newton_raphson_method.cpp

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#include <cmath>
#include <cstdint>
#include <ctime>
#include <iostream>
#include <limits>
 
constexpr double EPSILON = 1e-10;              
constexpr int16_t MAX_ITERATIONS = INT16_MAX;  
 
static double eq(double i) {
    return (std::pow(i, 3) - (4 * i) - 9);  // original equation
}
 
static double eq_der(double i) {
    return ((3 * std::pow(i, 2)) - 4);  // derivative of equation
}
 
int main() {
    std::srand(std::time(nullptr));  // initialize randomizer
 
    double z = NAN, c = std::rand() % 100, m = NAN, n = NAN;
    int i = 0;
 
    std::cout << "\nInitial approximation: " << c;
 
    // start iterations
    for (i = 0; i < MAX_ITERATIONS; i++) {
        m = eq(c);
        n = eq_der(c);
 
        z = c - (m / n);
        c = z;
 
        if (std::abs(m) < EPSILON) {  // stoping criteria
            break;
        }
    }
 
    std::cout << "\n\nRoot: " << z << "\t\tSteps: " << i << std::endl;
    return 0;
}