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