NextLA.jl

NextLA.jl is a high-performance, hardware-agnostic, and datatype-flexible dense linear algebra package implemented in Julia. It provides a unified API for linear algebra operations, enabling users to efficiently execute fundamental matrix computations across CPUs and GPUs without sacrificing performance.

🚀 Features

• Unified API: Implements LAPACK/BLAS subroutines in Julia, avoiding type- and hardware-specific implementations.
• Multi-Architecture Support: Efficiently runs on CPUs and GPUs, leveraging Julia's LLVM-based compilation.
• High Performance: Benchmarks show that Julia-based implementations achieve performance on par with or exceeding LAPACK/CUSOLVER.
• Broad Datatype Support: Supports Float64, Float32, Float16, complex numbers, and other numerical types seamlessly.
• Future-Proof & Composable: Designed for extensibility, allowing new data types and hardware architectures to be integrated with minimal modifications.

📌 Why Julia for Dense Linear Algebra?

Traditionally, linear algebra libraries have been optimized for Fortran and C, requiring separate implementations for different hardware and data types. NextLA.jl leverages Julia’s multiple dispatch, type inference, and metaprogramming capabilities to dynamically generate optimized machine code, making it a future-proof alternative.

📈 Performance

Benchmarks indicate that NextLA.jl achieves performance comparable to or better than state-of-art for medium to large problem sizes. Key highlights:

• Close to native performance across different data types.
• No need for separate CPU/GPU implementations—a single API works across both.
• Efficient parallel execution, taking advantage of Julia's multi-threading and GPU acceleration.

📚 References

@inproceedings{nextla1,
  title={{Synthesizing Numerical Linear Algebra using Julia}},
  author={Xuan, Sophie and Ringoot, Evelyne and Alomairy, Rabab and Tome, Felipe and Samaroo, Julian and Edelman, Alan},
  booktitle={2024 IEEE High Performance Extreme Computing Conference (HPEC)},
  year={2024},
  organization={IEEE}
}

@inproceedings{nextla2,
  title={{Toward Portable GPU Performance: Julia Recursive Implementation of TRMM and TRSM}},
  author={Vicki Carrica⋆, Maxwell Onyango⋆, Rabab Alomairy, Evelyne Ringoot, James Schloss, and Alan Edelman},
  booktitle={Asynchronous Many-Task Systems and Applications (WAMTA)},
  year={2025},
  organization={Springer Nature}
}

👥 Contributors

• Rabab Alomairy (@Rabab53)
• Sophie Xuan (@Azura-yuwi)
• Evelyne Ringoot (@evelyne-ringoot)
• Vicki Carrica (@vickicarrica)
• Maxwell Onyango (@maxmlewa)
• Julian Samaroo (@jpsamaroo)