Bisection and Regula Falsi Methods in C Programming

Bisection Method Implementation

#include <stdio.h>
#include <math.h>

#define f(x) (cos(x) - (x * exp(x)))

int main() {
    float x0, x1, x2, f0, f1, f2, e;
    int step = 1;

    /* Inputs */
    up:
    printf("\nEnter two initial guesses:\n");
    scanf("%f%f", &x0, &x1);
    printf("Enter tolerable error:\n");
    scanf("%f", &e);

    f0 = f(x0);
    f1 = f(x1);

    if (f0 * f1 > 0.0) {
        printf("Incorrect Initial Guesses. Try again.\n");
        goto up;
    }

    printf("\nStep\t\tx0\t\tx1\t\tx2\t\tf(x2)\n");
    do {
        x2 = (x0 + x1) / 2;
        f2 = f(x2);
        printf("%d\t\t%f\t%f\t%f\t%f\n", step, x0, x1, x2, f2);

        if (f0 * f2 < 0) {
            x1 = x2;
            f1 = f2;
        } else {
            x0 = x2;
            f0 = f2;
        }
        step++;
    } while (fabs(f2) > e);

    printf("\nRoot is: %f\n", x2);
    return 0;
}

Regula Falsi Method Implementation

#include <stdio.h>
#include <math.h>

// Define the function: x * log10(x) - 1.2
#define f(x) ((x) * log10(x) - 1.2)

int main() {
    float x0, x1, x2, f0, f1, f2, e;
    int step = 1;

    /* Inputs */
    up:
    printf("\nEnter two initial guesses:\n");
    scanf("%f%f", &x0, &x1);
    printf("Enter tolerable error:\n");
    scanf("%f", &e);

    /* Calculate functional values */
    f0 = f(x0);
    f1 = f(x1);

    /* Check if initial guesses bracket the root */
    if (f0 * f1 > 0.0) {
        printf("Incorrect Initial Guesses. The function does not change sign. Try again.\n");
        goto up;
    }

    /* Regula Falsi Method */
    printf("\nStep\t\tx0\t\tx1\t\tx2\t\tf(x2)\n");
    do {
        x2 = x0 - (x0 - x1) * f0 / (f0 - f1);
        f2 = f(x2);

        printf("%d\t\t%f\t%f\t%f\t%f\n", step, x0, x1, x2, f2);

        if (f0 * f2 < 0) {
            x1 = x2;
            f1 = f2;
        } else {
            x0 = x2;
            f0 = f2;
        }
        step++;
    } while (fabs(f2) > e);

    printf("\nRoot is: %f\n", x2);
    return 0;
}