Which is the fastest way to get the absolute value of a number

Question

Which is the fastest way to implement an operation that returns the absolute value of a number?

x=root(x²)

or

if !isPositiv         


        

Answer 1

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 .

Answer 2

The if variant will almost certainly be blindingly fast compared to the square root, since it normally translates to a conditional jump instruction at the machine code level (following the evaluation of the expression, which may be complex, but not in this case since it's a simple check for less than 0).

Taking the square root of a number is likely to be much slower (Newton's method, for example, would use many many if statements at the machine code level).

The likely source of confusion is the fact that if invariably lead to changing the instruction pointer in a non-sequential manner. This can slow down processors that pre-fetch instructions into a pipeline since they have to re-populate the pipeline when the address changes unexpectedly.

However, the cost of that would be minuscule compared to performing a square root operation as opposed to a simple check-and-negate.