/*

* stirling.c

* This program checks Stirling's formula.

*/

#include <stdio.h>

#include <math.h>

#define PI 3.14159265

#define N 20

/* Prototypes: */

double log_fact (int n);

int main ()

{

int n;

double exact_res;

double stirling_res;

for (n = 1; n <= N; n++)

{

/* Compute the exact value of ln(n!): */

exact_res = log_fact(n);

/* n^(n+0.5)

* Use Stirling's formula: n! ~ sqrt(2*PI) * -----------

* e^n

*

* Therefore: ln(n!) ~ 0.5*ln(2*PI) + (n+0.5)*ln(n) - n

*/

stirling_res = 0.5*log(2*PI) + (n + 0.5)*log(n) - n;

/* Print the results. */

printf ("ln(%d!) = %.6lf\t", n, exact_res);

printf ("Stirling's apporximation is %.6lf\n", stirling_res);

}

return (0);

}

/* ------------------------------------------------------------------------

* Function: log_fact

* Purpose : Compute the natural logarithm of a factorial.

* Input : n - The factorial base.

* Returns : The value of ln(n!).

*/

double log_fact (int n)

{

if (n <= 1)

/* Since 0! = 1! = 1, we can simple return ln(1) = 0: */

return (0);

/* Use the equality: ln(n!) = ln((n-1)!) + ln(n) */

return (log_fact(n - 1) + log (n));

}