Which is the fastest way to implement an operation that returns the absolute value of a number?
x=root(x²)
or
if !isPositiv
Which is the fastest way to get the absolute value of a number
I think the "right" answer isn't here actually. The fastest way to get the absolute number is probably to use the Intel Intrinsic. See https://software.intel.com/sites/landingpage/IntrinsicsGuide/ and look for 'vpabs' (or another intrinsic that does the job for your CPU). I'm pretty sure it'll beat all the other solutions here.
If you don't like intrinsics (or cannot use them or ...), you might want to check if the Compiler is smart enough to figure out if a call to 'native absolute value' (std::abs in C++ or Math.Abs(x) in C#) will change automagically into the intrinsic - basically that involves looking at the disassembled (compiled) code. If you're in a JIT, be sure that JIT optimizations aren't disabled.
If that also doesn't give you the optimized instructions, you can use the method described here: https://graphics.stanford.edu/~seander/bithacks.html#IntegerAbs .