Pow is not working for two double digit numbers - c

Question

I have made a code to read two long integers (A and B) from standard input and output (to standard output) A to the power of B.
It works for 1^some huge number, 3^3 etc.
But not for 13^16.
I've tried to put long int ans to solve it, it gave me a different value but not the right one.
#include <stdio.h>
#include <math.h>
int main()
{
int x, n;
long int ans;
scanf("%d \n %d",&x, &n);
ans = pow(x,n);
printf("%d", ans);
return 0;
}

Answer 1

pow(1,anything) is always 1. pow(3, 3) is 27. These are both quite small numbers and easily fit into a 32 bit integer. pow(13,16) is (approximately) 6.65 x 1017. This is too big for a 32 bit integer to contain. It will go into a 64 bit integer (although pow(14, 17) will not). It's likely that your compiler treats a long as a 32 bit value, which is not uncommon. You could try long long which is likely to be 64 bits or int64_t which is explicitly 64 bits long.
Note though that the prototype for pow() is
double pow(double x, double y);
which means that it is returning a double precision floating point number and then coercing it into the type of your variable. double (a 64 bit floating point number) only has 53 bits of precision in its mantissa, which means you are not going to get the exact number when you cast it back to even a 64 bit integer. You could use powl() whose prototype is
long double powl(long double x, long double y);
But long double might be defined as 80 bits or 128 bits or even only 64 bits (Microsoft). It might give you the precision you need, but such is the nature of power operations, your input numbers won't have to get much bigger to overflow the precision of even the longest long double.
If you really need to raise large numbers to large powers, you are going to need a big integer library.

Answer 2

Rather than use floating point pow() and friends with their potential limited precision for an integer problem within 64 bits (1316 needs 60 bits), use an integer power function.
unsigned long long upow(unsigned x, unsigned y) {
unsigned long long z = 1;
unsigned long long xx = x;
while (y) {
if (y % 2) {
z *= xx;
}
y /= 2;
xx *= xx;
}
return z;
}
int main() {
printf("%llu\n", upow(3, 3));
printf("%llu\n", upow(13, 16));
}
Output
27
665416609183179841
If code needs to handle answers more the 64 bits, consider long double (with potential loss of precision) or big_integer libraries.

Answer 3

You have defined "ans" as long int then you are trying to print it as int (%d - Take the next argument and print it as an int ) So change printf("%d", ans) to printf("%ld",ans) . your code would look something like this :
#include <stdio.h>
#include <math.h>
int main()
{
int x, n;
long int ans;
scanf("%d \n %d",&x, &n);
ans = pow(x,n);
printf("%ld", ans);
return 0;
}