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

#include <stdio.h>
#include <stdlib.h>
#include "pico/stdlib.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).
 */
int main() {

#ifndef WOKWI
    // Initialise the IO as we will be using the UART
    // Only required for hardware and not needed for Wokwi
    stdio_init_all();
#endif  
    // call function wallis
    wallis();
   // Returning zero indicates everything went okay.
    wallisDouble();
    return 0;
}
// function wallis returns the digits of pi using floats
void wallis (){
    //pi=1, this enables us to add onto pi through multiplication (x * 1 = still x)
    float pi=1;
    //for loop with 100000 iterations each adding to pi
    for(int i=1; i<=100000; i++){
        // formula for pi=(4.0i^2/4.0i^2-1) pi*pi each iteration
        pi= pi* ((4.0* i * i)/((4.0* i * i)-1));
    }
    //real value
   float piReal = 3.14159265359;
   //times by 2 to get value of pi
   pi=pi*2.0;
   //print statements
   printf("for Floats\n");
   printf("my calculated value of PI is %f\n",pi);
   pi=piReal - pi;
   printf("the approximate error is %f\n",pi*2.0);
}

// function wallis returns the digits of pi using doubles
void wallisDouble (){
    //pi=1, this enables us to add onto pi through multiplication (x * 1 = still x)
    double pi=1;
    //for loop with 100000 iterations each adding to pi
    for(int i=1; i<=100000; i++){
        // formula for pi=(4.0i^2/4.0i^2-1) pi*pi each iteration
        pi= pi* ((4.0* i * i)/((4.0* i * i)-1));
    }
    //real value
   double piReal = 3.14159265359;
   //times by 2 to get value of pi
   pi=pi*2.0;
   //print statements
   printf("for Doubles\n");
   printf("my calculated value of PI is %f\n",pi);
   pi=piReal - pi;
   printf("the approximate error is %f\n",pi*2);


}