Zoltan Ivanfi commented on PARQUET-1222:

[~jbapple] Indeed, the proposed order does not match the IEEE 754 totalOrder 
for the following reasons:
* In case of subnormal values, different bit patterns may correspond to the 
same numeric value, similar to how one can write 0.005 as 0.5 * 10^-2 or 0.05 * 
10^-1 or ... The IEEE 754 totalOrder predicate orders these numerically equal 
values according to the exponents used in their representation. This 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. Since both the 
corresponding numeric values and their presentation to the user are identical, 
this would lead to behaviour that I consider incorrect, or at least unintuitive.
* No programming languages or libraries I know of implement the totalOrder 
predicate. I am also not aware of any hardware implementation, and if there 
were one, it would still be virtually impossible to use it without proper 
exposure through a library or some very low-level wizardry.
* The definition of the totalOrder predicate looks very complicated. I think 
any implementation is prone to be complicated, error-prone and inefficient.

The proposed order, on the other hand, is sufficient for sorting and seems to 
be easy to implement. If the regular (normally hardware-accelerated) floating 
point comparison operators can decide the order, then it returns those. 
Otherwise it orders by the exponent part of the bit pattern.

However, depending on one's point of view, the proposed ordering may not really 
be considered a total ordering as both zeros are equivalent to each other and 
all NaN are equivalent to each other as well. However, it is a (strict) weak 
ordering for sure and maybe the enum should be renamed as such. However, my 
understanding is that the only difference between weak ordering and total 
ordering is whether equivalence by ordering is the same as equality by value. 
But then the totalOrder defined by IEEE 754 is not a total order either, since 
it defines NaN-s of the same bit pattern to be equivalent for ordering, while 
it also defines a NaN value to not be equal to itself at the same time. Since 
the equality defined by IEEE 754 is already inconsistent in the mathematical 
sense (because of x != x), there really is no proper equality operation to use 
for judging whether the proposed ordering is weak or total. From a more 
practical point of view, we could consider an ordering weak if it is sufficient 
for sorting but not for hashing, while a total ordering would be sufficient for 
both. This, however, depends on how we calculate the hash values and is also 
entirely out of scope for min/max values or indexes.

> 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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