Power function giving different answer than math.pow function in C

Question

I was trying to write a program to calculate the value of x^n using a while loop:

#include <stdio.h>
#include <math.h>
int main()
{
    float x = 3, power = 1, copyx;
    int n = 22, copyn;
    copyx = x;
    copyn = n;

    while (n)
    {
        if ((n % 2) == 1)
        {
            power = power * x;
        }
        n = n / 2;
        x *= x;
    }

    printf("%g^%d = %f\n", copyx, copyn, power);
    printf("%g^%d = %f\n", copyx, copyn, pow(copyx, copyn));

    return 0;
}

Up until the value of 15 for n, the answer from my created function and the pow function (from math.h) gives the same value; but, when the value of n exceeds 15, then it starts giving different answers.

I cannot understand why there is a difference in the answer. Is it that I have written the function in the wrong way or it is something else?

Answer 1

You are mixing up two different types of floating-point data. The pow function uses the double type but your loop uses the float type (which has less precision).

You can make the results coincide by either using the double type for your x, power and copyx variables, or by calling the powf function (which uses the float type) instead of pow.

The latter adjustment (using powf) gives the following output (clang-cl compiler, Windows 10, 64-bit):

3^22 = 31381059584.000000
3^22 = 31381059584.000000

And, changing the first line of your main to double x = 3, power = 1, copyx; gives the following:

3^22 = 31381059609.000000
3^22 = 31381059609.000000

Note that, with larger and larger values of n, you are increasingly likely to get divergence between the results of your loop and the value calculated using the pow or powf library functions. On my platform, the double version gives the same results, right up to the point where the value overflows the range and becomes Infinity. However, the float version starts to diverge around n = 55:

3^55 = 174449198498104595772866560.000000
3^55 = 174449216944848669482418176.000000