Efficient implementation of fixed-point power (pow) function with argument constraints

I'm looking for an efficient implementation of the function pow(a, b), where a is limited to the interval (0,1), and b is >= 1 (both are real numbers—i.e., not necessarily integers).

If it helps, b is not a high number—let's say it is less than 10-20. That would open up the possibility of solving this problem iteratively, with a small number of iterations ~= b

The code should work on a 32-bit microcontroller, possibly without a floating-point unit (i.e., using a fixed-point implementation).

How can I implement such a function, optimized for the following constraints? I'm looking for the algorithm itself, so pseudocode is acceptable.

Read more here: https://stackoverflow.com/questions/64941736/efficient-implementation-of-fixed-point-power-pow-function-with-argument-const

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