[jira] [Resolved] (ARROW-11758) [C++][Compute] Summation kernel round-off error

["Yibo Cai (Jira)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/ARROW-11758?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Yibo Cai resolved ARROW-11758.
------------------------------
    Fix Version/s: 4.0.0
       Resolution: Fixed

Issue resolved by pull request 9635
[https://github.com/apache/arrow/pull/9635]

> [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
>          Components: C++
>            Reporter: Yibo Cai
>            Assignee: Yibo Cai
>            Priority: Major
>              Labels: pull-request-available
>             Fix For: 4.0.0
>
>          Time Spent: 3h 20m
>  Remaining Estimate: 0h
>
> 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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