How do I programmatically return the max of two integers without using any comparison operators and without using if, else, etc?

Question

How do I programmatically return the maximum of two integers without using any comparison operators and without using if, else, etc?

Answer 1

In the math world:

max(a+b) = ( (a+b) + |(a-b)| ) / 2
min(a-b) = ( (a+b) - |(a-b)| ) / 2

Apart from being mathematically correct it is not making assumptions about the bit size as shifting operations need to do.

|x| stands for the absolute value of x.

Comment:

You are right, the absolute value was forgotten. This should be valid for all a, b positive or negative