Efficient sparse matrix multiple-vector multiplication using a bitmapped format

The problem of obtaining high computational throughput from sparse matrix multiple-vector multiplication routines is considered. Current sparse matrix formats and algorithms have high bandwidth requirements and poor reuse of cache and register loaded entries, which restrict their performance. We propose the mapped blocked row format: a bitmapped sparse matrix format that stores entries as blocks without a fill overhead, thereby offering blocking without additional storage and bandwidth overheads. An efficient algorithm decodes bitmaps using de Bruijn sequences and minimizes the number of conditionals evaluated. Performance is compared with that of popular formats, including vendor implementations of sparse BLAS. Our sparse matrix multiple-vector multiplication algorithm achieves high throughput on all platforms and is implemented using platform neutral optimizations.