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Annotation of OpenXM_contrib/gmp/mpfr/zeta.c, Revision 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: }