//#define WOKWI             // Uncomment if running on Wokwi RP2040 emulator.

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


/**
 * @brief EXAMPLE - HELLO_C
 *        Simple example to initialise the IOs and then 
 *        print a "Hello World!" message to the console.
 * 
 * @return int  Application return code (zero for success).
 */
float wallis_productsp(int iter)
{
    float product = 1.0f; // Intiliase the product to 1;
    for (int n = 1; n <= iter; n++)
    {
        float term1 = (2.0f * n) / (2.0f * n - 1.0f);// First term: (2n)/(2n-1)
        float term2 = (2.0f * n) / (2.0f * n + 1.0f);// Second term: (2n)/(2n+1)
        product *= term1 * term2;// Multiply the terms into the product
    }
    return product * 2.0f; // Multiply by 2 to approximate π
}

double wallis_productdp(int iter)
{
    double product = 1.0f; // Intiliase the product to 1;
    for (int n = 1; n <= iter; n++)
    {
        double term1 = (2.0f * n) / (2.0f * n - 1.0f);// First term: (2n)/(2n-1)
        double term2 = (2.0f * n) / (2.0f * n + 1.0f);// Second term: (2n)/(2n+1)
        product *= term1 * term2;// Multiply the terms into the product
    }
    return product * 2.0f; // Multiply by 2 to approximate π
}

int main() {
 stdio_init_all();
    int iterations = 100000;
    float pi_ref = 3.14159265359;

    float pi_w = wallis_productsp(iterations);
    float float_error = pi_w - pi_ref;
    double pi_w2 = wallis_productdp(iterations);
    double double_error = pi_w2 - pi_ref;

    printf("PI using wallis product (float): %.10f",pi_w);
    printf(" approx error: %.10f\n", float_error);
    printf("PI using wallis product (double): %.10f",pi_w2);
    printf(" approx error:: %.10f",double_error);
        // returning 0 indicates everything went okay
        return 0;
    // Initialise the IO as we will be using the UART
    // Only required for hardware and not needed for Wokwi
    // Print a console message to inform user what's going on.

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