/***************************************************
* Program to demonstrate the Chi-Square() Function *
* ------------------------------------------------ *
* Reference: BASIC Scientific Subroutines, Vol. II *
* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
*                                                  *
*             C++ Version by J.-P. Moreau, Paris.  *
*                     (www.jpmoreau.fr)            *
* ------------------------------------------------ *
* SAMPLE RUN:                                      *
* How many degrees of freedom: 100                 *
* What is the range (X1,X2):                       *
*   X1: 50                                         *
*   X2: 150                                        *
* What is the table step size: 5                   *
*                                                  *
*    X       Chi-Square PDF                        *
*   ------------------------                       *
*    50        0.00000                             *
*    55        0.00003                             *
*    60        0.00018                             *
*    65        0.00076                             *
*    70        0.00237                             *
*    75        0.00571                             *
*    80        0.01107                             *
*    85        0.01772                             *
*    90        0.02393                             *
*    95        0.02779                             *
*   100        0.02816                             *
*   105        0.02525                             *
*   110        0.02025                             *
*   115        0.01468                             *
*   120        0.00970                             *
*   125        0.00588                             *
*   130        0.00330                             *
*   135        0.00172                             *
*   140        0.00084                             *
*   145        0.00038                             *
*   150        0.00017                             *
*                                                  *
***************************************************/
#include <stdio.h>
#include <math.h>

double m1,x,x1,x2,x3,y;
int    m;


/**************************************************
* Series approximation subroutine 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;
}


/*****************************************************
* Chi-square function subroutine. This program takes *
* a given degree of freedom, m and value, x, and     *
* calculates the chi-square density distribution     *
* function value, y.                                 *
* Reference: Texas Instruments SR-51 owners Manual,  *
* 1974.                                              *
* Subroutine used: LN(X!).                           *
*****************************************************/
void Chi_Square()  {
  double c;
  //Save X
  m1 = x;
  //Perform calculation
  x = (double) (m / 2 - 1);
  //Call LN(X!) subroutine
  LN_FactX();
  x = m1;
  c = -x / 2 + (m / 2 - 1) * log(x) - (m / 2) * log(2) - y;
  y = exp(c);
}

void main()  {
  printf("\n How many degrees of freedom: "); scanf("%d",&m);
  printf(" What is the range (X1,X2):\n");
  printf("   X1: "); scanf("%lf",&x1);
  printf("   X2: "); scanf("%lf",&x2);
  printf(" What is the table step size: "); scanf("%lf",&x3);
  printf("\n   X       Chi-Square PDF ");
  printf("\n -------------------------\n");
  x=x1;
  while (x <= x2)  {
    Chi_Square();
    printf("  %3.0f        %7.5f\n",x,y);
    x +=  x3;
  }
}


// End of file chi-sqr.cpp