I have been looking for a Julia equivalent of Python’s fsum and have thus far been unable to find one. Is there an implementation already available? If not I will write my own and put it on Github for others to use. From the Python docs: math.fsum ( iterable ) Return an accurate floating point su…

[image] StefanKarpinski: See also Radford Neal’s paper on exact summation with superaccumulators: https://arxiv.org/abs/1505.05571 If someone wants to implement exact summation, it might be worth comparing different approaches. I put together a Julia wrapper for his C code at: [im…

Not my idea, I’ve only described the technique as told here - as far as I understand, any derivation of GPL’d code has to be GPL’d itself. By describing the algorithm with various sources without directly translating it to make it as easy as possible to reimplement it, it’s possible to (somewhat) ci…

Thanks for the feedback everyone — looks like I have plenty of alternatives to choose from at the moment. The default sum function in Julia is also quite accurate because it uses pairwise summation I didn’t realize the regular sum function uses pairwise summation, this will probably be adequate…

[image] Sukera: Not my idea, I’ve only described the technique as told here - as far as I understand, any derivation of GPL’d code has to be GPL’d itself Please do not do that. Translating GPL code to pseudocode that “looks suspiciously like Python” and then having someone else translate that…

[image] anon32405968: I need to hand in a PhD thesis in the 2 months time so it sounds like someone else will get to implementing Shewchuck’s (or Neal’s) algorithm before me. What better time for procrastination? :grimacing:

(Note that the published code by Radford is not GPL—in fact, it has no license statement at all, which means that you cannot redistribute it, or code derived from it, in any form. Clean-room re-implementation is not about “GPL avoidance,” it’s about working around copyright law’s definition of “deri…

A Kahan / Pairwise polyalgorithm seems like it could still be pretty fast, it might be +15*3 operations for summing 256 numbers depending on where you switch. Not sure how much extra precision you’d get

Pairwise summation is the default in Julia; it is just as fast as naive summation and much more accurate. Kahan summation is even more accurate but significantly slower, which is why it is not the default.

It’s a pretty neat trick too, and definitely a hard default to argue against. I was just noticing that each pass of the pairwise sum makes a partial Kahan sum on the remaining values 50% cheaper Another approach function finiteDif_sum(arr, d= 0.0) x = 0.0; y=0.0; y += d; for i in arr x =…

I have posted a copy of Radford’s paper with all C code removed. https://github.com/JeffreySarnoff/SuperaccumulatorPaperNoC/blob/master/superaccumulator.pdf

Radford’s C code has now been posted under an MIT license: gitlab.com/radfordneal/xsum

Julia equivalent of Python's "fsum" for floating point summation

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Julia equivalent of Python's "fsum" for floating point summation

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