Another way is just to add d to the exponent bits. Probably fastest to do this in a mex routine where edge checking can easily be done and of course you can multithread it, but in m-code one can use typecast to demonstrate the process. E.g.,
x = rand(1000000,1);
d = 44;
tic
y1 = pow2(x,d);
toc
tic
y2 = x * 2^d;
toc
tic
y = typecast(x,'uint64'); % interpret double bits as uint64
p = bitshift(uint64(d),52); % shift d into exponent bits location (demo assumes d >= 0)
y3 = typecast(y+p,'double'); % but no edge checking here to see if we overrun exponent bits
toc
max(abs(y1-y2))
max(abs(y1-y3))
A production algorithm would have to account for overrunning to inf, or underrunning to denormals, etc. But if you are going to go through all the trouble of checking the overrun or underrun, you may as well just use the standard multiply instead because all of that is built in to the chip microcode.
