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https://issues.apache.org/jira/browse/PARQUET-1222?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16373429#comment-16373429
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Jim Apple commented on PARQUET-1222:
------------------------------------

I do not think the order proposed matches the IEEE 754 totalOrder. It would be 
good to match that order so as to avoid creating yet one more thing for users 
to track. Also, it is possible that the IEEE totalOrder is also faster in some 
hardware.

I haven't checked, but it is possible that IEEE-754 is actually a 
lexicographical compare of the bit representations in some endianess or another.

> Definition of float and double sort order is ambigious
> ------------------------------------------------------
>
>                 Key: PARQUET-1222
>                 URL: https://issues.apache.org/jira/browse/PARQUET-1222
>             Project: Parquet
>          Issue Type: Bug
>          Components: parquet-format
>            Reporter: Zoltan Ivanfi
>            Priority: Critical
>             Fix For: format-2.5.0
>
>         Attachments: ordering.png
>
>
> Currently parquet-format specifies the sort order for floating point numbers 
> as follows:
> {code:java}
>    *   FLOAT - signed comparison of the represented value
>    *   DOUBLE - signed comparison of the represented value
> {code}
> The problem is that the comparison of floating point numbers is only a 
> partial ordering with strange behaviour in specific corner cases. For 
> example, according to IEEE 754, -0 is neither less nor more than \+0 and 
> comparing NaN to anything always returns false. This ordering is not suitable 
> for statistics. Additionally, the Java implementation already uses a 
> different (total) ordering that handles these cases correctly but differently 
> than the C\+\+ implementations, which leads to interoperability problems.
> TypeDefinedOrder for doubles and floats should be deprecated and a new 
> TotalFloatingPointOrder should be introduced. The default for writing doubles 
> and floats would be the new TotalFloatingPointOrder. The proposed ordering is 
> the following:
>  * -∞
>  * negative numbers in their natural order
>  * -0 and +0 in the same equivalence class \(!)
>  * positive numbers in their natural order
>  * +∞
>  * all NaN values, including the negative ones \(!), in the same equivalence 
> class \(!)
> This ordering should be effective and easy to implement in all programming 
> languages. A visual representation of the ordering of some example values:
> !ordering.png|width=640px!
> For reading existing stats created using TypeDefinedOrder, the following 
> compatibility rules should be applied:
> * When looking for NaN values, min and max should be ignored.
> * If the min is a NaN, it should be ignored.
> * If the max is a NaN, it should be ignored.
> * If the min is \+0, the row group may contain -0 values as well.
> * If the max is -0, the row group may contain \+0 values as well.



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