Efficient high-precision integer multiplication on the GPU

Abstract

Dieguez AP, Amor M, Doallo R, Nukada A, Matsuoka S. Efficient high precision integer multiplication on the GPU. The International Journal of High Performance Computing Applications. 2022;36(3):356-369.© The Author(s) 2022. Publisher: SAGE Publications. https://doi.org/10.1177/10943420221077964[Abstract]: The multiplication of large integers, which has many applications in computer science, is an operation that can be expressed as a polynomial multiplication followed by a carry normalization. This work develops two approaches for efficient polynomial multiplication: one approach is based on tiling the classical convolution algorithm, but taking advantage of new CUDA architectures, a novelty approach to compute the multiplication using integers without accuracy lossless; the other one is based on the Strassen algorithm, an algorithm that multiplies large polynomials using the FFT operation, but adapting the fastest FFT libraries for current GPUs and working on the complex field. Previous studies reported that the Strassen algorithm is an effective implementation for “large enough” integers on GPUs. Additionally, most previous studies do not examine the implementation of the carry normalization, but this work describes a parallel implementation for this operation. Our results show the efficiency of our approaches for short, medium, and large sizes.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has been supported by the Ministry of Science and Innovation of Spain (PID2019-104184RB-I00), by the Galician Government and FEDER funds under the Consolidation Program of Competitive Reference Groups (UDC/GI-000265, ref. ED431C 2021/30), by the Consolidation Program of Competitive Research Units (ED431G2019/01), and by the FPU Program of the Ministry of Education of Spain (FPU14/02801). It is also partially supported by JST CREST [JPMJCR1303 and JPMJCR1687] and NVIDIA GPU Center of Excellence and conducted as research activities of AIST-TokyoTech Real World Big-Data Computation Open Innovation Laboratory (RWBC-OIL).Xunta de Galicia; ED431C 2021/3