argument type problem with plpgsql function

I wrote a little function that has to work with big numbers

CREATE OR REPLACE FUNCTION blast_evalue(seq_len bigint, db_size bigint,
bit_score double precision)
RETURNS double precision AS $$
BEGIN
RETURN 2^(bit_score) * db_size * seq_len;
END;
$$
LANGUAGE 'plpgsql'
IMMUTABLE
RETURNS NULL ON NULL INPUT;

but it doesn't work properly unless I cast the db_size parameter when I call
the function:

select blast_evalue(273, 8903836, -55.4546);
blast_evalue
--------------
2430747228 <- wrong number. This is 273 * 8903836
(1 row)

select blast_evalue(273, 8903836::bigint, -55.4546);
blast_evalue
---------------------
4.9231356421437e-08 <- that's correct
(1 row)

I don't understand why the cast is necessary. Is there a way to make this
work without it?

Thanks

Luca