NaN being equal to itself in PG probably isn't a huge deal (though it is quite surprising). Not supporting NaN or Infinity at all seems more likely to cause issues, but even then it's still niche. But not implementing floating point types to spec seems like such a weird omission
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MySQL's behavior here is especially weird. It absolutely implements IEEE 754 under the hood, including NaN not equaling itself. But you cannot insert NaN, Infinity, or -Infinity into a table, nor is there a literal form. So you can only observe this with bind params.
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Google BigQuery implements IEEE-754 for all finite values and all operations where at least one input is non-finite. Not sure the use case here but could be worth a try

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No use case. Curiosity of an orm maintainer
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