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/* mpfr_zeta -- Riemann Zeta function at a floating-point number
Copyright 1999, 2000, 2001, 2002, 2003 Free Software Foundation.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */
#include <stdio.h>
#include <math.h>
#include "gmp.h"
#include "mpfr.h"
#include "gmp-impl.h"
#include "longlong.h"
int
mpfr_zeta (mpfr_ptr result, mpfr_srcptr op, mp_rnd_t rnd_mode)
{
mpfr_t s,s2,x,y,u,b,v,nn,z,z2;
int i, n, succes;
int cmp1;
if (MPFR_IS_NAN(op) || MPFR_SIGN(op) < 0)
{
MPFR_SET_NAN(result);
MPFR_RET_NAN;
}
if (MPFR_IS_INF(op)) /* +infinity */
return mpfr_set_ui(result, 1, rnd_mode);
cmp1 = mpfr_cmp_ui(op, 1);
if (cmp1 < 0)
{
MPFR_SET_NAN(result);
MPFR_RET_NAN;
}
if (cmp1 == 0)
{
MPFR_CLEAR_NAN(result);
MPFR_SET_INF(result);
MPFR_SET_POS(result);
return 0;
}
/* 1 < op < +infinity */
/* first version */
if (mpfr_get_d1 (op) != 2.0 || rnd_mode != GMP_RNDN
|| MPFR_PREC(result) != 53) {
fprintf(stderr, "not yet implemented\n"); exit(1);
}
mpfr_set_default_prec(67);
mpfr_init(x); mpfr_init(y); mpfr_init(s); mpfr_init(s2);
mpfr_init(u); mpfr_init(b); mpfr_init(v); mpfr_init(nn);
mpfr_init(z); mpfr_init(z2);
mpfr_set_ui(u,1,GMP_RNDN);
mpfr_set_ui(s,0,GMP_RNDN);
/* s=Somme des 1/i^2 (i=100...2) */
n=100;
for (i=n; i>1; i--)
{
mpfr_div_ui(y,u,i*i,GMP_RNDN);
mpfr_add(s,s,y,GMP_RNDN);
}
/* Application d'Euler-Maclaurin, jusqu'au terme 1/n^7 - n=100) */
/* mpfr_set_ui(nn,n,GMP_RNDN); */
mpfr_div_ui(z,u,n,GMP_RNDN);
mpfr_mul(z2,z,z,GMP_RNDN);
mpfr_div_2ui(v,z2,1,GMP_RNDN);
mpfr_set(s2,z,GMP_RNDN);
mpfr_sub(s2,s2,v,GMP_RNDN);
mpfr_mul(z,z,z2,GMP_RNDN);
mpfr_div_ui(v,z,6,GMP_RNDN);
mpfr_add(s2,s2,v,GMP_RNDN);
mpfr_mul(z,z,z2,GMP_RNDN);
mpfr_div_ui(v,z,30,GMP_RNDN);
mpfr_sub(s2,s2,v,GMP_RNDN);
mpfr_mul(z,z,z2,GMP_RNDN);
mpfr_div_ui(v,z,42,GMP_RNDN);
mpfr_add(s2,s2,v,GMP_RNDN);
mpfr_add(s,s,s2,GMP_RNDN);
mpfr_add(s,s,u,GMP_RNDN);
/*Peut-on arrondir ? La reponse est oui*/
succes=mpfr_can_round(s, 57, GMP_RNDN,GMP_RNDN, 53);
if (succes) mpfr_set(result,s,GMP_RNDN);
else {
fprintf(stderr, "can't round in mpfr_zeta\n"); exit(1);
}
mpfr_clear(x); mpfr_clear(y); mpfr_clear(s); mpfr_clear(s2);
mpfr_clear(u); mpfr_clear(b); mpfr_clear(v); mpfr_clear(nn);
mpfr_clear(z); mpfr_clear(z2);
return 1; /* result is inexact */
}
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