Nth root

Implement the algorithm to compute the principal nth root ${\sqrt[{n}]{A}}$ of a positive real number A, as explained at the Wikipedia page.

Nth root
You are encouraged to solve this task according to the task description, using any language you may know.

This page uses content from Wikipedia. The original article was at Nth root algorithm. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

Fortran

<lang fortran>program NthRootTest

 implicit none

 print *, nthroot(10, 7131.5**10)
 print *, nthroot(5, 34.0)

contains

 function nthroot(n, A, p)
   real :: nthroot
   integer, intent(in)        :: n
   real, intent(in)           :: A
   real, intent(in), optional :: p

   real :: rp, x(2)

   if ( A < 0 ) then
      stop "A < 0"       ! we handle only real positive numbers
   elseif ( A == 0 ) then
      nthroot = 0
      return
   end if

   if ( present(p) ) then
      rp = p
   else
      rp = 0.001
   end if

   x(1) = A
   x(2) = A/n   ! starting "guessed" value...

   do while ( abs(x(2) - x(1)) > rp )
      x(1) = x(2)
      x(2) = ((n-1.0)*x(2) + A/(x(2) ** (n-1.0)))/real(n)
   end do

   nthroot = x(2)

 end function nthroot

end program NthRootTest</lang>