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Posted to jira@arrow.apache.org by "Yibo Cai (Jira)" <ji...@apache.org> on 2021/02/25 06:12:00 UTC
[jira] [Assigned] (ARROW-11758) [C++][Compute] Summation kernel
round-off error
[ https://issues.apache.org/jira/browse/ARROW-11758?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Yibo Cai reassigned ARROW-11758:
--------------------------------
Assignee: Yibo Cai
> [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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