Day 69: Occupancy-Based Tuning for Large Problems

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1459 字

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10 分钟

When working on large-scale kernels—like a massive matrix multiplication—achieving optimal occupancy on the GPU can significantly improve performance. However, register usage, shared memory allocation, and block size choices can all limit occupancy and reduce overall throughput. In this lesson, we’ll discuss how to tune large workloads, such as a matrix multiplication, by analyzing occupancy constraints using tools like Nsight Compute’s occupancy analysis.

Overview
Occupancy and Large-Scale Kernels
- a) What is Occupancy?
- b) Impact on Large Matrix Multiplication
Key Tuning Parameters
Implementation Steps for Matrix Multiplication Tuning
Code Example: Occupancy-Tuned Matrix Multiply
- Explanation & Comments
Performance Considerations & Common Pitfalls
Conceptual Diagram
References & Further Reading
Conclusion
Next Steps

1. Overview

Matrix multiplication is a staple in HPC and AI, often involving very large matrices that heavily stress the GPU’s compute and memory subsystems. Occupancy-based tuning aims to maximize the number of warps resident on each Streaming Multiprocessor (SM) by refining register usage, shared memory allocation, and kernel launch configurations. However, these optimizations must balance arithmetic intensity and memory access patterns to ensure improved performance without excessive spills or overhead.

2. Occupancy and Large-Scale Kernels

a) What is Occupancy?

Occupancy is the ratio of active warps per SM to the maximum possible warps the SM can support. High occupancy can help hide memory latency by enabling the GPU scheduler to switch to another warp when one warp is stalled, thus improving throughput.

b) Impact on Large Matrix Multiplication

For large matrix multiplies:

Arithmetic Intensity: The ratio of compute operations to memory operations is typically high, but memory inefficiencies can still cause stalls.
Resource Usage: Shared memory tile-based approaches (with register-blocked sub-tiles) can consume significant registers, limiting occupancy.

3. Key Tuning Parameters

a) Register Usage

Launch Bounds: Decorate your kernel with __launch_bounds__() to guide the compiler on maximum threads per block and register usage.
-maxrregcount: A compiler flag to limit the number of registers per thread, possibly raising occupancy but risking register spills to local memory.

b) Shared Memory Allocation

Tile Size: Larger tile-based matrix multiply might lead to heavy shared memory usage. Minimizing unused shared memory helps preserve occupancy.
Bank Conflicts: Even if you achieve high occupancy, excessive bank conflicts in shared memory can hamper performance.

c) Block and Grid Dimensions

Block Size: Typically a multiple of warp size (e.g., 256 or 128). Adjusting block size can find a sweet spot between occupancy and register usage.
Grid Size: Determined by the matrix dimensions, but ensuring each SM gets enough blocks to saturate the GPU remains key.

4. Implementation Steps for Matrix Multiplication Tuning

a) Baseline Kernel

Implement a tile-based matrix multiply that uses shared memory for sub-tiles of A and B.
Determine block size (e.g., 16×16 or 32×32 threads) and shared memory usage.

b) Using Nsight Compute’s Occupancy Analysis

Profile the baseline kernel.
Examine “Occupancy” metrics—compare achieved occupancy vs. theoretical occupancy.
Look for constraints: excessive registers or shared memory usage that limit active warps.

c) Iterative Optimization

Adjust block tile size to reduce register or shared memory usage if occupancy is too low.
Evaluate -maxrregcount or __launch_bounds__().
Re-profile to confirm if occupancy and performance improved.

5. Code Example: Occupancy-Tuned Matrix Multiply

Below is a simplified matrix multiplication kernel with a tile-based approach, annotated with potential occupancy-based tweaks.

cpp

// File: occupancy_tuned_matrix_mul.cu
#include <cuda_runtime.h>
#include <stdio.h>

// __launch_bounds__(128, 2) is an example to limit register usage 
// and hint to the compiler that each block has at most 128 threads 
// with at least 2 blocks per SM.
__launch_bounds__(128, 2)
__global__ void matrixMulKernel(const float* A, const float* B, float* C,
                                int N) {
    extern __shared__ float sdataA[]; // Tiled approach
    float* sdataB = &sdataA[blockDim.x * blockDim.y];

    int tx = threadIdx.x;
    int ty = threadIdx.y;
    int row = blockIdx.y * blockDim.y + ty;
    int col = blockIdx.x * blockDim.x + tx;
    float sum = 0.0f;

    // For demonstration, assume blockDim.x == blockDim.y = tileSize
    int tileSize = blockDim.x;

    for (int tile = 0; tile < N / tileSize; tile++) {
        // Load sub-tile of A, B into shared memory
        int A_idx = row * N + (tile * tileSize + tx);
        int B_idx = (tile * tileSize + ty) * N + col;

        sdataA[ty * tileSize + tx] = (row < N && tile * tileSize + tx < N) ?
                                     A[A_idx] : 0.0f;
        sdataB[ty * tileSize + tx] = (col < N && tile * tileSize + ty < N) ?
                                     B[B_idx] : 0.0f;

        __syncthreads();

        // Compute partial sums
        for (int k = 0; k < tileSize; k++) {
            sum += sdataA[ty * tileSize + k] * sdataB[k * tileSize + tx];
        }
        __syncthreads();
    }

    // Write result
    if (row < N && col < N) {
        C[row * N + col] = sum;
    }
}

int main() {
    // For demonstration: an NxN matrix, e.g., N=2048
    int N = 2048;
    size_t matrixSize = N * N * sizeof(float);

    float *d_A, *d_B, *d_C;
    cudaMalloc(&d_A, matrixSize);
    cudaMalloc(&d_B, matrixSize);
    cudaMalloc(&d_C, matrixSize);

    // ... host code to initialize and copy data omitted ...

    // Example: 16x16 tile
    dim3 block(16, 16);
    dim3 grid((N + block.x - 1)/ block.x,
              (N + block.y - 1)/ block.y);

    // Shared memory usage: 2 tiles of size tileSize^2 * sizeof(float)
    int sharedMemBytes = 2 * block.x * block.y * sizeof(float);

    // Launch kernel 
    matrixMulKernel<<<grid, block, sharedMemBytes>>>(d_A, d_B, d_C, N);
    cudaDeviceSynchronize();

    // ... copy results back, verify correctness ...
    // ... free memory, etc. ...
    return 0;
}

Explanation & Comments

__launch_bounds__(128, 2): This attribute is an occupancy optimization hint to the compiler, limiting block size to at most 128 threads and aiming for at least 2 blocks per SM.
Shared Memory: The kernel uses 2 sub-tiles (for A and B) each sized tileSize * tileSize.
Block Size: 16×16 is a common tile dimension for matrix multiplication, but it can be tuned for occupancy or arithmetic throughput.
Tile Loop: Each iteration loads a sub-tile of A and B, accumulates partial sums, and repeats until the entire dimension is covered.

6. Performance Considerations & Common Pitfalls

Register Usage: Overly large blocks or unrolled loops might inflate register usage, capping occupancy below the ideal.
Shared Memory: If you allocate too much, blocks may not all fit on an SM simultaneously.
Tuning: Sometimes a suboptimal occupancy can still yield the best performance if arithmetic intensity is high enough. Always measure real performance, not just theoretical occupancy.
Over-optimization: Attempting to forcibly raise occupancy with -maxrregcount can lead to register spills to local memory, negating any gains.

7. Conceptual Diagram

mermaid

flowchart TD
    A[Kernel Launch: matrixMulKernel<<<grid, block, sharedMem>>>]
    B[Thread block loads sub-tiles from A, B into shared memory]
    C[Compute partial sums tile by tile]
    D[Write partial sum to global memory (C)]
    E[Nsight Compute Occupancy Analysis -> Adjust tile/block]

    A --> B
    B --> C
    C --> D
    D --> E

Explanation:

Each block processes a tile of A and B in shared memory.
The final partial sum is written to global memory.
Occupancy analysis with Nsight Compute helps identify if resource usage is limiting concurrency.

8. References & Further Reading

9. Conclusion

Occupancy-based tuning is crucial for large, compute-intensive kernels like matrix multiplication. By balancing register usage, shared memory allocations, and block dimensions, you can achieve higher concurrency and better performance. Tools like Nsight Compute’s occupancy analysis help pinpoint resource constraints—be it registers or shared memory. Yet, real-world performance is ultimately measured by kernel runtime, so iterative testing and profiling remain key to truly optimizing large-scale GPU workloads.

10. Next Steps

Profile: Use Nsight Compute to verify if your matrix multiply kernel is limited by register usage, shared memory, or another factor.
Experiment: Try different block/tile sizes (e.g., 16×16, 32×16, etc.) and measure resulting occupancy and performance.
Explore Launch Bounds: Adjust __launch_bounds__() or -maxrregcount to see if capping register usage raises occupancy enough to improve runtime.
Analyze Memory Patterns: Confirm coalesced loads/stores for sub-tiles and reduce bank conflicts in shared memory.
Extend: Use the same approach for other large HPC kernels (e.g., multi-dimensional FFTs or reductions) that can benefit from occupancy-based tuning.



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## 文件历史

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Day 69: Occupancy-Based Tuning for Large Problems ​

Table of Contents ​

1. Overview ​

2. Occupancy and Large-Scale Kernels ​

a) What is Occupancy? ​

b) Impact on Large Matrix Multiplication ​

3. Key Tuning Parameters ​

a) Register Usage ​

b) Shared Memory Allocation ​

c) Block and Grid Dimensions ​

4. Implementation Steps for Matrix Multiplication Tuning ​

a) Baseline Kernel ​

b) Using Nsight Compute’s Occupancy Analysis ​

c) Iterative Optimization ​

5. Code Example: Occupancy-Tuned Matrix Multiply ​

Explanation & Comments ​

6. Performance Considerations & Common Pitfalls ​

7. Conceptual Diagram ​

8. References & Further Reading ​

9. Conclusion ​

10. Next Steps ​