MaxGekk opened a new pull request #29784:
URL: https://github.com/apache/spark/pull/29784


   ### What changes were proposed in this pull request?
   1. Change the target error calculation according to the paper 
[Space-Efficient Online Computation of Quantile 
Summaries](http://infolab.stanford.edu/~datar/courses/cs361a/papers/quantiles.pdf).
 It says that the error `e = max(gi, deltai)/2` (see the page 59). Also this 
has clear explanation [ε-approximate 
quantiles](http://www.mathcs.emory.edu/~cheung/Courses/584/Syllabus/08-Quantile/Greenwald.html#proofprop1).
   2. Added a test to check different accuracies.
   3. Added an input CSV file `percentile_approx-input.csv.bz2` to the resource 
folder `sql/catalyst/src/main/resources` for the test.
   
   ### Why are the changes needed?
   To fix incorrect percentile calculation, see an example in SPARK-32908.
   
   ### Does this PR introduce _any_ user-facing change?
   Yes
   
   ### How was this patch tested?
   - By running existing tests in `QuantileSummariesSuite` and in 
`ApproximatePercentileQuerySuite`.
   - Added new test `SPARK-32908: maximum target error in percentile_approx` to 
`ApproximatePercentileQuerySuite`.


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