Fast Multiple-Precision Integer Division Using Intel AVX-512

Abstract

This paper reports on the implementation of a large integer division method that uses Intel Advanced Vector Extensions 512 (AVX-512), which is a 512-bit Single Instruction Multiple Data (SIMD) instruction set, and proposes a modification to a conventional division algorithm that makes it more SIMD instruction-friendly. More specifically, we use the Integer Fused Multiply-Add AVX-512 (AVX-512IFMA) subset, which is an instruction set that works well with large integer multiplication, to compute large integer divisions via a multiplication-based approach with a reciprocal. For the division process, we apply the most basic algorithm and divide-and-conquer methods and then use several techniques to compute efficiently with SIMD instructions in our implementation. We then combine these techniques and methods to implement our division function so that it can flexibly handle various sizes. To evaluate the performance of our proposed implementation, we executed our division program and the GNU Multiple Precision Arithmetic Library (GMP) on a Cannon Lake microarchitecture processor. A comparison of the execution times for our division program and GMP with various sizes showed that our method resulted in performance improvements of 25% to 35% on average, thus indicating that SIMD instructions are effective for fast arbitrary precision integer divisions.