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