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SQLite doesn't use indexes for bitwise clauses?
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Yes, I assumed bit expressions involved positive integers only indeed.  
I thought the bitwise operators required that. That's my only use-case for them in fact.

Perhaps the OP want to look into [expression-based indexes](https://sqlite.org/expridx.html) and/or [partial indexes](https://sqlite.org/partialindex.html) instead?  
That does assume his (or her) `?` values have very low cardinality.

Anyways, as I wrote, I was just thinking aloud.