Precise sum of floating point numbers

Question

I am aware of a similar question, but I want to ask for people opinion on my algorithm to sum floating point numbers as accurately as possible with practical costs.

Answer 1

Kahan's summation algorithm is significantly more precise than straightforward summation, and it runs in O(n) (somewhere between 1-4 times slower than straightforward summation depending how fast floating-point is compared to data access. Definitely less than 4 times slower on desktop hardware, and without any shuffling around of data).

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Alternately, if you are using the usual x86 hardware, and if your compiler allows access to the 80-bit long double type, simply use the straightforward summation algorithm with the accumulator of type long double. Only convert the result to double at the very end.

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If you really need a lot of precision, you can combine the above two solutions by using long double for variables c, y, t, sum in Kahan's summation algorithm.