Annotation of OpenXM_contrib/gmp/mpfr/atanh.c, Revision 1.1.1.1
1.1 ohara 1: /* mpfr_atanh -- Inverse Hyperbolic Tangente of Unsigned Integer Number
2:
3: Copyright 2001, 2002 Free Software Foundation.
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 Lesser General Public License as published by
9: the Free Software Foundation; either version 2.1 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 Lesser General Public
15: License for more details.
16:
17: You should have received a copy of the GNU Lesser 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 "gmp.h"
23: #include "gmp-impl.h"
24: #include "mpfr.h"
25: #include "mpfr-impl.h"
26:
27: /* The computation of acosh is done by
28:
29: atanh= 1/2*ln(x+1)-1/2*ln(1-x)
30: */
31:
32: int
33: mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
34: {
35: int inexact =0;
36: mpfr_t x;
37: int flag_neg=0;
38:
39: mp_prec_t Nx=MPFR_PREC(xt); /* Precision of input variable */
40: mpfr_init2(x,Nx);
41: mpfr_set(x,xt,GMP_RNDN);
42:
43: if (MPFR_SIGN(x) < 0)
44: {
45: MPFR_CHANGE_SIGN(x);
46: flag_neg=1;
47: }
48:
49: if (MPFR_IS_NAN(x))
50: {
51: MPFR_SET_NAN(y);
52: mpfr_clear(x);
53: MPFR_RET_NAN;
54: }
55: MPFR_CLEAR_NAN(y);
56:
57:
58: if (MPFR_IS_INF(x))
59: {
60: MPFR_SET_INF(y);
61: MPFR_SET_SAME_SIGN(y,x);
62: if(flag_neg)
63: MPFR_CHANGE_SIGN(y);
64: mpfr_clear(x);
65: MPFR_RET(0);
66: }
67:
68: MPFR_CLEAR_INF(y);
69:
70: if (MPFR_IS_ZERO(x))
71: {
72: MPFR_SET_ZERO(y); /* atanh(0) = 0 */
73: MPFR_SET_SAME_SIGN(y,x);
74: if(flag_neg)
75: MPFR_CHANGE_SIGN(y);
76: mpfr_clear(x);
77: MPFR_RET(0);
78: }
79:
80: /* General case */
81: {
82: /* Declaration of the intermediary variable */
83: mpfr_t t, te,ti;
84:
85: /* Declaration of the size variable */
86: mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
87: mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
88:
89: mp_prec_t Nt; /* Precision of the intermediary variable */
90: long int err; /* Precision of error */
91:
92: /* compute the precision of intermediary variable */
93: Nt=MAX(Nx,Ny);
94: /* the optimal number of bits : see algorithms.ps */
95: Nt=Nt+4+_mpfr_ceil_log2(Nt);
96:
97: /* initialise of intermediary variable */
98: mpfr_init(t);
99: mpfr_init(te);
100: mpfr_init(ti);
101:
102: /* First computation of cosh */
103: do {
104:
105: /* reactualisation of the precision */
106: mpfr_set_prec(t,Nt);
107: mpfr_set_prec(te,Nt);
108: mpfr_set_prec(ti,Nt);
109:
110: /* compute atanh */
111: mpfr_ui_sub(te,1,x,GMP_RNDU); /* (1-xt)*/
112: mpfr_add_ui(ti,x,1,GMP_RNDD); /* (xt+1)*/
113: mpfr_div(te,ti,te,GMP_RNDN); /* (1+xt)/(1-xt)*/
114: mpfr_log(te,te,GMP_RNDN); /* ln((1+xt)/(1-xt))*/
115: mpfr_div_2ui(t,te,1,GMP_RNDN); /* (1/2)*ln((1+xt)/(1-xt))*/
116:
117: /* estimation of the error see- algorithms.ps*/
118: /* err=Nt-_mpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
119: err=Nt-(MAX(4-MPFR_EXP(t),0)+1);
120:
121: /* actualisation of the precision */
122: Nt += 10;
123:
124: } while ((err < 0) || (!mpfr_can_round(t,err,GMP_RNDN,rnd_mode,Ny) || (MPFR_IS_ZERO(t))));
125:
126: if(flag_neg)
127: MPFR_CHANGE_SIGN(t);
128:
129: inexact = mpfr_set(y,t,rnd_mode);
130:
131: mpfr_clear(t);
132: mpfr_clear(ti);
133: mpfr_clear(te);
134: }
135: mpfr_clear(x);
136: return inexact;
137: }
138:
139:
140:
141:
142:
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