If the algorithm of these functions executes literally, then bitshift is actually adding to the exponential segment of the double, and pow2 is the same as the operator. While bitshifts should theoretically have lower power consumption, the difference in the time they consume is very small and far less than the overhead of the function call itself.
Yes, the main amount of time you observe that bitshift and pow2 spend is on function calls. MATLAB's function calls are very expensive because they don't optimize simple functions inline like C++ does.
If you use the vectorization method to calculate:
n = 1e6;
x = floor(rand(1,n)*2^8);
tic;
x1=bitshift(x,16);
toc
tic;
x2=pow2(x,16);
toc
x=uint32(x);
tic;
x3= x*2^16;
toc
You will observe that, as I said, pow2 and operators consume almost the same amount of time. However, bitshift still consumes the most time, which may be due to the fact that MATLAB adds more logical judgment steps to bitshift.
An interesting way to compare this is to use the doc command to look at the document length of bitshift and pow2, and you will find that the bitshift document is longer. Although not absolutely, I believe that in general, the longer the document, the more likely the logic of a function to be more complex. This means that bitshift has to deal with more different and more complex scenarios than pow2, and these judgment operations take more time.
MATLAB's expensive function call overhead feature tells us to try to avoid frequent calls to functions in loops and make the most of the vectorization support features of the functions themselves.
