goldmedal commented on issue #10838:
URL: https://github.com/apache/datafusion/issues/10838#issuecomment-2156419089

   Hi @jayzhan211
   I tried to convert `ApproxPercentileCont`, but I encountered some 
challenges. `ApproxPercentileCont` creates the accumulator based on the 
`percentile` parameter, but I couldn't find a way to access this parameter when 
defining the UDAF.
   
https://github.com/goldmedal/datafusion/blob/24a08465e12bc07275cafe5310a7ac44898e39de/datafusion/physical-expr/src/aggregate/approx_percentile_cont.rs#L104
   
   The `AccumulatorArgs` doesn't carry the original argument expression, making 
it difficult to create the accumulator for `ApproxPercentileCont`.
   
https://github.com/goldmedal/datafusion/blob/24a08465e12bc07275cafe5310a7ac44898e39de/datafusion/expr/src/function.rs#L45
   
   I think we need another PR to address this issue. For now, I just moved 
`TDigest` and `ApproxPercentileAccumulator` in #10840 so that I can convert 
`approx_median` to a UDAF.


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