Cadillac Repair: 2001 Deville engine smoke, engine smoke, cadillac deville

Question
Hello
I just purchased a 2001 Cadillac Deville with 131000 miles. When the engine is cold and you first crank it up it starts out with a little rough idle. When you accelerate,it starts smoking (white smoke with a strong gas smell) after the engine warms up the engine runs smooth with no smoke. Do have any idea what cause this.
Thanks you
Larry

Answer
IS or HAS the CHECK ENGINE light ever illuminated while driving the vehicle and or has any other lights illuminated or any messages from the message display center ?.

What work or diagnostics of ANYKIND WHAT-SO-EVER have been performed on the vehicle trying to fix this problem ?.