[SPARK-55557][SQL][3.5] Hyperbolic functions should not overflow withlarge inputs#54803
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mgaido91 wants to merge 1 commit intoapache:branch-3.5from
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[SPARK-55557][SQL][3.5] Hyperbolic functions should not overflow withlarge inputs#54803mgaido91 wants to merge 1 commit intoapache:branch-3.5from
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… large inputs As mentioned in https://issues.apache.org/jira/browse/SPARK-55557, for large values (namely, larger than the square root of `Double.MAX:_VALUE`) the `asinh` and `acosh` functions return Infinity, due to overflow. This happens because of the `x * x` operation in the formula to compute them. However, for such large numbers, the expression can be simplified. Indeed, `x +\- 1` for such large numbers has no effect, since the precision is not enough to be sensitive to this operaiton. Hence, `log(x + sqrt(x * x +/- 1))` can be written as `log(2x) = (log(2) + log(x))` in such cases. Current code overflows and returns Infinity for asinh and acosh for large values. Yes, SQL with asinh and acosh with large values do not return infinity anymore. For large negative values as input of acosh, `NaN` is returned. Added UTs. No. Closes apache#54676 from mgaido91/SPARK-55557. Authored-by: Marco Gaido <mgaido@fbk.eu> Signed-off-by: Peter Toth <peter.toth@gmail.com>
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What changes were proposed in this pull request?
As mentioned in https://issues.apache.org/jira/browse/SPARK-55557, for large values (namely, larger than the square root of
Double.MAX:_VALUE) theasinhandacoshfunctions return Infinity, due to overflow. This happens because of thex * xoperation in the formula to compute them. However, for such large numbers, the expression can be simplified. Indeed,x +\- 1for such large numbers has no effect, since the precision is not enough to be sensitive to this operaiton. Hence,log(x + sqrt(x * x +/- 1))can be written aslog(2x) = (log(2) + log(x))in such cases.Why are the changes needed?
Current code overflows and returns Infinity for asinh and acosh for large values.
Does this PR introduce any user-facing change?
Yes, SQL with asinh and acosh with large values do not return infinity anymore. For large negative values as input of acosh,
NaNis returned.How was this patch tested?
Added UTs.
Was this patch authored or co-authored using generative AI tooling?
No.