1/* mpfr_asinh -- inverse hyperbolic sine
2
3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4Contributed by the AriC and Caramel projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
22
23#define MPFR_NEED_LONGLONG_H
24#include "mpfr-impl.h"
25
26/* The computation of asinh is done by  *
27 *    asinh = ln(x + sqrt(x^2 + 1))     */
28
29int
30mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
31{
32  int inexact;
33  int signx, neg;
34  mpfr_prec_t Ny, Nt;
35  mpfr_t t; /* auxiliary variables */
36  mpfr_exp_t err;
37  MPFR_SAVE_EXPO_DECL (expo);
38  MPFR_ZIV_DECL (loop);
39
40  MPFR_LOG_FUNC (
41    ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
42    ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
43     inexact));
44
45  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
46    {
47      if (MPFR_IS_NAN (x))
48        {
49          MPFR_SET_NAN (y);
50          MPFR_RET_NAN;
51        }
52      else if (MPFR_IS_INF (x))
53        {
54          MPFR_SET_INF (y);
55          MPFR_SET_SAME_SIGN (y, x);
56          MPFR_RET (0);
57        }
58      else /* x is necessarily 0 */
59        {
60          MPFR_ASSERTD (MPFR_IS_ZERO (x));
61          MPFR_SET_ZERO (y);   /* asinh(0) = 0 */
62          MPFR_SET_SAME_SIGN (y, x);
63          MPFR_RET (0);
64        }
65    }
66
67  /* asinh(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
68  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0,
69                                    rnd_mode, {});
70
71  Ny = MPFR_PREC (y);   /* Precision of output variable */
72
73  signx = MPFR_SIGN (x);
74  neg = MPFR_IS_NEG (x);
75
76  /* General case */
77
78  /* compute the precision of intermediary variable */
79  /* the optimal number of bits : see algorithms.tex */
80  Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);
81
82  MPFR_SAVE_EXPO_MARK (expo);
83
84  /* initialize intermediary variables */
85  mpfr_init2 (t, Nt);
86
87  /* First computation of asinh */
88  MPFR_ZIV_INIT (loop, Nt);
89  for (;;)
90    {
91      /* compute asinh */
92      mpfr_mul (t, x, x, MPFR_RNDD);                    /* x^2 */
93      mpfr_add_ui (t, t, 1, MPFR_RNDD);                 /* x^2+1 */
94      mpfr_sqrt (t, t, MPFR_RNDN);                      /* sqrt(x^2+1) */
95      (neg ? mpfr_sub : mpfr_add) (t, t, x, MPFR_RNDN); /* sqrt(x^2+1)+x */
96      mpfr_log (t, t, MPFR_RNDN);                       /* ln(sqrt(x^2+1)+x)*/
97
98      if (MPFR_LIKELY (MPFR_IS_PURE_FP (t)))
99        {
100          /* error estimate -- see algorithms.tex */
101          err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
102          if (MPFR_LIKELY (MPFR_IS_ZERO (t)
103                           || MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
104            break;
105        }
106
107      /* actualisation of the precision */
108      MPFR_ZIV_NEXT (loop, Nt);
109      mpfr_set_prec (t, Nt);
110    }
111  MPFR_ZIV_FREE (loop);
112
113  inexact = mpfr_set4 (y, t, rnd_mode, signx);
114
115  mpfr_clear (t);
116
117  MPFR_SAVE_EXPO_FREE (expo);
118  return mpfr_check_range (y, inexact, rnd_mode);
119}
120