Factorial Frequencies

Now how many digits in the factorial of N numbers..?

#include<stdio.h>
#include <math.h>
/*******************************************************************/
double count_digit(long a){
 double sum;
 long i;
 if(a==0) return 1;
 else{
 sum=0;
 for(i=1;i<=a;i++){
 sum+=log10(double(i));
 }
 return floor(sum)+1;
 }
}
/*******************************************************************/
int main(){
 double sum;
 long n;
 while(scanf("%ld",&n)==1){
 sum=count_digit(n);
 printf("%.0lf\n",sum);
 }
 return 0;
}
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