A Quantitative Evaluation of Vector Transcendental Functions on ARMv8-Based Processors

Transcendental functions are important functions in various high performance computing applications. Because these functions are time-consuming and the vector units on modern processors become wider and more scalable, there is an increasing demand for developing and using vector transcendental functions in such performance-hungry applications. However, the performance of vector transcendental functions as well as their accuracy remain largely unexplored. To address this issue, we perform a comprehensive evaluation of two Single Instruction Multiple Data (SIMD) intrinsics based vector math libraries on two ARMv8 compatible processors. We first design dedicated microbenchmarks that help us understand the performance behavior of vector transcendental functions. Then, we propose a piecewise, quantitative evaluation method with a set of meaningful metrics to quantify their performance and accuracy. By analyzing the experimental results, we find that vector transcendental functions achieve good performance speedups thanks to the vectorization and algorithm optimization. Moreover, vector math libraries can replace scalar math libraries in many cases because of improved performance and satisfactory accuracy. Despite this, the implementations of vector math libraries are still immature, which means further optimization is needed, and our evaluation reveals feasible optimization solutions for future vector math libraries.