# Why is pow2() slow? Fastest way?

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Jim Svensson on 12 Oct 2023
Edited: Jim Svensson on 13 Oct 2023
The pow2(x, d) built in function seems unreasonable slow with a floating point vector x. It is about ten times slower than just doing x*2^d.
Is it like that because the used cpu instruction can only operate on one float at a time, but multiplication can be vectorized?
Is there a faster (fastest) way to scale a floating point vector by a power of 2?

James Tursa on 12 Oct 2023
Edited: James Tursa on 12 Oct 2023
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
Elapsed time is 0.015516 seconds.
tic
y2 = x * 2^d;
toc
Elapsed time is 0.005390 seconds.
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
Elapsed time is 0.012423 seconds.
max(abs(y1-y2))
ans = 0
max(abs(y1-y3))
ans = 0
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.

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