

PROJECT 10 Completed (24 days) Completed (57 days) Completed (26 days) Completed (47 days) Completed (19 days) Completed (14 days)  Nonfloatingpoint fractional exponentiation approach Completed on 16Nov2016 (24 days) The NewtonRaphson method is an iterative methodology for finding the roots of real functions, defined by x_i+1 = x_i  f(x_i) / f'(x_i) and starting from an initial guess x0. In the current implementation (i.e., GetNRoot ), the goal is solving the function f(x) = x^n  value, what yields:f(x) = x^n  value f'(x) = n*x^(n1) x_i+1 = ((n  1) * x_i + value / x_i^(n1)) / n GetNRoot includes a Number based version of the aforementioned equation inside a loop exited when the difference between the x_i+1 and x_i values is smaller or equal than the target accuracy of 1e28m . Note that this is assumed to be the smallest positive value with which the most precise type (i.e., decimal ) can reliably deal.This approach has only one relevant limitation: the initial guess x0 has to be similar enough to the final result. A bad initial guess would provoke (practically speaking) infinite loops in quite a few scenarios. The methodology with which I came up to address this issue is undoubtedly the most important part of the current implementation. The following two sections (Exponential proportionality and Method improvement) include detailed explanations about it, but some points should already be clear:
