Computing the sparse matrix vector product using block-based kernels without zero padding on processors with AVX-512...

Area of Science:

• Computer Science
• Numerical Analysis
• High Performance Computing

Background:

• Sparse matrix-vector product (SpMV) is crucial for scientific applications.
• Existing block-based SpMV kernels achieve high performance but require zero padding.
• Zero padding complicates practical implementation and memory storage.

Purpose of the Study:

• To develop efficient SpMV kernels utilizing AVX-512 instruction sets.
• To enable block-based SpMV without zero padding in matrix storage.
• To enhance the performance of SpMV operations on modern CPU architectures.

Main Methods:

• Proposed new SpMV kernels leveraging the AVX-512 instruction set.
• Introduced mask-based sparse matrix formats and assembly-optimized kernels.
• Developed a predictive method for optimal kernel selection via interpolation.
• Compared performance against Intel MKL CSR and CSR5 on benchmark matrices.

Main Results:

• Achieved significant performance improvements for SpMV operations.
• Demonstrated effectiveness in both sequential and parallel execution scenarios.
• Eliminated the need for zero padding in block-based SpMV implementations.
• Validated performance gains on standard benchmark matrices.

Conclusions:

• The proposed AVX-512 kernels offer a practical and efficient solution for SpMV.
• The mask-based formats and predictive method enhance usability and performance.
• The open-source library SPC5 provides access to these optimized kernels.