you can do the non smart way test it like I did(not recommended but I didnt really care) start car, pull the positive cable and see if the car stays on.
On new cars doing this will turn off the car as there are failsafes, but not in the e46.
take it to an alternator shop/ independent
"So I'm drifting away like a feather in air, letting my soul take me away from the hurt and despair.
So I'm, keepin' it vertical forever elevator, riding the escalator to something that is greater.."
Official E46 OT Podcast