Logging in function with exception

Hello,

I write funktions in pl/pgsql and want to abort it. For this I use raise
exception, to undo all changes for this transaction. Now I want to log
these exceptions somewhere.

DECLARE
a integer;
log_id integer;
BEGIN
SELECT a INTO b FROM c WHERE d = 10;
IF NOT FOUND THEN
INSERT INTO log (logtype, logtext)
VALUES ('error', 'Dit not found 10 in table')
RETURNING id INTO log_id;
RAISE EXCEPTION 'internal_error: %', log_id;
END IF;
-- anything else
END;

I know that these logs well be discard, if the commit rolls back.

Is there a possible way to implement something like this?

Thanks,
Gerhard