Alias in the HAVING clause

I am in the middle of switching a bunch of queries over from MySQL to
PostgreSQL and have hit a little snag. The following query works fine
in MySQL but raises an error in postgres:

SELECT COUNT(*), id % 3 AS f1 FROM table GROUP BY f1 HAVING f1 <> 0;

It seems that Postgres does not recognize the alias in the HAVING
clause. Rewriting it like this works in postgres:

SELECT COUNT(*), id % 3 AS f1 FROM table GROUP BY f1 HAVING event_id % 3 <> 0;

I am wondering if I am missing something because this looks like my
expression (id % 3) is getting evaluated twice when it really only
should be done once. Now, this query is obviously watered down from
what I am really doing and the expression is fairly lengthy and
complex so I would prefer to not have to evaluate it more times than
necessary.

Is this the correct way to do this, or is there a better way / a way
to get PostgreSQL to recognize an alias in the HAVING clause?

Thanks,
Nate