#define WOKWI  // Uncomment if running on Wokwi RP2040 emulator
#define PI 3.14159265359
#define MAX_ITERATIONS 100000

#include <stdio.h>
#include <stdlib.h>


/**
 * @brief Function to calculate pi using the Wallis product, using single-precision floating-point 
 * representation
 *
 * This function estimates the value of PI using the Wallis algorithm. It iteratively computes 
 * the product of fractions based on the Wallis formula and uses this to optimize Pi. This
 * function uses single-precision floating-point representation
 *
 * @return the calculated value of PI
 *
*/

float single_precision() {
    float pi = 1.0;
    for (int i = 1; i <= MAX_ITERATIONS; i++) {
        float numerator = 4.0 * i * i;
        float denominator = numerator - 1;
        pi = pi * (numerator / denominator);
    }
    pi = pi * 2.0;

    return pi;
}

/**
 * @brief Function to calculate pi using the Wallis product, using double-precision floating-point 
 * representation
 *
 * This function estimates the value of PI using the Wallis algorithm. It iteratively computes 
 * the product of fractions based on the Wallis formula and uses this to optimize Pi. This
 * function uses double- precision floating-point representation
 *
 * @return the calculated value of PI
 *
*/

double double_precision() {
    double pi = 1.0;
    for (int i = 1; i <= MAX_ITERATIONS; i++) {
        double numerator = 4.0 * i * i;
        double denominator = numerator - 1;
        pi = pi * (numerator / denominator);
    }
    pi = pi * 2.0;

    return pi;
}


/**
 * @brief Main function that outputs the values to the serial monitor
 *
 * This is the main function of the program. It calls the Wallis functions and calculates
 * the approximate error between these results and the defined PI. It submits these results
 * to the serial monitor.
 * 
 * @return always returns 0.
 */

int main() {

    float singlePI = single_precision();
    float comparedSingle = PI - singlePI;
    double doublePI = double_precision();
    double comparedDouble = PI - doublePI;

    // Print a console message to inform user what's going on.
    printf("Calculated value of PI using single-precision = %f\n", singlePI);
    printf("Approximation error = %f\n", comparedSingle);

    printf("Calculated value of PI using double-precision = %lf\n", doublePI);
    printf("Approximation error = %lf\n", comparedDouble);

    // Returning zero indicates everything went okay.
    return 0;
}