// #include <stdio.h>
// #include <stdlib.h>
// #include <math.h>
// #include "pico/stdlib.h"
// #include "pico/float.h"     // Required for using single-precision variables.
// #include "pico/double.h"    // Required for using double-precision variables.


/**
 * @brief LAB #02 - TEMPLATE
 *        Main entry point for the code.
 * 
 * @return int      Returns exit-status zero on completion.
 */

float wallisProductFloat(int limit){
    float n=0;
    float final=1;
    float varOne;
    float varTwo;
    //FORMULA 2
    for(n=1; n<limit; n++)
    {
        varOne = (n*2)/((2*n)-1);
        varTwo = (n*2)/((2*n)+1);
        final *= varOne*varTwo;
    }
    return final*2;
}

double wallisProductDouble(int limit){
    double n=0;
    double final=1;
    double varOne;
    double varTwo;
    //FORMULA 2
    for(n=1; n<limit; n++)
    {
        varOne = (n*2)/((2*n)-1);
        varTwo = (n*2)/((2*n)+1);
        final *= varOne*varTwo;
    }
    return final*2;
}

int main() {
    #ifndef WOKWI
        // Initialise the IO as we will be using the UART
        // Only required for hardware and not needed for Wokwi
        gpio_put_all;
    #endif

        // Print a console message to inform user what's going on.
        //printf("Hello World!\n");

        float wallisFloat = wallisProductFloat(100000);
        float floatError = abs((3.14159265359-wallisFloat)/3.14159265359);

        double wallisDouble = wallisProductDouble(100000);
        double doubleError = abs((3.14159265359-wallisDouble)/3.14159265359);

        printf("Rosemary Doyle Results: Student No.22335687 \n");
        printf("Single Precion Result: %f \n", wallisFloat);
        printf("Single Precision Approximation Error %f \n", floatError);

        printf("Double Precion Result: %f \n", wallisDouble);
        printf("Double Precision Approximation Error %f \n", doubleError);
        // Returning zero indicates everything went okay.
        return 0;
}