Performance Analysis

Benchmark Methodology

Test Environment

Component	Specification
GPU	NVIDIA RTX 3090 (Ampere, SM 8.6)
Theoretical Bandwidth	936 GB/s
CUDA Version	12.0
CPU	AMD Ryzen 9 5900X
OS	Ubuntu 22.04 LTS

Metrics

• Execution Time: Median of 100 runs after 10 warmup iterations
• Effective Bandwidth: (bytes_read + bytes_written) / time
• Utilization: effective_bandwidth / theoretical_bandwidth

Matrix Test Suite

Matrix Type	Description	Generation Method
Diagonal	Non-zeros only on diagonal	Synthetic
Uniform	Random uniform distribution	sprand(n, n, density)
Power-Law	Scale-free distribution	sprand(n, n, density, 'power')
Band	Banded matrix	Synthetic
Real-World	SuiteSparse matrices	Downloaded

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Kernel Performance Comparison

By Matrix Pattern

Pattern	Size	NNZ	Scalar	Vector	Merge	ELL
Diagonal	100K	100K	37.2%	69.1%	72.4%	74.8%
Uniform	100K	5M	41.5%	71.8%	70.9%	82.3%
Power-Law	100K	5M	32.1%	45.6%	69.2%	34.7%
Band	100K	5M	28.4%	64.9%	58.1%	41.2%

Key Observations:

1. ELL excels on uniform matrices (82.3%) due to coalesced access
2. Merge Path is most robust across irregular patterns
3. Scalar CSR is only viable for very sparse matrices

Performance Visualization

Uniform Matrix (100K × 100K)

ELL Kernel

82.3%

Vector CSR

71.8%

Merge Path

70.9%

Scalar CSR

41.5%

Power-Law Matrix (100K × 100K)

Merge Path

69.2%

Vector CSR

45.6%

ELL Kernel

34.7%

Scalar CSR

32.1%

By Matrix Size

Size	NNZ	Scalar	Vector	Merge	ELL
10K × 10K	500K	42.1%	70.2%	68.5%	78.3%
100K × 100K	5M	36.7%	68.7%	71.5%	73.7%
1M × 1M	50M	34.8%	65.5%	70.8%	71.2%
10M × 10M	500M	33.2%	62.1%	69.4%	68.9%

Scaling Analysis:

• All kernels maintain >60% utilization at scale
• Vector CSR shows slight degradation at 10M (L2 cache pressure)
• Merge Path maintains consistent performance

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Kernel Selection Accuracy

The auto-selection algorithm achieves optimal or near-optimal selection in 95%+ of cases:

Selection Accuracy by Pattern

Pattern	Correct Selection	Performance vs. Optimal
Diagonal	98%	99.2%
Uniform	96%	98.5%
Power-Law	94%	97.1%
Mixed	92%	96.3%

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Memory Access Analysis

Coalescing Efficiency

Kernel	Avg. Threads per Transaction	Efficiency
Scalar CSR	1.2	Low
Vector CSR	8.4	Medium
Merge Path	12.1	High
ELL Kernel	16.0	Perfect

L2 Cache Hit Rate

Kernel	Hit Rate	Notes
Scalar CSR	45%	Poor locality
Vector CSR	72%	Moderate reuse
Merge Path	68%	Balanced
ELL Kernel	85%	Excellent locality

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Comparison with Reference Implementations

vs. cuSPARSE

Matrix	GPU SpMV	cuSPARSE	Speedup
Uniform 100K	71.5%	68.2%	1.05×
Power-Law 100K	69.2%	52.1%	1.33×
Real-World (webbase)	67.8%	61.4%	1.10×

Advantages:

• Better on irregular matrices (Merge Path algorithm)
• Automatic kernel selection (no manual tuning)
• Open source (full transparency)

vs. Generic SpMV

Matrix	GPU SpMV	Generic	Speedup
Uniform 100K	71.5%	35.2%	2.03×
Power-Law 100K	69.2%	28.7%	2.41×

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Performance Optimization Tips

1. Matrix Format Selection

// For uniform matrices, convert to ELL
if (is_uniform(csr)) {
    ELLMatrix* ell = csr_to_ell(csr);
    // Use ELL kernel for better performance
}

2. Batch Processing

For multiple SpMV operations, reuse the configuration:

SpMVConfig config = spmv_auto_config(csr);

for (int i = 0; i < num_iterations; i++) {
    spmv_csr(csr, x[i], y[i], &config, n);
}

3. Memory Pre-allocation

Pre-allocate output vectors to avoid repeated allocations:

CudaBuffer<float> y(num_rows);  // Allocate once
for (auto& x : inputs) {
    spmv_csr(csr, x, y.device_ptr(), &config, n);
    // Process y...
}

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Benchmark Reproduction

To reproduce the library build and collect your own timings:

# Clone and build
git clone https://github.com/AICL-Lab/gpu-spmv.git
cd gpu-spmv
cmake --preset release
cmake --build --preset release

After that, profile the exact spmv_csr or spmv_ell call path you care about inside your own driver or application. The repository no longer ships a dedicated benchmark executable because keeping measurement logic outside the core library makes the maintenance surface smaller.