1. Is this a recommended approach for this sort of issue?  Is there another
approach that works better and requires less customization of the library?
2. Does POI already have a facility for adding new functions to the library or
overriding existing ones?


The feature you want is called User-Defined Function (UDF) and is supported by POI. A good example how to use UDF can be found in POI test cases:

https://svn.apache.org/repos/asf/poi/trunk/src/testcases/org/apache/poi/hssf/record/formula/eval/TestExternalFunction.java

This code was contributed a year back in https://issues.apache.org/bugzilla/show_bug.cgi?id=47809 Please read the last comment by Josh Micich to better understand how this API is organized.



I'll also throw this out there: my team might be able to contribute something to
POI that formalizes this - the ability to add or override existing functions
provided it doesn't force us to re-design/re-write large portions of POI.  As
such we're interested in knowing what would need to be done (assuming this is a
good idea).


Patches are always welcome. If you have an idea how to improve the work with UDF - please share it on poi-dev or submit a patch to Bugzilla.

Regards,
Yegor


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