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

max: // Will put MAX(a,b) into a

a -= b;
a &= (~a) >> 31;
a += b;

And:

int a, b;

min: // Will put MIN(a,b) into a

a -= b;
a &= a >> 31;
a += b;

from here.

http://www.graphics.stanford.edu/~seander/bithacks.html#IntegerMinOrMax

r = x - ((x - y) & -(x < y)); // max(x, y)

You can have fun with arithmetically shifting (x - y) to saturate the sign bit, but this is usually enough. Or you can test the high bit, always fun.

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