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Annotation of OpenXM_contrib/gmp/mpfr/zeta.c, Revision 1.1.1.1

1.1       maekawa     1: /* mpfr_zeta -- Riemann Zeta function at a floating-point number
                      2:
                      3: Copyright (C) 1999 PolKA project, Inria Lorraine and Loria
                      4:
                      5: This file is part of the MPFR Library.
                      6:
                      7: The MPFR Library is free software; you can redistribute it and/or modify
                      8: it under the terms of the GNU Library General Public License as published by
                      9: the Free Software Foundation; either version 2 of the License, or (at your
                     10: option) any later version.
                     11:
                     12: The MPFR Library is distributed in the hope that it will be useful, but
                     13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
                     14: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Library General Public
                     15: License for more details.
                     16:
                     17: You should have received a copy of the GNU Library General Public License
                     18: along with the MPFR Library; see the file COPYING.LIB.  If not, write to
                     19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
                     20: MA 02111-1307, USA. */
                     21:
                     22: #include <stdio.h>
                     23: #include <math.h>
                     24: #include "gmp.h"
                     25: #include "gmp-impl.h"
                     26: #include "longlong.h"
                     27: #include "mpfr.h"
                     28:
                     29: int
                     30: #if __STDC__
                     31: mpfr_zeta(mpfr_ptr result, mpfr_srcptr op, unsigned char rnd_mode)
                     32: #else
                     33: mpfr_zeta(result, op, rnd_mode)
                     34:      mpfr_ptr result;
                     35:      mpfr_srcptr op;
                     36:      unsigned char rnd_mode;
                     37: #endif
                     38: {
                     39:        mpfr_t s,s2,x,y,u,b,v,nn,z,z2;
                     40:        int i,n,succes;
                     41:
                     42:        /* first version */
                     43:        if (mpfr_get_d(op) != 2.0 || rnd_mode != GMP_RNDN
                     44:        || PREC(result) != 53) {
                     45:           fprintf(stderr, "not yet implemented\n"); exit(1);
                     46:        }
                     47:
                     48: mpfr_set_default_prec(67);
                     49: mpfr_init(x);
                     50: mpfr_init(y);
                     51: mpfr_init(s);
                     52: mpfr_init(s2);
                     53: mpfr_init(u);
                     54: mpfr_init(b);
                     55: mpfr_init(v);
                     56: mpfr_init(nn);
                     57: mpfr_init(z);
                     58: mpfr_init(z2);
                     59: mpfr_set_ui(u,1,GMP_RNDN);
                     60: mpfr_set_ui(s,0,GMP_RNDN);
                     61: /*s=Somme des 1/i^2 (i=100...2)*/
                     62: n=100;
                     63: for (i=n; i>1; i--)
                     64: {
                     65: mpfr_set_ui(x,i*i,GMP_RNDN);
                     66: mpfr_div(y,u,x,GMP_RNDN);
                     67: mpfr_add(s,s,y,GMP_RNDN);
                     68: };
                     69: /*mpfr_print_raw(s);printf("\n");
                     70: t=mpfr_out_str(stdout,10,0,s,GMP_RNDN);printf("\n");*/
                     71: /*Application d'Euler-Maclaurin, jusqu'au terme 1/n^7 - n=100)*/
                     72: mpfr_set_ui(nn,n,GMP_RNDN);
                     73: mpfr_div(z,u,nn,GMP_RNDN);
                     74: mpfr_set(s2,z,GMP_RNDN);
                     75: mpfr_mul(z2,z,z,GMP_RNDN);
                     76: mpfr_div_2exp(v,z2,1,GMP_RNDN);
                     77: mpfr_sub(s2,s2,v,GMP_RNDN);
                     78: mpfr_set_ui(b,6,GMP_RNDN);
                     79: mpfr_mul(z,z,z2,GMP_RNDN);
                     80: mpfr_div(v,z,b,GMP_RNDN);
                     81: mpfr_add(s2,s2,v,GMP_RNDN);
                     82: mpfr_set_si(b,-30,GMP_RNDN);
                     83: mpfr_mul(z,z,z2,GMP_RNDN);
                     84: mpfr_div(v,z,b,GMP_RNDN);
                     85: mpfr_add(s2,s2,v,GMP_RNDN);
                     86: mpfr_set_si(b,42,GMP_RNDN);
                     87: mpfr_mul(z,z,z2,GMP_RNDN);
                     88: mpfr_div(v,z,b,GMP_RNDN);
                     89: mpfr_add(s2,s2,v,GMP_RNDN);
                     90: /*mpfr_print_raw(s2);printf("\n");
                     91: t=mpfr_out_str(stdout,10,0,s2,GMP_RNDN);printf("\n");*/
                     92: mpfr_add(s,s,s2,GMP_RNDN);
                     93: /*mpfr_print_raw(s);printf("\n");
                     94: t=mpfr_out_str(stdout,10,0,s,GMP_RNDN);printf("\n");*/
                     95: mpfr_add(s,s,u,GMP_RNDN);
                     96: /*mpfr_print_raw(s);printf("\n");
                     97: t=mpfr_out_str(stdout,10,0,s,GMP_RNDN);printf("\n");*/
                     98: /*Peut-on arrondir ? La reponse est oui*/
                     99: succes=mpfr_can_round(s,57,GMP_RNDN,GMP_RNDN,53);
                    100: if (succes) mpfr_set(result,s,GMP_RNDN);
                    101: else {
                    102:   fprintf(stderr, "can't round in mpfr_zeta\n"); exit(1);
                    103: }
                    104:
                    105: mpfr_clear(x);
                    106: mpfr_clear(y);
                    107: mpfr_clear(s);
                    108: mpfr_clear(s2);
                    109: mpfr_clear(u);
                    110: mpfr_clear(b);
                    111: mpfr_clear(v);
                    112: mpfr_clear(nn);
                    113: mpfr_clear(z);
                    114: mpfr_clear(z2);
                    115: return 1; /* result is inexact */
                    116: }