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

["Joris Van den Bossche (Jira)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/ARROW-11758?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17289761#comment-17289761 ] 

Joris Van den Bossche edited comment on ARROW-11758 at 2/24/21, 8:11 AM:
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+1 on using pairwise summation. Also Julia uses that as the default sum. 
(only not fully sure it would be easy to use if we integrate with hash/grouped aggregations)


was (Author: jorisvandenbossche):
+1 on using pairwise summation. Also Julia uses that as the default 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
>            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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