// SquareRoot.cpp - CALCULATE A SQUARE ROOT BY TRIAL AND ERROR
//
// MODULE INDEX
// NAME			CONTENTS
// SquareRoot		Calculate the square root of a number by trial and error
// main			Testing main line
//
// MAINTENANCE HISTORY
// DATE		PROGRAMMER AND DETAILS
// 06-09-11	JS	Original
//
//-----------------------------------------------------------------------------

#include <cstring>		// C-style string manipulation functions
#include <cstdlib>		// C-style standard library
#include <iostream>		// C++ input/output stream declarations
using namespace std;		// Expand the standard namespace
#include "dtime.h"		// Double time functions

//-----------------------------------------------------------------------------

// CALCULATE THE SQUARE ROOT OF A NUMBER BY TRIAL AND ERROR

double
SquareRoot (
	double		x)		// Value to be square rooted
{
	double		l, u;		// Lower and upper limits
	double		m;		// Midpoint
	double		m2;		// Midpoint squared

	if (x < 0) {
		cerr << "Error: square root of negative number\n";
		abort ();
	}
	if (x == 0)
		return 0;
	if (x < 1.0) {
		l = x;
		u = 1.0;
	} else if (x > 1.0) {
		l = 1.0;
		u = x;
	} else
		return 1.0;
	while (fabs((l - u) / l) >= 1.0e-8) {
		m = (l + u) / 2.0;
		m2 = m * m;
		if (m2 > x)
			u = m;
		else
			l = m;
	}
	return (l + u) / 2.0;
}

//-----------------------------------------------------------------------------

// TESTING MAIN LINE

int
main ()
{
	double		x;		// The value to be square rooted

	for (x = 0.0; x < 20.0; x += 0.5)
		cout << "x=" << x << "  root=" << SquareRoot(x) << '\n';
	return 0;
}