GPU SpMV

High-Performance CUDA Sparse Matrix-Vector Multiplication Library

4 optimized kernels · 2 sparse formats · 70%+ bandwidth utilization · Production-ready

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Quick Start · Features · Performance · Documentation · Contributing

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🎯 What is GPU SpMV?

GPU SpMV is a production-ready C++ library that accelerates sparse matrix-vector multiplication on NVIDIA GPUs. It automatically selects the optimal kernel based on matrix characteristics, delivering up to 70%+ of theoretical memory bandwidth.

Perfect for: Graph algorithms · Scientific computing · Machine learning · Data analytics

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✨ Why Choose GPU SpMV?

🚀 Intelligent Kernel Selection

Four optimized kernels with automatic selection based on matrix features:

Matrix Pattern	Kernel	Strategy	Performance
Very sparse (avg_nnz < 4)	Scalar CSR	1 thread/row	★★★☆☆
Uniform (skewness < 10)	Vector CSR	1 warp/row	★★★★☆
Skewed (skewness ≥ 10)	Merge Path	Perfect balance	★★★★★
ELL format	ELL Kernel	Coalesced access	★★★★★

📊 Multi-Format Support

• CSR (Compressed Sparse Row) - General-purpose sparse matrices
• ELL (ELLPACK) - Uniform row lengths with maximum performance

🎯 Production-Grade Quality

// RAII resource management - automatic cleanup
CudaBuffer<float> d_x(1000);  // GPU memory auto-freed
SpMVResult result = spmv_csr(csr, d_x, d_y, &config, n);

// Semantic error handling - clear diagnostics
if (result.error != SpMVError::SUCCESS) {
    printf("Error: %s\n", spmv_error_string(result.error));
}

• ✅ RAII Management - CudaBuffer, SpMVExecutionContext
• 🔍 Error Codes - Semantic SpMVError enum
• 🖥️ Cross-Platform - Windows & Linux
• 🔧 Modern Build - CMake Presets, one-click build
• ✅ Full Testing - Google Test + 100+ property tests

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🚀 Quick Start

Prerequisites

Component	Minimum	Recommended
CUDA Toolkit	11.0	12.0+
CMake	3.18	3.25+
NVIDIA GPU	CC 7.0 (Volta)	CC 8.6+ (Ampere)

3-Step Installation

# 1. Clone
git clone https://github.com/LessUp/gpu-spmv.git && cd gpu-spmv

# 2. Build
cmake --preset release && cmake --build --preset release

# 3. Test
ctest --preset default  # All tests should pass ✅

⏱️ Build time: ~2 minutes on modern machine

💻 30-Second Example

#include <spmv/spmv.h>

int main() {
    // 1. Create 3×3 sparse matrix: [1 0 2; 0 3 4; 0 0 5]
    float data[] = {1, 0, 2, 0, 3, 4, 0, 0, 5};
    CSRMatrix* csr = csr_create(3, 3, 5);
    csr_from_dense(csr, data, 3, 3);
    csr_to_gpu(csr);

    // 2. Prepare vectors
    CudaBuffer<float> d_x(3), d_y(3);
    float h_x[] = {1, 1, 1};
    cudaMemcpy(d_x.data(), h_x, sizeof(h_x), cudaMemcpyHostToDevice);

    // 3. Execute (auto-selects optimal kernel)
    SpMVConfig config = spmv_auto_config(csr);
    SpMVResult result = spmv_csr(csr, d_x.data(), d_y.data(), &config, 3);
    // result.time_ms ≈ 0.05ms, result.error == SUCCESS

    // 4. Get result: y = [3, 7, 5]
    csr_destroy(csr);
}

📚 More examples: Documentation Site

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📊 Performance

Benchmark on NVIDIA RTX 3090 (Ampere, 936 GB/s peak):

Matrix Size	NNZ	Kernel	Time	Bandwidth	Utilization
10K × 10K	500K	Vector CSR	2.3ms	68.5 GB/s	70.2%
100K × 100K	5M	Merge Path	23.5ms	69.8 GB/s	71.5%
1M × 1M	50M	Merge Path	235ms	69.1 GB/s	70.8%

# Run your own benchmarks
./build-release/spmv_benchmark

# Output example:
# GPU: NVIDIA GeForce RTX 3090
# Matrix: 100000x100000, NNZ: 5000000
# Avg time: 23.5 ms | Bandwidth: 69.8 GB/s (71.5% of peak)

📈 Full performance guide: Performance Optimization

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🏗️ Architecture

gpu-spmv/
├── include/spmv/          # Public headers (10 files)
│   ├── spmv.h             # Main SpMV interface
│   ├── csr_matrix.h       # CSR format
│   ├── ell_matrix.h       # ELL format
│   ├── cuda_buffer.h      # RAII GPU memory
│   ├── benchmark.h        # Performance testing
│   └── pagerank.h         # PageRank algorithm
├── src/                   # Implementations (7 files)
├── tests/                 # Google Test suite (8 files)
├── benchmarks/            # Performance benchmarks
└── specs/                 # SDD specifications

🔧 Spec-Driven Development: All features defined in /specs/ before implementation

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📚 Documentation

Complete documentation is available at https://lessup.github.io/gpu-spmv/:

Document	Description
📦 Installation Guide	System requirements, detailed installation
📚 API Reference	Complete API documentation, data structures
📝 Examples	7 complete code examples (basic → advanced)
🚀 Performance Guide	Tuning strategies, benchmark data
🏗️ Architecture	System design, kernel selection
📋 Changelog	Version history, migration guide

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🧪 Testing

# Run all tests
ctest --preset default

# Or run directly
./build-release/spmv_tests

# Run specific tests
./build-release/spmv_tests --gtest_filter="CSR*"
./build-release/spmv_tests --gtest_filter="ELL*"

Test Coverage:

• ✅ CSR/ELL format conversion
• ✅ SpMV computation correctness (vs CPU reference)
• ✅ Dimension validation
• ✅ Kernel selection logic
• ✅ Bandwidth metrics
• ✅ PageRank invariants
• ✅ 100+ property-based tests with random matrices

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💡 Real-World Application: PageRank

#include <spmv/pagerank.h>

// Build adjacency matrix for graph
CSRMatrix* adj = build_graph_adjacency();
csr_to_gpu(adj);

// Run PageRank
PageRankConfig config = {.damping = 0.85f, .tolerance = 1e-6f};
PageRankResult result = pagerank(adj, &config);

// Get top-10 ranked nodes
auto top_10 = get_top_k(result, 10);
for (const auto& node : top_10) {
    printf("Node %d: %.6f\n", node.id, node.rank);
}

pagerank_free(&result);
csr_destroy(adj);

📊 Use cases: Social network analysis · Web search · Recommendation systems · Fraud detection

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🤝 Contributing

We welcome contributions! GPU SpMV follows Spec-Driven Development - specs are the single source of truth.

Quick Contributing Guide

1. 🍴 Fork the repository
2. 📖 Read specs in /specs/ for the feature you want
3. 🌿 Create branch (git checkout -b feature/your-feature)
4. 📝 Update specs first (if modifying behavior)
5. 💻 Implement code following spec
6. ✅ Run tests (ctest --preset default)
7. 🚀 Open PR with spec changes

📋 Full guide: CONTRIBUTING.md

Development Setup

# Format code (required before commit)
find src include tests benchmarks -type f \( -name "*.cpp" -o -name "*.h" -o -name "*.cu" \) \
  | xargs clang-format -i

# Build & test
cmake --preset default && cmake --build --preset default && ctest --preset default

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📄 License

MIT License © 2024-2026 LessUp. See LICENSE for details.

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🙏 Acknowledgments

• Algorithm based on Merge-based Parallel SpMV by Merrill & Garland (NVIDIA)
• CUDA optimizations from NVIDIA official documentation
• Inspired by cuSPARSE and modern sparse library design patterns

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_{Built with ❤️ by the GPU SpMV contributors}

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