In 2's complement arithmetic, the smallest negative number of a given size is one larger in magnitude than the largest positive number of the same size. For example, a long runs from -9223372036854775808 to 9223372036854775807. If you take the absolute value of Long.MIN_VALUE, there is no correct answer representable as a Long.
From the Java 5 API for Math.abs():
Note that if the argument is equal to the value of Long.MIN_VALUE, the most negative representable long value, the result is that same value, which is negative.
[ December 04, 2004: Message edited by: Mike Gershman ]