🧠 Advanced Cluster Algorithms

fn advanced_cluster_patterns[
    in_layout: Layout, out_layout: Layout, tpb: Int
](
    output: LayoutTensor[mut=True, dtype, out_layout],
    input: LayoutTensor[mut=False, dtype, in_layout],
    size: Int,
):
    """Advanced cluster programming using cluster masks and relaxed synchronization.
    """
    global_i = block_dim.x * block_idx.x + thread_idx.x
    local_i = thread_idx.x
    my_block_rank = Int(block_rank_in_cluster())
    block_id = Int(block_idx.x)

    shared_data = tb[dtype]().row_major[tpb]().shared().alloc()

    # Compute cluster mask for advanced coordination
    # base_mask = cluster_mask_base()  # Requires cluster_shape parameter

    # FIX: Process data with block_idx-based scaling for guaranteed uniqueness
    var data_scale = Float32(block_id + 1)
    if global_i < size:
        shared_data[local_i] = input[global_i] * data_scale
    else:
        shared_data[local_i] = 0.0

    barrier()

    # Advanced pattern: Use elect_one_sync for efficient coordination
    if elect_one_sync():  # Only one thread per warp does this work
        var warp_sum: Float32 = 0.0
        var warp_start = (local_i // 32) * 32  # Get warp start index
        for i in range(32):  # Sum across warp
            if warp_start + i < tpb:
                warp_sum += shared_data[warp_start + i][0]
        shared_data[local_i] = warp_sum

    barrier()

    # Use cluster_arrive for staged synchronization in sm90+
    cluster_arrive()

    # Only first thread in each block stores result
    if local_i == 0:
        var block_total: Float32 = 0.0
        for i in range(0, tpb, 32):  # Sum warp results
            if i < tpb:
                block_total += shared_data[i][0]
        output[block_id] = block_total

    # Wait for all blocks to complete their calculations in sm90+
    cluster_wait()

The advanced cluster patterns solution demonstrates a sophisticated three-level hierarchical optimization that combines warp, block, and cluster coordination for maximum GPU utilization:

Level 1: Warp-Level Optimization (Thread Election)

Data preparation and scaling:

var data_scale = Float32(block_id + 1)  # Block-specific scaling factor
if global_i < size:
    shared_data[local_i] = input[global_i] * data_scale
else:
    shared_data[local_i] = 0.0  # Zero-pad for out-of-bounds
barrier()  # Ensure all threads complete data loading

Warp-level thread election:

if elect_one_sync():  # Hardware elects exactly 1 thread per warp
    var warp_sum: Float32 = 0.0
    var warp_start = (local_i // 32) * 32  # Calculate warp boundary
    for i in range(32):  # Process entire warp's data
        if warp_start + i < tpb:
            warp_sum += shared_data[warp_start + i][0]
    shared_data[local_i] = warp_sum  # Store result at elected thread's position

Warp boundary calculation explained:

• Thread 37 (in warp 1): warp_start = (37 // 32) * 32 = 1 * 32 = 32
• Thread 67 (in warp 2): warp_start = (67 // 32) * 32 = 2 * 32 = 64
• Thread 199 (in warp 6): warp_start = (199 // 32) * 32 = 6 * 32 = 192

Election pattern visualization (TPB=256, 8 warps):

Warp 0 (threads 0-31):   elect_one_sync() → Thread 0   processes elements 0-31
Warp 1 (threads 32-63):  elect_one_sync() → Thread 32  processes elements 32-63
Warp 2 (threads 64-95):  elect_one_sync() → Thread 64  processes elements 64-95
Warp 3 (threads 96-127): elect_one_sync() → Thread 96  processes elements 96-127
Warp 4 (threads 128-159):elect_one_sync() → Thread 128 processes elements 128-159
Warp 5 (threads 160-191):elect_one_sync() → Thread 160 processes elements 160-191
Warp 6 (threads 192-223):elect_one_sync() → Thread 192 processes elements 192-223
Warp 7 (threads 224-255):elect_one_sync() → Thread 224 processes elements 224-255

Level 2: Block-level aggregation (Warp Leader Coordination)

Inter-warp synchronization:

barrier()  # Ensure all warps complete their elected computations

Warp leader aggregation (Thread 0 only):

if local_i == 0:
    var block_total: Float32 = 0.0
    for i in range(0, tpb, 32):  # Iterate through warp leader positions
        if i < tpb:
            block_total += shared_data[i][0]  # Sum warp results
    output[block_id] = block_total

Memory access pattern:

• Thread 0 reads from: shared_data[0], shared_data[32], shared_data[64], shared_data[96], shared_data[128], shared_data[160], shared_data[192], shared_data[224]
• These positions contain the warp sums computed by elected threads
• Result: 8 warp sums → 1 block total

Level 3: Cluster-level staged synchronization

Staged synchronization approach:

cluster_arrive()  # Non-blocking: signal this block's completion
# ... Thread 0 computes and stores block result ...
cluster_wait()    # Blocking: wait for all blocks to complete

Why staged synchronization?

• cluster_arrive() called before final computation allows overlapping work
• Block can compute its result while other blocks are still processing
• cluster_wait() ensures deterministic completion order
• More efficient than cluster_sync() for independent block computations

Advanced pattern characteristics

Hierarchical computation reduction:

1. 256 threads → 8 elected threads (32x reduction per block)
2. 8 warp sums → 1 block total (8x reduction per block)
3. 4 blocks → staged completion (synchronized termination)
4. Total efficiency: 256x reduction in redundant computation per block

Memory access optimization:

• Level 1: Coalesced reads from input[global_i], scaled writes to shared memory
• Level 2: Elected threads perform warp-level aggregation (8 computations vs 256)
• Level 3: Thread 0 performs block-level aggregation (1 computation vs 8)
• Result: Minimized memory bandwidth usage through hierarchical reduction

Synchronization hierarchy:

1. barrier(): Intra-block thread synchronization (after data loading and warp processing)
2. cluster_arrive(): Inter-block signaling (non-blocking, enables work overlap)
3. cluster_wait(): Inter-block synchronization (blocking, ensures completion order)

Why this is “advanced”:

• Multi-level optimization: Combines warp, block, and cluster programming techniques
• Hardware efficiency: Leverages elect_one_sync() for optimal warp utilization
• Staged coordination: Uses advanced cluster APIs for flexible synchronization
• Production-ready: Demonstrates patterns used in real-world GPU libraries

Real-world performance benefits:

• Reduced memory pressure: Fewer threads accessing shared memory simultaneously
• Better warp utilization: Elected threads perform focused computation
• Scalable coordination: Staged synchronization handles larger cluster sizes
• Algorithm flexibility: Foundation for complex multi-stage processing pipelines

Complexity analysis:

• Warp level: O(32) operations per elected thread = O(256) total per block
• Block level: O(8) aggregation operations per block
• Cluster level: O(1) synchronization overhead per block
• Total: Linear complexity with massive parallelization benefits