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🚀 Performance Optimization

Tuning strategies, benchmark testing, and best practices.

Table of Contents

1. Performance Overview
   1. Core Performance Metrics
2. Kernel Selection Strategy
   1. 1. Scalar CSR Kernel
   2. 2. Vector CSR Kernel
   3. 3. Merge Path Kernel
   4. 4. ELL Kernel
3. Performance Tuning Guide
   1. 1. Auto Configuration (Recommended)
   2. 2. Manual Kernel Selection
   3. 3. Format Conversion
4. Benchmarking
   1. Running Benchmarks
   2. Example Output
   3. Custom Benchmark
5. Performance Optimization Best Practices
   1. 1. Memory Optimization
   2. 2. Execution Context Reuse
   3. 3. Batch Processing
   4. 4. Data Transfer Optimization
6. Benchmark Data
   1. NVIDIA RTX 3090 (Ampere) Test Results
   2. Different GPU Architecture Comparison
7. Troubleshooting
   1. Common Reasons for Poor Performance
   2. Performance Analysis Tools

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Performance Overview

GPU SpMV library achieves extreme performance through multiple kernel intelligent scheduling.

Core Performance Metrics

Metric	Description	Target
Bandwidth Utilization	Actual memory bandwidth / theoretical peak	> 60%
Compute Density	FLOPS / byte access	Matrix-dependent
Scalability	Performance growth with matrix size	Linear scaling

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Kernel Selection Strategy

1. Scalar CSR Kernel

Use Case: Very sparse matrices (avg_nnz < 4)

// Auto-selection
SpMVConfig config = spmv_auto_config(csr);
// config.kernel_type == KernelType::SCALAR_CSR

Performance Characteristics:

• Each thread processes one row
• Minimizes inter-thread coordination overhead
• Suitable for cases with very few non-zero elements

Bandwidth Utilization: ~40-50%

2. Vector CSR Kernel

Use Case: Moderate sparsity matrices (skewness < 10)

Performance Characteristics:

• Each warp collaboratively processes one row
• Coalesced memory access pattern
• Balanced load distribution

Bandwidth Utilization: ~65-75%

3. Merge Path Kernel

Use Case: Highly skewed matrices (skewness ≥ 10)

Performance Characteristics:

• Perfect load balancing
• Binary search partition points
• Adaptive to matrix features

Bandwidth Utilization: ~70-80%

4. ELL Kernel

Use Case: ELL format matrices

Performance Characteristics:

• Fully coalesced memory access
• Column-major storage
• Highest bandwidth utilization

Bandwidth Utilization: ~80-90%

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Performance Tuning Guide

1. Auto Configuration (Recommended)

// Let the library automatically select optimal kernel
SpMVConfig config = spmv_auto_config(csr);
SpMVResult result = spmv_csr(csr, d_x, d_y, &config, n);

Advantages:

• No manual tuning required
• Intelligent selection based on matrix features
• Suitable for most scenarios

2. Manual Kernel Selection

// Manually select for specific scenarios
SpMVConfig config;
config.kernel_type = KernelType::MERGE_PATH;
config.auto_select = false;

SpMVResult result = spmv_csr(csr, d_x, d_y, &config, n);

Use Cases:

• Known stable matrix features
• Need extreme performance
• Auto-selection results not ideal

3. Format Conversion

// CSR -> ELL conversion
ELLMatrix* ell = ell_create(num_rows, num_cols, max_nnz_per_row);
ell_from_csr(ell, csr);
ell_to_gpu(ell);

// ELL format usually performs better
SpMVResult result = spmv_ell(ell, d_x, d_y, n);

When to Convert:

• Matrix row lengths are uniform
• Non-zero elements per row variation < 20%
• Pursuing extreme performance

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Benchmarking

Running Benchmarks

#include <spmv/benchmark.h>

BenchmarkConfig config;
config.iterations = 100;      // 100 iterations
config.warmup = true;         // Warmup
config.print_details = true;  // Detailed information

spmv_benchmark(csr, &config);

Example Output

=== GPU SpMV Benchmark ===
Matrix: 10000 x 10000, nnz = 500000
Kernel: Vector CSR
Iterations: 100 (10 warmup)

Results:
  Avg:  2.34 ms
  Min:  2.12 ms
  Max:  2.89 ms
  Std:  0.15 ms

Bandwidth: 68.5 GB/s (70.2% of peak)
GFLOPS: 42.8

Custom Benchmark

#include <spmv/spmv.h>
#include <chrono>

void custom_benchmark(const CSRMatrix* csr, 
                     const float* d_x, 
                     float* d_y, 
                     int n,
                     int iterations) {
    // Warmup
    SpMVConfig config = spmv_auto_config(csr);
    for (int i = 0; i < 5; i++) {
        spmv_csr(csr, d_x, d_y, &config, n);
    }
    
    // Official test
    cudaDeviceSynchronize();
    auto start = std::chrono::high_resolution_clock::now();
    
    for (int i = 0; i < iterations; i++) {
        spmv_csr(csr, d_x, d_y, &config, n);
    }
    
    cudaDeviceSynchronize();
    auto end = std::chrono::high_resolution_clock::now();
    
    auto duration = std::chrono::duration_cast<std::chrono::microseconds>(
                        end - start).count();
    
    printf("Avg: %.3f ms\n", duration / 1000.0 / iterations);
}

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Performance Optimization Best Practices

1. Memory Optimization

// ✅ Recommended: Use RAII
void process() {
    CudaBuffer<float> d_x(1000000);
    CudaBuffer<float> d_y(1000000);
    // Automatic lifecycle management
}

// ❌ Avoid: Manual management
void process() {
    float *d_x, *d_y;
    cudaMalloc(&d_x, 1000000 * sizeof(float));
    cudaMalloc(&d_y, 1000000 * sizeof(float));
    // Easy to forget cudaFree
    cudaFree(d_x);
    cudaFree(d_y);
}

2. Execution Context Reuse

// ✅ Recommended: Reuse context
SpMVExecutionContext ctx;
for (int i = 0; i < 100; i++) {
    spmv_csr(csr, d_x, d_y, &config, n, &ctx);
    // Texture objects and cache configuration are reused
}

// ❌ Avoid: Create each time
for (int i = 0; i < 100; i++) {
    SpMVResult result = spmv_csr(csr, d_x, d_y, &config, n);
    // Repeatedly create texture objects
}

3. Batch Processing

// ✅ Recommended: Batch process multiple matrices
void process_batch(const std::vector<CSRMatrix*>& matrices) {
    for (auto* csr : matrices) {
        csr_to_gpu(csr);
        SpMVConfig config = spmv_auto_config(csr);
        spmv_csr(csr, d_x, d_y, &config, csr->num_rows);
    }
}

// ❌ Avoid: Process one by one
for (int i = 0; i < 100; i++) {
    CSRMatrix* csr = load_matrix(i);
    csr_to_gpu(csr);
    spmv_csr(csr, d_x, d_y, &config, n);
    csr_destroy(csr);
}

4. Data Transfer Optimization

// ✅ Recommended: Async transfer
cudaMemcpyAsync(d_x.data(), h_x.data(), 
                n * sizeof(float), 
                cudaMemcpyHostToDevice, 
                stream);

// ❌ Avoid: Sync transfer blocks
cudaMemcpy(d_x.data(), h_x.data(), 
           n * sizeof(float), 
           cudaMemcpyHostToDevice);

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Benchmark Data

NVIDIA RTX 3090 (Ampere) Test Results

Matrix Size	Non-Zero Elements	Kernel	Time (ms)	Bandwidth (GB/s)	Utilization
10K × 10K	500K	Vector CSR	2.34	68.5	70.2%
50K × 50K	2.5M	Merge Path	11.8	71.2	72.9%
100K × 100K	5M	Merge Path	23.5	69.8	71.5%
500K × 500K	25M	Merge Path	118.3	70.5	72.2%
1M × 1M	50M	Merge Path	235.7	69.1	70.8%

Different GPU Architecture Comparison

GPU Architecture	Representative Model	Theoretical Bandwidth	Actual Utilization
Volta	V100	900 GB/s	~65%
Turing	RTX 2080	448 GB/s	~68%
Ampere	RTX 3090	936 GB/s	~70%
Ada Lovelace	RTX 4090	1008 GB/s	~72%

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Troubleshooting

Common Reasons for Poor Performance

1. Not using auto configuration

   // ❌ Wrong
   SpMVConfig config;
   config.kernel_type = KernelType::SCALAR_CSR;  // Manually selected inefficient kernel
   

2. Data not transferred to GPU

   // ❌ Wrong
   csr_to_gpu(csr);  // Forgot to call
   spmv_csr(csr, d_x, d_y, &config, n);  // Executing on CPU data
   

3. Matrix size too small

   // Warning: 100x100 matrix has high overhead ratio
   CSRMatrix* csr = csr_create(100, 100, 500);
   

4. Frequent memory allocation

   // ❌ Wrong: Allocate in loop
   for (int i = 0; i < 100; i++) {
       CudaBuffer<float> buf(1000);  // Allocate each iteration
   }
   

Performance Analysis Tools

# Use nvprof for analysis
nvprof ./spmv_benchmark

# Use Nsight Systems
nsys profile ./spmv_benchmark

# Use Nsight Compute
ncu --kernel-name spmv ./spmv_benchmark

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Complete performance data see benchmarks/ directory