/*************************************************************************************************************************************/
/*                                                                                                                                   */
/*        C A L C U L   D E   ' P I '   P A R   L A   F O R M U L E   D E                                                            */
/*        S A L A M I N - B R E N T   Q U A D R A T I Q U E  :                                                                       */
/*                                                                                                                                   */
/*                                                                                                                                   */
/*        Author of '$xtc/pi_SalBr2.01$c' :                                                                                          */
/*                                                                                                                                   */
/*                    Jean-Francois COLONNA (LACTAMME, AAAAMMJJhhmmss).                                                              */
/*                                                                                                                                   */
/*************************************************************************************************************************************/

#include  <stdio.h>

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

#define   UN        1.0
#define   DEUX      2.0

#define   ITER      4

main()
     {
     double    k;
     double    A_k_1=UN;
     double    A_k;
     double    B_k_1=UN/sqrt(DEUX);
     double    B_k;
     double    C_k;
     double    S_k_1=UN/DEUX;
     double    S_k;
     double    P_k;
     double    pi;

     for       (k=1 ; k<=ITER ; k++)
               {
               A_k = (A_k_1 + B_k_1)/DEUX;
               B_k = sqrt(A_k_1*B_k_1);
               C_k = (A_k*A_k) - (B_k*B_k);
               S_k = S_k_1 - (pow(DEUX,k)*C_k);

               P_k = (DEUX*A_k*A_k)/S_k;

               A_k_1 = A_k;
               B_k_1 = B_k;
               S_k_1 = S_k;
                                        /* Formule donnee a la page 52 du numero 1, volume 19 de The Mathematical Intelligencer.     */
               }

     pi = P_k;
     printf("\n pi = %.12f",pi);
     }