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

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

Yibo Cai created ARROW-11758:
--------------------------------

             Summary: [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


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



--
This message was sent by Atlassian Jira
(v8.3.4#803005)