Algorithm                        tmin    tavg    tmax   (in us)
square root algo, optimized       161     176     191
brute force                       244     246     249
table based approximation           6     363     399
square root algo, unoptimized    1058    1077    1092

tested with input values from 0 to 4294840760, step size 10357.

but these two facts reveal that aginst what you think the original programmers were not stupid.

As I said before, the code was never intended for a '51, I just did that for fun. The "slowest" thing the code ever ran on was a 68000, which can (at least from a look at its instruction set) natively shift 32 bit variables, which speeds up the algorithm quite a bit since it eliminates library calls for the shifts and adds. The square root calculation is rarely needed (the main task of the code is doing FFTs) and space was usually more of a concern than CPU cycles.