Nth root of A. `gst nth-root-a.st -a N A`

nth-root-a.st

Number extend [
    nthRoot: n [
        |x0 m x1|
        x0 := (self / n) asFloatD.
        m := n - 1.
        [true] whileTrue: [
            x1 := ((m * x0) + (self/(x0 raisedTo: m))) / n.
            ((x1 - x0) abs) < ((x0 * 1e-9) abs)
                ifTrue: [ ^ x1 ].
            x0 := x1.
        ]
    ]
].

(((Smalltalk getArgv: 2) asNumber) nthRoot: ((Smalltalk getArgv: 1) asNumber)) displayNl.

Pseudocode:

extend Number class {
  method nthRoot(n) {
    vars (x0 m x1);
    set x0 = float(self / n);
    set m = n - 1;
    while (true) {
      set x1 = ((m * x0) + (self / (x0 ^ m))) / n;
      if (abs(x1 - x0) < abs(x0 * 1e-9)) {
        return(x1);
      }
      set x0 = x1
    }
  }
}

println(nthRoot(sys.argv[1], sys.argv[2]));