// NewtonSolver by Walter Bislin, 07.10.2015
// http://walter.bislins.ch
// You may do what ever you want with this file and code!

function SolveWithNewton( fn, target, guess, prec, data ) {
  // function aFunction( x, data )
  // aData: user data passed to aFunction
  // In data you can specify properties:
  //   { MaxLoops: 1000 }
  // Solver returns in aData:
  //   { Result, Status, NLoops }
  var dx, X, Y, Y1, Y2, Xnew, slope;

  data = data || NewtonSolver;
  data.Result = 0;
  data.Status = '';
  data.NLoops = 0;
  fn = fn || function(x,d){ d.Status='no function defined'; return x; };
  target = target || 0;
  guess = guess || 0;
  prec = prec || 0.0001;
  var maxLoops = data.MaxLoops || 1000;
  var nLoops = 0;
  var eps = prec / 2.0;
  var eps2 = eps / 2;
  Xnew = guess;
  do {
    X = Xnew;
    try {
      Y = fn( X, data ) - target;
      if (Y == 0) break; // exact solution found

      Y1 = fn( X-eps2, data ) - target;
      if (Y1 == 0) { // exact solution found
        Xnew = X - eps2;
        break;
      }

      Y2 = fn( X + eps2, data ) - target;
      if (Y2 == 0) { // exact solution found
        Xnew = X + eps2;
        break;
      }

      slope = (Y2 - Y1) / eps;
      if (slope == 0) { // slope zero, cant find a solution
        data.Status = 'extremum found';
        break;
      }

      Xnew = X - (Y / slope);

    } catch(err) {
      data.Status = err.message;
      break;
    }

    nLoops++;
    dx = Math.abs( Xnew - X );

  } while ((dx > prec) && (nLoops < maxLoops));

  if (data.Status == '' && nLoops >= maxLoops) data.Status = 'max loops exceedet';

  data.NLoops = nLoops;
  data.Result = (data.Status == '') ? Xnew : 0;

  return data.Result;
}

var NewtonSolver = { MaxLoops: 1000, Result: 0, Status: '', NLoops: 0 };