{
  "summary": "Beginning the top-k kernel optimization for Blackwell GPU. First step is reading the reference implementation (reference.py), problem prompt (PROMPT.txt), and verification script (check.py) to understand the input shapes, constraints, and interface.",
  "title": "Analyzing Reference and Requirements",
  "strategic_intent": "Analyzing the reference implementation, prompt, and testing environment to plan the top-k optimization."
}

{
  "file_path": "reference.py"
}

{
  "file_path": "PROMPT.txt"
}

{
  "file_path": "check.py"
}

{
  "file_path": "shapes.py"
}

{
  "file_path": "problem.yaml"
}

{
  "file_path": "benchmark.py"
}

{
  "pattern": "solution.py"
}

{
  "file_path": "sota.py"
}

{
  "command": "uv run python -c \"import torch; import triton; print('Torch:', torch.__version__, 'CUDA:', torch.version.cuda); print('Triton:', triton.__version__)\"",
  "description": "Checking PyTorch and Triton versions in the workspace uv environment"
}

{
  "content": "<846 chars \u2014 see below>",
  "file_path": "test_triton.py"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_sort_kernel(
    X_ptr, Y_vals_ptr, Y_idxs_ptr,
    N: tl.constexpr,
):
    # Load 1D row
    cols = tl.arange(0, N)
    x = tl.load(X_ptr + cols)
    
    # Sort
    # Triton tl.sort can sort multiple tensors (like values and their indices)
    sorted_vals, sorted_idxs = tl.sort((x, cols), descending=True)
    
    # Store
    tl.store(Y_vals_ptr + cols, sorted_vals)
    tl.store(Y_idxs_ptr + cols, sorted_idxs)

def run():
    N = 16
    x = torch.randn(N, device='cuda')
    y_vals = torch.empty(N, device='cuda')
    y_idxs = torch.empty(N, dtype=torch.int32, device='cuda')
    
    test_sort_kernel[(1,)](x, y_vals, y_idxs, N=N)
    
    print("x:", x)
    print("sorted_vals:", y_vals)
    print("sorted_idxs:", y_idxs)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py to verify Triton multi-tensor sort functionality",
  "command": "uv run python test_triton.py"
}

{
  "command": "uv run python -c \"import triton.language as tl; import inspect; print(inspect.getsource(tl.sort))\"",
  "description": "Inspecting triton.language.sort source code"
}

{
  "pattern": "def sort\\(",
  "dir_path": "/workspace/.venv/lib/python3.11/site-packages/triton"
}

{
  "command": "grep -rn \"def sort\" /workspace/.venv/lib/python3.11/site-packages/triton/",
  "description": "Searching for \"def sort\" in virtual environment Triton packages"
}

{
  "description": "Viewing the sort implementation details in Triton's standard.py",
  "command": "sed -n '420,480p' /workspace/.venv/lib/python3.11/site-packages/triton/language/standard.py"
}

{
  "file_path": "test_triton.py",
  "content": "<3221 chars \u2014 see below>"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_pack_kernel(
    X_ptr, Y_vals_ptr, Y_idxs_ptr,
    N: tl.constexpr,
):
    cols = tl.arange(0, N)
    x = tl.load(X_ptr + cols)
    
    # Bitcast float32 to int32
    x_i32 = x.to(tl.int32, bitcast=True)
    
    # Map to sortable uint32/int32
    # mask = 0x80000000 if x_i32 >= 0 else 0xFFFFFFFF
    # Let's do this using bitwise ops
    # if sign bit is set (negative), we want 0xFFFFFFFF, else 0x80000000
    # sign bit is x_i32 >> 31 (arithmetic shift)
    # If negative, sign_mask is all 1s (0xFFFFFFFF)
    # If positive, sign_mask is all 0s (0x00000000)
    sign_mask = x_i32 >> 31
    # mask = sign_mask | 0x80000000
    # Note: in Python/Triton, 0x80000000 might be treated as unsigned or signed.
    # To be safe, we can use signed hex or decimal: -2147483648 is 0x80000000
    # Let's write it out:
    mask = sign_mask ^ 0x80000000
    mapped = x_i32 ^ mask
    
    # Cast mapped to uint64 and shift to high 32 bits
    mapped_u64 = mapped.to(tl.int64) & 0xFFFFFFFF
    shifted = mapped_u64 << 32
    
    # Combine with column indices (0 to N-1)
    cols_u64 = cols.to(tl.int64) & 0xFFFFFFFF
    packed = shifted | cols_u64
    
    # Sort descending
    sorted_packed = tl.sort(packed, descending=True)
    
    # Unpack
    unpacked_mapped = (sorted_packed >> 32) & 0xFFFFFFFF
    # Convert back to i32:
    # If unpacked_mapped >= 0x80000000: mask = 0x80000000
    # else: mask = 0xFFFFFFFF
    # We can determine the mask from the unpacked_mapped sign bit (bit 31)
    # If bit 31 is 1: mask is 0x80000000. If bit 31 is 0: mask is 0xFFFFFFFF.
    # So mask = (unpacked_mapped >> 31 ^ 1) * 0x7FFFFFFF ^ 0xFFFFFFFF or similar.
    # Let's simplify:
    # If original float >= 0, mapped >= 0x80000000. So unpacked_mapped >= 0x80000000.
    # If so, original sign bit was 0, and we XORed with 0x80000000.
    # If unpacked_mapped < 0x80000000, original sign bit was 1, and we XORed with 0xFFFFFFFF.
    # Let's check:
    # If unpacked_mapped & 0x80000000:
    #    orig = unpacked_mapped ^ 0x80000000
    # else:
    #    orig = unpacked_mapped ^ 0xFFFFFFFF
    is_pos = (unpacked_mapped & 0x80000000) != 0
    # In Triton, we can use select:
    orig_mask = tl.where(is_pos, 0x80000000, 0xFFFFFFFF)
    unpacked_i32 = (unpacked_mapped ^ orig_mask).to(tl.int32)
    
    # Bitcast back to float32
    unpacked_x = unpacked_i32.to(tl.float32, bitcast=True)
    unpacked_idx = sorted_packed & 0xFFFFFFFF
    
    # Store
    tl.store(Y_vals_ptr + cols, unpacked_x)
    tl.store(Y_idxs_ptr + cols, unpacked_idx)

def run():
    N = 16
    x = torch.tensor([-3.5, 2.1, 0.0, -0.0, 1.5, -1.2, 5.4, -10.0, 12.0, -1.5, 2.1, 0.5, -0.5, 0.1, -0.1, 10.0], device='cuda')
    y_vals = torch.empty(N, device='cuda')
    y_idxs = torch.empty(N, dtype=torch.int64, device='cuda')
    
    test_pack_kernel[(1,)](x, y_vals, y_idxs, N=N)
    
    print("x:", x)
    print("sorted_vals (triton):", y_vals)
    print("sorted_idxs (triton):", y_idxs)
    
    ref_vals, ref_idxs = torch.topk(x, k=N, descending=True)
    print("sorted_vals (ref):   ", ref_vals)
    print("sorted_idxs (ref):   ", ref_idxs)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py to check packed float sorting via Triton",
  "command": "uv run python test_triton.py"
}

{
  "file_path": "test_triton.py",
  "content": "<2645 chars \u2014 see below>"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_pack_kernel(
    X_ptr, Y_vals_ptr, Y_idxs_ptr,
    N: tl.constexpr,
):
    cols = tl.arange(0, N)
    x = tl.load(X_ptr + cols)
    
    # Bitcast float32 to uint32
    x_u32 = x.to(tl.uint32, bitcast=True)
    
    # If negative (highest bit is 1), mask is 0xFFFFFFFF.
    # If positive/zero (highest bit is 0), mask is 0x80000000.
    is_neg = (x_u32 & 0x80000000) != 0
    mask = tl.where(is_neg, 0xFFFFFFFF, 0x80000000)
    mapped = x_u32 ^ mask
    
    # Cast mapped to uint64 and shift to high 32 bits
    mapped_u64 = mapped.to(tl.uint64)
    shifted = mapped_u64 << 32
    
    # Combine with column indices (0 to N-1)
    cols_u64 = cols.to(tl.uint64)
    packed = shifted | cols_u64
    
    # Sort descending
    sorted_packed = tl.sort(packed, descending=True)
    
    # Unpack
    unpacked_mapped = (sorted_packed >> 32).to(tl.uint32)
    
    # Convert back to uint32:
    # If unpacked_mapped & 0x80000000 != 0, then original sign was positive/zero, and mask was 0x80000000.
    # If unpacked_mapped & 0x80000000 == 0, then original sign was negative, and mask was 0xFFFFFFFF.
    # Let's verify:
    # If original was positive, mapped >= 0x80000000. So unpacked_mapped & 0x80000000 != 0.
    # If original was negative, mapped < 0x80000000. So unpacked_mapped & 0x80000000 == 0.
    is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
    orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
    unpacked_u32 = unpacked_mapped ^ orig_mask
    
    # Bitcast back to float32
    unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
    unpacked_idx = (sorted_packed & 0xFFFFFFFF).to(tl.int64)
    
    # Store
    tl.store(Y_vals_ptr + cols, unpacked_x)
    tl.store(Y_idxs_ptr + cols, unpacked_idx)

def run():
    N = 16
    x = torch.tensor([-3.5, 2.1, 0.0, -0.0, 1.5, -1.2, 5.4, -10.0, 12.0, -1.5, 2.1, 0.5, -0.5, 0.1, -0.1, 10.0], device='cuda')
    y_vals = torch.empty(N, device='cuda')
    y_idxs = torch.empty(N, dtype=torch.int64, device='cuda')
    
    test_pack_kernel[(1,)](x, y_vals, y_idxs, N=N)
    
    print("x:", x)
    print("sorted_vals (triton):", y_vals)
    print("sorted_idxs (triton):", y_idxs)
    
    ref_vals, ref_idxs = torch.topk(x, k=N, descending=True)
    print("sorted_vals (ref):   ", ref_vals)
    print("sorted_idxs (ref):   ", ref_idxs)
    
    # Check if correct
    correct_vals = torch.allclose(y_vals, ref_vals, atol=1e-5)
    print("Vals correct?", correct_vals)
    correct_idxs = torch.equal(y_idxs, ref_idxs)
    print("Idxs correct?", correct_idxs)

if __name__ == "__main__":
    run()

{
  "command": "uv run python test_triton.py",
  "description": "Running test_triton.py to check if mapped-float sorting works and matches torch.topk exactly"
}

{
  "file_path": "test_triton.py",
  "content": "<587 chars \u2014 see below>"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_slice_kernel(X_ptr, Y_ptr, B: tl.constexpr, P: tl.constexpr):
    cols = tl.arange(0, B)
    x = tl.load(X_ptr + cols)
    
    # Try indexing
    slice_indices = tl.arange(0, P)
    # Can we do x[slice_indices]?
    # Let's try:
    y = x[slice_indices]
    
    tl.store(Y_ptr + slice_indices, y)

def run():
    x = torch.randn(16, device='cuda')
    y = torch.zeros(4, device='cuda')
    test_slice_kernel[(1,)](x, y, B=16, P=4)
    print("x:", x)
    print("y:", y)

if __name__ == "__main__":
    run()

{
  "command": "uv run python test_triton.py",
  "description": "Running test_triton.py to check register tensor slicing in Triton"
}

{
  "file_path": "test_triton.py",
  "content": "<587 chars \u2014 see below>"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_topk_kernel(X_ptr, Y_ptr, B: tl.constexpr, P: tl.constexpr):
    cols = tl.arange(0, B)
    x = tl.load(X_ptr + cols)
    
    # Try tl.topk
    # Wait, tl.topk sorts descending and returns top k
    y = tl.topk(x, k=P)
    
    slice_indices = tl.arange(0, P)
    tl.store(Y_ptr + slice_indices, y)

def run():
    x = torch.randn(16, device='cuda')
    y = torch.zeros(4, device='cuda')
    test_topk_kernel[(1,)](x, y, B=16, P=4)
    print("x:", x)
    print("y:", y)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py to check tl.topk functionality in Triton",
  "command": "uv run python test_triton.py"
}

{
  "content": "<667 chars \u2014 see below>",
  "file_path": "test_triton.py"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_topk_u64_kernel(X_ptr, Y_ptr, B: tl.constexpr, P: tl.constexpr):
    cols = tl.arange(0, B)
    x = tl.load(X_ptr + cols)
    
    # Cast to uint64
    x_u64 = x.to(tl.uint64)
    y = tl.topk(x_u64, k=P)
    
    slice_indices = tl.arange(0, P)
    tl.store(Y_ptr + slice_indices, y)

def run():
    # Make sure we use uint64 values
    x = torch.randint(0, 1000000, (16,), dtype=torch.int64, device='cuda')
    y = torch.zeros(4, dtype=torch.int64, device='cuda')
    test_topk_u64_kernel[(1,)](x, y, B=16, P=4)
    print("x:", x)
    print("y:", y)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py to check tl.topk on uint64 tensors",
  "command": "uv run python test_triton.py"
}

{
  "command": "grep -rn \"def cat\" /workspace/.venv/lib/python3.11/site-packages/triton/",
  "description": "Searching for \"def cat\" in Triton source files"
}

{
  "file_path": "test_triton.py",
  "content": "<542 chars \u2014 see below>"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_cat_kernel(X_ptr, Y_ptr, P: tl.constexpr):
    cols1 = tl.arange(0, P)
    cols2 = tl.arange(P, 2*P)
    
    x1 = tl.load(X_ptr + cols1)
    x2 = tl.load(X_ptr + cols2)
    
    # Try tl.cat
    y = tl.cat(x1, x2)
    
    tl.store(Y_ptr + tl.arange(0, 2*P), y)

def run():
    x = torch.randn(8, device='cuda')
    y = torch.zeros(8, device='cuda')
    test_cat_kernel[(1,)](x, y, P=4)
    print("x:", x)
    print("y:", y)

if __name__ == "__main__":
    run()

{
  "command": "uv run python test_triton.py",
  "description": "Running test_triton.py to check register tensor concatenation using tl.cat"
}

{
  "description": "Searching for examples of tl.cat in Triton's virtual environment files",
  "command": "grep -rn \"tl.cat\" /workspace/.venv/lib/python3.11/site-packages/triton/ 2>/dev/null | head -n 30"
}

{
  "description": "Listing Triton language functions related to concatenation or joining",
  "command": "uv run 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])\""
}

{
  "command": "uv run python -c \"import triton.language as tl; help(tl.join); help(tl.cat)\"",
  "description": "Printing the docstrings of tl.join and tl.cat to understand their parameters"
}

{
  "description": "Checking GPU status and process usage with nvidia-smi",
  "command": "nvidia-smi"
}

{
  "description": "Listing all system processes with ps aux",
  "command": "ps aux"
}

{
  "description": "Checking for stale lock files in common temporary directories",
  "command": "ls -la /tmp /var/tmp /dev/shm 2>/dev/null"
}

{
  "command": "uv run python -c \"import triton.language as tl; print('JOIN:', tl.join.__doc__); print('CAT:', tl.cat.__doc__)\"",
  "description": "Printing docstrings of tl.join and tl.cat directly"
}

{
  "command": "/workspace/.venv/bin/python -c \"import torch; print(torch.__version__)\"",
  "description": "Directly checking Python and Torch from the virtual environment without uv"
}

{
  "description": "Printing docstrings for tl.join and tl.cat using the direct Python binary",
  "command": "/workspace/.venv/bin/python -c \"import triton.language as tl; print('JOIN:', tl.join.__doc__); print('CAT:', tl.cat.__doc__)\""
}

{
  "content": "<689 chars \u2014 see below>",
  "file_path": "test_triton.py"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_join_reshape_kernel(X_ptr, Y_ptr, P: tl.constexpr):
    cols1 = tl.arange(0, P)
    cols2 = tl.arange(P, 2*P)
    
    x1 = tl.load(X_ptr + cols1)
    x2 = tl.load(X_ptr + cols2)
    
    # Join into (P, 2)
    joined = tl.join(x1, x2)
    
    # Reshape into (2 * P,)
    y = tl.reshape(joined, [2 * P])
    
    tl.store(Y_ptr + tl.arange(0, 2*P), y)

def run():
    x = torch.tensor([10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0], device='cuda')
    y = torch.zeros(8, device='cuda')
    test_join_reshape_kernel[(1,)](x, y, P=4)
    print("x:", x)
    print("y:", y)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py to check the join-reshape pattern",
  "command": "/workspace/.venv/bin/python test_triton.py"
}

{
  "file_path": "solution.py",
  "content": "<6324 chars \u2014 see below>"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

def next_power_of_2(n):
    return 1 if n <= 1 else 2**(n - 1).bit_length()

@triton.jit
def topk_phase1_kernel(
    X_ptr,
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    N: tl.constexpr,
    P: tl.constexpr,
    K: tl.constexpr,
    B: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    SINGLE_PASS: tl.constexpr,
):
    pid = tl.program_id(0)
    row_idx = pid // BLOCKS_PER_ROW
    block_col_idx = pid % BLOCKS_PER_ROW
    
    N_per_block = (N + BLOCKS_PER_ROW - 1) // BLOCKS_PER_ROW
    cols_start = block_col_idx * N_per_block
    
    # Initialize running top-P with 0
    running_top = tl.zeros([P], dtype=tl.uint64)
    
    steps = (N_per_block + B - 1) // B
    
    for s in range(steps):
        chunk_cols = cols_start + s * B + tl.arange(0, B)
        # Load values
        mask = (chunk_cols < N) & (chunk_cols < cols_start + N_per_block)
        vals = tl.load(X_ptr + row_idx * N + chunk_cols, mask=mask, other=-1e38)
        
        # Pack float to sortable uint32
        vals_u32 = vals.to(tl.uint32, bitcast=True)
        is_neg = (vals_u32 & 0x80000000) != 0
        mask_xor = tl.where(is_neg, 0xFFFFFFFF, 0x80000000)
        mapped = vals_u32 ^ mask_xor
        
        # Combine mapped float and column index
        packed = (mapped.to(tl.uint64) << 32) | chunk_cols.to(tl.uint64)
        
        # Find top-P of this chunk
        chunk_top = tl.topk(packed, k=P)
        
        # Merge running_top and chunk_top
        joined = tl.join(running_top, chunk_top)
        combined = tl.reshape(joined, [2 * P])
        running_top = tl.topk(combined, k=P)
        
    if SINGLE_PASS:
        # Unpack and write directly to output
        unpacked_mapped = (running_top >> 32).to(tl.uint32)
        is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
        orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
        unpacked_u32 = unpacked_mapped ^ orig_mask
        
        unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
        unpacked_idx = (running_top & 0xFFFFFFFF).to(tl.int64)
        
        out_cols = tl.arange(0, P)
        mask = out_cols < K
        tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x, mask=mask)
        tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx, mask=mask)
    else:
        # Write running_top to Workspace
        out_cols = tl.arange(0, P)
        tl.store(Workspace_ptr + (row_idx * BLOCKS_PER_ROW + block_col_idx) * P + out_cols, running_top)


@triton.jit
def topk_phase2_kernel(
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    P: tl.constexpr,
    K: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
):
    row_idx = tl.program_id(0)
    
    # Each row has BLOCKS_PER_ROW * P intermediate results in Workspace
    M = BLOCKS_PER_ROW * P
    cols = tl.arange(0, M)
    
    packed = tl.load(Workspace_ptr + row_idx * M + cols)
    
    # Find top-K
    top_packed = tl.topk(packed, k=K)
    
    # Unpack
    unpacked_mapped = (top_packed >> 32).to(tl.uint32)
    is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
    orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
    unpacked_u32 = unpacked_mapped ^ orig_mask
    
    unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
    unpacked_idx = (top_packed & 0xFFFFFFFF).to(tl.int64)
    
    out_cols = tl.arange(0, K)
    tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x)
    tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx)


class Model(nn.Module):
    def __init__(self, batch: int, n: int, k: int):
        super().__init__()
        self.batch = batch
        self.n = n
        self.k = k
        self.register_buffer("_dummy", torch.zeros(1))
        
        # Decide BLOCKS_PER_ROW dynamically
        if self.batch >= 64:
            self.blocks_per_row = 1
        elif self.batch >= 32:
            self.blocks_per_row = 2
        elif self.batch >= 16:
            self.blo

... (2324 more chars)

{
  "description": "Running check.py to test solution.py across all shapes",
  "command": "/workspace/.venv/bin/python check.py"
}

{
  "old_string": "<393 chars \u2014 see below>",
  "new_string": "<387 chars \u2014 see below>",
  "allow_multiple": false,
  "file_path": "solution.py",
  "instruction": "Add M: tl.constexpr as a parameter to topk_phase2_kernel and pass it during launching to satisfy Triton arange constexpr requirement."
}

@triton.jit
def topk_phase2_kernel(
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    P: tl.constexpr,
    K: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
):
    row_idx = tl.program_id(0)
    
    # Each row has BLOCKS_PER_ROW * P intermediate results in Workspace
    M = BLOCKS_PER_ROW * P
    cols = tl.arange(0, M)
    
    packed = tl.load(Workspace_ptr + row_idx * M + cols)

@triton.jit
def topk_phase2_kernel(
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    P: tl.constexpr,
    K: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    M: tl.constexpr,
):
    row_idx = tl.program_id(0)
    
    # Each row has BLOCKS_PER_ROW * P intermediate results in Workspace
    cols = tl.arange(0, M)
    
    packed = tl.load(Workspace_ptr + row_idx * M + cols)

{
  "dir_path": "/workspace/problems/05_topk_bitonic",
  "pattern": "topk_phase2_kernel",
  "include_pattern": "solution.py"
}

{
  "allow_multiple": false,
  "file_path": "solution.py",
  "instruction": "Pass M as a parameter in topk_phase2_kernel call.",
  "old_string": "<269 chars \u2014 see below>",
  "new_string": "<317 chars \u2014 see below>"
}

            grid2 = (self.batch,)
            topk_phase2_kernel[grid2](
                workspace,
                out_vals,
                out_idxs,
                P=self.p,
                K=self.k,
                BLOCKS_PER_ROW=self.blocks_per_row,
            )

            grid2 = (self.batch,)
            topk_phase2_kernel[grid2](
                workspace,
                out_vals,
                out_idxs,
                P=self.p,
                K=self.k,
                BLOCKS_PER_ROW=self.blocks_per_row,
                M=self.blocks_per_row * self.p,
            )

{
  "description": "Running check.py to test the modified topk_phase2_kernel launch",
  "command": "/workspace/.venv/bin/python check.py"
}

{
  "description": "Inspecting standard.py imports to see how max/min are defined",
  "command": "head -n 20 /workspace/.venv/lib/python3.11/site-packages/triton/language/standard.py"
}

{
  "content": "<520 chars \u2014 see below>",
  "file_path": "test_triton.py"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_topk_k1_kernel(X_ptr, Y_ptr, B: tl.constexpr, P: tl.constexpr):
    cols = tl.arange(0, B)
    x = tl.load(X_ptr + cols)
    
    y = tl.topk(x, k=P)
    
    slice_indices = tl.arange(0, P)
    tl.store(Y_ptr + slice_indices, y)

def run():
    x = torch.randn(16, device='cuda')
    y = torch.zeros(1, device='cuda')
    test_topk_k1_kernel[(1,)](x, y, B=16, P=1)
    print("x:", x)
    print("y:", y)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py with P=1 (k=1) to reproduce the compiler error",
  "command": "/workspace/.venv/bin/python test_triton.py"
}

{
  "file_path": "test_triton.py",
  "content": "<592 chars \u2014 see below>"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_max_kernel(X_ptr, Y_ptr, B: tl.constexpr):
    cols = tl.arange(0, B)
    x = tl.load(X_ptr + cols)
    
    # Try tl.max
    # Note: tl.max requires axis parameter
    y = tl.max(x, axis=0)
    
    # Store y (which is a 0D tensor / scalar)
    tl.store(Y_ptr, y)

def run():
    x = torch.randn(16, device='cuda')
    y = torch.zeros(1, device='cuda')
    test_max_kernel[(1,)](x, y, B=16)
    print("x:", x)
    print("max(x) ref:", x.max())
    print("max(x) triton:", y)

if __name__ == "__main__":
    run()

{
  "command": "/workspace/.venv/bin/python test_triton.py",
  "description": "Running test_triton.py to check tl.max functionality on 1D tensors"
}

{
  "content": "<914 chars \u2014 see below>",
  "file_path": "test_triton.py"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_p1_kernel(X_ptr, Y_ptr, B: tl.constexpr):
    cols1 = tl.arange(0, B)
    cols2 = tl.arange(B, 2*B)
    
    x1 = tl.load(X_ptr + cols1)
    x2 = tl.load(X_ptr + cols2)
    
    # Each is shape [16]
    # Find max of each
    max1 = tl.expand_dims(tl.max(x1, axis=0), 0) # shape [1]
    max2 = tl.expand_dims(tl.max(x2, axis=0), 0) # shape [1]
    
    # Join and reshape to [2]
    joined = tl.join(max1, max2)
    combined = tl.reshape(joined, [2])
    
    # Find global max
    global_max = tl.expand_dims(tl.max(combined, axis=0), 0) # shape [1]
    
    tl.store(Y_ptr, global_max)

def run():
    x = torch.randn(32, device='cuda')
    y = torch.zeros(1, device='cuda')
    test_p1_kernel[(1,)](x, y, B=16)
    print("x:", x)
    print("max(x) ref:", x.max())
    print("max(x) triton:", y)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py with P=1 workaround to verify correctness",
  "command": "/workspace/.venv/bin/python test_triton.py"
}

{
  "content": "<932 chars \u2014 see below>",
  "file_path": "test_triton.py"
}

import torch
import triton
import triton.language as tl

@triton.jit
def test_p1_kernel(X_ptr, Y_ptr, B: tl.constexpr):
    cols1 = tl.arange(0, B)
    cols2 = tl.arange(B, 2*B)
    
    x1 = tl.load(X_ptr + cols1)
    x2 = tl.load(X_ptr + cols2)
    
    # Each is shape [16]
    # Find max of each
    max1 = tl.expand_dims(tl.max(x1, axis=0), 0) # shape [1]
    max2 = tl.expand_dims(tl.max(x2, axis=0), 0) # shape [1]
    
    # Join and reshape to [2]
    joined = tl.join(max1, max2)
    combined = tl.reshape(joined, [2])
    
    # Find global max
    global_max = tl.expand_dims(tl.max(combined, axis=0), 0) # shape [1]
    
    tl.store(Y_ptr + tl.arange(0, 1), global_max)

def run():
    x = torch.randn(32, device='cuda')
    y = torch.zeros(1, device='cuda')
    test_p1_kernel[(1,)](x, y, B=16)
    print("x:", x)
    print("max(x) ref:", x.max())
    print("max(x) triton:", y)

if __name__ == "__main__":
    run()

{
  "description": "Running test_triton.py to verify block store and top-1 logic workaround",
  "command": "/workspace/.venv/bin/python test_triton.py"
}

{
  "file_path": "solution.py",
  "content": "<6668 chars \u2014 see below>"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

def next_power_of_2(n):
    return 1 if n <= 1 else 2**(n - 1).bit_length()

@triton.jit
def topk_phase1_kernel(
    X_ptr,
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    N: tl.constexpr,
    P: tl.constexpr,
    K: tl.constexpr,
    B: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    SINGLE_PASS: tl.constexpr,
):
    pid = tl.program_id(0)
    row_idx = pid // BLOCKS_PER_ROW
    block_col_idx = pid % BLOCKS_PER_ROW
    
    N_per_block = (N + BLOCKS_PER_ROW - 1) // BLOCKS_PER_ROW
    cols_start = block_col_idx * N_per_block
    
    # Initialize running top-P with 0
    running_top = tl.zeros([P], dtype=tl.uint64)
    
    steps = (N_per_block + B - 1) // B
    
    for s in range(steps):
        chunk_cols = cols_start + s * B + tl.arange(0, B)
        # Load values
        mask = (chunk_cols < N) & (chunk_cols < cols_start + N_per_block)
        vals = tl.load(X_ptr + row_idx * N + chunk_cols, mask=mask, other=-1e38)
        
        # Pack float to sortable uint32
        vals_u32 = vals.to(tl.uint32, bitcast=True)
        is_neg = (vals_u32 & 0x80000000) != 0
        mask_xor = tl.where(is_neg, 0xFFFFFFFF, 0x80000000)
        mapped = vals_u32 ^ mask_xor
        
        # Combine mapped float and column index
        packed = (mapped.to(tl.uint64) << 32) | chunk_cols.to(tl.uint64)
        
        # Find top-P of this chunk
        if P == 1:
            chunk_top = tl.expand_dims(tl.max(packed, axis=0), 0)
        else:
            chunk_top = tl.topk(packed, k=P)
        
        # Merge running_top and chunk_top
        joined = tl.join(running_top, chunk_top)
        combined = tl.reshape(joined, [2 * P])
        if P == 1:
            running_top = tl.expand_dims(tl.max(combined, axis=0), 0)
        else:
            running_top = tl.topk(combined, k=P)
        
    if SINGLE_PASS:
        # Unpack and write directly to output
        unpacked_mapped = (running_top >> 32).to(tl.uint32)
        is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
        orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
        unpacked_u32 = unpacked_mapped ^ orig_mask
        
        unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
        unpacked_idx = (running_top & 0xFFFFFFFF).to(tl.int64)
        
        out_cols = tl.arange(0, P)
        mask = out_cols < K
        tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x, mask=mask)
        tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx, mask=mask)
    else:
        # Write running_top to Workspace
        out_cols = tl.arange(0, P)
        tl.store(Workspace_ptr + (row_idx * BLOCKS_PER_ROW + block_col_idx) * P + out_cols, running_top)


@triton.jit
def topk_phase2_kernel(
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    P: tl.constexpr,
    K: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    M: tl.constexpr,
):
    row_idx = tl.program_id(0)
    
    # Each row has BLOCKS_PER_ROW * P intermediate results in Workspace
    cols = tl.arange(0, M)
    
    packed = tl.load(Workspace_ptr + row_idx * M + cols)
    
    # Find top-K
    if K == 1:
        top_packed = tl.expand_dims(tl.max(packed, axis=0), 0)
    else:
        top_packed = tl.topk(packed, k=K)
    
    # Unpack
    unpacked_mapped = (top_packed >> 32).to(tl.uint32)
    is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
    orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
    unpacked_u32 = unpacked_mapped ^ orig_mask
    
    unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
    unpacked_idx = (top_packed & 0xFFFFFFFF).to(tl.int64)
    
    out_cols = tl.arange(0, K)
    tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x)
    tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx)


class Model(nn.Module):
    def __init__(self, batch: int, n: int, k: int):
        super().__init__()
        self.batch = batch
        self.n = n
        self.k

... (2668 more chars)

{
  "command": "/workspace/.venv/bin/python check.py",
  "description": "Running check.py to test our optimized solution across all test cases"
}

{
  "strategic_intent": "Benchmarking and tuning the performance of the Triton top-k kernel to optimize memory bandwidth and compute efficiency.",
  "title": "Benchmarking and Performance Tuning",
  "summary": "Successfully implemented a custom, two-pass Triton-based top-k kernel utilizing highly optimized parallel bitonic merge-select and float-to-sortable-uint32 packing/unpacking. Verified correctness across all shape scenarios (including batched argmax and non-power-of-two limits), successfully passing check.py. Now transitioning to benchmarking and performance tuning."
}

{
  "description": "Running benchmark.py to measure throughput and peak bandwidth fraction",
  "command": "/workspace/.venv/bin/python benchmark.py"
}

{
  "file_path": "time_all.py",
  "content": "<1399 chars \u2014 see below>"
}

import torch
import reference
import solution
import shapes
import time

def main():
    device = torch.device("cuda:0")
    for i, shape in enumerate(shapes.SHAPES):
        batch, n, k = shape["batch"], shape["n"], shape["k"]
        print(f"Shape {i}: batch={batch}, n={n}, k={k}")
        
        # Inputs
        x = torch.randn(batch, n, device=device)
        
        # Warmup reference
        ref_model = reference.Model(batch, n, k).to(device)
        for _ in range(10):
            ref_model(x)
        
        # Measure reference
        torch.cuda.synchronize()
        t0 = time.perf_counter()
        iters = 100
        for _ in range(iters):
            ref_vals, ref_idxs = ref_model(x)
        torch.cuda.synchronize()
        ref_ms = (time.perf_counter() - t0) * 1000 / iters
        
        # Warmup solution
        sol_model = solution.Model(batch, n, k).to(device)
        for _ in range(10):
            sol_model(x)
            
        # Measure solution
        torch.cuda.synchronize()
        t0 = time.perf_counter()
        for _ in range(iters):
            sol_vals, sol_idxs = sol_model(x)
        torch.cuda.synchronize()
        sol_ms = (time.perf_counter() - t0) * 1000 / iters
        
        print(f"  Reference: {ref_ms:.4f} ms")
        print(f"  Solution:  {sol_ms:.4f} ms (Speedup: {ref_ms / sol_ms:.2f}x)")

if __name__ == "__main__":
    main()

{
  "command": "/workspace/.venv/bin/python time_all.py",
  "description": "Running time_all.py to evaluate speedup compared to eager baseline"
}

{
  "file_path": "tune.py",
  "content": "<1881 chars \u2014 see below>"
}

import torch
import reference
import solution
import shapes
import time

def main():
    device = torch.device("cuda:0")
    for i, shape in enumerate(shapes.SHAPES):
        batch, n, k = shape["batch"], shape["n"], shape["k"]
        print(f"\nShape {i}: batch={batch}, n={n}, k={k}")
        
        # Inputs
        x = torch.randn(batch, n, device=device)
        
        # Try different blocks_per_row
        best_ms = 9999.0
        best_cfg = None
        
        for bpr in [1, 2, 4, 8, 16, 32, 64]:
            # Make sure we don't have too many blocks or invalid configs
            n_per_block = (n + bpr - 1) // bpr
            if n_per_block < k:
                continue
                
            for b in [512, 1024, 2048]:
                # Test configuration
                model = solution.Model(batch, n, k).to(device)
                model.blocks_per_row = bpr
                model.b = b
                
                # Warmup
                try:
                    for _ in range(5):
                        model(x)
                        
                    torch.cuda.synchronize()
                    t0 = time.perf_counter()
                    iters = 50
                    for _ in range(iters):
                        model(x)
                    torch.cuda.synchronize()
                    ms = (time.perf_counter() - t0) * 1000 / iters
                    
                    if ms < best_ms:
                        best_ms = ms
                        best_cfg = (bpr, b)
                    print(f"  blocks_per_row={bpr:2d}, B={b:4d} -> {ms:.4f} ms")
                except Exception as e:
                    print(f"  blocks_per_row={bpr:2d}, B={b:4d} -> Error: {e}")
                    
        print(f"  ==> Best: blocks_per_row={best_cfg[0]}, B={best_cfg[1]} ({best_ms:.4f} ms)")

if __name__ == "__main__":
    main()

{
  "description": "Running tune.py to sweep and identify optimal configurations for each shape",
  "command": "/workspace/.venv/bin/python tune.py"
}

{
  "file_path": "solution.py",
  "content": "<7358 chars \u2014 see below>"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

def next_power_of_2(n):
    return 1 if n <= 1 else 2**(n - 1).bit_length()

@triton.jit
def topk_phase1_kernel(
    X_ptr,
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    N: tl.constexpr,
    P: tl.constexpr,
    K: tl.constexpr,
    B: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    SINGLE_PASS: tl.constexpr,
):
    pid = tl.program_id(0)
    row_idx = pid // BLOCKS_PER_ROW
    block_col_idx = pid % BLOCKS_PER_ROW
    
    N_per_block = (N + BLOCKS_PER_ROW - 1) // BLOCKS_PER_ROW
    cols_start = block_col_idx * N_per_block
    
    # Initialize running top-P with 0
    running_top = tl.zeros([P], dtype=tl.uint64)
    
    steps = (N_per_block + B - 1) // B
    
    for s in range(steps):
        chunk_cols = cols_start + s * B + tl.arange(0, B)
        # Load values
        mask = (chunk_cols < N) & (chunk_cols < cols_start + N_per_block)
        vals = tl.load(X_ptr + row_idx * N + chunk_cols, mask=mask, other=-1e38)
        
        # Pack float to sortable uint32
        vals_u32 = vals.to(tl.uint32, bitcast=True)
        is_neg = (vals_u32 & 0x80000000) != 0
        mask_xor = tl.where(is_neg, 0xFFFFFFFF, 0x80000000)
        mapped = vals_u32 ^ mask_xor
        
        # Combine mapped float and column index
        packed = (mapped.to(tl.uint64) << 32) | chunk_cols.to(tl.uint64)
        
        # Find top-P of this chunk
        if P == 1:
            chunk_top = tl.expand_dims(tl.max(packed, axis=0), 0)
        else:
            chunk_top = tl.topk(packed, k=P)
        
        # Merge running_top and chunk_top
        joined = tl.join(running_top, chunk_top)
        combined = tl.reshape(joined, [2 * P])
        if P == 1:
            running_top = tl.expand_dims(tl.max(combined, axis=0), 0)
        else:
            running_top = tl.topk(combined, k=P)
        
    if SINGLE_PASS:
        # Unpack and write directly to output
        unpacked_mapped = (running_top >> 32).to(tl.uint32)
        is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
        orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
        unpacked_u32 = unpacked_mapped ^ orig_mask
        
        unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
        unpacked_idx = (running_top & 0xFFFFFFFF).to(tl.int64)
        
        out_cols = tl.arange(0, P)
        mask = out_cols < K
        tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x, mask=mask)
        tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx, mask=mask)
    else:
        # Write running_top to Workspace
        out_cols = tl.arange(0, P)
        tl.store(Workspace_ptr + (row_idx * BLOCKS_PER_ROW + block_col_idx) * P + out_cols, running_top)


@triton.jit
def topk_phase2_kernel(
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    P: tl.constexpr,
    K: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    M: tl.constexpr,
):
    row_idx = tl.program_id(0)
    
    # Each row has BLOCKS_PER_ROW * P intermediate results in Workspace
    cols = tl.arange(0, M)
    
    packed = tl.load(Workspace_ptr + row_idx * M + cols)
    
    # Find top-K
    if K == 1:
        top_packed = tl.expand_dims(tl.max(packed, axis=0), 0)
    else:
        top_packed = tl.topk(packed, k=K)
    
    # Unpack
    unpacked_mapped = (top_packed >> 32).to(tl.uint32)
    is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
    orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
    unpacked_u32 = unpacked_mapped ^ orig_mask
    
    unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
    unpacked_idx = (top_packed & 0xFFFFFFFF).to(tl.int64)
    
    out_cols = tl.arange(0, K)
    tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x)
    tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx)


class Model(nn.Module):
    def __init__(self, batch: int, n: int, k: int):
        super().__init__()
        self.batch = batch
        self.n = n
        self.k

... (3358 more chars)

{
  "command": "/workspace/.venv/bin/python time_all.py",
  "description": "Running time_all.py to measure performance with the optimal configurations"
}

{
  "description": "Running check.py to confirm correctness remains PASS",
  "command": "/workspace/.venv/bin/python check.py"
}

{
  "command": "/workspace/.venv/bin/python benchmark.py",
  "description": "Running benchmark.py to get the official scored peak fraction and results"
}

{
  "content": "<1141 chars \u2014 see below>",
  "file_path": "tune_warps.py"
}

import torch
import reference
import solution
import shapes
import time

def main():
    device = torch.device("cuda:0")
    for i, shape in enumerate(shapes.SHAPES):
        batch, n, k = shape["batch"], shape["n"], shape["k"]
        print(f"\nShape {i}: batch={batch}, n={n}, k={k}")
        
        x = torch.randn(batch, n, device=device)
        best_ms = 9999.0
        best_warps = None
        
        # We can temporarily modify the launch calls in solution.py or write a custom test
        # Let's write a custom test inside solution.py's forward or just sweep here.
        # Wait, since solution.py is imported, we can patch the forward method or edit it.
        # Let's test different warps by defining a custom launch inside a copy of the model.
        for w1 in [4, 8, 16]:
            for w2 in [4, 8, 16]:
                # Patch launch or run
                # To keep it simple, we can just edit solution.py to use different warps and run time_all.py.
                # But we can also test it here if we use a modified version of forward.
                pass
                
if __name__ == "__main__":
    main()

{
  "file_path": "tune_warps.py",
  "content": "<3149 chars \u2014 see below>"
}

import torch
import triton
import triton.language as tl
import solution
import shapes
import time

def next_power_of_2(n):
    return 1 if n <= 1 else 2**(n - 1).bit_length()

def run_custom_forward(x, model, w1, w2):
    batch, n, k = model.batch, model.n, model.k
    p, b, blocks_per_row = model.p, model.b, model.blocks_per_row
    
    out_vals = torch.empty(batch, k, dtype=torch.float32, device=x.device)
    out_idxs = torch.empty(batch, k, dtype=torch.int64, device=x.device)
    
    if blocks_per_row == 1:
        grid = (batch,)
        solution.topk_phase1_kernel[grid](
            x,
            None,
            out_vals,
            out_idxs,
            N=n,
            P=p,
            K=k,
            B=b,
            BLOCKS_PER_ROW=1,
            SINGLE_PASS=True,
            num_warps=w1,
        )
    else:
        workspace = torch.empty(batch, blocks_per_row, p, dtype=torch.int64, device=x.device)
        
        grid1 = (batch * blocks_per_row,)
        solution.topk_phase1_kernel[grid1](
            x,
            workspace,
            None,
            None,
            N=n,
            P=p,
            K=k,
            B=b,
            BLOCKS_PER_ROW=blocks_per_row,
            SINGLE_PASS=False,
            num_warps=w1,
        )
        
        grid2 = (batch,)
        solution.topk_phase2_kernel[grid2](
            workspace,
            out_vals,
            out_idxs,
            P=p,
            K=k,
            BLOCKS_PER_ROW=blocks_per_row,
            M=blocks_per_row * p,
            num_warps=w2,
        )
        
    return out_vals, out_idxs

def main():
    device = torch.device("cuda:0")
    for i, shape in enumerate(shapes.SHAPES):
        batch, n, k = shape["batch"], shape["n"], shape["k"]
        print(f"\nShape {i}: batch={batch}, n={n}, k={k}")
        
        x = torch.randn(batch, n, device=device)
        model = solution.Model(batch, n, k).to(device)
        
        # Determine the set of w1 and w2 to try
        w1_options = [2, 4, 8, 16]
        w2_options = [2, 4, 8, 16] if model.blocks_per_row > 1 else [4]
        
        best_ms = 9999.0
        best_w = None
        
        for w1 in w1_options:
            for w2 in w2_options:
                try:
                    # Warmup
                    for _ in range(5):
                        run_custom_forward(x, model, w1, w2)
                    
                    torch.cuda.synchronize()
                    t0 = time.perf_counter()
                    iters = 100
                    for _ in range(iters):
                        run_custom_forward(x, model, w1, w2)
                    torch.cuda.synchronize()
                    ms = (time.perf_counter() - t0) * 1000 / iters
                    
                    print(f"  w1={w1:2d}, w2={w2:2d} -> {ms:.4f} ms")
                    if ms < best_ms:
                        best_ms = ms
                        best_w = (w1, w2)
                except Exception as e:
                    pass
                    
        print(f"  ==> Best: w1={best_w[0]}, w2={best_w[1]} ({best_ms:.4f} ms)")

if __name__ == "__main__":
    main()

{
  "description": "Running tune_warps.py to sweep num_warps parameter combinations",
  "command": "/workspace/.venv/bin/python tune_warps.py"
}

{
  "content": "<7766 chars \u2014 see below>",
  "file_path": "solution.py"
}

import torch
import torch.nn as nn
import triton
import triton.language as tl

def next_power_of_2(n):
    return 1 if n <= 1 else 2**(n - 1).bit_length()

@triton.jit
def topk_phase1_kernel(
    X_ptr,
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    N: tl.constexpr,
    P: tl.constexpr,
    K: tl.constexpr,
    B: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    SINGLE_PASS: tl.constexpr,
):
    pid = tl.program_id(0)
    row_idx = pid // BLOCKS_PER_ROW
    block_col_idx = pid % BLOCKS_PER_ROW
    
    N_per_block = (N + BLOCKS_PER_ROW - 1) // BLOCKS_PER_ROW
    cols_start = block_col_idx * N_per_block
    
    # Initialize running top-P with 0
    running_top = tl.zeros([P], dtype=tl.uint64)
    
    steps = (N_per_block + B - 1) // B
    
    for s in range(steps):
        chunk_cols = cols_start + s * B + tl.arange(0, B)
        # Load values
        mask = (chunk_cols < N) & (chunk_cols < cols_start + N_per_block)
        vals = tl.load(X_ptr + row_idx * N + chunk_cols, mask=mask, other=-1e38)
        
        # Pack float to sortable uint32
        vals_u32 = vals.to(tl.uint32, bitcast=True)
        is_neg = (vals_u32 & 0x80000000) != 0
        mask_xor = tl.where(is_neg, 0xFFFFFFFF, 0x80000000)
        mapped = vals_u32 ^ mask_xor
        
        # Combine mapped float and column index
        packed = (mapped.to(tl.uint64) << 32) | chunk_cols.to(tl.uint64)
        
        # Find top-P of this chunk
        if P == 1:
            chunk_top = tl.expand_dims(tl.max(packed, axis=0), 0)
        else:
            chunk_top = tl.topk(packed, k=P)
        
        # Merge running_top and chunk_top
        joined = tl.join(running_top, chunk_top)
        combined = tl.reshape(joined, [2 * P])
        if P == 1:
            running_top = tl.expand_dims(tl.max(combined, axis=0), 0)
        else:
            running_top = tl.topk(combined, k=P)
        
    if SINGLE_PASS:
        # Unpack and write directly to output
        unpacked_mapped = (running_top >> 32).to(tl.uint32)
        is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
        orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
        unpacked_u32 = unpacked_mapped ^ orig_mask
        
        unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
        unpacked_idx = (running_top & 0xFFFFFFFF).to(tl.int64)
        
        out_cols = tl.arange(0, P)
        mask = out_cols < K
        tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x, mask=mask)
        tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx, mask=mask)
    else:
        # Write running_top to Workspace
        out_cols = tl.arange(0, P)
        tl.store(Workspace_ptr + (row_idx * BLOCKS_PER_ROW + block_col_idx) * P + out_cols, running_top)


@triton.jit
def topk_phase2_kernel(
    Workspace_ptr,
    Out_vals_ptr,
    Out_idxs_ptr,
    P: tl.constexpr,
    K: tl.constexpr,
    BLOCKS_PER_ROW: tl.constexpr,
    M: tl.constexpr,
):
    row_idx = tl.program_id(0)
    
    # Each row has BLOCKS_PER_ROW * P intermediate results in Workspace
    cols = tl.arange(0, M)
    
    packed = tl.load(Workspace_ptr + row_idx * M + cols)
    
    # Find top-K
    if K == 1:
        top_packed = tl.expand_dims(tl.max(packed, axis=0), 0)
    else:
        top_packed = tl.topk(packed, k=K)
    
    # Unpack
    unpacked_mapped = (top_packed >> 32).to(tl.uint32)
    is_pos_or_zero = (unpacked_mapped & 0x80000000) != 0
    orig_mask = tl.where(is_pos_or_zero, 0x80000000, 0xFFFFFFFF)
    unpacked_u32 = unpacked_mapped ^ orig_mask
    
    unpacked_x = unpacked_u32.to(tl.float32, bitcast=True)
    unpacked_idx = (top_packed & 0xFFFFFFFF).to(tl.int64)
    
    out_cols = tl.arange(0, K)
    tl.store(Out_vals_ptr + row_idx * K + out_cols, unpacked_x)
    tl.store(Out_idxs_ptr + row_idx * K + out_cols, unpacked_idx)


class Model(nn.Module):
    def __init__(self, batch: int, n: int, k: int):
        super().__init__()
        self.batch = batch
        self.n = n
        self.k

... (3766 more chars)

{
  "description": "Running check.py to confirm the correctness of our final solution",
  "command": "/workspace/.venv/bin/python check.py"
}

{
  "description": "Running benchmark.py to get the official scored peak fraction",
  "command": "/workspace/.venv/bin/python benchmark.py"
}

{
  "file_path": "framework.txt"
}

{
  "description": "Cleaning up temporary scratch files",
  "command": "rm test_triton.py tune.py tune_warps.py time_all.py"
}

{
  "title": "Final Verification and Summary",
  "summary": "Successfully designed, implemented, and optimized a custom top-k selection kernel in Triton for the RTX PRO 6000 (SM120 Blackwell). Utilized a mathematically rigorous float-to-sortable-uint32 bitwise mapping to pack floating-point values and their original column indices into 64-bit unsigned integers. Performed a two-pass parallel reduction utilizing Triton's highly-optimized bitonic top-k select primitives. Conducted automated sweeps to fine-tune `BLOCKS_PER_ROW`, chunk sizes, and warp counts (`num_warps`) for each target shape. Ach

... (298 more chars)