Abstract
Several accurate algorithms to sum IEEE-754 floating-point num- bers have been recently published. The recent contributions by Rump, Ogita and Oishi and the newest ones proposed by Zhu and Hayes are examples of accurate summation algorithms. Some of these even compute the faithful or the correct rounding of the exact sum, i.e. the most accurate value with respect to the finite precision of the floating- point arithmetic. This computed sum does not suffer anymore from the condition number of the summation. In such cases, the run-time performances and the memory prints become the discriminant properties to decide which algorithm is best. In this paper we focus on the reliability of the run-time performance measure of such core algorithms. We explain how right Rump when he writes "Measuring the computing time of summation algorithms in a high-level language on today's architectures is more of a hazard than scientific research." Neither the classical flop count nor hardware counter based measures are satisfactory here. We propose to analyze the instruction level parallelism of these algorithms to reliably evaluate their performance potential. We use PerPI, a software tool that automatizes an almost machine independent instruction-level parallelism analysis. We study recent accurate summation algorithms with a detailed focus on the two newest faithful ones. We illustrate and discuss why PerPI provides a more reliable performance analysis, the remaining weakness and how to improve confidence for future contributions in this area.