jonahgao opened a new issue, #11596:
URL: https://github.com/apache/datafusion/issues/11596

   ### Describe the bug
   
   As pointed by @2010YOUY01 in 
https://github.com/apache/datafusion/pull/11571#discussion_r1685702554
   
   For binary expressions or multi-input functions , if their args are ordered 
but the `nulls_first` option in `SortOptions` differs, they are still very 
likely to be unordered.
   
   
   
   ### To Reproduce
   
   Need to examine the code. 
   
   - The methods of `SortProperties`, such as 
[add](https://github.com/apache/datafusion/blob/81d06f2e103385fe744fb909563d4fb4c4b13d49/datafusion/expr/src/sort_properties.rs#L48),
 `sub`, seem to not consider nulls_first.
   - Similar to 
[log.rs](https://github.com/apache/datafusion/blob/81d06f2e103385fe744fb909563d4fb4c4b13d49/datafusion/functions/src/math/log.rs#L84)
 (should be fixed in PR 11571), the implementation of 
`ScalarUDFImpl::output_ordering` also needs to be reviewed.
   
   ### Expected behavior
   
   _No response_
   
   ### Additional context
   
   _No response_


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