Summation algorithm

A summation algorithm is an algorithm that computes the sum of a finite list of numbers ${\textstyle \sum L[i]}$. It is especially relevant in floating-point arithmetic where the associative property $(a+b)+c=a+(b+c)$ does not hold like it does in (mathematical) real numbers, rational numbers, fixed-point numbers, and unsigned integers, so that the order of calculation can affect the final result. A closely related problem is the calculation of dot products, both of which have numerous proposed algorithms that differ in terms of simplicity, speed (single-thread and parallelized), and accuracy.