As explained in
the previous section, the n-root calculation is the most relevant part of the described fractional exponentiation algorithm.
GetNRoot takes care of this through a
Number-adapted optimised version of the Newton-Raphson method dealing with
f(x) = x^n - value.
The last three sections of this project describe this algorithm in detail.
- The next section explains this approach and its implementation in
GetNRoot. - The last two sections (Exponential proportionality and Method improvement) analyse the Math2_Private_New_PowSqrt_RootIni.cs contents; a file which includes all the code in charge of determining the most adequate initial guess. Without this part, the Newton-Raphson method wouldn't be able to deliver what is required because of failing (i.e., getting stuck in an infinite-loop-like situation) under virtually any scenario involving a relevant number of digits.
Additionally, note that
GetNRoot isn't meant to calculate any root for any number. It can only deal with certain inputs.
- Its algorithm assumes that
value will always be a positive number. The whole approach determining the most adequate initial guess also comes from this assumption. - Its heavy dependence upon the corresponding initial guess restricts the possible values of
n to 2 and numbers which are divisible by 10. Note that this is just a consequence of the current implementation, not an absolute limitation.