evaluateApproximateSqrtAlgorithm.cpp

// must use gcc  ¯\_(ツ)_/¯
#include <bits/stdc++.h>

using namespace std;

int closestSquare(int num) {
	double root = sqrt((double)num);
	double lowerBoundRoot = (int)(root);
	double upperBoundRoot = (int)(root + 0.5);
	int lowerBound = lowerBoundRoot * lowerBoundRoot;
	int upperBound = upperBoundRoot * upperBoundRoot;
	int distanceLower = abs(lowerBound - num);
	int distanceUpper = abs(upperBound - num);
	if (distanceLower <= distanceUpper) {
		return lowerBound;
	} else {
		return upperBound;
	}
}

int main(int argc, char const *argv[])
{
	int n, squareNear;
	double realSqrt, squareRootOfNearSquare, generatedSqrt;
	if (argc == 1) {
		while(true) {
			cout << "Enter a number: ";
			cin >> n;
			int squareNear = closestSquare(n);
			realSqrt = sqrt((double)n);
			squareRootOfNearSquare = sqrt((double)squareNear);
			generatedSqrt = ((double)(n + squareNear))/(2.0 * squareRootOfNearSquare);
			cout << "Real Square root: " << realSqrt;
			cout << "\nSquare root generated: " << generatedSqrt;
			cout << "\nDifference: " << generatedSqrt - realSqrt << endl;
		}
		
	} else if (argc == 2) {
		stringstream val(argv[1]);
		val >> n;
		squareNear = closestSquare(n);
		realSqrt = sqrt((double)n);
		squareRootOfNearSquare = sqrt((double)squareNear);
		generatedSqrt = ((double)(n + squareNear))/(2.0 * squareRootOfNearSquare);
		cout << "Real Square root: " << realSqrt;
		cout << "\nSquare root generated: " << generatedSqrt;
		cout << "\nDifference: " << generatedSqrt - realSqrt << endl;
	} else if (argc == 3) {
		stringstream begin(argv[1]);
		stringstream finish(argv[2]);
		int start, end;
		begin >> start;
		finish >> end;
		if (start > end) {
			cout << "Sorry, you started before you ended." << endl;
			return 2;
		}
		double sumAbsDeviation, sumDeviationSquared, absDeviation, deviation;
		int maxDevNum, minDevNum;
		double maxDev = 0;
		double minDev = 1;
		double numSamples = (end-start+1); // is an int, but cast as double for convenience
		for (int n = start; n <= end; n++) {
			squareNear = closestSquare(n);
			realSqrt = sqrt((double)n);
			squareRootOfNearSquare = sqrt((double)n);
			generatedSqrt = ((double)(n + squareNear))/(2.0 * squareRootOfNearSquare);
			deviation = generatedSqrt - realSqrt;
			absDeviation = abs(deviation);
			if (absDeviation > maxDev) {
				maxDev = absDeviation;
				maxDevNum = n;
			}
			if (absDeviation > 0 && absDeviation < minDev) {
				minDev = absDeviation;
				minDevNum = n;
			}
			if(n % 30 == 0) {
				cout << "\r" << n;
			}
			/*cerr << "(" << n << ")\t";
			cerr.precision(3);
			
			cerr << realSqrt << "\t" << generatedSqrt << "\t" << deviation << "\n";
			if (n % 20 == 0) {
				cout.flush();
			}
			sumAbsDeviation += absDeviation;
			sumDeviationSquared += absDeviation * absDeviation;*/
		}
		cerr << endl;
		cout.precision(10);
		cout << "Average deviation: " << sumAbsDeviation/numSamples << "\n";
		cout << "RMSE (Root Mean Squared Error): " << sqrt(sumDeviationSquared/numSamples) << "\n";
		cout << "Maximum deviation (at " << maxDevNum << "): " << maxDev << "\n";
		cout << "Minimum non-zero deviation (at " << minDevNum << "): " << minDev << "\n";

		cout << endl;
	} else {
		cout << "Sorry, there was an error." << endl;
		return 1;
	}
	return 0;
}