Improving accuracy of summation using parallel vectorized Kahan's and Gill‐Møller algorithms.

The aim of this paper is to show that Kahan's and Gill‐Møller compensated summation algorithms that allow to achieve high accuracy of summing long sequences of floating‐point numbers can be efficiently vectorized and parallelized using Intel AVX‐512 intrinsics together with OpenMP constructs in order to utilize SIMD extension of modern multicore processors. Numerical experiments show that the new implementations of the algorithms achieve much better accuracy than ordinary summation in both double and single precision and their performance is comparable with the performance of the ordinary summation algorithm optimized automatically. The vectorized Gill‐Møller algorithm is faster than the vectorized Kahan's algorithm. However, in case of single precision, the accuracy of the Gill‐Møller algorithm is worse than Kahan's but it can be fixed by the use of mixed‐precision. Then the accuracy of both compensated summation algorithms is the same and the Gill‐Møller algorithm is still faster than Kahan's. [ABSTRACT FROM AUTHOR]