#define MAX_ITERATIONS 100000
#define PI 3.14159265359

#include <stdio.h>
#include <stdlib.h>
#include "pico/float.h"
#include "pico/double.h"



/**
 * @brief Print pi to the console
 * 
 * @return int  Application return code (zero for success).
 */



/**
 * @brief Computes pi using the Wallis Product using single-precision
 *
 * @param n The amount of terms to sum
 *
 * @return float pi (calculates using Wallis Product
 */
float wallis_product_float(int n) {
    float pi = 1.0;

    for (int i = 1; i <= n; i++) {
        float two_n = 2.0 * (float) i;
        pi *= (two_n / (two_n - 1.0)) * (two_n / (two_n + 1.0)); 
    }

    return pi * 2.0;
}


/**
 * @brief Computes pi using the Wallis Product using double-precision
 *
 * @param n The amount of terms to sum
 *
 * @return double pi (calculates using Wallis Product
 */
double wallis_product_double(int n) {
    double pi = 1.0;

    for (int i = 1; i <= n; i++) {
        double two_n = 2.0 * (double) i;
        pi *= (two_n / (two_n - 1.0)) * (two_n / (two_n + 1.0)); 
    }

    return pi * 2.0;
}



int main() {

    stdio_init_all();

    // Calculate pi using Wallis Product using single-precision
    float pi_f = wallis_product_float(MAX_ITERATIONS);

    // Calculate approximation error
    float error_f = pi_f - PI;

    // Get absolute value of error
    if (error_f < 0.0) {
        error_f = - error_f;
    }

    // Calculate pi using Wallis Product using double-precision
    double pi_d = wallis_product_double(MAX_ITERATIONS);

    // Calculate approximation error
    double error_d = pi_d - PI;

    // Get absolute value of error
    if (error_d < 0.0) {
        error_d = - error_d;
    }

    while (true) {

        // Print values and approximation errors to console.
        printf("Single-Precision: \nCalculated Value: %f \nApproximation Error: %f \n \nDouble-Precision: \nCalculated Value: %lf \nApproximation Error: %lf \n---------------------- \n", pi_f, error_f, pi_d, error_d);
        sleep_ms(1000);
    }


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