bisection_method.cpp

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#include <cmath>
#include <iostream>
#include <limits>
 
#define EPSILON \
    1e-6  // std::numeric_limits<double>::epsilon()  ///< system accuracy limit
#define MAX_ITERATIONS 50000  
 
static double eq(double i) {
    return (std::pow(i, 3) - (4 * i) - 9);  // original equation
}
 
template <typename T>
int sgn(T val) {
    return (T(0) < val) - (val < T(0));
}
 
int main() {
    double a = -1, b = 1, x, z;
    int i;
 
    // loop to find initial intervals a, b
    for (int i = 0; i < MAX_ITERATIONS; i++) {
        z = eq(a);
        x = eq(b);
        if (sgn(z) == sgn(x)) {  // same signs, increase interval
            b++;
            a--;
        } else {  // if opposite signs, we got our interval
            break;
        }
    }
 
    std::cout << "\nFirst initial: " << a;
    std::cout << "\nSecond initial: " << b;
 
    // start iterations
    for (i = 0; i < MAX_ITERATIONS; i++) {
        x = (a + b) / 2;
        z = eq(x);
        std::cout << "\n\nz: " << z << "\t[" << a << " , " << b
                  << " | Bisect: " << x << "]";
 
        if (z < 0) {
            a = x;
        } else {
            b = x;
        }
 
        if (std::abs(z) < EPSILON)  // stoping criteria
            break;
    }
 
    std::cout << "\n\nRoot: " << x << "\t\tSteps: " << i << std::endl;
    return 0;
}