[ARROW-10263] [C++][Compute] Improve numerical stability of variances merging

• Type: Improvement
• Status: Resolved
• Priority: Major
• Resolution: Fixed
• Fix Version/s: 3.0.0
• Component/s: C++
• Labels: pull-request-available
• External issue URL: https://github.com/apache/arrow/issues/26259
• Assignee: Yibo Cai
• Reporter: Yibo Cai
• Created: 10/Oct/20 07:12
• Updated: 11/Jan/23 08:12
• Resolved: 13/Oct/20 09:11

Description

For chunked array, variance kernel needs to merge variances.
Tested with two single value chunk, [40000008000000490], [40000008000000400]. The merged variance is 3872. If treated as single array with two values, the variance is 3904, same as numpy outputs.
So current merging method is not stable in extreme cases when chunks are very short and with approximate mean values.

Issue Links

• links to: GitHub Pull Request #8437