emkornfield commented on issue #35576:
URL: https://github.com/apache/arrow/issues/35576#issuecomment-1547404763

   the first part of the error is down-casting from float64 (python default 
representation to)->float32
   ```
   a = pa.array([545803904.0], type=pa.float32())
   a
   <pyarrow.lib.FloatArray object at 0x3ebb737bb400>
   [
     545803900
   ]
   ```
   Same happens with numpy:
   ```
   numpy.float32(545803904.0)
   545803900.0
   ```
   
   The second part of the error I think is likely due to implementation which 
looks like we somehow might do an extra cast through an intermediate value:
   
   ```
   a = pa.array([545803900.0], type=pa.float64())
   print(a.cast(pa.decimal128(38, 18)))
   print(a.cast(pa.float32()).cast(pa.decimal128(38, 18)))
   ```
   gives:
   [
     545803899.999999976169013248
   ]
   [
     545803886.966396699654750208
   ]
   
   I think the second source of error might be: 
https://github.com/apache/arrow/blob/cd6e2a4d2b9373b942da18b4cc82cb41431764d9/cpp/src/arrow/util/decimal.cc#L158
   since this looks like it it is done in float space (instead of casting to 
double) which potentially causes further loss of precision.
   
   
   


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