IFastSum.jl

correctly rounded summation (Yuhang Zhao's iFastSum)

####use:

sum_of_xs = iFastSum(x::Vector{AbstractFloat})

####notes:

This should work correctly for vectors of any size. The time used relative to sum() is somewhat host dependant. On one machine, I found it likely to range from ~2x (500 values) to ~4x-~6x (25_000 values) to ~9x-~12x (10_000_000 values). To get accurate relative timings, I used @CPUelapsed from CPUTime in a loop that looked for the shortest time. This implementation follows the original description. With two minor exceptions, there has been no effort to speed it up. It ran 8-12 times faster than sum using BigFloats.

####reference:

"Some Highly Accurate Basic Linear Algebra Subroutines" by Yuhang Zhao (c) 2010 McMaster University, Canada