A simple calculation: 3^20%15.

The answer, according to a calculator, is 6.

The following code generates answer 7.

#include <stdio.h>

#include <math.h>

int main() {

        int i = 20;

        printf("%dn", ((int)pow(3,20)%15));

        return 0;

}

If I replace 20 in the printf statement with the variable i, it gives -8 as output.

Assuming that the calculator is corrent (or not?), what is the problem in the program?

Thank you.

The result of pow(3,20) can't fit in an int on your platform (or mine for that matter). Because of that, you're experiencing unexpected results.

Changing to a larger integer type such as long long will do the job.

Moreover, pow works with floating-point numbers which aren't represented exactly in memory (look that up). During conversion to an integer, that can cause certain errors. For example, for printf("%fln", (pow(3,20))); I get 3486784401.000000l which is not a precise integer value.

What likely happened here is:

• In your C implementation, int is 32 bits, with a minimum of −2,147,483,648 and a maximum of 2,147,483,647.


• The result of pow(3, 20) is 3486784401. (See note 1 below.)


• 3486784401 is too large for an int, so there is an overflow. In case of integer overflow, the C standard permits an implementation to do anything.


• In (int) pow(3, 20), the conversion to int may have been computed at a compile time by producing the maximum, 2,147,483,647. Then the remainder of that divided by 15 is 7.


• In (int) pow(3, i), the conversion to int may have been computed at run time by producing the minimum, −2,147,483,648. (Some processors produce such a result for integer overflows.) Then the remainder of that divided by 15 is −8.

In summary:

• Your code overflows, so the C standard does not define the behavior.


• The compiler likely behaves differently for pow(3, 20) and pow(3, i) because it evaluates the former at compile time and the latter at execution time.

Note

1. Good implementations of pow return exactly 3486784401 for pow(3, 20). Unfortunately, poor implementations may return inaccurate values such as 3486784401.000000476837158203125 or 3486784400.999999523162841796875.