Fast exact summation using small and large superaccumulators

arxiv.org

31 points·nanis··7 comments

As someone who has worked with building, testing, and numerical software, this seems like a great thing. Generally floating point computations are effectively non-deterministic: you (or the compiler) change something that doesn't seem like it matters and all of a sudden your result changes. Having more methods available that give you the deterministically best right thing at little additional expense is great!

You might be interested in ReproBLAS too.(http://bebop.cs.berkeley.edu/reproblas/)

It uses a different approach than superaccumulators, which as far as I know was first explored for the purpose of determinizing parallel floating-point sums by the folks working on ExBLAS (https://exblas.lip6.fr/)

Was the software you worked on a general numerics platform, or something more specialised? I'm trying to learn more about the topic myself, from a finance perspective.

This technique seems like overkill for most finance applications - you can fit nearly any sensible currency amount into a 64-bit fixed-point number (or a 128-bit if you're doing whole-economy calculations).

Funny coincidence. I happened to point to some papers and code for superaccumulators in a StackOverflow answer yesterday: http://stackoverflow.com/a/41741276/392585

Thank you. That's where I saw this.

Sort/bucket the abosute value within some epsilon then merge pairwise in a binary tree.

Or split FloatMax into 32-2048 bins. Start all at zero. Add incoming numbers to the corresponding bin. If a bin goes out of range zero it and add the sum where it needs to go. When you are done keep adding the lowest magnitude bin to the next highest.

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