pow() function in C problems

Question

I am having some problems with pow() function in C. When ever run this code, 153 as input, the sum evaluates to 152. However if I dont use pow() function and instead use a for loop to get the value of Nⁿ, the sum evaluates to 153. Can anyone help please explain me this difference?

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>

int main(void) {
    unsigned int i, n, sum = 0, N, a = 1, j;
    char num[100], x[2] = { 0 };
    printf("Determining an armstrong number\n\n"
           "Enter a number: ");
    fflush(stdin);
    gets(num);
    n = strlen(num);
    for (i = 0; i < n; i++) {
        a = 1;
        x[0] = num[i];
        N = atoi(x);
        /* for (j = 1; j <= n; j++)
            a *= N;
        */
        sum += pow(N, n);
    }
    n = atoi(num);
    if (sum == n)
        printf("\nIt is an Armstrong number!\n");
    else
        printf("\nIt is not an Armstrong number!\n");
    return 0;
}

Answer 1

Your C implementation, including its math library, has a bad implementation of pow that returns inaccurate results. (A good pow implementation returns an exact result when the mathematical result is exactly representable in the floating-point format.) For example, for pow(7, 2), your pow may be returning a value slightly under 49. When this is converted to an unsigned int (in the addition to sum), it is truncated, resulting in 48.

To work around this defect in your library, do not use pow for integer arithmetic. Write your own integer arithmetic to get the result you desire. In some circumstances, using round(pow(N, n)) may suffice, but there are considerations of the range of values for which this will work (wide integers may be able to represent integers that double cannot) and sometimes performance. (Another workaround is to get a better C implementation.)