Question

I wrote this piece of code. I think that is all right but when I run it, I obtain a bad result. This code is for calculate the Euler number. I will appreciate your answer.

The result that I expect is approximately 2.718281828459045 and I obtain the result 2.718281745910644:

• 2.718281828459045 (expected)
• 2.718281745910644 (actual)

Code:

#include <stdio.h>

main() {

    int factor, counter, n = 1;
    float total = 0, division;

    while ( n <= 20 ) {
        counter = 1;
        factor = n;

    while ( counter < n ) {
        factor *= ( n - counter );
        counter++;
    } 

    division = 1.0 / factor;
    total = total + division;
    n++;
    }

    total = total + 1;

    printf( "La constante matematica e vale aproximadamente: %.20f\n", total);

    return 0;  

} /* Finaliza funcion main */

Answer 1

while ( n <= 20 ) {
    contador = 1;
    factorial = n;

    while ( contador < n ) {
        factorial *= ( n - contador );
        contador++;
    } 
    // snip
    n++;

int, if it is a 32-bit integer type, can only hold the factorials up to 12!. 13! = 6227020800 is too large for a 32-bit integer. Thus you have overflow, and the results are completely wrong.

You could get somewhat good results if factorial were a double or a 64-bit integer instead of an int.

The (relatively small) error your computation gives you is due to using float instead of double for total and division:

We compute a good approximation to e as a double

Prelude Text.FShow.RealFloat> FD $ exp 1
2.718281828459045090795598298427648842334747314453125

and convert that to a float:

Prelude Text.FShow.RealFloat> FF $ realToFrac it
2.71828174591064453125

Which is the value you got: 2.718281745910644 modulo the different precision in printing. And it’s the same we get when computing exp 1 as a float:

Prelude Text.FShow.RealFloat> FF $ exp 1
2.71828174591064453125

the closest float value to the desired result:

Prelude Text.FShow.RealFloat> FF 2.718281828459045
2.71828174591064453125