High‐performance SIMD modular arithmetic for polynomial evaluation

Two essential problems in computer algebra, namely polynomial factorization and greatest common divisor computation, can be efficiently solved thanks to multiple evaluations two variables using modular arithmetic. In this article, we focus on the efficient computation of such one single CPU core. We first show how leverage SIMD (single instruction, data) computing for arithmetic AVX2 AVX-512 units, both intrinsics OpenMP compiler directives. Then manage increase operational intensity exploit instruction-level parallelism order compute efficiency these evaluations. All results end performance gains up about 5x 10x AVX-512.