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: }
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