////////////////////////////////////////////////////////////////////////////////
// File: testlngamma.c                                                        //
//                                                                            //
// Test the functions Ln_Gamma_Function() and xLn_Gamma_Function() in the file//
// ln_gamma_function.c                                                        //
//                                                                            //
// A table of log Gamma function can be found in "Handbook of Mathematical    //
// Functions with Formulas, Graphs, and Mathematical Tables" by Abramowitz    //
// and Stegun on page 274 Table 6.4 (note the table is the log Gamma Function,//
// where the log is the common log i.e. log10).                               //
////////////////////////////////////////////////////////////////////////////////
#include <math.h>
#include <float.h>
#include <stdio.h>

extern long double xGamma_Function(long double x);
extern double Gamma_Function(double x);
extern double Gamma_Function_Max_Arg( void );
extern double Ln_Gamma_Function(double x);
extern long double xLn_Gamma_Function(long double x);

int main() {

   double est;
   long double x,g;
   long double estL;
   long double onethird = 1.0L / 3.0L;
   long double half = 0.5L;
   long double twothirds = 2.0L / 3.0L;
   long double ln10 = logl(10.0);
   int i;
  
   printf("Program: testlngamma.c\n\n");
   printf("See Abramowitz and Stegan - Handbook of Mathematical Functions with Formulas,\n                            Graphs, and Mathematical Tables\n                            Page 274 Table 6.4\n\n");
   printf("Table of Log10(Gamma(x))  (double)\n\n");
   printf("   x  Log10(Gamma(x)) Log10(Gamma(x+1/3)) Log10(Gamma(x+1/2)) Log10(Gamma(x+2/3)\n");
   for (i = 1; i <= 101; i++) {
      x = (long double) i;
      printf("%4i",i);
      est = Ln_Gamma_Function((double) x) / ln10;
      printf("%+14.8f",est);
      est = Ln_Gamma_Function((double) (x + onethird)) / ln10;
      printf("%+17.8f",est);
      est = Ln_Gamma_Function((double) (x + half)) / ln10;
      printf("%+20.8f",est);
      est = Ln_Gamma_Function((double) (x + twothirds)) / ln10;
      printf("%+20.8f\n",est);
   }
   printf("\n\n");
   printf("Table of Log10(Gamma(x))  (long double)\n\n");
   printf("   x  Log10(Gamma(x)) Log10(Gamma(x+1/3)) Log10(Gamma(x+1/2)) Log10(Gamma(x+2/3)\n");
   for (i = 1; i <= 101; i++) {
      x = (long double) i;
      printf("%4i",i);
      estL = xLn_Gamma_Function(x) / ln10;
      printf("%+14.8Lf",estL);
      estL = xLn_Gamma_Function(x + onethird) / ln10; 
      printf("%+17.8Lf",estL);
      estL = xLn_Gamma_Function(x + half) / ln10; 
      printf("%+20.8Lf",estL);
      estL = xLn_Gamma_Function(x + twothirds) / ln10; 
      printf("%+20.8Lf\n",estL);
   }
   printf("\n\n");
}