Optimizations on synchronized methods in java/C++

I was wondering whether any optimizations are automatically done by
the compiler or VM in Java in classes where methods are defined as
synchronized. I'm working with a library where a typical function is
defined so,


class Foo
{
private int a = 0;
private int b = 0;
public synchronized doSomethingWithA( int var )
{
        int tmp = some_function( var ); // heavy computation
        a += tmp;
}
public synchronized doSomethingWithB( int var )
{
        int tmp = some_function( var ); // heavy computation
        b += tmp;
}
};


Can the compiler see that the first statement in the methods are local
and therefore not lock the object for that statement, and hold the
lock only for the actual addition part, so that it saves time?

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