Finding x from y = log₂(x) efficiently for calibration

[macilak]

Hello All,

I have a very impotant question for you. Any help is appreciated.

Given is a logarithmical function: y = log2x (2 is the base) and the y value is known.
I have to find out what is the x value in the fewest steps possible. It can be made by giving sample values for x and applying to the function, but the performance (timing) is a key value, so the process must be very quick. The known solution is to split the curve to lines and shrink the range of possibilities.

Later on I have to translate the solution into C++ and apply it for calibration.

Many thanks in advance for your help!

 

[Tide]

Are you constrained to solving the problem by iteration? You could just write $x=2^y$ and use the built-in functions.