## Abstract

Dense General Matrix-Matrix (GEMM) multiplication is a core operation of the Basic Linear Algebra Subroutines (BLAS) library, and therefore, often resides at the bottom of the traditional software stack for many scientific applications. In fact, chip manufacturers give a special attention to the GEMM kernel implementation since this is exactly where most of the high-performance software libraries extract hardware performance. With the emergence of big data applications involving large data-sparse, hierarchically low-rank matrices, the off-diagonal tiles can be compressed to reduce the algorithmic complexity and the memory footprint. The resulting tile low-rank (TLR) data format is composed of small data structures, which retain the most significant information for each tile. However, to operate on low-rank tiles, a new GEMM operation and its corresponding API have to be designed on GPUs so that the data sparsity structure of the matrix can be exploited while leveraging the underlying TLR compression format. The main idea consists of aggregating all operations into a single kernel launch to compensate for their low arithmetic intensities and to mitigate the data transfer overhead on GPUs. The new TLR-GEMM kernel outperforms the cuBLAS dense batched GEMM by more than an order of magnitude and creates new opportunities for TLR advanced algorithms.

Original language | English (US) |
---|---|

Title of host publication | Euro-Par 2018 |

Subtitle of host publication | Parallel Processing - 24th International Conference on Parallel and Distributed Computing, Proceedings |

Editors | Massimo Torquati, Marco Aldinucci, Luca Padovani |

Publisher | Springer-Verlag |

Pages | 811-825 |

Number of pages | 15 |

ISBN (Print) | 9783319969824 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 24th International European Conference on Parallel and Distributed Computing, Euro-Par 2018 - Turin, Italy Duration: Aug 27 2018 → Aug 31 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 11014 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 24th International European Conference on Parallel and Distributed Computing, Euro-Par 2018 |
---|---|

Country | Italy |

City | Turin |

Period | 08/27/18 → 08/31/18 |

## Keywords

- GPU Computing
- Hierarchical low-rank matrix computations
- High performance computing
- KBLAS
- Matrix multiplication - GEMM

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)