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https://issues.apache.org/jira/browse/ARROW-11758?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17292078#comment-17292078
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Yibo Cai commented on ARROW-11758:
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Implemented recursive and non-recursive pairwise summation, also naive
summation.
Naive summation suffers from severe round-off errors, and worse performance.
*Non-recursive pairwise summation* is of best performance, it above 1x faster
than recursive one. We should adopt it.
Details at https://github.com/cyb70289/sum/
> [C++][Compute] Summation kernel round-off error
> -----------------------------------------------
>
> Key: ARROW-11758
> URL: https://issues.apache.org/jira/browse/ARROW-11758
> Project: Apache Arrow
> Issue Type: Bug
> Reporter: Yibo Cai
> Assignee: Yibo Cai
> Priority: Major
>
> From below test, summation kernel is of lower precision than numpy.sum.
> Numpy implements pairwise summation [1] with O(logn) round-off error, better
> than O(n) error from naive summation.
> *sum.py*
> {code:python}
> import numpy as np
> import pyarrow.compute as pc
> t = np.arange(321000, dtype='float64')
> t2 = t - np.mean(t)
> t2 *= t2
> print('numpy sum:', np.sum(t2))
> print('arrow sum:', pc.sum(t2))
> {code}
> *test result*
> {noformat}
> # Verified with wolfram alpha (arbitrary precision), Numpy's result is
> correct.
> $ ARROW_USER_SIMD_LEVEL=SSE4_2 python sum.py
> numpy sum: 2756346749973250.0
> arrow sum: 2756346749973248.0
> $ ARROW_USER_SIMD_LEVEL=AVX2 python sum.py
> numpy sum: 2756346749973250.0
> arrow sum: 2756346749973249.0
> {noformat}
> [1] https://en.wikipedia.org/wiki/Pairwise_summation
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