Task

Implement the algorithm to compute the principal   nth   root   





A

n





{\displaystyle {\sqrt[{n}]{A}}}

   of a positive real number   A,   as explained at the   Wikipedia page.



data 10, 1024, 3, 27, 2, 2, 125, 5642, 4, 16, 0, 0
 
do
    read e, b
    if e = 0 break
    print "The ", e, "th root of ", b, " is ", b^(1/e), " (", nthroot(b, e), ")"
loop
 
 
sub nthroot(y, n)
    local eps, x, d, e
 
    eps = 1e-15     // relative accuracy
    x   = 1
    repeat
        d  = ( y / ( x^(n-1) ) - x ) / n
        x = x + d
        e = eps * x // absolute accuracy
 
    until(not(d < -e or d > e ))
 
    return x
end sub