Mathematically Find Max Value without Conditional Comparison

I guess this one would be the most simplest if we manage to find difference between two numbers (only the magnitude not sign)

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

where |a-b| is a magnitude of difference between a and b.

finding the maximum of 2 variables:

max = a-((a-b)&((a-b)>>31))

where >> is bitwise right-shift (also called SHR or ASR depeding on signedness).

Instead of 31 you use the number of bits your numbers have minus one.