Question about integer out of range in function

Hello ppl,

I have a question about ERROR: integer out of range in one function.
I modify the generate_ulid() function to accept also UNIX timestamp as
input parameter.

I drop old function and make new one:

CREATE FUNCTION generate_ulid(fromtime bigint default 0)

Then I declare two new variables:

rand_int INTEGER;
new_time BIGINT;

and then begin:

BEGIN
-- 6 timestamp bytes
IF fromtime = 0 THEN
unix_time = (EXTRACT(EPOCH FROM NOW()) * 1000)::BIGINT;
ELSE
rand_int = (random() * 1000)::INT;
new_time = fromtime * 1000; -- here is line 19
unix_time = (new_time + rand_int)::BIGINT;
END IF;

(Yes, I know it's can be one line, but this is for debug)

When I start the function I receive error:

test_db=# select generate_ulid(extract(epoch from now())::int);
ERROR: integer out of range
CONTEXT: PL/pgSQL function generate_ulid(integer) line 19 at assignment

If I modify line 19 to : new_time = (fromtime * 1000)::BIGINT;

Everything is work. Well, until I write the email I figured out, but I
don't know is this normal behavior or just a problem.

I think, this is happened because I send INT to function
generate_ulid(extract(epoch from now())::int) but in function I expect
this to be BIGINT and my variable is cast automatic to INT.

My question is this normal and should input param not be treated as
bigint automatic as defined ? Did I can change whit this way input type
to other functions for example
get_random_bytes(34423423423423423424234::BIGINT) ?

Version: PostgreSQL 13.2 on x86_64-slackware-linux-gnu, compiled by
x86_64-slackware-linux-gcc (GCC) 10.3.0, 64-bit

Regards,
HS