/*************************************************************************************************************************************/
/*                                                                                                                                   */
/*        C A L C U L   D E   ' P I '   P A R   L A   F O R M U L E                                                                  */
/*        D ' O R D R E   5   ( " Q U I N T I Q U E " )  :                                                                           */
/*                                                                                                                                   */
/*                                                                                                                                   */
/*        Author of '$xtc/pi_quintique.01$c' :                                                                                       */
/*                                                                                                                                   */
/*                    Jean-Francois COLONNA (LACTAMME, AAAAMMJJhhmmss).                                                              */
/*                                                                                                                                   */
/*************************************************************************************************************************************/

#include  "INCLUDES.01.I"
                                        /* Introduit le 20051116101907...                                                            */

extern    double    sqrt();
extern    double    pow();

#define   UN        1.0
#define   DEUX      2.0
#define   CINQ      5.0
#define   SIX       6.0
#define   SEPT      7.0

#define   ITER      2

main()
     {
     double    k;
     double    A_k_1=UN / DEUX;
     double    A_k;
     double    S_k_1=CINQ*(sqrt(CINQ) - DEUX);
     double    S_k;
     double    x,y,z;
     double    pi;

     for       (k=0 ; k<ITER ; k++)
               {
               x = (CINQ / S_k_1) - UN;
               y = EXP2(x - UN) + SEPT;
               z = pow((x*(y + sqrt(EXP2(y) - 4*EXP3(x)))/DEUX),UN/CINQ);

               S_k = EXP2(CINQ) / (EXP2(z + (x/z) + UN)*S_k_1);
               A_k = (EXP2(S_k_1)*A_k_1) - (pow(CINQ,k)*(((EXP2(S_k_1) - CINQ)/DEUX) + sqrt(S_k_1*(EXP2(S_k_1) - (DEUX*S_k_1) + CINQ))));

               A_k_1 = A_k;
               S_k_1 = S_k;
                                        /* Formule donnee a la page 624 de "PI a Source Book" des freres Borwein.                    */
               }

     pi = UN / A_k;
     printf("\n pi = %.12f",pi);
     }