What complexity are operations on BigInteger?

There is a new "better" BigInteger class that is not being used by the sun jdk for conservateism and lack of useful regression tests (huge data sets). The guy that did the better algorithms might have discussed the old BigInteger in the comments.

Here you go http://futureboy.us/temp/BigInteger.java

If you look at the code for BigInteger (provided with JDK), it appears to me that multiply(..) has O(n^2) (actually the method is multiplyToLen(..)). The code for the other methods is a bit more complex, but you can see yourself.

Note: this is for Java 6. I assume it won't differ in Java 7.