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

#include <stdio.h>
#include <stdlib.h>
// #include "pico/stdlib.h"
#include "pico/float.h"     
#include "pico/double.h"   
#include <math.h>
#define FACTOR 2.0f
#define DOUBLE_FACTOR 2.0

/**
 * @brief Calculate Pi by using Wallis product in Single precision 
 *        this function implements calculating the approximate value of pi by using single precision float points
 *        
 * @param precision the iteration number of the calculation which is the precision
 * @return Calculated value of PI in single precision.
 */

 float singlePrecisionForPi(int iterations) 
 {
    float halfPi = 1.0f;                                                            //initialize half pi as 1 but a float 1.0 
    for (int i = 1; i <= iterations; i++)                                           //loop number of iterations times 
    {
        float numerator = (FACTOR * i) * (FACTOR * i);                              //calculate numerator by using Wallis product formula
        float denominator = ((FACTOR * i) - 1) * ((FACTOR * i) + 1);                // (2n/2n-1)*(2/2n+1) such that n is from 1 to the number of iterations
        halfPi *= numerator / denominator;                                          //cumulative multiplication by using formula
    }
    float result = halfPi * 2.0f;                                                   //calculate pi value by multiply halpPi by 2
    return result;                                                                  //calculated Pi value
}


/**
 * @brief Calculate Pi by using 1 product in Double precision 
 *        this function implements calculating the approximate value of pi by using Double precision double
 *        
 * @param precision the iteration number of the calculation which is the precision
 * @return Calculated value of PI in double precision.
 */

 double doublePrecisionForPi(int iterations) 
 {
    double halfPi = 1.0;                                                            //initialize half pi as 1
    for (int i = 1; i <= iterations; i++)                                           //loop number of iterations times
    {
        double numerator = (DOUBLE_FACTOR * i) * (DOUBLE_FACTOR * i);               //calculate numerator by using Wallis product formula
        double denominator = ((DOUBLE_FACTOR * i) - 1) * ((DOUBLE_FACTOR * i) + 1); // (2n/2n-1)*(2/2n+1) such that n is from 1 to the number of iterations
        halfPi *= numerator / denominator;                                          //cumulative multiplication by using formula
    }
    double result = halfPi * 2.0;                                                   //calculate pi value by multiply halpPi by 2
    return result;                                                                  //calculated Pi value
}


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

int n_Value = 100000;
float singleCal = singlePrecisionForPi(n_Value);                                  //calculate pi by using single precision
double doubleCal = doublePrecisionForPi(n_Value);                                 //calculate pi by using double precision
double piDefult = 3.14159265359;                                                  //defult value of pi

printf("pi calculated by using single precision is: %.55f\n", singleCal);         //print calculated pi by using single precision
printf("approximation error for single precision is: %.55f\n", fabs(singleCal - piDefult));//get positive error value


printf("pi calculated by using double precision is: %.55f\n", doubleCal);          //print calculated pi by using single precisio
printf("approximation error for double precision is: %.55f\n", fabs(doubleCal - piDefult));//get positive error value


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