Accurate Sum and Dot Product with New Instruction for High-Precision Computing on ARMv8 Processor

The accumulation of rounding errors can lead to unreliable results. Therefore, accurate and efficient algorithms are required. A processor from the ARMv8 architecture has introduced new instructions for high-precision computation. We have redesigned and implemented accurate summation and the accurate dot product. The number of floating-point operations has been reduced from 7 n − 5 and 10 n − 5 to 4 n − 2 and 7 n − 2 , compared with the classic compensated precision algorithms. It has been proven that our accurate summation and dot algorithms’ error bounds are γ n − 1 γ n cond + u and γ n γ n + 1 cond + u , where ‘cond’ denotes the condition number, γ n = n · u / ( 1 − n · u ) , and u denotes the relative rounding error unit. Our accurate summation and dot product achieved a 1.69× speedup and a 1.14× speedup, respectively, on a simulation platform. Numerical experiments also illustrate that, under round-towards-zero mode, our algorithms are as accurate as the classic compensated precision algorithms.