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https://issues.apache.org/jira/browse/PARQUET-1222?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16376924#comment-16376924
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Zoltan Ivanfi commented on PARQUET-1222:
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[~jbapple] The proposed order was intentionally different from IEEE 754
totalOrder, because of the following rules of totalOrder:
{noformat}
3) If x and y represent the same floating-point datum:
i) If x and y have negative sign,
totalOrder(x, y) is true if and only if the exponent of x ≥ the
exponent of y
ii) otherwise
totalOrder(x, y) is true if and only if the exponent of x ≤ the
exponent of y.
{noformat}
This has led me to believe that different bit patterns may correspond to the
same numeric value, in which case considering them different would be
problematic, as it could lead to row groups being dropped or not based on what
bit pattern was used to save the data and what bit pattern is used for looking
them up. However, thinking more about it, it seems to me that apart from +0/-0
and the various NaNs, all other bit patterns correspond to different numbers.
Since the opposite assumption was the reason for the proposed order, I am
removing it for now.
> 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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