The Xsum package is a Julia wrapper around Radford Neal's xsum package
for exactly rounded double-precision floating-point summation. The xsum algorithm takes n double precision (Float64 or smaller) floating-point values as input and computes the "exactly rounded sum" — equivalent to summing the values in infinite precision and rounding the result to the nearest Float64 value.
By clever use of additional precision, xsum can compute the exactly rounded sum only a few times more slowly than the naive summation algorithm (or the pairwise summation used in the built-in sum function), much faster than using generic arbitrary precision (like BigFloat operations).
The Xsum package provides a function xsum to perform the summation. To use it, simply do:
using Xsum
xsum(iterator)where you can pass any iteratable collection (arrays, generators, tuples, etcetera). Real or complex collections can be summed, but note that each element is converted to double precision (Float64 or ComplexF64) before it is summed, and the result is always double precision.
The variant xsum(function, iterator) is also supported, similar to sum(function, iterator), which sums the result of the
given function applied to each element of the iterator.