/* Title      - Square Root Function
 * File name  - Lab17
 * Programmer - 415 Erich Musick
 * IPO        - Input   - User inputs a positive real number
 *              Process - Approximate square root value of user inputed number
 *                is calculated, within .01 of the acutal value
 *              Output  - Approx square root value and actual value (calculated
 *                using the sqrt() function) are displayed
*/

/*************************** H E A D E R  F I L E S ***************************/
//#include "iostream.h"
#include "waittoclose.h"    // Add to project waittoclose.cpp
#include "apstring.h"       // Add to project apstring.cpp
//#include "randgen.h"       // Add to project randgen.cpp
#pragma hdrstop
//#include "apvector.h"     // DO NOT ADD TO PROJECT apvector.cpp
//#include "apmatrix.h"     // DO NOT ADD TO PROJECT apmatrix.cpp

/******************** F U N C T I O N  P R O T O T Y P E S ********************/
void SqrtEst(double a, double &approxSquareRoot, double actualSquareRoot);
void displayResult(double a, double approxSquareRoot, double actualSquareRoot);

/****************************** F U N C T I O N S *****************************/
// SQUARE ROOT ESTIMATE
 /* purpose    - Calculate the approximate square root of the number entered
  *            -  by the user.
  * parameters - a - double containing number entered by the user.
  *            - approxSquareRoot - double where approx sqrt value will be placed
  *            - actualSquareRoot - double containing value of function sqrt(a)
  * input      - None.
  * process    - Approximate value for square root of a is calculated using a
  *               recursive series.
  * output     - None.
  * return     - estimatedSquareRoot - double containing the approximate value
  *               of the square root of the number entered by the user. The
  *               approximate value is the actual value +/- .01
  */
void SqrtEst(double a, double &approxSquareRoot, double actualSquareRoot) {
  double accuracy;

  approxSquareRoot = a/2.;
  do {
    approxSquareRoot = .5 * (approxSquareRoot + (a / approxSquareRoot));
    accuracy = fabs(actualSquareRoot - approxSquareRoot);
  } while (accuracy > .01);

  return;
}

// DISPLAY RESULT
 /* purpose    - Display the calculated and actual values for the sqrt of a
  * parameters - a - double containing number entered by the user.
  *            - approxSquareRoot - double containing approx square root of a
  *            - actualSquareRoot - double containing value of function sqrt(a)
  * input      - None.
  * process    - None.
  * output     - Calculated and acutal values for square root of a are displayed
  * return     - None.
  */
void displayResult(double a, double approxSquareRoot, double actualSquareRoot) {
   cout << endl;
  cout << "Approximate square root of ";
  cout << a;
  cout << " is                     : ";
  cout << approxSquareRoot;
  cout << " +/- .01";
  cout << endl;

  cout << "Actual square root using the C++ function sqrt(";
  cout << a;
  cout << ") is: ";
  cout << actualSquareRoot;
  cout << endl;
  cout << endl;
}

int main() {
  apstring goAgain;         // Contains user input (calculate another?)
  double a;
  double approxSquareRoot;
  double actualSquareRoot;
  int yLocation;

  cout << "SQUARE ROOT FUNCTION";
  cout << endl;
  cout << "Estimates the square root of a positive number.";
  cout << endl;
  cout << endl;

  do {
    // USER INPUT: get values for base and power
    cout << "Enter a positive number: ";
    yLocation = wherey();
    do {                    // Ask for number > 0 until one is entered
      gotoxy(26,yLocation);
      clreol();
      cin >> a;
    } while (a <= 0);

    actualSquareRoot = sqrt(a);

    // CALCULATION: calculate the value of the base raised to the power
    SqrtEst(a,approxSquareRoot,actualSquareRoot);

    // DISPLAY: display the result of the calculation
    displayResult(a,approxSquareRoot,actualSquareRoot);

    // USER INPUT: Loop through again?
    cout << "Again (y/n)? ";
    cin >> goAgain;

    // DISPLAY: Leave an extra space if user would like to loop through again.
    if (goAgain == "y" || goAgain == "Y") {
      cout << endl;
    }
  } while (goAgain == "y" || goAgain == "Y");

  return 0;
}

/************************** S A M P L E  O U T P U T **************************/

/*               LAB17 by 415 ERICH MUSICK   11:11 on Nov 27 2001

SQUARE ROOT FUNCTION
Estimates the square root of a positive number.

Enter a positive number: 25

Approximate square root of 25 is                     : 5.00001 +/- .01
Actual square root using the C++ function sqrt(25) is: 5

Again (y/n)? y

Enter a positive number: 10

Approximate square root of 10 is                     : 3.16232 +/- .01
Actual square root using the C++ function sqrt(10) is: 3.16228

Again (y/n)? y

Enter a positive number: 2.5

Approximate square root of 2.5 is                     : 1.58173 +/- .01
Actual square root using the C++ function sqrt(2.5) is: 1.58114

Again (y/n)? y

Enter a positive number: 2.25

Approximate square root of 2.25 is                     : 1.50125 +/- .01
Actual square root using the C++ function sqrt(2.25) is: 1.5

Again (y/n)? y

Enter a positive number: 100

Approximate square root of 100 is                     : 10 +/- .01
Actual square root using the C++ function sqrt(100) is: 10

Again (y/n)? y

Enter a positive number: 5463

Approximate square root of 5463 is                     : 73.9123 +/- .01
Actual square root using the C++ function sqrt(5463) is: 73.9121

Again (y/n)? n

'Esc' closes window.*/