/***************************************************
*      Program to demonstrate LN(X!) Function      *
* ------------------------------------------------ *
* Reference: BASIC Scientific Subroutines, Vol. II *
* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
*                                                  *
*             C++ Version by J.-P. Moreau, Paris.  *
* ------------------------------------------------ *
* SAMPLE RUN:                                      *
*                                                  *
*    X     LN(X!)        EXP(LN(X!))               *
*  ----------------------------------              *
*    1    -0.000307                1               *
*    2     0.693146                2               *
*    3     1.791759                6               *
*    4     3.178054               24               *
*    5     4.787492              120               *
*    6     6.579251              720               *
*    7     8.525161             5040               *
*    8    10.604603            40320               *
*    9    12.801827           362880               *
*   10    15.104413          3628800               *
*   11    17.502308         39916800               *
*   12    19.987214        479001600               *
*   13    22.552164       6227020800               *
*   14    25.191221      87178291200               *
*   15    27.899271    1307674368000               *
*                                                  *
****************************************************
See file chi-sq.txt, equation (2.3.9)             */

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

int i; double x,y;

/**************************************************
* Series approximation subroutine for LN(X!)      *
* Accuracy better then 6 places for x>=3          *
* Accuracy better than 12 places for x>10         *
* Advantage is that very large values of the      *
* argument can be used without fear of over flow. *
* Reference: CRC Math Tables.                     *
* x is the input, y is the output.                *
**************************************************/
void LN_FactX()  {
  double x1;
  x1 = 1.0 / (x * x);
  y = (x + 0.5) * log(x) - x * (1 - x1 / 12 + x1 * x1 / 360 - x1 * x1 * x1 / 1260 + x1 * x1 * x1 * x1 / 1680);
  y += 0.918938533205;
}


void main() {
  printf("\n  X     LN(X!)        EXP(LN(X!))\n");
  printf("---------------------------------\n");
  for (i = 1; i<16; i++) {
	x = (double) i;

    LN_FactX();

    printf(" %2d    %9.6f    %13.0f\n",i,y,exp(y));
  }
  printf("---------------------------------\n\n");
}

// End of file Logn!.cpp