Implement square root function.

#include <iostream>
#include <cmath>

double customSqrt(double x, double epsilon = 1e-6) {
    if (x < 0.0) {
        std::cerr << "Square root is undefined for negative numbers.\n";
        return std::numeric_limits<double>::quiet_NaN(); // Return NaN for undefined result
    }

    // Handle special cases: square root of 0 or 1
    if (x == 0.0 || x == 1.0) {
        return x;
    }

    double low = 0.0;
    double high = x;

    // Perform binary search until the range is small enough
    while (high - low > epsilon) {
        double mid = (low + high) / 2.0;
        double square = mid * mid;

        if (square < x) {
            low = mid;
        } else {
            high = mid;
        }
    }

    return low + (high - low) / 2.0; // Final approximation
}

int main() {
    // Test the custom square root function
    double number;

    std::cout << "Enter a number: ";
    std::cin >> number;

    double customResult = customSqrt(number);
    double stdResult = std::sqrt(number);

    std::cout << "Custom square root: " << customResult << "\n";
    std::cout << "std::sqrt result: " << stdResult << "\n";

    return 0;
}

#include <iostream>

//using Newton-Raphson method.

double customSqrt(double x) {
    // Initial guess
    double guess = x / 2.0;

    // Iterate until convergence or a maximum number of iterations
    for (int i = 0; i < 100; ++i) {
        // Update the guess using the Newton-Raphson formula
        guess = 0.5 * (guess + x / guess);
    }

    return guess;
}

int main() {
    // Test the custom square root function
    double number;
    
    std::cout << "Enter a number: ";
    std::cin >> number;

    if (number < 0) {
        std::cout << "Square root is undefined for negative numbers.\n";
    } else {
        double result = customSqrt(number);
        std::cout << "Custom square root of " << number << " is approximately: " << result << "\n";
    }

    return 0;
}