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Reproducible Floating-Point Summations

Floating-point sums are non-associative. That is,

(a+b)+c != a+(b+c)

This is problematic for performing reductions in which the ordering of the reduction or the partitioning of the data is non-deterministic, such as with internode communication or atomics.

This repo provides implementations of two papers which pre-round floating-point numbers to achieve reproducible results with (often) small reductions in accuracy versus a perfectly accurate summation (simulated in the test suite using Kahan summation). Both implementations' accuracy is likely to be greater than a simple summation.

The papers implemented are

  • Demmel and Nguyen (2013). "Fast Reproducible Floating-Point Summation".
  • Ahrens, Demmel, and Nguyen (2020). "Algorithms for Efficient Reproducible Floating Point Summation"

Building

mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=RelWithDebInfo ..
make