> Kahan’s summation algorithm Radford Neal (2015) has an approach to computing sums exactly (to the correct rounded floating point number) in less than twice t

> Kahan’s summation algorithm Radford Neal (2015) has an approach to computing sums exactly (to the correct rounded floating point number) in less than twice the time to do it naively. In some situations it can do work in parallel and saturate memory bandwidth, so takes roughly the same time: http://www.cs.toronto.edu/~radford/xsum.abstract.html http://www.cs.toronto.edu/~radford/xsum.abstract.html "Kahan’s (1965) method for reducing summation error (but without producing the exact result) was also tested on all systems. On modern 64-bit processors, computing the exact sum with the large superaccumulator method was faster than Kahan’s method for summations of more than about 1000 terms. Kahan’s method was significantly faster than the small superaccumulator method only for summations of less than about 100 terms."