How to replace recursive functions using stack and while-loop to avoid the stack-overflow

/*! 
@file NestedRecursion.h
@author Woong Gyu La a.k.a Chris. <juhgiyo@gmail.com>
@date July 11, 2012
@brief Nested Recursion to Loop example
@version 1.0

@section LICENSE

The MIT License (MIT)

Copyright (c) 2008-2013 Woong Gyu La <juhgiyo@gmail.com>

Permission is hereby granted, free of charge, to any person obtaining a copy
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@section DESCRIPTION

Nested Recursion to Loop version example.

@section REFERENCE

http://www.dreamincode.net/forums/topic/51296-types-of-recursion/

*/
#ifndef __NESTED_RECURSION_H__
#define __NESTED_RECURSION_H__
#include <stack>
using namespace std;

int Ackermann(int x, int y)
{
	// Base or Termination Condition
	if (0 == x)
	{
		return y + 1;
	}   
	// Error Handling condition
	if (x < 0  ||  y < 0)
	{
		return -1;
	}  
	// Recursive call by Linear method 
	else if (x > 0 && 0 == y) 
	{
		return Ackermann(x-1, 1);
	}
	// Recursive call by Nested method
	else
	{
		// int midVal = Ackermann(x, y-1);
		// return Ackermann(x-1, midVal);
		return Ackermann(x-1, Ackermann(x, y-1));
	}
}



int AckermannLoop(int x, int y)
{
	// (First rule)
	struct SnapShotStruct // this can be declared as local structure 
		                  //   since it will be only used within this function.
	{
		int inputX;       // parameter that changes
		int inputY;       // parameter that changes
		int stage;
		                  // no local variable
	};

	// (Second rule)
	int returnVal;        // the return value at the point

	// (Third rule)
	stack<SnapShotStruct> snapshotStack;

	// (Fourth rule)
	SnapShotStruct currentSnapshot;
	currentSnapshot.inputX = x;
	currentSnapshot.inputY = y;
	currentSnapshot.stage = 0;

	snapshotStack.push(currentSnapshot);

	// (Fifth rule)
	while(!snapshotStack.empty())
	{
		currentSnapshot=snapshotStack.top();
		snapshotStack.pop();

		// (Sixth rule)
		switch(currentSnapshot.stage)
		{
			// (Seventh rule)
		case 0:
			// Base or Termination Condition
			if(currentSnapshot.inputX == 0)
			{
				// (Eighth rule && Ninth rule)
				returnVal = currentSnapshot.inputY + 1;
				continue;             // Since the function should return here
			}
			// Error Handling condition			
			if (currentSnapshot.inputX < 0  ||  currentSnapshot.inputY < 0)
			{
				// (Eighth rule && Ninth rule)
				returnVal = -1;
				continue;             // Since the function should return here
			}  
			// Recursive call by Linear method 
			else if (currentSnapshot.inputX > 0 && 0 == currentSnapshot.inputY) 
			{
				// (Tenth rule)

				// Create a new snapshot for calling itself
				SnapShotStruct newSnapshot;
				newSnapshot.inputX= currentSnapshot.inputX - 1; // give parameter as parameter given 
																//   when calling itself ( Ackermann(x-1, 1) )
				newSnapshot.inputY= 1;                          // give parameter as parameter given 
																//   when calling itself ( Ackermann(x-1, 1) )
				newSnapshot.stage= 0;
				snapshotStack.push(newSnapshot);
				continue;
			}
			// Recursive call by Nested method
			else
			{
				// (Tenth rule)

				currentSnapshot.stage=1;                        // current snapshot is done processing 
																//   and only waiting for result of calling 
																//   itself, so becomes stage "1"
				snapshotStack.push(currentSnapshot);

				// Create a new snapshot for calling itself
				SnapShotStruct newSnapshot;
				newSnapshot.inputX= currentSnapshot.inputX;	    // give parameter as parameter given 
																//   when calling itself ( Ackermann(x, y-1) )
				newSnapshot.inputY= currentSnapshot.inputY - 1; // give parameter as parameter given 
																//   when calling itself ( Ackermann(x, y-1) )
				newSnapshot.stage = 0;
				snapshotStack.push(newSnapshot);
				continue;
			}
			break;
		case 1:
			// (Tenth rule)

			// Create a new snapshot for calling itself
			SnapShotStruct newSnapshot;
			newSnapshot.inputX= currentSnapshot.inputX - 1;   // give parameter as parameter given 
															  //   when calling itself ( Ackermann(x-1,  Ackermann(x, y-1)) )
			newSnapshot.inputY= returnVal;                    // give parameter as parameter given 
															  //   when calling itself ( Ackermann(x-1,  Ackermann(x, y-1)) )
			newSnapshot.stage = 0;
			snapshotStack.push(newSnapshot);
			continue;
			break;
		}
	}
	// (Second rule)
	return returnVal;
}     
#endif //__NESTED_RECURSION_H__