bit|varbit #, xor operator

Related to [1], I want to add an operator that returns the count of set
(or unset) bits in a bit|varbit input. Given the number of times people
ask "how can I get a count of NULL fields" and similar, I expect this to
become quite popular. The obvious choice would be to use #, but I was
rather surprised to discover # is already used for XOR.

I think ^ is a pretty standard convention for XOR, but I can understand
why we wouldn't want to just use that. But I also think the choice of #
is pretty unfortunate.

# is currently mixed between XOR and counting[2]. IMHO we should
disambiguate it. My bet is that the XOR versions are very seldom used
and could be renamed without much grumbling. The versions that actually
do counting are presumably more popular. I'm not sure about the
intersection versions.

Personally I think it was a mistake to use # for intersection. Range
doesn't do that (using * instead), and AFAICT PostGIS doesn't either
(preferring &). So I propose renaming those operators, as well as the
XOR ones. I think ^^ is pretty logical for XOR. I'm not sure about
intersect... * doesn't seem like a good idea, && is overlaps, maybe &*.

Related to this I'd also like to add a boolean XOR operator as that's a
relatively common request/question.

1:
https://www.postgresql.org/message-id/9f1db94a-fa18-5975-3a6c-6850fabb3865%40BlueTreble.com
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Jim Nasby, Data Architect, Blue Treble Consulting, Austin TX
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