{
  "command": "ls -la",
  "description": "List workspace contents"
}

{
  "file_path": "/workspace/problems/03_paged_attention/reference.py"
}

{
  "file_path": "/workspace/problems/03_paged_attention/check.py"
}

{
  "file_path": "/workspace/problems/03_paged_attention/benchmark.py"
}

{
  "file_path": "/workspace/problems/03_paged_attention/shapes.py"
}

{
  "file_path": "/workspace/problems/03_paged_attention/sota.py"
}

{
  "file_path": "/workspace/problems/03_paged_attention/problem.yaml"
}

{
  "file_path": "/workspace/problems/03_paged_attention/PROMPT.txt"
}

{
  "command": "<472 chars \u2014 see below>",
  "description": "Check GPU and torch environment"
}

echo "=== nvidia-smi ===" && nvidia-smi 2>/dev/null | head -20
echo "=== uv python ===" && uv run python -c "import torch; print('torch', torch.__version__); print('cuda', torch.version.cuda); print('dev', torch.cuda.get_device_name(0) if torch.cuda.is_available() else 'NONE'); print('capability', torch.cuda.get_device_capability(0) if torch.cuda.is_available() else 'NONE'); print('props:', torch.cuda.get_device_properties(0) if torch.cuda.is_available() else 'NONE')"

{
  "command": "<542 chars \u2014 see below>",
  "description": "Check triton/cutlass/flashinfer/nvcc/nsight availability"
}

cd /workspace/problems/03_paged_attention
uv run python -c "
import importlib
for m in ['triton','flashinfer','vllm','cutlass','cuda']:
    try:
        mod=importlib.import_module(m)
        print(m, 'OK', getattr(mod,'__version__','?'))
    except Exception as e:
        print(m, 'MISSING', type(e).__name__, str(e)[:80])
"
echo "=== nvcc ==="
which nvcc && nvcc --version 2>/dev/null | tail -4
echo "=== nsight ==="
which ncu nsys 2>/dev/null
echo "=== GPU clocks ==="
nvidia-smi -q -d CLOCK 2>/dev/null | grep -A2 "Max Clocks" | head -20

{
  "command": "<160 chars \u2014 see below>",
  "description": "Explore repo structure for eval utilities"
}

cd /workspace
echo "=== repo root ===" && ls -la
echo "=== src/eval ===" && ls -la src/eval/ 2>/dev/null
echo "=== hardware ===" && ls src/hardware* 2>/dev/null

{
  "file_path": "/workspace/src/eval/timing.py"
}

{
  "file_path": "/workspace/src/eval/roofline.py"
}

{
  "file_path": "/workspace/src/hardware/rtx_pro_6000.py"
}

{
  "file_path": "/workspace/src/eval/correctness.py"
}

{
  "file_path": "/workspace/src/eval/numeric_stress.py"
}

{
  "subject": "Triton split-K paged-decode kernel v1",
  "description": "Write flash-decoding style Triton kernel: main kernel computes per-split partial output (m, l, acc) with online softmax over paged KV; reduction kernel merges splits. Get it correct (check.py PASS).",
  "activeForm": "Writing v1 Triton split-K kernel"
}

{
  "subject": "Tune split-K params + BLOCK_N/warps/stages",
  "description": "Autotune BLOCK_N, num_warps, num_stages. Choose num_splits to fill ~4-8x SMs. Profile with ncu for bandwidth utilization.",
  "activeForm": "Tuning split-K and tile params"
}

{
  "subject": "Optimize launch overhead + persistent buffers",
  "description": "Cache partial/output buffers, consider CUDA graph capture to eliminate per-call launch overhead (dominant for small shapes). Minimize kernel count.",
  "activeForm": "Optimizing launch overhead"
}

{
  "subject": "Push peak_fraction toward SOTA",
  "description": "Iterate profiling/timing via benchmark.py, target >70% of 1800 GB/s. Compare against compiled/eager baselines.",
  "activeForm": "Pushing bandwidth utilization"
}

{
  "taskId": "1",
  "status": "in_progress"
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "content": "<9935 chars \u2014 see diff>"
}

{
  "command": "uv run python check.py 2>&1 | tail -40",
  "description": "Run correctness checker on v1"
}

{
  "command": "<141 chars \u2014 see below>",
  "description": "Benchmark v1 solution"
}

cd /workspace/problems/03_paged_attention
uv run python benchmark.py 2>&1 | grep -E "variant=solution|peak_fraction|RESULT|shape=" | head -40

{
  "command": "<1560 chars \u2014 see below>",
  "description": "Profile kernel times vs launch overhead for small and large shapes"
}

cd /workspace/problems/03_paged_attention
cat > prof_trace.py << 'EOF'
import torch, reference, solution, shapes
from pathlib import Path
dev=torch.device("cuda:0")

def run(shape_idx):
    s=shapes.SHAPES[shape_idx]
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    # warmup
    for _ in range(20): sol(*inp)
    torch.cuda.synchronize()
    # CUDA-event time
    import statistics
    ts=[]
    for _ in range(100):
        s_=torch.cuda.Event(enable_timing=True); e=torch.cuda.Event(enable_timing=True)
        s_.record(); sol(*inp); e.record(); torch.cuda.synchronize(); ts.append(s_.elapsed_time(e))
    print(f"shape{shape_idx} {s}: median GPU-event {statistics.median(ts)*1000:.1f}us  min {min(ts)*1000:.1f}us")
    # torch profiler breakdown
    with torch.profiler.profile(activities=[torch.profiler.ProfilerActivity.CUDA,torch.profiler.ProfilerActivity.CPU]) as p:
        for _ in range(5): sol(*inp)
        torch.cuda.synchronize()
    print("  kernel rows (top cuda):")
    for r in [x for x in p.key_averages() if x.device_time_total>0][:6]:
        print(f"    {r.key[:50]:50s} cuda {r.cuda_time_total/5:7.1f}us  cnt {r.count//5}")

for i in [0,1,4]:
    run(i)
EOF
uv run python prof_trace.py 2>&1 | grep -v Warning | head -50

{
  "command": "<1217 chars \u2014 see below>",
  "description": "Per-kernel GPU time breakdown"
}

cd /workspace/problems/03_paged_attention
cat > prof_trace.py << 'EOF'
import torch, reference, solution, shapes
dev=torch.device("cuda:0")

def run(shape_idx):
    s=shapes.SHAPES[shape_idx]
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    for _ in range(20): sol(*inp)
    torch.cuda.synchronize()
    with torch.profiler.profile(activities=[torch.profiler.ProfilerActivity.CUDA]) as p:
        for _ in range(10): sol(*inp)
        torch.cuda.synchronize()
    print(f"\nshape{shape_idx} {s}")
    evs=[x for x in p.key_averages() if x.self_device_time_total>0]
    evs.sort(key=lambda r:-r.self_device_time_total)
    tot=sum(r.self_device_time_total for r in evs)
    for r in evs[:5]:
        print(f"  {r.key[:48]:48s} dev {r.self_device_time_total/10:7.2f}us  cnt/iter {r.count/10:.0f}")

for i in [0,1,4]:
    run(i)
EOF
uv run python prof_trace.py 2>&1 | grep -vE "Warning|_warn" | head -40

{
  "command": "<1368 chars \u2014 see below>",
  "description": "ncu DRAM bandwidth metrics for shape 0 decode kernel"
}

cd /workspace/problems/03_paged_attention
cat > prof_ncu.py << 'EOF'
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
# Shape 0 cold (do a flush before each call)
 FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
def run(shape_idx, flush=False, tag=""):
    s=shapes.SHAPES[shape_idx]
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    for _ in range(10): sol(*inp)
    torch.cuda.synchronize()
    # profile region
    for _ in range(3):
        if flush: FlushBuf.zero_(); torch.cuda.synchronize()
        sol(*inp)
    torch.cuda.synchronize()
run(0, flush=True, tag="shape0 cold")
EOF
uv run ncu --target-processes all --kernel-name regex:"_decode_kernel" \
  --metrics dram__bytes_read.sum,dram__bytes_write.sum,gpc__cycles_elapsed.avg,sm__warps_active.avg.pct_of_peak_sustained_active,sm__pipe_tensor_op_hmma_cycles_active.avg.pct_of_peak_sustained_active \
  --csv --print-units base --launch-count 2 \
  uv run python prof_ncu.py 2>&1 | grep -vE "Warning|warn|==WARNING|Register|Sanitizer" | tail -20

{
  "command": "<1322 chars \u2014 see below>",
  "description": "ncu DRAM bandwidth metrics for shape 0 decode kernel (fixed)"
}

cd /workspace/problems/03_paged_attention
cat > prof_ncu.py << 'EOF'
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
def run(shape_idx, flush=False):
    s=shapes.SHAPES[shape_idx]
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    for _ in range(10): sol(*inp)
    torch.cuda.synchronize()
    for _ in range(3):
        if flush: FlushBuf.zero_(); torch.cuda.synchronize()
        sol(*inp)
    torch.cuda.synchronize()
run(0, flush=True)
EOF
uv run ncu --target-processes all --kernel-name regex:"_decode_kernel" \
  --metrics dram__bytes_read.sum,dram__bytes_write.sum,gpc__cycles_elapsed.max,sm__warps_active.avg.pct_of_peak_sustained_active,sm__pipe_tensor_op_hmma_cycles_active.avg.pct_of_peak_sustained_active,launch__waves_per_multiprocessor \
  --csv --print-units base --launch-count 2 --launch-skip 10 \
  uv run python prof_ncu.py 2>&1 | grep -vE "Warning|warn|==WARNING|Sanitizer|gpu_id" | tail -15

{
  "command": "<448 chars \u2014 see below>",
  "description": "ncu memory workload + occupancy for shape 0"
}

cd /workspace/problems/03_paged_attention
uv run ncu --target-processes all --kernel-name regex:"_decode_kernel" \
  --section MemoryWorkloadAnalysis --section LaunchStats --section Occupancy \
  --launch-count 1 --launch-skip 12 \
  uv run python prof_ncu.py 2>&1 | grep -vE "Warning|warn|==WARNING|Sanitizer|==PROF|gpu_id|Avtex|Copyright" | grep -iE "dram|mem|bandwidth|occupancy|peak|achieved|theoretical|active|warps|block|reg|share" | head -40

{
  "command": "<3605 chars \u2014 see below>",
  "description": "Sweep decode kernel configs cold bandwidth"
}

cd /workspace/problems/03_paged_attention
cat > sweep.py << 'EOF'
import torch, reference, solution, shapes
import triton
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)

import math
def make_sol(shape, **cfg):
    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"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    return sol

def cold_time(sol, inp, iters=50):
    for _ in range(15): sol(*inp)
    torch.cuda.synchronize()
    import statistics
    ts=[]
    for _ in range(iters):
        FlushBuf.zero_(); torch.cuda.synchronize()
        s=torch.cuda.Event(enable_timing=True); e=torch.cuda.Event(enable_timing=True)
        s.record(); sol(*inp); e.record(); torch.cuda.synchronize()
        ts.append(s.elapsed_time(e))
    return statistics.median(ts)*1000  # us

def bytes_of(s):
    return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2

import importlib
for sidx in [0,1,4]:
    s=shapes.SHAPES[sidx]
    print(f"\n=== shape{sidx} {s} bytes={bytes_of(s)/1e6:.1f}MB ideal(1800)={bytes_of(s)/1.8e6:.1f}us ===")
    sol=make_sol(s)
    importlib.reload(reference); importlib.reload(shapes)
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    for bn, nw, ns in [(16,4,2),(32,4,2),(64,4,2),(128,4,2),(64,8,2),(128,8,2),(64,8,3),(32,8,2),(128,4,3),(64,4,3),(32,4,3),(16,8,2)]:
        # monkeypatch forward to use config
        orig=sol.forward
        def mkfwd(sol, bn,nw,ns):
            def fwd(q,kv,bt,sl):
                B,H,D=q.shape; Hkv=sol.num_kv_heads; G=sol.group_size; P=sol.page_size
                sol._ensure_buffers(q.device, q.dtype)
                grid=(sol.num_splits,B,Hkv)
                solution._decode_kernel[grid](
                    q,kv,bt,sl,sol._o_partial,sol._m_partial,sol._l_partial,
                    q.stride(0),q.stride(1),kv.stride(0),kv.stride(1),kv.stride(2),bt.stride(0),
                    sol._o_partial.stride(0),sol._o_partial.stride(1),sol._o_partial.stride(2),
                    sol._m_partial.stride(0),sol._m_partial.stride(1),sol._m_partial.stride(2),
                    sol.scale,sol.split_size,HEAD_DIM=D,GROUP=G,BLOCK_M=16,BLOCK_N=bn,PAGE_SIZE=P,
                    num_warps=nw,num_stages=ns)
                solution._reduce_kernel[(B,H)](
                    sol._o_partial,sol._m_partial,sol._l_partial,sol._out,
                    sol._o_partial.stride(0),sol._o_partial.stride(1),sol._o_partial.stride(2),
                    sol._m_partial.stride(0),sol._m_partial.stride(1),sol._m_partial.stride(2),
                    sol._out.stride(0),sol._out.stride(1),sol.num_splits,HEAD_DIM=D,num_warps=4)
                return sol._out
            return fwd
        sol.forward=mkfwd(sol,bn,nw,ns)
        try:
            t=cold_time(sol,inp)
            gbps=bytes_of(s)/t/1e3
            print(f"  BN={bn:3d} w={nw} st={ns}: {t:6.1f}us  {gbps:6.0f} GB/s  frac={gbps/1800:.3f}")
        except Exception as e:
            print(f"  BN={bn:3d} w={nw} st={ns}: ERR {type(e).__name__} {str(e)[:60]}")
EOF
uv run python sweep.py 2>&1 | grep -vE "Warning|warn" | head -70

{
  "command": "<1817 chars \u2014 see below>",
  "description": "Test CUDA graph capture/replay correctness and timing"
}

cd /workspace/problems/03_paged_attention
cat > test_graph.py << 'EOF'
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
s=shapes.SHAPES[0]
reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
torch.manual_seed(2026)
inp=[t.to(dev) for t in reference.get_inputs()]
# direct launch
ref_out = sol(*inp).clone()
# capture
for _ in range(3): sol(*inp)
torch.cuda.synchronize()
g=torch.cuda.CUDAGraph()
with torch.cuda.graph(g):
    sol(*inp)
# replay - inputs same address
g.replay(); torch.cuda.synchronize()
graph_out = sol._out.clone()
print("graph vs direct allclose:", torch.allclose(ref_out.float(), graph_out.float(), atol=1e-3, rtol=1e-3))
print("max diff", (ref_out.float()-graph_out.float()).abs().max().item())
# timing
import statistics
FlushBuf=torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
ts=[]
for _ in range(100):
    FlushBuf.zero_(); torch.cuda.synchronize()
    a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
    a.record(); g.replay(); b.record(); torch.cuda.synchronize()
    ts.append(a.elapsed_time(b))
print(f"graph replay median cold: {statistics.median(ts)*1000:.1f}us min {min(ts)*1000:.1f}us")
# compare direct cold
ts2=[]
for _ in range(100):
    FlushBuf.zero_(); torch.cuda.synchronize()
    a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
    a.record(); sol(*inp); b.record(); torch.cuda.synchronize()
    ts2.append(a.elapsed_time(b))
print(f"direct median cold: {statistics.median(ts2)*1000:.1f}us")
EOF
uv run python test_graph.py 2>&1 | grep -vE "Warning|warn" | head

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "content": "<11448 chars \u2014 see diff>"
}

{
  "command": "<79 chars \u2014 see below>",
  "description": "Run correctness checker with graph path"
}

cd /workspace/problems/03_paged_attention
uv run python check.py 2>&1 | tail -5

{
  "command": "<131 chars \u2014 see below>",
  "description": "Benchmark with graphs + BN=16"
}

cd /workspace/problems/03_paged_attention
uv run python benchmark.py 2>&1 | grep -E "variant=solution|peak_fraction:|RESULT" | head

{
  "command": "<130 chars \u2014 see below>",
  "description": "Get peak fractions with graphs"
}

cd /workspace/problems/03_paged_attention
uv run python benchmark.py 2>&1 | grep -E "solution_peak_fraction|peak_fraction:|RESULT"

{
  "status": "completed",
  "taskId": "1"
}

{
  "status": "completed",
  "taskId": "3"
}

{
  "status": "in_progress",
  "taskId": "2"
}

{
  "command": "<2592 chars \u2014 see below>",
  "description": "Comprehensive per-shape config sweep with graphs"
}

cd /workspace/problems/03_paged_attention
cat > sweep2.py << 'EOF'
import torch, reference, solution, shapes, importlib, statistics
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)

def bytes_of(s):
    return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2

def setup(s):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp

def cold_replay(sol, inp, iters=80):
    for _ in range(20): sol(*inp)
    torch.cuda.synchronize()
    ts=[]
    for _ in range(iters):
        FlushBuf.zero_(); torch.cuda.synchronize()
        a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
        a.record(); sol(*inp); b.record(); torch.cuda.synchronize()
        ts.append(a.elapsed_time(b))
    return statistics.median(ts)*1000

for sidx in range(5):
    s=shapes.SHAPES[sidx]
    print(f"\n=== shape{sidx} B={s['batch']} H={s['num_heads']} Hkv={s['num_kv_heads']} D={s['head_dim']} L={s['seq_len']} bytes={bytes_of(s)/1e6:.1f}MB ideal={bytes_of(s)/1.8e6:.1f}us ===")
    sol, inp = setup(s)
    best=None
    cfgs=[]
    D=s['head_dim']
    bns = [16,32,64] if D==64 else [16,32,64,128]
    for tps in [2,4,6,8]:
        for bn in bns:
            for nw in [4,8]:
                for ns_ in [1,2,3]:
                    sol2, inp2 = setup(s)
                    sol2.num_splits, sol2.split_size = solution._choose_splits(
                        s['seq_len'], s['batch'], s['num_kv_heads'], sol2.num_sms, tps, s['page_size'])
                    sol2.block_n=bn; sol2.num_warps=nw; sol2.num_stages=ns_
                    sol2._graph=None; sol2._gkeys=None; sol2._o_partial=None
                    try:
                        t=cold_replay(sol2, inp2)
                        frac=bytes_of(s)/t/1e3/1800
                        cfgs.append((frac,t,bn,nw,ns_,tps,sol2.num_splits))
                    except Exception as e:
                        pass
    cfgs.sort(key=lambda x:-x[0])
    by=bytes_of(s)
    for frac,t,bn,nw,ns_,tps,nsp in cfgs[:6]:
        print(f"  frac={frac:.3f}  {t:6.1f}us  BN={bn:3d} w={nw} st={ns_} tps={tps} nsplits={nsp}")
EOF
timeout 580 uv run python sweep2.py 2>&1 | grep -vE "Warning|warn" | tail -50

{
  "command": "cat /tmp/claude-1002/-workspace-problems-03-paged-attention/d28083b8-ae68-4576-8388-410d228e627e/tasks/bgf6olfl0.output 2>/dev/null | grep -vE \"Warning|warn\" | tail -45",
  "description": "Read config sweep results"
}

{
  "command": "cat /tmp/claude-1002/-workspace-problems-03-paged-attention/d28083b8-ae68-4576-8388-410d228e627e/tasks/bgf6olfl0.output 2>/dev/null | grep -vE \"Warning|warn|_warn\" | tail -45; echo \"---STATUS---\"; ls -la /tmp/claude-1002/-workspace-problems-03-paged-attention/d28083b8-ae68-4576-8388-410d228e627e/tasks/bgf6olfl0.output",
  "description": "Read sweep output file"
}

{
  "task_id": "bgf6olfl0",
  "block": true,
  "timeout": 420000
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<913 chars \u2014 see diff>",
  "new_string": "<1027 chars \u2014 see diff>"
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<280 chars \u2014 see diff>",
  "new_string": "<302 chars \u2014 see diff>"
}

{
  "command": "<193 chars \u2014 see below>",
  "description": "Check correctness and benchmark with tuned configs"
}

cd /workspace/problems/03_paged_attention
uv run python check.py 2>&1 | tail -2 && echo "===BENCH===" && uv run python benchmark.py 2>&1 | grep -E "solution_peak_fraction|peak_fraction:|RESULT"

{
  "command": "<1332 chars \u2014 see below>",
  "description": "ncu memory+occupancy for shapes 0 and 4 decode+reduce"
}

cd /workspace/problems/03_paged_attention
cat > prof_ncu2.py << 'EOF'
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
import sys
sidx=int(sys.argv[1])
s=shapes.SHAPES[sidx]
reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
torch.manual_seed(2026)
inp=[t.to(dev) for t in reference.get_inputs()]
for _ in range(10): sol(*inp)
torch.cuda.synchronize()
for _ in range(3):
    FlushBuf.zero_(); torch.cuda.synchronize(); sol(*inp)
torch.cuda.synchronize()
print(f"shape{sidx} nsplits={sol.num_splits} split_size={sol.split_size} BN={sol.block_n} cfg done", flush=True)
EOF
for SI in 0 4; do
echo "########## SHAPE $SI ##########"
uv run ncu --target-processes all --kernel-name regex:"decode|reduce" \
  --section MemoryWorkloadAnalysis --section Occupancy \
  --launch-count 2 --launch-skip 11 \
  uv run python prof_ncu2.py $SI 2>&1 | grep -iE "decode_kernel|reduce_kernel|Memory Throughput|Mem Busy|Max Bandwidth|Achieved Occupancy|Theoretical Occupancy|Registers Per Thread|Dynamic Shared|Block Limit" | head -30
done

{
  "command": "<2060 chars \u2014 see below>",
  "description": "Test Triton scalar atomic per-program and GPU fence building blocks"
}

cd /workspace/problems/03_paged_attention
cat > test_atomics.py << 'EOF'
import torch, triton, triton.language as tl

@triton.jit
def test_count(counter_ptr, out_ptr, N: tl.constexpr):
    pid = tl.program_id(0)
    # scalar atomic - does it count programs or threads?
    tl.atomic_add(counter_ptr, 1)
    # write pid so all threads do something
    tl.store(out_ptr + pid, pid)

@triton.jit
def test_fence(counter_ptr, done_ptr, val_ptr, out_ptr, N: tl.constexpr, NS: tl.constexpr):
    pid = tl.program_id(0)
    # each program writes a value, fences, then atomic-increments
    tl.store(val_ptr + pid, pid * 100 + 7)
    # fence
    tl.inline_asm_elementwise("fence.acq_rel.gpu;", "=r", [], dtype=tl.int32, is_pure=False, pack=1)
    prev = tl.atomic_add(counter_ptr, 1)
    # last program reads all values
    if prev == N - 1:
        offs = tl.arange(0, N)
        vals = tl.load(val_ptr + offs)
        tl.store(out_ptr + offs, vals)
        tl.store(done_ptr, 1)

dev = torch.device("cuda:0")
N = 256
counter = torch.zeros(1, dtype=torch.int32, device=dev)
out = torch.full((N,), -1, dtype=torch.int32, device=dev)
test_count[(N,)](counter, out, N)
torch.cuda.synchronize()
print(f"atomic count: counter={counter.item()} (expect {N} if per-program, {N*128} if per-thread)")

# fence test: NS programs each write val[fence] then atomic; last reads all
NS = 64
counter2 = torch.zeros(1, dtype=torch.int32, device=dev)
done = torch.zeros(1, dtype=torch.int32, device=dev)
vals = torch.full((NS,), -1, dtype=torch.int32, device=dev)
out2 = torch.zeros((NS,), dtype=torch.int32, device=dev)
# launch NS programs across many SMs to test cross-CTA visibility
test_fence[(NS,)](counter2, done, vals, out2, NS, NS)
torch.cuda.synchronize()
print(f"fence: done={done.item()} counter={counter2.item()} (expect done=1, counter={NS})")
print(f"  out2 == vals? {torch.equal(out2, vals)}  (expect True)")
print(f"  vals sample: {vals[:5].tolist()}")
print(f"  out2 sample: {out2[:5].tolist()}")
EOF
uv run python test_atomics.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "offset": 37,
  "limit": 10
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 45,
  "offset": 118
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<362 chars \u2014 see diff>",
  "new_string": "<4943 chars \u2014 see diff>"
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<334 chars \u2014 see diff>",
  "new_string": "<358 chars \u2014 see diff>"
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 12,
  "offset": 205
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 12,
  "offset": 227
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<553 chars \u2014 see diff>",
  "new_string": "<486 chars \u2014 see diff>"
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 60,
  "offset": 330
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<1772 chars \u2014 see diff>",
  "new_string": "<1669 chars \u2014 see diff>"
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<117 chars \u2014 see diff>",
  "new_string": "<291 chars \u2014 see diff>"
}

{
  "command": "<79 chars \u2014 see below>",
  "description": "Correctness of fused kernel"
}

cd /workspace/problems/03_paged_attention
uv run python check.py 2>&1 | tail -5

{
  "command": "<130 chars \u2014 see below>",
  "description": "Benchmark fused kernel (tps=2)"
}

cd /workspace/problems/03_paged_attention
uv run python benchmark.py 2>&1 | grep -E "solution_peak_fraction|peak_fraction:|RESULT"

{
  "command": "<2090 chars \u2014 see below>",
  "description": "Sweep target_per_sm for fused kernel"
}

cd /workspace/problems/03_paged_attention
cat > sweep3.py << 'EOF'
import torch, reference, solution, shapes, statistics
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn=None, nw=None, ns_=None):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    if bn: sol.block_n=bn
    if nw: sol.num_warps=nw
    if ns_: sol.num_stages=ns_
    bs=1
    while bs < sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
def cold(sol, inp, iters=80):
    for _ in range(20): sol(*inp)
    torch.cuda.synchronize()
    ts=[]
    for _ in range(iters):
        FlushBuf.zero_(); torch.cuda.synchronize()
        a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
        a.record(); sol(*inp); b.record(); torch.cuda.synchronize()
        ts.append(a.elapsed_time(b))
    return statistics.median(ts)*1000
for sidx in range(5):
    s=shapes.SHAPES[sidx]
    by=bytes_of(s)
    print(f"\n=== shape{sidx} D={s['head_dim']} B*Hkv={s['batch']*s['num_kv_heads']} L={s['seq_len']} ideal={by/1.8e6:.1f}us ===")
    res=[]
    for tps in [1,2,3,4,6,8,12]:
        try:
            sol,inp=setup(s,tps); t=cold(sol,inp); res.append((by/t/1e3/1800, t, tps, sol.num_splits))
        except Exception as e: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,ns in res[:5]:
        print(f"  frac={f:.3f} {t:6.1f}us  tps={tps} nsplits={ns}")
EOF
timeout 400 uv run python sweep3.py 2>&1 | grep -vE "Warning|warn" | tail -45

{
  "command": "<1733 chars \u2014 see below>",
  "description": "ncu decode bandwidth vs splits for shape 0"
}

cd /workspace/problems/03_paged_attention
cat > prof_splits.py << 'EOF'
import torch, reference, solution, shapes, sys
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
sidx=int(sys.argv[1]); tps=int(sys.argv[2])
s=shapes.SHAPES[sidx]
reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
bs=1
while bs<sol.num_splits: bs<<=1
sol.block_s=bs
torch.manual_seed(2026)
inp=[t.to(dev) for t in reference.get_inputs()]
for _ in range(10): sol(*inp)
torch.cuda.synchronize()
for _ in range(3):
    FlushBuf.zero_(); torch.cuda.synchronize(); sol(*inp)
torch.cuda.synchronize()
EOF
echo "=== shape0 tps=1 (nsplits=3) ==="
uv run ncu --target-processes all --kernel-name regex:"decode_reduce" \
  --section MemoryWorkloadAnalysis --section Occupancy \
  --launch-count 1 --launch-skip 11 \
  uv run python prof_splits.py 0 1 2>&1 | grep -iE "Memory Throughput|Mem Busy|Max Bandwidth|Achieved Occupancy|Theoretical Occupancy|Dynamic Shared|Registers Per" | head
echo "=== shape0 tps=8 (nsplits=16) ==="
uv run ncu --target-processes all --kernel-name regex:"decode_reduce" \
  --section MemoryWorkloadAnalysis --section Occupancy \
  --launch-count 1 --launch-skip 11 \
  uv run python prof_splits.py 0 8 2>&1 | grep -iE "Memory Throughput|Mem Busy|Max Bandwidth|Achieved Occupancy|Theoretical Occupancy|Dynamic Shared|Registers Per" | head

{
  "command": "<2150 chars \u2014 see below>",
  "description": "Focused sweep warps/stages/BN for weak shapes"
}

cd /workspace/problems/03_paged_attention
cat > sweep4.py << 'EOF'
import torch, reference, solution, shapes, statistics
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
def cold(sol, inp, iters=80):
    for _ in range(20): sol(*inp)
    torch.cuda.synchronize()
    ts=[]
    for _ in range(iters):
        FlushBuf.zero_(); torch.cuda.synchronize()
        a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
        a.record(); sol(*inp); b.record(); torch.cuda.synchronize()
        ts.append(a.elapsed_time(b))
    return statistics.median(ts)*1000
for sidx in [0,4,2]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s); D=s['head_dim']
    print(f"\n=== shape{sidx} D={D} ===")
    res=[]
    bns=[16,32,64,128] if D==128 else [16,32,64,128]
    for tps in [1,2,3]:
      for bn in bns:
        for nw in ([4,8] if D==128 else [4,8]):
          for ns_ in [2,3]:
            try:
              sol,inp=setup(s,tps,bn,nw,ns_); t=cold(sol,inp)
              res.append((by/t/1e3/1800,t,tps,bn,nw,ns_))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_ in res[:6]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_}")
EOF
timeout 560 uv run python sweep4.py 2>&1 | grep -vE "Warning|warn" | tail -25

{
  "command": "<2337 chars \u2014 see below>",
  "description": "Final tight fused sweep, all 5 shapes, geomean"
}

cd /workspace/problems/03_paged_attention
cat > sweep5.py << 'EOF'
import torch, reference, solution, shapes, statistics
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
def cold(sol, inp, iters=100):
    for _ in range(25): sol(*inp)
    torch.cuda.synchronize()
    ts=[]
    for _ in range(iters):
        FlushBuf.zero_(); torch.cuda.synchronize()
        a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
        a.record(); sol(*inp); b.record(); torch.cuda.synchronize()
        ts.append(a.elapsed_time(b))
    return statistics.median(ts)*1000
import math
allf=[]
for sidx in range(5):
    s=shapes.SHAPES[sidx]; by=bytes_of(s); D=s['head_dim']
    res=[]
    cfgset = [(tps,bn,nw,ns_) for tps in [1,2] for bn in ([64,128] if D==64 else [32,64]) for nw in [4,8] for ns_ in [2,3]]
    for tps,bn,nw,ns_ in cfgset:
        try:
            sol,inp=setup(s,tps,bn,nw,ns_); t=cold(sol,inp)
            res.append((by/t/1e3/1800,t,tps,bn,nw,ns_))
        except Exception: pass
    res.sort(key=lambda x:-x[0])
    f=res[0][0]; allf.append(f)
    print(f"shape{sidx} D={D} B*Hkv={s['batch']*s['num_kv_heads']} L={s['seq_len']}: best frac={f:.3f}")
    for ff,t,tps,bn,nw,ns_ in res[:3]:
        print(f"    {ff:.3f} {t:6.1f}us tps={tps} BN={bn} w={nw} st={ns_}")
gm=math.exp(sum(math.log(x) for x in allf)/len(allf))
print(f"\nGEOMEAN of per-shape bests: {gm:.4f}")
EOF
timeout 580 uv run python sweep5.py 2>&1 | grep -vE "Warning|warn" | tail -25

{
  "command": "<988 chars \u2014 see below>",
  "description": "Measure with official time_fn, 200 iters"
}

cd /workspace/problems/03_paged_attention
cat > meas_official.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
for sidx in range(5):
    s=shapes.SHAPES[sidx]
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    ms=time_fn(sol, inp, iters=200, warmup=20)
    by=2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
    print(f"shape{sidx}: official time_fn {ms*1000:.2f}us  gbps={by/(ms*1e-3)/1e9:.0f}  frac={by/(ms*1e-3)/1e9/1800:.4f}")
EOF
uv run python meas_official.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "command": "<1578 chars \u2014 see below>",
  "description": "Measure kernel-only GPU time for weak shapes"
}

cd /workspace/problems/03_paged_attention
cat > meas_kern.py << 'EOF'
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
FlushBuf = torch.empty(128*1024*1024//4, dtype=torch.float32, device=dev)
for sidx in [0,4,2]:
    s=shapes.SHAPES[sidx]
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    for _ in range(20): sol(*inp)
    torch.cuda.synchronize()
    # GPU kernel time (excludes graph replay dispatch gap)
    with torch.profiler.profile(activities=[torch.profiler.ProfilerActivity.CUDA]) as p:
        for _ in range(100):
            FlushBuf.zero_(); torch.cuda.synchronize(); sol(*inp)
        torch.cuda.synchronize()
    evs=[x for x in p.key_averages() if x.self_device_time_total>0 and 'elementwise' not in x.key.lower() and 'zero' not in x.key.lower()]
    tot=sum(r.self_device_time_total for r in evs)/100
    by=2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
    print(f"shape{sidx}: kernel GPU={tot:.1f}us -> {by/tot/1e3:.0f}GB/s frac={by/tot/1e3/1800:.3f}  (kernels: {[(r.key.split('_')[1], round(r.self_device_time_total/100,1)) for r in sorted(evs,key=lambda x:-x.self_device_time_total)[:2]]})")
EOF
uv run python meas_kern.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "command": "<490 chars \u2014 see below>",
  "description": "ncu profile shape 4 decode kernel"
}

cd /workspace/problems/03_paged_attention
echo "=== shape4 fused decode_reduce (D=64, BN=128) ==="
uv run ncu --target-processes all --kernel-name regex:"decode_reduce" \
  --section MemoryWorkloadAnalysis --section Occupancy --section WarpStateStats \
  --launch-count 1 --launch-skip 11 \
  uv run python prof_splits.py 4 1 2>&1 | grep -iE "Memory Throughput|Mem Busy|Max Bandwidth|Achieved Occupancy|Theoretical Occup|Dynamic Shared|Registers Per|Warp Cycles Per Issued|Stall" | head -15

{
  "command": "<1755 chars \u2014 see below>",
  "description": "Official time_fn sweep for weak shapes 4,0,2"
}

cd /workspace/problems/03_paged_attention
cat > sweep6.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx in [4,0,2]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s); D=s['head_dim']
    print(f"\n=== shape{sidx} D={D} ===")
    res=[]
    bns=[16,32,64,128]
    for tps in [1,2,3,4]:
      for bn in bns:
        for nw in [4,8]:
          for ns_ in [1,2,3]:
            try:
              sol,inp=setup(s,tps,bn,nw,ns_)
              ms=time_fn(sol, inp, iters=60, warmup=15)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_ in res[:5]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_}")
EOF
timeout 590 uv run python sweep6.py 2>&1 | grep -vE "Warning|warn" | tail -25

{
  "command": "<1789 chars \u2014 see below>",
  "description": "Official sweep shapes 1 and 3"
}

cd /workspace/problems/03_paged_attention
cat > sweep7.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx in [1,3]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s); D=s['head_dim']
    print(f"\n=== shape{sidx} D={D} B*Hkv={s['batch']*s['num_kv_heads']} L={s['seq_len']} ===")
    res=[]
    for tps in [1,2]:
      for bn in [16,32,64,128]:
        for nw in [4,8]:
          for ns_ in [2,3]:
            try:
              sol,inp=setup(s,tps,bn,nw,ns_)
              ms=time_fn(sol, inp, iters=60, warmup=15)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_ in res[:4]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_}")
EOF
timeout 500 uv run python sweep7.py 2>&1 | grep -vE "Warning|warn" | tail -12

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<597 chars \u2014 see diff>",
  "new_string": "<966 chars \u2014 see diff>"
}

{
  "command": "<191 chars \u2014 see below>",
  "description": "Check + benchmark per-shape configs"
}

cd /workspace/problems/03_paged_attention
uv run python check.py 2>&1 | tail -1
uv run python benchmark.py 2>&1 | grep -E "solution_peak_fraction|peak_fraction:|RESULT" | tr '\n' ' '; echo ""

{
  "command": "<1748 chars \u2014 see below>",
  "description": "Sweep warps and deeper stages for shapes 0,4,2"
}

cd /workspace/problems/03_paged_attention
cat > sweep8.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx, bns in [(0,[32,64]), (4,[64,128]), (2,[32,64])]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"\n=== shape{sidx} ===")
    res=[]
    for tps in [1,2]:
      for bn in bns:
        for nw in [4,8,16]:
          for ns_ in [2,3,4,5]:
            try:
              sol,inp=setup(s,tps,bn,nw,ns_)
              ms=time_fn(sol, inp, iters=50, warmup=12)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_ in res[:5]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_}")
EOF
timeout 590 uv run python sweep8.py 2>&1 | grep -vE "Warning|warn" | tail -22

{
  "command": "<1613 chars \u2014 see below>",
  "description": "Test BN=32 st=5 on shapes 1 and 3"
}

cd /workspace/problems/03_paged_attention
cat > sweep9.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx in [1,3]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"=== shape{sidx} ===")
    for tps,bn,nw,ns_ in [(1,64,4,3),(1,32,4,5),(1,32,4,3),(1,32,8,5),(1,64,4,2),(1,32,4,4)]:
        try:
            sol,inp=setup(s,tps,bn,nw,ns_)
            ms=time_fn(sol, inp, iters=50, warmup=12)
            print(f"  tps={tps} BN={bn:3d} w={nw} st={ns_}: {ms*1000:.1f}us frac={by/(ms*1e-3)/1e9/1800:.3f}")
        except Exception as e: print(f"  tps={tps} BN={bn} w={nw} st={ns_}: ERR {type(e).__name__}")
EOF
timeout 300 uv run python sweep9.py 2>&1 | grep -vE "Warning|warn" | tail -15

{
  "command": "<2077 chars \u2014 see below>",
  "description": "Measure graph replay vs forward overhead vs kernel time"
}

cd /workspace/problems/03_paged_attention
cat > meas_overhead.py << 'EOF'
import torch, reference, solution, shapes, statistics, time
dev=torch.device("cuda:0")
s=shapes.SHAPES[4]
reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
for _ in range(20): sol(*inp)
torch.cuda.synchronize()
g = sol._graph
# 1. bare replay GPU-event time
ts=[]
for _ in range(200):
    a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
    a.record(); g.replay(); b.record(); torch.cuda.synchronize()
    ts.append(a.elapsed_time(b))
print(f"bare g.replay() GPU-event: {statistics.median(ts)*1000:.2f}us")
# 2. forward() GPU-event time
ts2=[]
for _ in range(200):
    a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
    a.record(); sol(*inp); b.record(); torch.cuda.synchronize()
    ts2.append(a.elapsed_time(b))
print(f"forward() GPU-event:       {statistics.median(ts2)*1000:.2f}us")
# 3. CPU-only timing of forward (no sync, just dispatch)
torch.cuda.synchronize(); t0=time.perf_counter()
for _ in range(1000): sol(*inp)
torch.cuda.synchronize(); t1=time.perf_counter()
print(f"forward() CPU dispatch:    {(t1-t0)/1000*1e6:.2f}us/call")
# 4. CPU-only of bare replay
torch.cuda.synchronize(); t0=time.perf_counter()
for _ in range(1000): g.replay()
torch.cuda.synchronize(); t1=time.perf_counter()
print(f"bare replay CPU dispatch:  {(t1-t0)/1000*1e6:.2f}us/call")
# kernel GPU time
with torch.profiler.profile(activities=[torch.profiler.ProfilerActivity.CUDA]) as p:
    for _ in range(100): sol(*inp)
    torch.cuda.synchronize()
ev=[x for x in p.key_averages() if 'decode' in x.key.lower()][0]
print(f"decode kernel GPU time:    {ev.self_device_time_total/100:.2f}us")
EOF
uv run python meas_overhead.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 35,
  "offset": 370
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<986 chars \u2014 see diff>",
  "new_string": "<1428 chars \u2014 see diff>"
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 15,
  "offset": 307
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 22,
  "offset": 321
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<81 chars \u2014 see diff>",
  "new_string": "<81 chars \u2014 see diff>"
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<115 chars \u2014 see diff>",
  "new_string": "<361 chars \u2014 see diff>"
}

{
  "command": "<206 chars \u2014 see below>",
  "description": "Check + benchmark streamlined forward + st=5"
}

cd /workspace/problems/03_paged_attention
uv run python check.py 2>&1 | tail -1
for i in 1 2; do
uv run python benchmark.py 2>&1 | grep -E "solution_peak_fraction|peak_fraction:" | tr '\n' ' '; echo ""
done

{
  "command": "<1796 chars \u2014 see below>",
  "description": "Deep sweep shapes 4 and 0 with streamlined forward"
}

cd /workspace/problems/03_paged_attention
cat > sweep10.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx, bns in [(4,[16,32,64,128]),(0,[16,32,64])]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"\n=== shape{sidx} D={s['head_dim']} ===")
    res=[]
    for tps in [1,2,3,4,6]:
      for bn in bns:
        for nw in [4,8]:
          for ns_ in [2,3,4,5]:
            try:
              sol,inp=setup(s,tps,bn,nw,ns_)
              ms=time_fn(sol, inp, iters=40, warmup=10)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_,sol.num_splits))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_,nsp in res[:6]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_} nspl={nsp}")
EOF
timeout 595 uv run python sweep10.py 2>&1 | grep -vE "Warning|warn" | tail -18

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<47 chars \u2014 see diff>",
  "new_string": "<47 chars \u2014 see diff>"
}

{
  "command": "<1625 chars \u2014 see below>",
  "description": "Test st=6 for shape 0 and st variants for shape 4"
}

cd /workspace/problems/03_paged_attention
cat > test_st.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def setup(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx,cfgs in [(0,[(32,8,5),(32,8,6),(32,4,6),(32,8,4)]),(4,[(128,4,4),(128,4,5),(64,4,5),(128,8,4)])]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"=== shape{sidx} ===")
    for bn,nw,ns_ in cfgs:
        try:
            sol,inp=setup(s,1,bn,nw,ns_)
            ms=time_fn(sol, inp, iters=60, warmup=15)
            print(f"  BN={bn} w={nw} st={ns_}: {ms*1000:.1f}us frac={by/(ms*1e-3)/1e9/1800:.3f}")
        except Exception as e: print(f"  BN={bn} w={nw} st={ns_}: ERR {type(e).__name__} {str(e)[:50]}")
EOF
timeout 200 uv run python test_st.py 2>&1 | grep -vE "Warning|warn" | tail -12

{
  "status": "completed",
  "taskId": "2"
}

{
  "status": "in_progress",
  "taskId": "4"
}

{
  "command": "<1486 chars \u2014 see below>",
  "description": "Test Triton reshape/split for combined KV load"
}

cd /workspace/problems/03_paged_attention
cat > test_split.py << 'EOF'
import torch, triton, triton.language as tl
@triton.jit
def k1(out_ptr, in_ptr, BN: tl.constexpr, D: tl.constexpr):
    # combined load then split via reshape
    offs_n = tl.arange(0, BN)
    offs_d = tl.arange(0, 2*D)
    kv = tl.load(in_ptr + offs_n[:,None]*2*D + offs_d[None,:])  # (BN, 2D)
    kv2 = tl.reshape(kv, (BN, 2, D))
    k = kv2[:, 0, :]   # static index
    v = kv2[:, 1, :]
    tl.store(out_ptr + offs_n[:,None]*2*D + offs_d[None,:], k*0+1 + v*0+2*1)  # dummy
dev=torch.device("cuda:0")
inp = torch.randn(64, 256, device=dev, dtype=torch.bfloat16)
out = torch.zeros(64, 256, device=dev, dtype=torch.bfloat16)
k1[(1,)](out, inp, 64, 128)
torch.cuda.synchronize()
print("reshape+static-index works:", out[0,:5].tolist())

@triton.jit
def k2(out_ptr, in_ptr, BN: tl.constexpr, D: tl.constexpr):
    offs_n = tl.arange(0, BN)
    offs_d = tl.arange(0, 2*D)
    kv = tl.load(in_ptr + offs_n[:,None]*2*D + offs_d[None,:])
    k, v = tl.split(kv)  # split last dim in half
    tl.store(out_ptr + offs_n[:,None]*D + tl.arange(0,D)[None,:], k+v*0)
dev=torch.device("cuda:0")
out2 = torch.zeros(64, 256, device=dev, dtype=torch.bfloat16)
try:
    k2[(1,)](out2, inp, 64, 128)
    torch.cuda.synchronize()
    print("tl.split works:", out2[0,:5].tolist())
except Exception as e:
    print("tl.split failed:", type(e).__name__, str(e)[:80])
EOF
uv run python test_split.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "command": "<1016 chars \u2014 see below>",
  "description": "Check tl.split API and test it"
}

cd /workspace/problems/03_paged_attention
uv run python -c "
import triton.language as tl
import inspect
print('split sig:', inspect.signature(tl.split) if hasattr(tl,'split') else 'NO split')
print('split doc:', (tl.split.__doc__ or '')[:300] if hasattr(tl,'split') else '')
" 2>&1 | grep -vE "Warning|warn" | tail
# test tl.split
cat >> test_split.py << 'EOF'

# retry k2 separately
EOF
uv run python -c "
import torch, triton, triton.language as tl
@triton.jit
def k2(out_ptr, in_ptr, BN: tl.constexpr, D: tl.constexpr):
    offs_n = tl.arange(0, BN)
    offs_d = tl.arange(0, 2*D)
    kv = tl.load(in_ptr + offs_n[:,None]*2*D + offs_d[None,:])
    k, v = tl.split(kv)
    tl.store(out_ptr + offs_n[:,None]*D + tl.arange(0,D)[None,:], k+v*0)
dev=torch.device('cuda:0')
inp=torch.randn(64,256,device=dev,dtype=torch.bfloat16)
out=torch.zeros(64,128,device=dev,dtype=torch.bfloat16)
k2[(1,)](out,inp,64,128); torch.cuda.synchronize()
print('tl.split OK:', out[0,:3].tolist())
" 2>&1 | grep -vE "Warning|warn" | tail

{
  "command": "<566 chars \u2014 see below>",
  "description": "Check global load efficiency for shape 0"
}

cd /workspace/problems/03_paged_attention
echo "=== shape0 load efficiency ==="
uv run ncu --target-processes all --kernel-name regex:"decode_reduce" \
  --metrics l1tex__t_sectors_pipe_lsu_mem_global_op_ld.sum,l1tex__sector_hit_rate.pct,l1tex__average_t_sectors_per_request_pipe_lsu_mem_global_op_ld.ratio,smsp__inst_executed_pipe_lsu_op_ld.sum,sm__inst_executed_pipe_lsu_op_ld.avg.pct_of_peak_sustained_active,dram__bytes_read.sum \
  --launch-count 1 --launch-skip 11 \
  uv run python prof_splits.py 0 1 2>&1 | grep -iE "sector|lsu|dram|inst_executed" | head -12

{
  "command": "<313 chars \u2014 see below>",
  "description": "Check which kernels are referenced"
}

cd /workspace/problems/03_paged_attention
# Verify _decode_kernel and _reduce_kernel are still defined & usable for a fair 2-kernel test
grep -n "^def _decode_kernel\|^def _reduce_kernel\|^@triton.jit" solution.py | head
echo "---"
grep -n "_decode_kernel\[\|_reduce_kernel\[\|_decode_reduce_kernel\[" solution.py

{
  "command": "<3473 chars \u2014 see below>",
  "description": "Compare 2-kernel vs fused for shapes 2,0,3"
}

cd /workspace/problems/03_paged_attention
cat > cmp_2k.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2

def make(s, tps, fused):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=bs
    sol._fused = fused
    sol._graph=None; sol._replay=None; sol._q_obj=None
    torch.manual_seed(2026)
    inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp

# monkeypatch a 2-kernel launch into the model
def launch2(self, query, kv_cache, block_table, seq_lens):
    B,H,D=query.shape; Hkv=self.num_kv_heads; G=self.group_size; P=self.page_size
    self._ensure_buffers(query.device, query.dtype)
    solution._decode_kernel[(self.num_splits,B,Hkv)](
        query,kv_cache,block_table,seq_lens,self._o_partial,self._m_partial,self._l_partial,
        query.stride(0),query.stride(1),kv_cache.stride(0),kv_cache.stride(1),kv_cache.stride(2),block_table.stride(0),
        self._o_partial.stride(0),self._o_partial.stride(1),self._o_partial.stride(2),
        self._m_partial.stride(0),self._m_partial.stride(1),self._m_partial.stride(2),
        self.scale,self.split_size,HEAD_DIM=D,GROUP=G,BLOCK_M=16,BLOCK_N=self.block_n,PAGE_SIZE=P,
        num_warps=self.num_warps,num_stages=self.num_stages)
    solution._reduce_kernel[(B,H)](
        self._o_partial,self._m_partial,self._l_partial,self._out,
        self._o_partial.stride(0),self._o_partial.stride(1),self._o_partial.stride(2),
        self._m_partial.stride(0),self._m_partial.stride(1),self._m_partial.stride(2),
        self._out.stride(0),self._out.stride(1),self.num_splits,HEAD_DIM=D,num_warps=4)
solution.Model.launch2 = launch2
orig_build = solution.Model._build_graph
def build2(self, q,kv,bt,sl):
    if getattr(self,'_fused',True):
        return orig_build(self,q,kv,bt,sl)
    self._ensure_buffers(q.device,q.dtype)
    try:
        for _ in range(2): self.launch2(q,kv,bt,sl)
        torch.cuda.synchronize()
        g=torch.cuda.CUDAGraph()
        with torch.cuda.graph(g): self.launch2(q,kv,bt,sl)
        self._replay=g.replay; self._q_obj=q
    except Exception: self._replay=None; self._q_obj=None; self.launch2(q,kv,bt,sl)
solution.Model._build_graph = build2

for sidx in [2,0,3]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"=== shape{sidx} ===")
    for fused,tps,bn,nw,ns_ in [(True,1,32,4,5),(False,2,32,8,3),(False,3,32,4,3),(False,1,64,4,3)]:
        try:
            sol,inp=make(s,tps,fused)
            sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
            ms=time_fn(sol, inp, iters=50, warmup=12)
            print(f"  fused={fused} tps={tps} BN={bn} w={nw} st={ns_}: {ms*1000:.1f}us frac={by/(ms*1e-3)/1e9/1800:.3f}")
        except Exception as e: print(f"  ERR {type(e).__name__} {str(e)[:60]}")
EOF
timeout 300 uv run python cmp_2k.py 2>&1 | grep -vE "Warning|warn" | tail -16

{
  "command": "<845 chars \u2014 see below>",
  "description": "Test 2-kernel vs fused for shapes 1 and 4"
}

cd /workspace/problems/03_paged_attention
cat >> cmp_2k.py << 'EOF'

print("\n=== shape1 and shape4 2-kernel vs fused ===")
for sidx in [1,4]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"--- shape{sidx} ---")
    cfgs = [(True,1,32,4,5),(False,1,64,4,3),(False,2,32,8,3),(False,2,64,4,3)] if sidx==1 else [(True,1,128,4,4),(False,2,64,4,3),(False,1,128,4,3)]
    for fused,tps,bn,nw,ns_ in cfgs:
        try:
            sol,inp=make(s,tps,fused)
            sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
            ms=time_fn(sol, inp, iters=40, warmup=10)
            print(f"  fused={fused} tps={tps} BN={bn} w={nw} st={ns_}: {ms*1000:.1f}us frac={by/(ms*1e-3)/1e9/1800:.3f}")
        except Exception as e: print(f"  ERR {type(e).__name__}")
EOF
timeout 200 uv run python cmp_2k.py 2>&1 | grep -vE "Warning|warn" | tail -10

{
  "command": "<3273 chars \u2014 see below>",
  "description": "2-kernel config sweep all shapes"
}

cd /workspace/problems/03_paged_attention
cat > sweep_2k.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def launch2(self, query, kv_cache, block_table, seq_lens):
    B,H,D=query.shape; Hkv=self.num_kv_heads; G=self.group_size; P=self.page_size
    self._ensure_buffers(query.device, query.dtype)
    solution._decode_kernel[(self.num_splits,B,Hkv)](
        query,kv_cache,block_table,seq_lens,self._o_partial,self._m_partial,self._l_partial,
        query.stride(0),query.stride(1),kv_cache.stride(0),kv_cache.stride(1),kv_cache.stride(2),block_table.stride(0),
        self._o_partial.stride(0),self._o_partial.stride(1),self._o_partial.stride(2),
        self._m_partial.stride(0),self._m_partial.stride(1),self._m_partial.stride(2),
        self.scale,self.split_size,HEAD_DIM=D,GROUP=G,BLOCK_M=16,BLOCK_N=self.block_n,PAGE_SIZE=P,
        num_warps=self.num_warps,num_stages=self.num_stages)
    solution._reduce_kernel[(B,H)](
        self._o_partial,self._m_partial,self._l_partial,self._out,
        self._o_partial.stride(0),self._o_partial.stride(1),self._o_partial.stride(2),
        self._m_partial.stride(0),self._m_partial.stride(1),self._m_partial.stride(2),
        self._out.stride(0),self._out.stride(1),self.num_splits,HEAD_DIM=D,num_warps=4)
solution.Model.launch2 = launch2
def make(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    sol._replay=None; sol._q_obj=None
    # repoint _launch to launch2
    sol._launch = lambda q,kv,bt,sl: launch2(sol,q,kv,bt,sl)
    torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx,bns in [(0,[32,64]),(4,[64,128]),(2,[32,64]),(3,[32,64]),(1,[32,64])]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    res=[]
    for tps in [1,2]:
      for bn in bns:
        for nw in [4,8]:
          for ns_ in [2,3,4,5,6]:
            try:
              sol,inp=make(s,tps,bn,nw,ns_)
              # build graph
              for _ in range(2): sol._launch(*inp)
              torch.cuda.synchronize()
              g=torch.cuda.CUDAGraph()
              with torch.cuda.graph(g): sol._launch(*inp)
              sol._replay=g.replay; sol._q_obj=inp[0]
              ms=time_fn(sol, inp, iters=40, warmup=10)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    print(f"shape{sidx}: best {res[0][0]:.3f}  cfg tps={res[0][2]} BN={res[0][3]} w={res[0][4]} st={res[0][5]}  (2nd {res[1][0]:.3f})")
EOF
timeout 595 uv run python sweep_2k.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 8,
  "offset": 154
}

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 8,
  "offset": 258
}

{
  "command": "<937 chars \u2014 see below>",
  "description": "Remove unused _decode_reduce_kernel"
}

cd /workspace/problems/03_paged_attention
python3 << 'EOF'
lines = open("solution.py").readlines()
# Lines 156-262 (1-indexed) are: blank(156? let's recompute). 
# Find the @triton.jit line preceding _decode_reduce_kernel and the end.
start = None
for i,l in enumerate(lines):
    if l.startswith("def _decode_reduce_kernel("):
        start = i-1  # the @triton.jit line
        break
# end: the line "tl.store(Counter_ptr + b * stride_cb + h, 0)"
end = None
for i,l in enumerate(lines):
    if "Counter_ptr + b * stride_cb + h, 0" in l:
        end = i
        break
print("removing lines (0-idx)", start, "to", end, "inclusive")
print("first removed:", repr(lines[start]))
print("last removed:", repr(lines[end]))
print("line after:", repr(lines[end+1]))
# Remove [start, end], and collapse surrounding blanks
new = lines[:start] + ["\n"] + lines[end+1:]
open("solution.py","w").writelines(new)
print("done; new length", len(new))
EOF

{
  "command": "<176 chars \u2014 see below>",
  "description": "Verify import and correctness after 2-kernel switch"
}

cd /workspace/problems/03_paged_attention
uv run python -c "import solution; print('imports OK')" 2>&1 | grep -vE "Warning|warn" | tail -3
uv run python check.py 2>&1 | tail -2

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 35,
  "offset": 123
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<1093 chars \u2014 see diff>",
  "new_string": "<1454 chars \u2014 see diff>"
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<149 chars \u2014 see diff>",
  "new_string": "<332 chars \u2014 see diff>"
}

{
  "replace_all": false,
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "old_string": "<129 chars \u2014 see diff>",
  "new_string": "<151 chars \u2014 see diff>"
}

{
  "command": "<227 chars \u2014 see below>",
  "description": "Check + benchmark vectorized reduce"
}

cd /workspace/problems/03_paged_attention
uv run python check.py 2>&1 | tail -2
echo "===BENCH==="
for i in 1 2 3; do
uv run python benchmark.py 2>&1 | grep -E "solution_peak_fraction|peak_fraction:" | tr '\n' ' '; echo ""
done

{
  "command": "<2075 chars \u2014 see below>",
  "description": "Focused decode sweep for shapes 4 and 0"
}

cd /workspace/problems/03_paged_attention
cat > sweep11.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def make(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=min(bs,16)
    sol._replay=None; sol._q_obj=None
    torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx, bns in [(4,[32,64,128]),(0,[16,32,64])]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"\n=== shape{sidx} D={s['head_dim']} ===")
    res=[]
    for tps in [1,2,3,4]:
      for bn in bns:
        for nw in [4,8]:
          for ns_ in [2,3,4,5,6]:
            try:
              sol,inp=make(s,tps,bn,nw,ns_)
              for _ in range(2): sol._launch(*inp)
              torch.cuda.synchronize()
              g=torch.cuda.CUDAGraph()
              with torch.cuda.graph(g): sol._launch(*inp)
              sol._replay=g.replay; sol._q_obj=inp[0]
              ms=time_fn(sol, inp, iters=50, warmup=12)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_,sol.num_splits))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_,nsp in res[:5]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_} nspl={nsp}")
EOF
timeout 595 uv run python sweep11.py 2>&1 | grep -vE "Warning|warn" | tail -16

{
  "command": "<1001 chars \u2014 see below>",
  "description": "Debug the sweep failure"
}

cd /workspace/problems/03_paged_attention
cat > test_one.py << 'EOF'
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
s=shapes.SHAPES[4]
reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, 1, s['page_size'])
sol.block_n=128; sol.num_warps=4; sol.num_stages=4
bs=1
while bs<sol.num_splits: bs<<=1
sol.block_s=min(bs,16)
sol._replay=None; sol._q_obj=None
torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
sol._launch(*inp)
print("launch OK")
torch.cuda.synchronize()
g=torch.cuda.CUDAGraph()
with torch.cuda.graph(g): sol._launch(*inp)
print("capture OK")
EOF
uv run python test_one.py 2>&1 | grep -vE "Warning|warn" | tail -15

{
  "command": "<2125 chars \u2014 see below>",
  "description": "Fixed decode sweep for shapes 4 and 0"
}

cd /workspace/problems/03_paged_attention
cat > sweep11.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def make(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=min(bs,16)
    sol._replay=None; sol._q_obj=None
    sol._ensure_buffers(dev, torch.bfloat16)
    torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx, bns in [(4,[32,64,128]),(0,[16,32,64])]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"\n=== shape{sidx} D={s['head_dim']} ===")
    res=[]
    for tps in [1,2,3,4]:
      for bn in bns:
        for nw in [4,8]:
          for ns_ in [2,3,4,5,6]:
            try:
              sol,inp=make(s,tps,bn,nw,ns_)
              for _ in range(2): sol._launch(*inp)
              torch.cuda.synchronize()
              g=torch.cuda.CUDAGraph()
              with torch.cuda.graph(g): sol._launch(*inp)
              sol._replay=g.replay; sol._q_obj=inp[0]
              ms=time_fn(sol, inp, iters=50, warmup=12)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_,sol.num_splits))
            except Exception as e: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_,nsp in res[:5]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_} nspl={nsp}")
EOF
timeout 595 uv run python sweep11.py 2>&1 | grep -vE "Warning|warn" | tail -16

{
  "command": "<2169 chars \u2014 see below>",
  "description": "Focused sweep shape4 and shape0"
}

cd /workspace/problems/03_paged_attention
cat > sweep12.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def make(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=min(bs,64)
    sol._replay=None; sol._q_obj=None
    sol._ensure_buffers(dev, torch.bfloat16)
    torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx in [4,0]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"\n=== shape{sidx} D={s['head_dim']} ===")
    res=[]
    for tps in ([2,3,4,6,8] if sidx==4 else [1,2,3]):
      for bn in ([16,32,64] if sidx==4 else [16,32]):
        for nw in [4,8]:
          for ns_ in ([4,5,6] if sidx==4 else [5,6]):
            try:
              sol,inp=make(s,tps,bn,nw,ns_)
              for _ in range(2): sol._launch(*inp)
              torch.cuda.synchronize()
              g=torch.cuda.CUDAGraph()
              with torch.cuda.graph(g): sol._launch(*inp)
              sol._replay=g.replay; sol._q_obj=inp[0]
              ms=time_fn(sol, inp, iters=50, warmup=12)
              f=by/(ms*1e-3)/1e9/1800
              res.append((f,ms*1000,tps,bn,nw,ns_,sol.num_splits))
            except Exception: pass
    res.sort(key=lambda x:-x[0])
    for f,t,tps,bn,nw,ns_,nsp in res[:6]:
        print(f"  frac={f:.3f} {t:6.1f}us tps={tps} BN={bn:3d} w={nw} st={ns_} nspl={nsp}")
EOF
timeout 595 uv run python sweep12.py 2>&1 | grep -vE "Warning|warn" | tail -16

{
  "command": "<1617 chars \u2014 see below>",
  "description": "Test shape2 with more splits (2-kernel)"
}

cd /workspace/problems/03_paged_attention
cat > test_s2.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
s=shapes.SHAPES[2]; by=bytes_of(s)
for tps,bn,nw,ns_ in [(1,32,4,6),(2,32,4,5),(2,32,4,6),(2,64,4,3),(3,32,4,5),(1,64,4,3)]:
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=min(bs,64); sol._replay=None; sol._q_obj=None
    sol._ensure_buffers(dev, torch.bfloat16)
    torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
    for _ in range(2): sol._launch(*inp)
    torch.cuda.synchronize()
    g=torch.cuda.CUDAGraph()
    with torch.cuda.graph(g): sol._launch(*inp)
    sol._replay=g.replay; sol._q_obj=inp[0]
    ms=time_fn(sol, inp, iters=50, warmup=12)
    print(f"  tps={tps} BN={bn} w={nw} st={ns_} nspl={sol.num_splits}: {ms*1000:.1f}us frac={by/(ms*1e-3)/1e9/1800:.3f}")
EOF
timeout 200 uv run python test_s2.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "command": "<105 chars \u2014 see below>",
  "description": "Re-run shape2 test directly"
}

cd /workspace/problems/03_paged_attention
timeout 200 uv run python test_s2.py 2>&1 | grep -E "tps=|frac"

{
  "file_path": "/workspace/problems/03_paged_attention/solution.py",
  "limit": 60,
  "offset": 1
}

{
  "command": "<221 chars \u2014 see below>",
  "description": "Final check + 5 benchmark runs for stability"
}

cd /workspace/problems/03_paged_attention
uv run python check.py 2>&1 | tail -1
echo "=== 5 benchmark runs ==="
for i in 1 2 3 4 5; do
uv run python benchmark.py 2>&1 | grep -E "peak_fraction:" | tr '\n' ' '; echo ""
done

{
  "command": "<1991 chars \u2014 see below>",
  "description": "Test num_warps=16 for shapes 0 and 4"
}

cd /workspace/problems/03_paged_attention
cat > test_w16.py << 'EOF'
import sys
sys.path.insert(0, "/workspace")
from src.eval.timing import time_fn
import torch, reference, solution, shapes
dev=torch.device("cuda:0")
def bytes_of(s): return 2*s["batch"]*s["seq_len"]*s["num_kv_heads"]*s["head_dim"]*2 + s["batch"]*s["num_heads"]*s["head_dim"]*2*2
def make(s, tps, bn, nw, ns_):
    reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
    reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
    sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
    sol.num_splits, sol.split_size = solution._choose_splits(s['seq_len'], s['batch'], s['num_kv_heads'], sol.num_sms, tps, s['page_size'])
    sol.block_n=bn; sol.num_warps=nw; sol.num_stages=ns_
    bs=1
    while bs<sol.num_splits: bs<<=1
    sol.block_s=min(bs,64); sol._replay=None; sol._q_obj=None
    sol._ensure_buffers(dev, torch.bfloat16)
    torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
    return sol, inp
for sidx, cfgs in [(0,[(1,32,8,6),(1,32,16,6),(1,32,16,5),(1,64,16,3)]),
                   (4,[(4,32,4,6),(4,32,8,6),(4,32,16,6),(4,64,8,4)])]:
    s=shapes.SHAPES[sidx]; by=bytes_of(s)
    print(f"=== shape{sidx} ===")
    for tps,bn,nw,ns_ in cfgs:
        try:
            sol,inp=make(s,tps,bn,nw,ns_)
            for _ in range(2): sol._launch(*inp)
            torch.cuda.synchronize()
            g=torch.cuda.CUDAGraph()
            with torch.cuda.graph(g): sol._launch(*inp)
            sol._replay=g.replay; sol._q_obj=inp[0]
            ms=time_fn(sol, inp, iters=50, warmup=12)
            print(f"  tps={tps} BN={bn} w={nw} st={ns_}: {ms*1000:.1f}us frac={by/(ms*1e-3)/1e9/1800:.3f}")
        except Exception as e: print(f"  tps={tps} BN={bn} w={nw} st={ns_}: ERR {type(e).__name__} {str(e)[:50]}")
EOF
timeout 250 uv run python test_w16.py 2>&1 | grep -E "shape|tps="

{
  "command": "<1266 chars \u2014 see below>",
  "description": "Measure PyTorch graph replay overhead precisely"
}

cd /workspace/problems/03_paged_attention
cat > test_rawreplay.py << 'EOF'
import torch, reference, solution, shapes, statistics, ctypes
dev=torch.device("cuda:0")
s=shapes.SHAPES[4]
reference.BATCH=s["batch"]; reference.NUM_HEADS=s["num_heads"]; reference.NUM_KV_HEADS=s["num_kv_heads"]
reference.HEAD_DIM=s["head_dim"]; reference.SEQ_LEN=s["seq_len"]; reference.PAGE_SIZE=s["page_size"]
sol=solution.Model(*reference.get_init_inputs()).to(dev).eval()
torch.manual_seed(2026); inp=[t.to(dev) for t in reference.get_inputs()]
for _ in range(20): sol(*inp)
torch.cuda.synchronize()
g = sol._graph
# PyTorch replay GPU-event
ts=[]
for _ in range(300):
    a=torch.cuda.Event(enable_timing=True); b=torch.cuda.Event(enable_timing=True)
    a.record(); g.replay(); b.record(); torch.cuda.synchronize()
    ts.append(a.elapsed_time(b))
print(f"PyTorch g.replay() GPU-event: {statistics.median(ts)*1000:.2f}us  min {min(ts)*1000:.2f}")
# CPU dispatch time of PyTorch replay
torch.cuda.synchronize(); 
import time
t0=time.perf_counter()
for _ in range(5000): g.replay()
torch.cuda.synchronize(); t1=time.perf_counter()
print(f"PyTorch replay CPU dispatch (pipelined): {(t1-t0)/5000*1e6:.2f}us/call")
EOF
uv run python test_rawreplay.py 2>&1 | grep -vE "Warning|warn" | tail

{
  "command": "<591 chars \u2014 see below>",
  "description": "Clean up scratch files"
}

cd /workspace/problems/03_paged_attention
ls *.py
echo "--- removing scratch files ---"
rm -f sweep.py sweep2.py sweep3.py sweep4.py sweep5.py sweep6.py sweep7.py sweep8.py sweep9.py sweep10.py sweep11.py sweep12.py sweep_2k.py
rm -f prof_trace.py prof_ncu.py prof_ncu2.py prof_splits.py meas_reduce.py meas_offhead.py meas_graph.py meas_kern.py meas_kern2.py meas_kern3.py meas_official.py test_graph.py test_atomics.py test_split.py test_st.py test_w16.py test_s2.py test_one.py test_rawreplay.py cmp_2k.py __pycache__ -rf
ls *.py
echo "--- framework.txt ---"
cat framework.txt 2>/dev/null