_N + tl.arange(0, BLOCK_N)[None, :])
    out = tl.dot(q, k)
    tl.store(Out + offs_h[:, None] * BLOCK_N + tl.arange(0, BLOCK_N)[None, :], out)

Q = torch.randn(4, 128, dtype=torch.bfloat16, device='cuda')
K = torch.randn(128, 16, dtype=torch.bfloat16, device='cuda')
Out = torch.empty(4, 16, dtype=torch.bfloat16, device='cuda')

test_kernel[(1,)](Q, K, Out, BLOCK_H=4, BLOCK_D=128, BLOCK_N=16)
print("BLOCK_H=4 works!")

test_kernel[(1,)](Q, K, Out, BLOCK_H=8, BLOCK_D=128, BLOCK_N=16)
print("BLOCK_H=8 works!")
EOF
uv run python /tmp/test_blockh.py

{
  "command": "<840 chars \u2014 see below>"
}

cat > /tmp/test_blockh1.py << 'EOF'
import torch
import triton
import triton.language as tl

@triton.jit
def test_kernel(Q, K, Out, BLOCK_H: tl.constexpr, BLOCK_D: tl.constexpr, BLOCK_N: tl.constexpr):
    offs_h = tl.arange(0, BLOCK_H)
    offs_d = tl.arange(0, BLOCK_D)
    q = tl.load(Q + offs_h[:, None] * BLOCK_D + offs_d[None, :])
    k = tl.load(K + offs_d[:, None] * BLOCK_N + tl.arange(0, BLOCK_N)[None, :])
    out = tl.dot(q, k)
    tl.store(Out + offs_h[:, None] * BLOCK_N + tl.arange(0, BLOCK_N)[None, :], out)

Q = torch.randn(1, 128, dtype=torch.bfloat16, device='cuda')
K = torch.randn(128, 16, dtype=torch.bfloat16, device='cuda')
Out = torch.empty(1, 16, dtype=torch.bfloat16, device='cuda')

test_kernel[(1,)](Q, K, Out, BLOCK_H=1, BLOCK_D=128, BLOCK_N=16)
print("BLOCK_H=1 works!")
EOF
uv run python /tmp/test_blockh1.py

{
  "command": "<1192 chars \u2014 see below>"
}

cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && cat > /tmp/profile_nsys.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")

# Profile shape 0
shape = shapes.SHAPES[0]
apply_shape(shape)
init_args = reference.get_init_inputs()
sol_model = solution.Model(*init_args).to(device).eval()

torch.manual_seed(42)
inputs = [t.to(device) for t in reference.get_inputs()]

# Warmup
for _ in range(10):
    sol_model(*inputs)
torch.cuda.synchronize()

# Profile
import torch.profiler
with torch.profiler.profile(
    activities=[torch.profiler.ProfilerActivity.CPU, torch.profiler.ProfilerActivity.CUDA],
    record_shapes=True,
) as prof:
    for _ in range(5):
        sol_model(*inputs)

print(prof.key_averages().table(sort_by="cuda_time_total", row_limit=20))
EOF
uv run python /tmp/profile_nsys.py

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "edit": [
    {
      "old": "def _decode_grouped_att_m_fwd(\n    q,\n    kv_cache,\n    block_table,\n    seq_lens,\n    mid_o,\n    num_kv_splits,\n    sm_scale,\n    page_size,\n):\n    batch, head_num = q.shape[0], q.shape[1]\n    num_kv_heads = kv_cache.shape[2]\n    head_dim = kv_cache.shape[3] // 2\n    kv_group_num = head_num // num_kv_heads\n\n    BLOCK_H = 16\n    grid = (\n        batch,\n        triton.cdiv(head_num, min(BLOCK_H, kv_group_num)),\n        num_kv_splits,\n    )\n\n    BLOCK

... (3681 more chars)

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python check.py 2>&1",
  "timeout": 120
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python benchmark.py 2>&1",
  "timeout": 180
}

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "edit": {
    "old": "    # Use BLOCK_H matching the group size for better tensor-core utilization.\n    # Round up to the next power of two if the group size is not a power of two,\n    # but all our shapes have power-of-two group sizes.\n    BLOCK_H = min(16, kv_group_num)\n    if BLOCK_H < 1:\n        BLOCK_H = 1",
    "new": "    BLOCK_H = 16"
  }
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python benchmark.py 2>&1",
  "timeout": 180
}

{
  "command": "<1473 chars \u2014 see below>"
}

cat > /tmp/sweep_params.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import triton

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")

# Test shape 0 and shape 4
for shape_idx in [0, 4]:
    shape = shapes.SHAPES[shape_idx]
    apply_shape(shape)
    init_args = reference.get_init_inputs()
    sol_model = solution.Model(*init_args).to(device).eval()
    
    torch.manual_seed(42)
    inputs = [t.to(device) for t in reference.get_inputs()]
    
    # Warmup
    for _ in range(10):
        sol_model(*inputs)
    torch.cuda.synchronize()
    
    # Time with L2 flush
    _l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")
    
    times = []
    for _ in range(30):
        _l2_scratch.zero_()
        torch.cuda.synchronize()
        s = torch.cuda.Event(enable_timing=True)
        e = torch.cuda.Event(enable_timing=True)
        s.record()
        sol_model(*inputs)
        e.record()
        torch.cuda.synchronize()
        times.append(s.elapsed_time(e))
    
    import statistics
    print(f"shape={shape_idx} baseline ms={statistics.median(times):.3f}")
EOF
uv run python /tmp/sweep_params.py

{
  "command": "<1383 chars \u2014 see below>"
}

cat > /tmp/test_variant.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import triton
import triton.language as tl
import reference
import shapes

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

# Copy the kernel and modify parameters
device = torch.device("cuda:0")
shape = shapes.SHAPES[0]
apply_shape(shape)
init_args = reference.get_init_inputs()

# Import solution to get the kernel code
import solution

# Time the current solution
sol_model = solution.Model(*init_args).to(device).eval()
torch.manual_seed(42)
inputs = [t.to(device) for t in reference.get_inputs()]

for _ in range(10):
    sol_model(*inputs)
torch.cuda.synchronize()

_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

times = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    sol_model(*inputs)
    e.record()
    torch.cuda.synchronize()
    times.append(s.elapsed_time(e))

import statistics
print(f"Current: ms={statistics.median(times):.3f}")
EOF
uv run python /tmp/test_variant.py

{
  "command": "<1404 chars \u2014 see below>"
}

cat > /tmp/test_reshape.py << 'EOF'
import torch
import triton
import triton.language as tl

@triton.jit
def test_kernel(KV, K_Out, V_Out, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr):
    page_base = KV + tl.arange(0, PAGE_SIZE * 2 * HEAD_DIM)
    page_data = tl.load(page_base)
    # Try reshape to (PAGE_SIZE, 2, HEAD_DIM)
    page_3d = tl.reshape(page_data, (PAGE_SIZE, 2, HEAD_DIM))
    k = page_3d[:, 0, :]
    v = page_3d[:, 1, :]
    
    # Store to verify
    k_flat = tl.reshape(k, (PAGE_SIZE * HEAD_DIM,))
    v_flat = tl.reshape(v, (PAGE_SIZE * HEAD_DIM,))
    tl.store(K_Out + tl.arange(0, PAGE_SIZE * HEAD_DIM), k_flat)
    tl.store(V_Out + tl.arange(0, PAGE_SIZE * HEAD_DIM), v_flat)

PAGE_SIZE = 16
HEAD_DIM = 128

kv = torch.randn(PAGE_SIZE, 2, HEAD_DIM, dtype=torch.bfloat16, device='cuda')
# Flatten to simulate packed layout: (PAGE_SIZE, 2*HEAD_DIM)
kv_packed = kv.view(PAGE_SIZE, 2 * HEAD_DIM)

k_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')
v_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')

test_kernel[(1,)](kv_packed, k_out, v_out, PAGE_SIZE=PAGE_SIZE, HEAD_DIM=HEAD_DIM)

k_expected = kv[:, 0, :].reshape(-1)
v_expected = kv[:, 1, :].reshape(-1)

print("K match:", torch.allclose(k_out, k_expected, atol=1e-5))
print("V match:", torch.allclose(v_out, v_expected, atol=1e-5))
EOF
uv run python /tmp/test_reshape.py

{
  "command": "<1411 chars \u2014 see below>"
}

cat > /tmp/test_gather.py << 'EOF'
import torch
import triton
import triton.language as tl

@triton.jit
def test_kernel(KV, K_Out, V_Out, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr):
    n = PAGE_SIZE * 2 * HEAD_DIM
    page_data = tl.load(KV + tl.arange(0, n))
    
    # Build 2D indices for K
    offs_t = tl.arange(0, PAGE_SIZE)[:, None]
    offs_d = tl.arange(0, HEAD_DIM)[None, :]
    idx_k = offs_t * (2 * HEAD_DIM) + offs_d
    k = page_data[idx_k]
    
    idx_v = offs_t * (2 * HEAD_DIM) + offs_d + HEAD_DIM
    v = page_data[idx_v]
    
    # Flatten and store
    tl.store(K_Out + tl.arange(0, PAGE_SIZE * HEAD_DIM), tl.reshape(k, (PAGE_SIZE * HEAD_DIM,)))
    tl.store(V_Out + tl.arange(0, PAGE_SIZE * HEAD_DIM), tl.reshape(v, (PAGE_SIZE * HEAD_DIM,)))

PAGE_SIZE = 16
HEAD_DIM = 128

kv = torch.randn(PAGE_SIZE, 2, HEAD_DIM, dtype=torch.bfloat16, device='cuda')
kv_packed = kv.view(PAGE_SIZE * 2 * HEAD_DIM)

k_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')
v_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')

test_kernel[(1,)](kv_packed, k_out, v_out, PAGE_SIZE=PAGE_SIZE, HEAD_DIM=HEAD_DIM)

k_expected = kv[:, 0, :].reshape(-1)
v_expected = kv[:, 1, :].reshape(-1)

print("K match:", torch.allclose(k_out, k_expected, atol=1e-5))
print("V match:", torch.allclose(v_out, v_expected, atol=1e-5))
EOF
uv run python /tmp/test_gather.py

{
  "command": "<1421 chars \u2014 see below>"
}

cat > /tmp/test_gather2.py << 'EOF'
import torch
import triton
import triton.language as tl

@triton.jit
def test_kernel(KV, K_Out, V_Out, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr):
    total = PAGE_SIZE * 2 * HEAD_DIM
    page_data = tl.load(KV + tl.arange(0, total))
    
    # Build 2D indices for K
    offs_t = tl.arange(0, PAGE_SIZE)[:, None]
    offs_d = tl.arange(0, HEAD_DIM)[None, :]
    idx_k = offs_t * (2 * HEAD_DIM) + offs_d
    k = page_data[idx_k]
    
    idx_v = offs_t * (2 * HEAD_DIM) + offs_d + HEAD_DIM
    v = page_data[idx_v]
    
    # Flatten and store
    tl.store(K_Out + tl.arange(0, PAGE_SIZE * HEAD_DIM), tl.reshape(k, (PAGE_SIZE * HEAD_DIM,)))
    tl.store(V_Out + tl.arange(0, PAGE_SIZE * HEAD_DIM), tl.reshape(v, (PAGE_SIZE * HEAD_DIM,)))

PAGE_SIZE = 16
HEAD_DIM = 128

kv = torch.randn(PAGE_SIZE, 2, HEAD_DIM, dtype=torch.bfloat16, device='cuda')
kv_packed = kv.view(PAGE_SIZE * 2 * HEAD_DIM)

k_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')
v_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')

test_kernel[(1,)](kv_packed, k_out, v_out, PAGE_SIZE=PAGE_SIZE, HEAD_DIM=HEAD_DIM)

k_expected = kv[:, 0, :].reshape(-1)
v_expected = kv[:, 1, :].reshape(-1)

print("K match:", torch.allclose(k_out, k_expected, atol=1e-5))
print("V match:", torch.allclose(v_out, v_expected, atol=1e-5))
EOF
uv run python /tmp/test_gather2.py

{
  "command": "<1432 chars \u2014 see below>"
}

cat > /tmp/test_gather3.py << 'EOF'
import torch
import triton
import triton.language as tl

@triton.jit
def test_kernel(KV, K_Out, V_Out, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr):
    total: tl.constexpr = PAGE_SIZE * 2 * HEAD_DIM
    page_data = tl.load(KV + tl.arange(0, total))
    
    # Build 2D indices for K
    offs_t = tl.arange(0, PAGE_SIZE)[:, None]
    offs_d = tl.arange(0, HEAD_DIM)[None, :]
    idx_k = offs_t * (2 * HEAD_DIM) + offs_d
    k = page_data[idx_k]
    
    idx_v = offs_t * (2 * HEAD_DIM) + offs_d + HEAD_DIM
    v = page_data[idx_v]
    
    # Flatten and store
    k_total: tl.constexpr = PAGE_SIZE * HEAD_DIM
    tl.store(K_Out + tl.arange(0, k_total), tl.reshape(k, (k_total,)))
    tl.store(V_Out + tl.arange(0, k_total), tl.reshape(v, (k_total,)))

PAGE_SIZE = 16
HEAD_DIM = 128

kv = torch.randn(PAGE_SIZE, 2, HEAD_DIM, dtype=torch.bfloat16, device='cuda')
kv_packed = kv.view(PAGE_SIZE * 2 * HEAD_DIM)

k_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')
v_out = torch.empty(PAGE_SIZE * HEAD_DIM, dtype=torch.bfloat16, device='cuda')

test_kernel[(1,)](kv_packed, k_out, v_out, PAGE_SIZE=PAGE_SIZE, HEAD_DIM=HEAD_DIM)

k_expected = kv[:, 0, :].reshape(-1)
v_expected = kv[:, 1, :].reshape(-1)

print("K match:", torch.allclose(k_out, k_expected, atol=1e-5))
print("V match:", torch.allclose(v_out, v_expected, atol=1e-5))
EOF
uv run python /tmp/test_gather3.py

{
  "command": "<10499 chars \u2014 see below>",
  "timeout": 300
}

cat > /tmp/sweep_blockh.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import triton
import triton.language as tl
import reference
import shapes
import math

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

# Kernel variants
@triton.jit
def _fwd_kernel_stage1_v2(
    Q,
    KV_Cache,
    block_table,
    seq_lens,
    sm_scale,
    Mid_O,
    stride_qb,
    stride_qh,
    stride_bt0,
    stride_bt1,
    stride_kv0,
    stride_kv1,
    stride_kv2,
    stride_kv3,
    stride_mid_ob,
    stride_mid_oh,
    stride_mid_os,
    kv_group_num: tl.constexpr,
    q_head_num: tl.constexpr,
    BLOCK_DMODEL: tl.constexpr,
    BLOCK_DV: tl.constexpr,
    BLOCK_H: tl.constexpr,
    NUM_KV_SPLITS: tl.constexpr,
    PAGE_SIZE: tl.constexpr,
    HEAD_DIM: tl.constexpr,
):
    cur_batch = tl.program_id(0)
    cur_head_id = tl.program_id(1)
    split_kv_id = tl.program_id(2)

    heads_per_kv = tl.cdiv(kv_group_num, BLOCK_H)
    cur_kv_head = cur_head_id // heads_per_kv

    if kv_group_num > BLOCK_H:
        VALID_BLOCK_H: tl.constexpr = BLOCK_H
    else:
        VALID_BLOCK_H: tl.constexpr = kv_group_num

    cur_head = cur_head_id * VALID_BLOCK_H + tl.arange(0, BLOCK_H)
    mask_h = cur_head < (cur_head_id + 1) * VALID_BLOCK_H
    mask_h = mask_h & (cur_head < q_head_num)

    offs_d = tl.arange(0, BLOCK_DMODEL)
    offs_dv = tl.arange(0, BLOCK_DV)
    mask_d = offs_d < HEAD_DIM
    mask_dv = offs_dv < HEAD_DIM

    cur_batch_seq_len = tl.load(seq_lens + cur_batch)

    offs_q = cur_batch * stride_qb + cur_head[:, None] * stride_qh + offs_d[None, :]
    q = tl.load(Q + offs_q, mask=mask_h[:, None] & mask_d[None, :], other=0.0)

    kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
    split_kv_start = kv_len_per_split * split_kv_id
    split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)

    e_max = tl.zeros([BLOCK_H], dtype=tl.float32) - float("inf")
    e_sum = tl.zeros([BLOCK_H], dtype=tl.float32)
    acc = tl.zeros([BLOCK_H, BLOCK_DV], dtype=tl.float32)

    if split_kv_end > split_kv_start:
        start_page = split_kv_start // PAGE_SIZE
        end_page = (split_kv_end + PAGE_SIZE - 1) // PAGE_SIZE

        offs_token_in_page = tl.arange(0, PAGE_SIZE)

        for page_idx in range(start_page, end_page):
            physical_page = tl.load(
                block_table + cur_batch * stride_bt0 + page_idx * stride_bt1,
            )

            global_token_idx = page_idx * PAGE_SIZE + offs_token_in_page
            token_mask = global_token_idx < split_kv_end

            page_base = (
                KV_Cache
                + physical_page * stride_kv0
                + cur_kv_head * stride_kv2
            )

            k = tl.load(
                page_base + offs_token_in_page[:, None] * stride_kv1 + offs_d[None, :],
                mask=token_mask[:, None] & mask_d[None, :],
                other=0.0,
            )
            v = tl.load(
                page_base + offs_token_in_page[:, None] * stride_kv1 + (HEAD_DIM + offs_dv)[None, :],
                mask=token_mask[:, None] & mask_dv[None, :],
                other=0.0,
            )

            qk = tl.dot(q, k.to(q.dtype).T)
            qk *= sm_scale
            qk = tl.where(
                mask_h[:, None] & token_mask[None, :],
                qk,
                float("-inf"),
            )

            n_e_max = tl.maximum(tl.max(qk, 1), e_max)
            re_scale = tl.exp(e_max - n_e_max)
            p = tl.exp(qk - n_e_max[:, None])

            acc *= re_scale[:, None]
            acc += tl.dot(p.to(v.dtype), v)

            e_sum = e_sum * re_scale + tl.sum(p, 1)
            e_max = n_e_max

        offs_mid_o = (
            cur_batch * stride_mid_ob
            + cur_head[:

... (6499 more chars)

{
  "command": "<8038 chars \u2014 see below>"
}

cat > /tmp/verify_bug.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import triton
import triton.language as tl
import reference
import math

shape = {"batch": 8, "num_heads": 32, "num_kv_heads": 8, "head_dim": 128, "seq_len": 1024, "page_size": 16}
B, H, Hkv, D, L, P = shape["batch"], shape["num_heads"], shape["num_kv_heads"], shape["head_dim"], shape["seq_len"], shape["page_size"]

device = torch.device("cuda:0")
pages_per_seq = (L + P - 1) // P
total_pages = max(B * pages_per_seq + 8, 64)

query = torch.randn(B, H, D, dtype=torch.bfloat16, device=device) * 0.1
kv_cache = torch.randn(total_pages, P, Hkv, 2 * D, dtype=torch.bfloat16, device=device) * 0.1
block_table = torch.randperm(total_pages)[:B * pages_per_seq].reshape(B, pages_per_seq).int().to(device)
seq_lens = torch.full((B,), L, dtype=torch.int32, device=device)

ref_model = reference.Model(B, H, Hkv, D, L, P).to(device).eval()
with torch.no_grad():
    ref_out = ref_model(query, kv_cache, block_table, seq_lens)

# Import the sweep kernel
import importlib.util
spec = importlib.util.spec_from_file_location("sweep", "/tmp/sweep_blockh.py")

# Actually, just run the kernel directly using the code from sweep
@triton.jit
def _fwd_kernel_stage1_v2(
    Q, KV_Cache, block_table, seq_lens, sm_scale, Mid_O,
    stride_qb, stride_qh, stride_bt0, stride_bt1,
    stride_kv0, stride_kv1, stride_kv2, stride_kv3,
    stride_mid_ob, stride_mid_oh, stride_mid_os,
    kv_group_num: tl.constexpr, q_head_num: tl.constexpr,
    BLOCK_DMODEL: tl.constexpr, BLOCK_DV: tl.constexpr, BLOCK_H: tl.constexpr,
    NUM_KV_SPLITS: tl.constexpr, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr,
):
    cur_batch = tl.program_id(0)
    cur_head_id = tl.program_id(1)
    split_kv_id = tl.program_id(2)
    heads_per_kv = tl.cdiv(kv_group_num, BLOCK_H)
    cur_kv_head = cur_head_id // heads_per_kv
    if kv_group_num > BLOCK_H:
        VALID_BLOCK_H: tl.constexpr = BLOCK_H
    else:
        VALID_BLOCK_H: tl.constexpr = kv_group_num
    cur_head = cur_head_id * VALID_BLOCK_H + tl.arange(0, BLOCK_H)
    mask_h = cur_head < (cur_head_id + 1) * VALID_BLOCK_H
    mask_h = mask_h & (cur_head < q_head_num)
    offs_d = tl.arange(0, BLOCK_DMODEL)
    offs_dv = tl.arange(0, BLOCK_DV)
    mask_d = offs_d < HEAD_DIM
    mask_dv = offs_dv < HEAD_DIM
    cur_batch_seq_len = tl.load(seq_lens + cur_batch)
    offs_q = cur_batch * stride_qb + cur_head[:, None] * stride_qh + offs_d[None, :]
    q = tl.load(Q + offs_q, mask=mask_h[:, None] & mask_d[None, :], other=0.0)
    kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
    split_kv_start = kv_len_per_split * split_kv_id
    split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)
    e_max = tl.zeros([BLOCK_H], dtype=tl.float32) - float("inf")
    e_sum = tl.zeros([BLOCK_H], dtype=tl.float32)
    acc = tl.zeros([BLOCK_H, BLOCK_DV], dtype=tl.float32)
    if split_kv_end > split_kv_start:
        start_page = split_kv_start // PAGE_SIZE
        end_page = (split_kv_end + PAGE_SIZE - 1) // PAGE_SIZE
        offs_token_in_page = tl.arange(0, PAGE_SIZE)
        for page_idx in range(start_page, end_page):
            physical_page = tl.load(block_table + cur_batch * stride_bt0 + page_idx * stride_bt1)
            global_token_idx = page_idx * PAGE_SIZE + offs_token_in_page
            token_mask = global_token_idx < split_kv_end
            page_base = KV_Cache + physical_page * stride_kv0 + cur_kv_head * stride_kv2
            k = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + offs_d[None, :],
                        mask=token_mask[:, None] & mask_d[None, :], other=0.0)
            v = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + (HEAD_DIM + offs_dv)[None, :],
                        mask=token_mask[:, None] & mask_dv[None, :], other=0.0)
            qk = tl.dot(q, k.to(q.dtype).T)
            qk *= sm_scale
            qk = tl.where(mask_h[:, None] & token_mask[None, :], qk, float("-inf"))
 

... (4038 more chars)

{
  "command": "<8481 chars \u2014 see below>"
}

cat > /tmp/verify_bug2.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import triton
import triton.language as tl
import reference
import math

shape = {"batch": 8, "num_heads": 32, "num_kv_heads": 8, "head_dim": 128, "seq_len": 1024, "page_size": 16}
B, H, Hkv, D, L, P = shape["batch"], shape["num_heads"], shape["num_kv_heads"], shape["head_dim"], shape["seq_len"], shape["page_size"]

device = torch.device("cuda:0")
pages_per_seq = (L + P - 1) // P
total_pages = max(B * pages_per_seq + 8, 64)

query = torch.randn(B, H, D, dtype=torch.bfloat16, device=device) * 0.1
kv_cache = torch.randn(total_pages, P, Hkv, 2 * D, dtype=torch.bfloat16, device=device) * 0.1
block_table = torch.randperm(total_pages)[:B * pages_per_seq].reshape(B, pages_per_seq).int().to(device)
seq_lens = torch.full((B,), L, dtype=torch.int32, device=device)

ref_model = reference.Model(B, H, Hkv, D, L, P).to(device).eval()
with torch.no_grad():
    ref_out = ref_model(query, kv_cache, block_table, seq_lens)

# Copy kernel code from sweep
@triton.jit
def _fwd_kernel_stage1_v2(
    Q, KV_Cache, block_table, seq_lens, sm_scale, Mid_O,
    stride_qb, stride_qh, stride_bt0, stride_bt1,
    stride_kv0, stride_kv1, stride_kv2, stride_kv3,
    stride_mid_ob, stride_mid_oh, stride_mid_os,
    kv_group_num: tl.constexpr, q_head_num: tl.constexpr,
    BLOCK_DMODEL: tl.constexpr, BLOCK_DV: tl.constexpr, BLOCK_H: tl.constexpr,
    NUM_KV_SPLITS: tl.constexpr, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr,
):
    cur_batch = tl.program_id(0)
    cur_head_id = tl.program_id(1)
    split_kv_id = tl.program_id(2)
    heads_per_kv = tl.cdiv(kv_group_num, BLOCK_H)
    cur_kv_head = cur_head_id // heads_per_kv
    if kv_group_num > BLOCK_H:
        VALID_BLOCK_H: tl.constexpr = BLOCK_H
    else:
        VALID_BLOCK_H: tl.constexpr = kv_group_num
    cur_head = cur_head_id * VALID_BLOCK_H + tl.arange(0, BLOCK_H)
    mask_h = cur_head < (cur_head_id + 1) * VALID_BLOCK_H
    mask_h = mask_h & (cur_head < q_head_num)
    offs_d = tl.arange(0, BLOCK_DMODEL)
    offs_dv = tl.arange(0, BLOCK_DV)
    mask_d = offs_d < HEAD_DIM
    mask_dv = offs_dv < HEAD_DIM
    cur_batch_seq_len = tl.load(seq_lens + cur_batch)
    offs_q = cur_batch * stride_qb + cur_head[:, None] * stride_qh + offs_d[None, :]
    q = tl.load(Q + offs_q, mask=mask_h[:, None] & mask_d[None, :], other=0.0)
    kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
    split_kv_start = kv_len_per_split * split_kv_id
    split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)
    e_max = tl.zeros([BLOCK_H], dtype=tl.float32) - float("inf")
    e_sum = tl.zeros([BLOCK_H], dtype=tl.float32)
    acc = tl.zeros([BLOCK_H, BLOCK_DV], dtype=tl.float32)
    if split_kv_end > split_kv_start:
        start_page = split_kv_start // PAGE_SIZE
        end_page = (split_kv_end + PAGE_SIZE - 1) // PAGE_SIZE
        offs_token_in_page = tl.arange(0, PAGE_SIZE)
        for page_idx in range(start_page, end_page):
            physical_page = tl.load(block_table + cur_batch * stride_bt0 + page_idx * stride_bt1)
            global_token_idx = page_idx * PAGE_SIZE + offs_token_in_page
            token_mask = global_token_idx < split_kv_end
            page_base = KV_Cache + physical_page * stride_kv0 + cur_kv_head * stride_kv2
            k = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + offs_d[None, :],
                        mask=token_mask[:, None] & mask_d[None, :], other=0.0)
            v = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + (HEAD_DIM + offs_dv)[None, :],
                        mask=token_mask[:, None] & mask_dv[None, :], other=0.0)
            qk = tl.dot(q, k.to(q.dtype).T)
            qk *= sm_scale
            qk = tl.where(mask_h[:, None] & token_mask[None, :], qk, float("-inf"))
            n_e_max = tl.maximum(tl.max(qk, 1), e_max)
            re_scale = tl.exp(e_max - n_e_max)
            p = tl.exp(qk - n_e_max[:, None])
            acc *

... (4481 more chars)

{
  "command": "<9690 chars \u2014 see below>",
  "timeout": 300
}

cat > /tmp/sweep_correct.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import triton
import triton.language as tl
import reference
import shapes
import math

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

@triton.jit
def _fwd_kernel_stage1_v2(
    Q, KV_Cache, block_table, seq_lens, sm_scale, Mid_O,
    stride_qb, stride_qh, stride_bt0, stride_bt1,
    stride_kv0, stride_kv1, stride_kv2, stride_kv3,
    stride_mid_ob, stride_mid_oh, stride_mid_os,
    kv_group_num: tl.constexpr, q_head_num: tl.constexpr,
    BLOCK_DMODEL: tl.constexpr, BLOCK_DV: tl.constexpr, BLOCK_H: tl.constexpr,
    NUM_KV_SPLITS: tl.constexpr, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr,
):
    cur_batch = tl.program_id(0)
    cur_head_id = tl.program_id(1)
    split_kv_id = tl.program_id(2)
    heads_per_kv = tl.cdiv(kv_group_num, BLOCK_H)
    cur_kv_head = cur_head_id // heads_per_kv
    if kv_group_num > BLOCK_H:
        VALID_BLOCK_H: tl.constexpr = BLOCK_H
    else:
        VALID_BLOCK_H: tl.constexpr = kv_group_num
    cur_head = cur_head_id * VALID_BLOCK_H + tl.arange(0, BLOCK_H)
    mask_h = cur_head < (cur_head_id + 1) * VALID_BLOCK_H
    mask_h = mask_h & (cur_head < q_head_num)
    offs_d = tl.arange(0, BLOCK_DMODEL)
    offs_dv = tl.arange(0, BLOCK_DV)
    mask_d = offs_d < HEAD_DIM
    mask_dv = offs_dv < HEAD_DIM
    cur_batch_seq_len = tl.load(seq_lens + cur_batch)
    offs_q = cur_batch * stride_qb + cur_head[:, None] * stride_qh + offs_d[None, :]
    q = tl.load(Q + offs_q, mask=mask_h[:, None] & mask_d[None, :], other=0.0)
    kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
    split_kv_start = kv_len_per_split * split_kv_id
    split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)
    e_max = tl.zeros([BLOCK_H], dtype=tl.float32) - float("inf")
    e_sum = tl.zeros([BLOCK_H], dtype=tl.float32)
    acc = tl.zeros([BLOCK_H, BLOCK_DV], dtype=tl.float32)
    if split_kv_end > split_kv_start:
        start_page = split_kv_start // PAGE_SIZE
        end_page = (split_kv_end + PAGE_SIZE - 1) // PAGE_SIZE
        offs_token_in_page = tl.arange(0, PAGE_SIZE)
        for page_idx in range(start_page, end_page):
            physical_page = tl.load(block_table + cur_batch * stride_bt0 + page_idx * stride_bt1)
            global_token_idx = page_idx * PAGE_SIZE + offs_token_in_page
            token_mask = global_token_idx < split_kv_end
            page_base = KV_Cache + physical_page * stride_kv0 + cur_kv_head * stride_kv2
            k = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + offs_d[None, :],
                        mask=token_mask[:, None] & mask_d[None, :], other=0.0)
            v = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + (HEAD_DIM + offs_dv)[None, :],
                        mask=token_mask[:, None] & mask_dv[None, :], other=0.0)
            qk = tl.dot(q, k.to(q.dtype).T)
            qk *= sm_scale
            qk = tl.where(mask_h[:, None] & token_mask[None, :], qk, float("-inf"))
            n_e_max = tl.maximum(tl.max(qk, 1), e_max)
            re_scale = tl.exp(e_max - n_e_max)
            p = tl.exp(qk - n_e_max[:, None])
            acc *= re_scale[:, None]
            acc += tl.dot(p.to(v.dtype), v)
            e_sum = e_sum * re_scale + tl.sum(p, 1)
            e_max = n_e_max
        offs_mid_o = cur_batch * stride_mid_ob + cur_head[:, None] * stride_mid_oh + split_kv_id * stride_mid_os + offs_dv[None, :]
        tl.store(Mid_O + offs_mid_o, acc / e_sum[:, None], mask=mask_h[:, None] & mask_dv[None, :])
        offs_mid_lse = cur_batch * stride_mid_ob + cur_head * stride_mid_oh + split_kv_id * stride_mid_os + HEAD_DIM
        tl.store(Mid_O + offs_mid_lse, e_max + tl.log(e_sum), mask=mask_h)

@tri

... (5690 more chars)

{
  "command": "<9703 chars \u2014 see below>",
  "timeout": 600
}

cat > /tmp/sweep_warps.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import triton
import triton.language as tl
import reference
import shapes
import math

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

@triton.jit
def _fwd_kernel_stage1_v2(
    Q, KV_Cache, block_table, seq_lens, sm_scale, Mid_O,
    stride_qb, stride_qh, stride_bt0, stride_bt1,
    stride_kv0, stride_kv1, stride_kv2, stride_kv3,
    stride_mid_ob, stride_mid_oh, stride_mid_os,
    kv_group_num: tl.constexpr, q_head_num: tl.constexpr,
    BLOCK_DMODEL: tl.constexpr, BLOCK_DV: tl.constexpr, BLOCK_H: tl.constexpr,
    NUM_KV_SPLITS: tl.constexpr, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr,
):
    cur_batch = tl.program_id(0)
    cur_head_id = tl.program_id(1)
    split_kv_id = tl.program_id(2)
    heads_per_kv = tl.cdiv(kv_group_num, BLOCK_H)
    cur_kv_head = cur_head_id // heads_per_kv
    if kv_group_num > BLOCK_H:
        VALID_BLOCK_H: tl.constexpr = BLOCK_H
    else:
        VALID_BLOCK_H: tl.constexpr = kv_group_num
    cur_head = cur_head_id * VALID_BLOCK_H + tl.arange(0, BLOCK_H)
    mask_h = cur_head < (cur_head_id + 1) * VALID_BLOCK_H
    mask_h = mask_h & (cur_head < q_head_num)
    offs_d = tl.arange(0, BLOCK_DMODEL)
    offs_dv = tl.arange(0, BLOCK_DV)
    mask_d = offs_d < HEAD_DIM
    mask_dv = offs_dv < HEAD_DIM
    cur_batch_seq_len = tl.load(seq_lens + cur_batch)
    offs_q = cur_batch * stride_qb + cur_head[:, None] * stride_qh + offs_d[None, :]
    q = tl.load(Q + offs_q, mask=mask_h[:, None] & mask_d[None, :], other=0.0)
    kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
    split_kv_start = kv_len_per_split * split_kv_id
    split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)
    e_max = tl.zeros([BLOCK_H], dtype=tl.float32) - float("inf")
    e_sum = tl.zeros([BLOCK_H], dtype=tl.float32)
    acc = tl.zeros([BLOCK_H, BLOCK_DV], dtype=tl.float32)
    if split_kv_end > split_kv_start:
        start_page = split_kv_start // PAGE_SIZE
        end_page = (split_kv_end + PAGE_SIZE - 1) // PAGE_SIZE
        offs_token_in_page = tl.arange(0, PAGE_SIZE)
        for page_idx in range(start_page, end_page):
            physical_page = tl.load(block_table + cur_batch * stride_bt0 + page_idx * stride_bt1)
            global_token_idx = page_idx * PAGE_SIZE + offs_token_in_page
            token_mask = global_token_idx < split_kv_end
            page_base = KV_Cache + physical_page * stride_kv0 + cur_kv_head * stride_kv2
            k = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + offs_d[None, :],
                        mask=token_mask[:, None] & mask_d[None, :], other=0.0)
            v = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + (HEAD_DIM + offs_dv)[None, :],
                        mask=token_mask[:, None] & mask_dv[None, :], other=0.0)
            qk = tl.dot(q, k.to(q.dtype).T)
            qk *= sm_scale
            qk = tl.where(mask_h[:, None] & token_mask[None, :], qk, float("-inf"))
            n_e_max = tl.maximum(tl.max(qk, 1), e_max)
            re_scale = tl.exp(e_max - n_e_max)
            p = tl.exp(qk - n_e_max[:, None])
            acc *= re_scale[:, None]
            acc += tl.dot(p.to(v.dtype), v)
            e_sum = e_sum * re_scale + tl.sum(p, 1)
            e_max = n_e_max
        offs_mid_o = cur_batch * stride_mid_ob + cur_head[:, None] * stride_mid_oh + split_kv_id * stride_mid_os + offs_dv[None, :]
        tl.store(Mid_O + offs_mid_o, acc / e_sum[:, None], mask=mask_h[:, None] & mask_dv[None, :])
        offs_mid_lse = cur_batch * stride_mid_ob + cur_head * stride_mid_oh + split_kv_id * stride_mid_os + HEAD_DIM
        tl.store(Mid_O + offs_mid_lse, e_max + tl.log(e_sum), mask=mask_h)

@trito

... (5703 more chars)

{
  "command": "<9667 chars \u2014 see below>",
  "timeout": 300
}

cat > /tmp/sweep_warps.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import triton
import triton.language as tl
import reference
import shapes
import math

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

@triton.jit
def _fwd_kernel_stage1_v2(
    Q, KV_Cache, block_table, seq_lens, sm_scale, Mid_O,
    stride_qb, stride_qh, stride_bt0, stride_bt1,
    stride_kv0, stride_kv1, stride_kv2, stride_kv3,
    stride_mid_ob, stride_mid_oh, stride_mid_os,
    kv_group_num: tl.constexpr, q_head_num: tl.constexpr,
    BLOCK_DMODEL: tl.constexpr, BLOCK_DV: tl.constexpr, BLOCK_H: tl.constexpr,
    NUM_KV_SPLITS: tl.constexpr, PAGE_SIZE: tl.constexpr, HEAD_DIM: tl.constexpr,
):
    cur_batch = tl.program_id(0)
    cur_head_id = tl.program_id(1)
    split_kv_id = tl.program_id(2)
    heads_per_kv = tl.cdiv(kv_group_num, BLOCK_H)
    cur_kv_head = cur_head_id // heads_per_kv
    if kv_group_num > BLOCK_H:
        VALID_BLOCK_H: tl.constexpr = BLOCK_H
    else:
        VALID_BLOCK_H: tl.constexpr = kv_group_num
    cur_head = cur_head_id * VALID_BLOCK_H + tl.arange(0, BLOCK_H)
    mask_h = cur_head < (cur_head_id + 1) * VALID_BLOCK_H
    mask_h = mask_h & (cur_head < q_head_num)
    offs_d = tl.arange(0, BLOCK_DMODEL)
    offs_dv = tl.arange(0, BLOCK_DV)
    mask_d = offs_d < HEAD_DIM
    mask_dv = offs_dv < HEAD_DIM
    cur_batch_seq_len = tl.load(seq_lens + cur_batch)
    offs_q = cur_batch * stride_qb + cur_head[:, None] * stride_qh + offs_d[None, :]
    q = tl.load(Q + offs_q, mask=mask_h[:, None] & mask_d[None, :], other=0.0)
    kv_len_per_split = tl.cdiv(cur_batch_seq_len, NUM_KV_SPLITS)
    split_kv_start = kv_len_per_split * split_kv_id
    split_kv_end = tl.minimum(split_kv_start + kv_len_per_split, cur_batch_seq_len)
    e_max = tl.zeros([BLOCK_H], dtype=tl.float32) - float("inf")
    e_sum = tl.zeros([BLOCK_H], dtype=tl.float32)
    acc = tl.zeros([BLOCK_H, BLOCK_DV], dtype=tl.float32)
    if split_kv_end > split_kv_start:
        start_page = split_kv_start // PAGE_SIZE
        end_page = (split_kv_end + PAGE_SIZE - 1) // PAGE_SIZE
        offs_token_in_page = tl.arange(0, PAGE_SIZE)
        for page_idx in range(start_page, end_page):
            physical_page = tl.load(block_table + cur_batch * stride_bt0 + page_idx * stride_bt1)
            global_token_idx = page_idx * PAGE_SIZE + offs_token_in_page
            token_mask = global_token_idx < split_kv_end
            page_base = KV_Cache + physical_page * stride_kv0 + cur_kv_head * stride_kv2
            k = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + offs_d[None, :],
                        mask=token_mask[:, None] & mask_d[None, :], other=0.0)
            v = tl.load(page_base + offs_token_in_page[:, None] * stride_kv1 + (HEAD_DIM + offs_dv)[None, :],
                        mask=token_mask[:, None] & mask_dv[None, :], other=0.0)
            qk = tl.dot(q, k.to(q.dtype).T)
            qk *= sm_scale
            qk = tl.where(mask_h[:, None] & token_mask[None, :], qk, float("-inf"))
            n_e_max = tl.maximum(tl.max(qk, 1), e_max)
            re_scale = tl.exp(e_max - n_e_max)
            p = tl.exp(qk - n_e_max[:, None])
            acc *= re_scale[:, None]
            acc += tl.dot(p.to(v.dtype), v)
            e_sum = e_sum * re_scale + tl.sum(p, 1)
            e_max = n_e_max
        offs_mid_o = cur_batch * stride_mid_ob + cur_head[:, None] * stride_mid_oh + split_kv_id * stride_mid_os + offs_dv[None, :]
        tl.store(Mid_O + offs_mid_o, acc / e_sum[:, None], mask=mask_h[:, None] & mask_dv[None, :])
        offs_mid_lse = cur_batch * stride_mid_ob + cur_head * stride_mid_oh + split_kv_id * stride_mid_os + HEAD_DIM
        tl.store(Mid_O + offs_mid_lse, e_max + tl.log(e_sum), mask=mask_h)

@trito

... (5667 more chars)

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "content": "<13593 chars \u2014 see diff>"
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python check.py 2>&1",
  "timeout": 120
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python benchmark.py 2>&1",
  "timeout": 180
}

{
  "command": "<2589 chars \u2014 see below>"
}

cat > /tmp/test_splits.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import shapes
import math

# Reuse the kernel from solution.py
import solution

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

# Test shape 4 with more splits
shape = shapes.SHAPES[4]
apply_shape(shape)

torch.manual_seed(42)
B = shape["batch"]
H = shape["num_heads"]
Hkv = shape["num_kv_heads"]
D = shape["head_dim"]
L = shape["seq_len"]
P = shape["page_size"]

pages_per_seq = (L + P - 1) // P
total_pages = max(B * pages_per_seq + 8, 64)

query = torch.randn(B, H, D, dtype=torch.bfloat16, device=device) * 0.1
kv_cache = torch.randn(total_pages, P, Hkv, 2 * D, dtype=torch.bfloat16, device=device) * 0.1
block_table = torch.randperm(total_pages)[:B * pages_per_seq].reshape(B, pages_per_seq).int().to(device)
seq_lens_tensor = torch.full((B,), L, dtype=torch.int32, device=device)

sm_scale = 1.0 / math.sqrt(D)

ref_model = reference.Model(B, H, Hkv, D, L, P).to(device).eval()
with torch.no_grad():
    ref_out = ref_model(query, kv_cache, block_table, seq_lens_tensor)

for num_kv_splits in [8, 12, 16, 20]:
    try:
        out = solution.paged_attention_decode(query, kv_cache, block_table, seq_lens_tensor, sm_scale, P, num_kv_splits)
        max_diff = (out - ref_out).abs().max().item()
        
        for _ in range(10):
            out = solution.paged_attention_decode(query, kv_cache, block_table, seq_lens_tensor, sm_scale, P, num_kv_splits)
        torch.cuda.synchronize()
        
        times = []
        for _ in range(30):
            _l2_scratch.zero_()
            torch.cuda.synchronize()
            s = torch.cuda.Event(enable_timing=True)
            e = torch.cuda.Event(enable_timing=True)
            s.record()
            out = solution.paged_attention_decode(query, kv_cache, block_table, seq_lens_tensor, sm_scale, P, num_kv_splits)
            e.record()
            torch.cuda.synchronize()
            times.append(s.elapsed_time(e))
        
        import statistics
        print(f"splits={num_kv_splits:2d} ms={statistics.median(times):.3f} max_diff={max_diff:.4f}")
    except Exception as e:
        print(f"splits={num_kv_splits} ERROR: {e}")
EOF
uv run python /tmp/test_splits.py

{
  "command": "<2815 chars \u2014 see below>",
  "timeout": 300
}

cat > /tmp/test_all_splits.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import shapes
import math
import solution

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

for shape_idx in range(5):
    shape = shapes.SHAPES[shape_idx]
    apply_shape(shape)
    
    torch.manual_seed(42)
    B = shape["batch"]
    H = shape["num_heads"]
    Hkv = shape["num_kv_heads"]
    D = shape["head_dim"]
    L = shape["seq_len"]
    P = shape["page_size"]
    
    pages_per_seq = (L + P - 1) // P
    total_pages = max(B * pages_per_seq + 8, 64)
    
    query = torch.randn(B, H, D, dtype=torch.bfloat16, device=device) * 0.1
    kv_cache = torch.randn(total_pages, P, Hkv, 2 * D, dtype=torch.bfloat16, device=device) * 0.1
    block_table = torch.randperm(total_pages)[:B * pages_per_seq].reshape(B, pages_per_seq).int().to(device)
    seq_lens_tensor = torch.full((B,), L, dtype=torch.int32, device=device)
    
    sm_scale = 1.0 / math.sqrt(D)
    
    ref_model = reference.Model(B, H, Hkv, D, L, P).to(device).eval()
    with torch.no_grad():
        ref_out = ref_model(query, kv_cache, block_table, seq_lens_tensor)
    
    print(f"\nshape={shape_idx} {shape}")
    for num_kv_splits in [1, 2, 4, 8, 12, 16, 20]:
        try:
            out = solution.paged_attention_decode(query, kv_cache, block_table, seq_lens_tensor, sm_scale, P, num_kv_splits)
            max_diff = (out - ref_out).abs().max().item()
            if max_diff > 0.02:
                continue
            
            for _ in range(10):
                out = solution.paged_attention_decode(query, kv_cache, block_table, seq_lens_tensor, sm_scale, P, num_kv_splits)
            torch.cuda.synchronize()
            
            times = []
            for _ in range(30):
                _l2_scratch.zero_()
                torch.cuda.synchronize()
                s = torch.cuda.Event(enable_timing=True)
                e = torch.cuda.Event(enable_timing=True)
                s.record()
                out = solution.paged_attention_decode(query, kv_cache, block_table, seq_lens_tensor, sm_scale, P, num_kv_splits)
                e.record()
                torch.cuda.synchronize()
                times.append(s.elapsed_time(e))
            
            import statistics
            print(f"  splits={num_kv_splits:2d} ms={statistics.median(times):.3f}")
        except Exception as e:
            pass
EOF
uv run python /tmp/test_all_splits.py 2>&1

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "edit": {
    "old": "        # Target ~256-512 stage-1 blocks for good occupancy on Blackwell.\n        head_groups = (self.num_heads + min(8, self.group_size) - 1) // min(8, self.group_size)\n        base_blocks = self.batch * head_groups\n\n        if base_blocks < 64:\n            num_kv_splits = 8\n        elif base_blocks < 128:\n            num_kv_splits = 4\n        elif base_blocks < 256:\n            num_kv_splits = 2\n        else:\n            num_kv_splits = 1\n\n        # Also increase 

... (775 more chars)

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python check.py 2>&1",
  "timeout": 120
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python benchmark.py 2>&1",
  "timeout": 180
}

{
  "command": "find /home -path \"*vllm*\" -name \"*.cu\" 2>/dev/null | head -20"
}

{
  "command": "find /home -path \"*vllm*\" -name \"paged_attention*.cu\" 2>/dev/null | head -10"
}

{
  "path": "/home/infatoshi/vllm/csrc/attention/paged_attention_v2.cu",
  "n_lines": 200
}

{
  "command": "find /home/infatoshi/vllm -name \"attention_kernels.cuh\" | head -5"
}

{
  "path": "/home/infatoshi/vllm/csrc/attention/attention_kernels.cuh",
  "n_lines": 300
}

{
  "path": "/home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention/solution.py",
  "edit": {
    "old": "        # Target a total stage-1 block count that keeps the GPU well occupied.\n        # With smaller head_dim each block does less work per page, so we need\n        # more blocks (hence more splits) to hide latency.\n        head_groups = (self.num_heads + min(8, self.group_size) - 1) // min(8, self.group_size)\n        base_blocks = self.batch * head_groups\n        target_blocks = 512 if self.head_dim <= 64 else 256\n        num_kv_splits = max(1, min(20, target_blocks // b

... (529 more chars)

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python check.py 2>&1",
  "timeout": 120
}

{
  "command": "cd /home/infatoshi/cuda/KernelBench-Hard/problems/03_paged_attention && uv run python benchmark.py 2>&1",
  "timeout": 180
}

{
  "command": "<2361 chars \u2014 see below>"
}

cat > /tmp/test_model_timing.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

for shape_idx in [2, 4]:
    shape = shapes.SHAPES[shape_idx]
    apply_shape(shape)
    
    torch.manual_seed(42)
    init_args = reference.get_init_inputs()
    ref_model = reference.Model(*init_args).to(device).eval()
    sol_model = solution.Model(*init_args).to(device).eval()
    
    torch.manual_seed(42)
    inputs = [t.to(device) for t in reference.get_inputs()]
    
    # Warmup
    for _ in range(10):
        sol_model(*inputs)
    torch.cuda.synchronize()
    
    # Time with L2 flush
    times = []
    for _ in range(30):
        _l2_scratch.zero_()
        torch.cuda.synchronize()
        s = torch.cuda.Event(enable_timing=True)
        e = torch.cuda.Event(enable_timing=True)
        s.record()
        sol_model(*inputs)
        e.record()
        torch.cuda.synchronize()
        times.append(s.elapsed_time(e))
    
    import statistics
    print(f"shape={shape_idx} {shape} ms={statistics.median(times):.3f}")
    
    # Also time paged_attention_decode directly with the heuristic's num_kv_splits
    import inspect
    src = inspect.getsource(solution.Model.forward)
    # Just call direct
    if shape_idx == 2:
        num_kv_splits = 16
    else:
        num_kv_splits = 16
    
    times2 = []
    for _ in range(30):
        _l2_scratch.zero_()
        torch.cuda.synchronize()
        s = torch.cuda.Event(enable_timing=True)
        e = torch.cuda.Event(enable_timing=True)
        s.record()
        solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], 1.0/math.sqrt(shape["head_dim"]), shape["page_size"], num_kv_splits)
        e.record()
        torch.cuda.synchronize()
        times2.append(s.elapsed_time(e))
    
    print(f"  direct splits={num_kv_splits} ms={statistics.median(times2):.3f}")
EOF
uv run python /tmp/test_model_timing.py

{
  "command": "<2478 chars \u2014 see below>"
}

cat > /tmp/test_overhead.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[2]
apply_shape(shape)

torch.manual_seed(42)
init_args = reference.get_init_inputs()
sol_model = solution.Model(*init_args).to(device).eval()

torch.manual_seed(42)
inputs = [t.to(device) for t in reference.get_inputs()]

# Warmup both
for _ in range(15):
    sol_model(*inputs)
    solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], 1.0/math.sqrt(128), 16, 16)
torch.cuda.synchronize()

# Time model
import statistics
times_model = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model(*inputs)
    e.record()
    torch.cuda.synchronize()
    times_model.append(s.elapsed_time(e))

print(f"Model: ms={statistics.median(times_model):.3f}")

# Time direct
times_direct = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], 1.0/math.sqrt(128), 16, 16)
    e.record()
    torch.cuda.synchronize()
    times_direct.append(s.elapsed_time(e))

print(f"Direct: ms={statistics.median(times_direct):.3f}")

# Time with state dict load
sd = sol_model.state_dict()
sol_model.load_state_dict(sd, strict=True)
torch.cuda.synchronize()

times_post_load = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model(*inputs)
    e.record()
    torch.cuda.synchronize()
    times_post_load.append(s.elapsed_time(e))

print(f"Post-load: ms={statistics.median(times_post_load):.3f}")
EOF
uv run python /tmp/test_overhead.py

{
  "command": "<2020 chars \u2014 see below>"
}

cat > /tmp/test_benchmark_mimic.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

# Mimic benchmark.py exactly for shape 4
shape_idx = 4
shape = shapes.SHAPES[shape_idx]
apply_shape(shape)

init_args = reference.get_init_inputs()
ref_model = reference.Model(*init_args).to(device).eval()
sol_model = solution.Model(*init_args).to(device).eval()
sd = ref_model.state_dict()
try:
    sol_model.load_state_dict(sd, strict=True)
except RuntimeError:
    pass

torch.manual_seed(2026)
inputs = [t.to(device) for t in reference.get_inputs()]

# Warmup exactly like time_fn
for _ in range(10):
    with torch.no_grad():
        sol_model(*inputs)
torch.cuda.synchronize()

# Time exactly like time_fn
times = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model(*inputs)
    e.record()
    torch.cuda.synchronize()
    times.append(s.elapsed_time(e))

print(f"shape={shape_idx} ms={statistics.median(times):.3f}")

# Also print num_kv_splits
head_groups = (shape["num_heads"] + min(8, shape["num_heads"]//shape["num_kv_heads"]) - 1) // min(8, shape["num_heads"]//shape["num_kv_heads"])
base_blocks = shape["batch"] * head_groups
target_blocks = 640 if shape["head_dim"] <= 64 else 512
num_kv_splits = max(1, min(24, target_blocks // base_blocks))
print(f"  base_blocks={base_blocks} num_kv_splits={num_kv_splits}")
EOF
uv run python /tmp/test_benchmark_mimic.py

{
  "command": "<1967 chars \u2014 see below>"
}

cat > /tmp/test_direct_20.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[4]
apply_shape(shape)

torch.manual_seed(2026)
B = shape["batch"]
H = shape["num_heads"]
Hkv = shape["num_kv_heads"]
D = shape["head_dim"]
L = shape["seq_len"]
P = shape["page_size"]
pages_per_seq = (L + P - 1) // P
total_pages = max(B * pages_per_seq + 8, 64)

query = torch.randn(B, H, D, dtype=torch.bfloat16, device=device) * 0.1
kv_cache = torch.randn(total_pages, P, Hkv, 2 * D, dtype=torch.bfloat16, device=device) * 0.1
block_table = torch.randperm(total_pages)[:B * pages_per_seq].reshape(B, pages_per_seq).int().to(device)
seq_lens = torch.full((B,), L, dtype=torch.int32, device=device)
sm_scale = 1.0 / math.sqrt(D)

for num_kv_splits in [8, 16, 20]:
    # Warmup
    for _ in range(15):
        solution.paged_attention_decode(query, kv_cache, block_table, seq_lens, sm_scale, P, num_kv_splits)
    torch.cuda.synchronize()
    
    times = []
    for _ in range(30):
        _l2_scratch.zero_()
        torch.cuda.synchronize()
        s = torch.cuda.Event(enable_timing=True)
        e = torch.cuda.Event(enable_timing=True)
        s.record()
        solution.paged_attention_decode(query, kv_cache, block_table, seq_lens, sm_scale, P, num_kv_splits)
        e.record()
        torch.cuda.synchronize()
        times.append(s.elapsed_time(e))
    
    print(f"splits={num_kv_splits} ms={statistics.median(times):.3f}")
EOF
uv run python /tmp/test_direct_20.py

{
  "command": "<2823 chars \u2014 see below>"
}

cat > /tmp/test_model_simple.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[4]
apply_shape(shape)

init_args = reference.get_init_inputs()

# Test 1: Model without load_state_dict
sol_model = solution.Model(*init_args).to(device).eval()

torch.manual_seed(2026)
inputs = [t.to(device) for t in reference.get_inputs()]

for _ in range(15):
    with torch.no_grad():
        sol_model(*inputs)
torch.cuda.synchronize()

times = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model(*inputs)
    e.record()
    torch.cuda.synchronize()
    times.append(s.elapsed_time(e))

print(f"Model (no load_state_dict): ms={statistics.median(times):.3f}")

# Test 2: Model with load_state_dict
ref_model = reference.Model(*init_args).to(device).eval()
sol_model2 = solution.Model(*init_args).to(device).eval()
sd = ref_model.state_dict()
sol_model2.load_state_dict(sd, strict=True)
torch.cuda.synchronize()

for _ in range(15):
    with torch.no_grad():
        sol_model2(*inputs)
torch.cuda.synchronize()

times2 = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model2(*inputs)
    e.record()
    torch.cuda.synchronize()
    times2.append(s.elapsed_time(e))

print(f"Model (with load_state_dict): ms={statistics.median(times2):.3f}")

# Test 3: Direct call
sm_scale = 1.0 / math.sqrt(128)
num_kv_splits = 16
for _ in range(15):
    solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], sm_scale, shape["page_size"], num_kv_splits)
torch.cuda.synchronize()

times3 = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], sm_scale, shape["page_size"], num_kv_splits)
    e.record()
    torch.cuda.synchronize()
    times3.append(s.elapsed_time(e))

print(f"Direct: ms={statistics.median(times3):.3f}")
EOF
uv run python /tmp/test_model_simple.py

{
  "command": "<1488 chars \u2014 see below>"
}

cat > /tmp/test_no_buffer.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")

# Temporarily modify solution.Model to not use register_buffer
class TestModel(solution.Model):
    def __init__(self, *args, **kwargs):
        torch.nn.Module.__init__(self)
        assert args[1] % args[2] == 0
        self.batch = args[0]
        self.num_heads = args[1]
        self.num_kv_heads = args[2]
        self.head_dim = args[3]
        self.seq_len = args[4]
        self.page_size = args[5]
        self.group_size = args[1] // args[2]
        import math
        self.scale = 1.0 / math.sqrt(args[3])
        # No buffer!

for shape in shapes.SHAPES:
    apply_shape(shape)
    init_args = reference.get_init_inputs()
    ref_model = reference.Model(*init_args).to(device).eval()
    test_model = TestModel(*init_args).to(device).eval()
    
    sd = ref_model.state_dict()
    try:
        test_model.load_state_dict(sd, strict=True)
        print(f"load_state_dict passed for {shape}")
    except RuntimeError as e:
        print(f"load_state_dict FAILED for {shape}: {e}")
EOF
uv run python /tmp/test_no_buffer.py

{
  "command": "python -c \"import torch; print(torch.__version__); m = torch.nn.Linear(2,2); m.register_buffer('b', torch.zeros(1)); sd = m.state_dict(); m2 = torch.nn.Linear(2,2); m2.load_state_dict(sd, strict=True); print('loaded')\""
}

{
  "path": "reference.py"
}

{
  "command": "<415 chars \u2014 see below>"
}

python -c "
import sys
sys.path.insert(0, '.')
import reference
import shapes

reference.BATCH = 8
reference.NUM_HEADS = 32
reference.NUM_KV_HEADS = 8
reference.HEAD_DIM = 128
reference.SEQ_LEN = 1024
reference.PAGE_SIZE = 16

ref_model = reference.Model(*reference.get_init_inputs())
print('ref state_dict keys:', list(ref_model.state_dict().keys()))
print('ref buffers:', dict(ref_model.named_buffers()).keys())
"

{
  "command": "<1548 chars \u2014 see below>"
}

cat > /tmp/test_page_aligned.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[4]
apply_shape(shape)

torch.manual_seed(2026)
init_args = reference.get_init_inputs()
inputs = [t.to(device) for t in reference.get_inputs()]

sm_scale = 1.0 / math.sqrt(64)

# Test with aligned splits
for num_kv_splits in [4, 8, 16, 20]:
    for _ in range(10):
        solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], sm_scale, 16, num_kv_splits)
    torch.cuda.synchronize()
    
    times = []
    for _ in range(30):
        _l2_scratch.zero_()
        torch.cuda.synchronize()
        s = torch.cuda.Event(enable_timing=True)
        e = torch.cuda.Event(enable_timing=True)
        s.record()
        solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], sm_scale, 16, num_kv_splits)
        e.record()
        torch.cuda.synchronize()
        times.append(s.elapsed_time(e))
    
    print(f"splits={num_kv_splits}: ms={statistics.median(times):.3f}")
EOF
uv run python /tmp/test_page_aligned.py

{
  "command": "<2201 chars \u2014 see below>"
}

cat > /tmp/test_verify_splits.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[4]
apply_shape(shape)

torch.manual_seed(2026)
init_args = reference.get_init_inputs()
inputs = [t.to(device) for t in reference.get_inputs()]

# Create model and check num_kv_splits
sol_model = solution.Model(*init_args).to(device).eval()
print(f"Model num_kv_splits heuristic:")
print(f"  head_dim={sol_model.head_dim}")
print(f"  seq_len={sol_model.seq_len}")
print(f"  batch={sol_model.batch}")
print(f"  num_heads={sol_model.num_heads}")
base_blocks = sol_model.num_kv_splits if hasattr(sol_model, 'num_kv_splits') else None
print(f"  base_blocks (num_kv_splits attr): {base_blocks}")

# Compute manually
kv_group_num = sol_model.num_heads // sol_model.num_kv_heads
head_groups = sol_model.num_heads // sol_model.num_kv_heads
base_blocks = (sol_model.batch * sol_model.num_kv_heads * head_groups * sol_model.seq_len) // sol_model.page_size
target_blocks = 640 if sol_model.head_dim <= 64 else 512
num_kv_splits = max(1, min(24, target_blocks // base_blocks))
print(f"  Manual: base_blocks={base_blocks}, target_blocks={target_blocks}, num_kv_splits={num_kv_splits}")

# Time it
for _ in range(15):
    with torch.no_grad():
        sol_model(*inputs)
torch.cuda.synchronize()

times = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model(*inputs)
    e.record()
    torch.cuda.synchronize()
    times.append(s.elapsed_time(e))

print(f"Model time: ms={statistics.median(times):.3f}")
EOF
uv run python /tmp/test_verify_splits.py

{
  "path": "solution.py"
}

{
  "command": "<3375 chars \u2014 see below>"
}

cat > /tmp/test_debug_overhead.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[4]
apply_shape(shape)

torch.manual_seed(2026)
init_args = reference.get_init_inputs()
inputs = [t.to(device) for t in reference.get_inputs()]

# Test 1: Direct call
sm_scale = 1.0 / math.sqrt(64)
num_kv_splits = 20

for _ in range(15):
    solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], sm_scale, 16, num_kv_splits)
torch.cuda.synchronize()

times1 = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], sm_scale, 16, num_kv_splits)
    e.record()
    torch.cuda.synchronize()
    times1.append(s.elapsed_time(e))

print(f"Direct: ms={statistics.median(times1):.3f}")

# Test 2: Model.call with identical args
sol_model = solution.Model(*init_args).to(device).eval()
print(f"Model.scale={sol_model.scale}, direct_scale={sm_scale}, match={sol_model.scale==sm_scale}")

for _ in range(15):
    with torch.no_grad():
        sol_model.forward(inputs[0], inputs[1], inputs[2], inputs[3])
torch.cuda.synchronize()

times2 = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model.forward(inputs[0], inputs[1], inputs[2], inputs[3])
    e.record()
    torch.cuda.synchronize()
    times2.append(s.elapsed_time(e))

print(f"Model.forward: ms={statistics.median(times2):.3f}")

# Test 3: Model.__call__ with identical args
for _ in range(15):
    with torch.no_grad():
        sol_model(inputs[0], inputs[1], inputs[2], inputs[3])
torch.cuda.synchronize()

times3 = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model(inputs[0], inputs[1], inputs[2], inputs[3])
    e.record()
    torch.cuda.synchronize()
    times3.append(s.elapsed_time(e))

print(f"Model.__call__: ms={statistics.median(times3):.3f}")

# Test 4: Model.__call__ without torch.no_grad
for _ in range(15):
    sol_model(inputs[0], inputs[1], inputs[2], inputs[3])
torch.cuda.synchronize()

times4 = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    sol_model(inputs[0], inputs[1], inputs[2], inputs[3])
    e.record()
    torch.cuda.synchronize()
    times4.append(s.elapsed_time(e))

print(f"Model.__call__ (no no_grad): ms={statistics.median(times4):.3f}")
EOF
uv run python /tmp/test_debug_overhead.py

{
  "command": "uv run python /tmp/test_debug_overhead.py"
}

{
  "command": "<2080 chars \u2014 see below>"
}

cat > /tmp/test_random_order.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics
import random

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[4]
apply_shape(shape)

torch.manual_seed(2026)
init_args = reference.get_init_inputs()
inputs = [t.to(device) for t in reference.get_inputs()]

sm_scale = 1.0 / math.sqrt(64)
num_kv_splits = 20

def run_test(name, fn, warmup=15, iters=30):
    for _ in range(warmup):
        with torch.no_grad():
            fn()
    torch.cuda.synchronize()
    times = []
    for _ in range(iters):
        _l2_scratch.zero_()
        torch.cuda.synchronize()
        s = torch.cuda.Event(enable_timing=True)
        e = torch.cuda.Event(enable_timing=True)
        s.record()
        with torch.no_grad():
            fn()
        e.record()
        torch.cuda.synchronize()
        times.append(s.elapsed_time(e))
    print(f"{name}: ms={statistics.median(times):.3f}")

sol_model = solution.Model(*init_args).to(device).eval()

# Run tests in random order multiple times
for i in range(5):
    order = ['direct', 'forward', 'call']
    random.shuffle(order)
    print(f"\nRun {i+1}, order: {order}")
    for name in order:
        if name == 'direct':
            run_test('direct', lambda: solution.paged_attention_decode(inputs[0], inputs[1], inputs[2], inputs[3], sm_scale, 16, num_kv_splits))
        elif name == 'forward':
            run_test('forward', lambda: sol_model.forward(inputs[0], inputs[1], inputs[2], inputs[3]))
        else:
            run_test('call', lambda: sol_model(inputs[0], inputs[1], inputs[2], inputs[3]))
EOF
uv run python /tmp/test_random_order.py

{
  "command": "nvidia-smi -q -d CLOCK | head -40"
}

{
  "command": "<1562 chars \u2014 see below>"
}

cat > /tmp/test_shape0.py << 'EOF'
import sys
sys.path.insert(0, '.')
import torch
import reference
import solution
import shapes
import math
import statistics

def apply_shape(shape):
    reference.BATCH = shape["batch"]
    reference.NUM_HEADS = shape["num_heads"]
    reference.NUM_KV_HEADS = shape["num_kv_heads"]
    reference.HEAD_DIM = shape["head_dim"]
    reference.SEQ_LEN = shape["seq_len"]
    reference.PAGE_SIZE = shape["page_size"]

device = torch.device("cuda:0")
_l2_scratch = torch.empty(128 * 1024 * 1024 // 4, dtype=torch.float32, device="cuda")

shape = shapes.SHAPES[0]
apply_shape(shape)

torch.manual_seed(2026)
init_args = reference.get_init_inputs()
inputs = [t.to(device) for t in reference.get_inputs()]

sol_model = solution.Model(*init_args).to(device).eval()

for _ in range(15):
    with torch.no_grad():
        sol_model(*inputs)
torch.cuda.synchronize()

times = []
for _ in range(30):
    _l2_scratch.zero_()
    torch.cuda.synchronize()
    s = torch.cuda.Event(enable_timing=True)
    e = torch.cuda.Event(enable_timing=True)
    s.record()
    with torch.no_grad():
        sol_model(*inputs)
    e.record()
    torch.cuda.synchronize()
    times.append(s.elapsed_time(e))

ms = statistics.median(times)
B, H, D = inputs[0].shape
Hkv = sol_model.num_kv_heads
L = sol_model.seq_len
bytes_moved = 2 * B * L * Hkv * D * 2 + B * H * D * 2 + B * H * D * 2  # KV + Q + Out in bytes
bw = bytes_moved / (ms / 1000) / 1e9
print(f"Shape 0: ms={ms:.3f}, BW={bw:.1f} GB/s, fraction={bw/1800:.3f}")
EOF
uv run python /tmp/test_shape0.py

{
  "command": "uv run python check.py"
}

{
  "command": "uv run python benchmark.py"
}