This method avoids loss of precision by tracking multiple intermediate partial sums. Based on python's math.fsum
rxPythonFsum(numbers)A vector of numbers to sum.
Sum of numbers without loss of precision
The algorithm's accuracy depends on IEEE-754 arithmetic guarantees and the typical case where the rounding mode is half-even. On some non-Windows builds, the underlying C library uses extended precision addition and may occasionally double-round an intermediate sum causing it to be off in its least significant bit.
https://docs.python.org/2/library/math.html
https://code.activestate.com/recipes/393090/
https://github.com/python/cpython/blob/a0ce375e10b50f7606cb86b072fed7d8cd574fe7/Modules/mathmodule.c
Shewchuk, JR. (1996) Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates. http://www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps