1/* mpfr_cosh -- hyperbolic cosine
2
3Copyright 2001, 2002, 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 cosh is done by    *
27 *  cosh= 1/2[e^(x)+e^(-x)]              */
28
29int
30mpfr_cosh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
31{
32  mpfr_t x;
33  int inexact;
34  MPFR_SAVE_EXPO_DECL (expo);
35
36  MPFR_LOG_FUNC (
37    ("x[%Pu]=%*.Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
38    ("y[%Pu]=%*.Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
39     inexact));
40
41  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(xt)))
42    {
43      if (MPFR_IS_NAN(xt))
44        {
45          MPFR_SET_NAN(y);
46          MPFR_RET_NAN;
47        }
48      else if (MPFR_IS_INF(xt))
49        {
50          MPFR_SET_INF(y);
51          MPFR_SET_POS(y);
52          MPFR_RET(0);
53        }
54      else
55        {
56          MPFR_ASSERTD(MPFR_IS_ZERO(xt));
57          return mpfr_set_ui (y, 1, rnd_mode); /* cosh(0) = 1 */
58        }
59    }
60
61  MPFR_SAVE_EXPO_MARK (expo);
62
63  /* cosh(x) = 1+x^2/2 + ... <= 1+x^2 for x <= 2.9828...,
64     thus the error < 2^(2*EXP(x)). If x >= 1, then EXP(x) >= 1,
65     thus the following will always fail. */
66  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, -2 * MPFR_GET_EXP (xt), 0,
67                                    1, rnd_mode, inexact = _inexact; goto end);
68
69  MPFR_TMP_INIT_ABS(x, xt);
70  /* General case */
71  {
72    /* Declaration of the intermediary variable */
73    mpfr_t t, te;
74    /* Declaration of the size variable */
75    mpfr_prec_t Ny = MPFR_PREC(y);   /* Precision of output variable */
76    mpfr_prec_t Nt;                  /* Precision of the intermediary variable */
77    long int err;                  /* Precision of error */
78    MPFR_ZIV_DECL (loop);
79    MPFR_GROUP_DECL (group);
80
81    /* compute the precision of intermediary variable */
82    /* The optimal number of bits : see algorithms.tex */
83    Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
84
85    /* initialise of intermediary variables */
86    MPFR_GROUP_INIT_2 (group, Nt, t, te);
87
88    /* First computation of cosh */
89    MPFR_ZIV_INIT (loop, Nt);
90    for (;;)
91      {
92        MPFR_BLOCK_DECL (flags);
93
94        /* Compute cosh */
95        MPFR_BLOCK (flags, mpfr_exp (te, x, MPFR_RNDD));  /* exp(x) */
96        /* exp can overflow (but not underflow since x>0) */
97        if (MPFR_OVERFLOW (flags))
98          /* cosh(x) > exp(x), cosh(x) underflows too */
99          {
100            inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
101            MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
102            break;
103          }
104        mpfr_ui_div (t, 1, te, MPFR_RNDU);   /* 1/exp(x) */
105        mpfr_add (t, te, t, MPFR_RNDU);      /* exp(x) + 1/exp(x)*/
106        mpfr_div_2ui (t, t, 1, MPFR_RNDN);   /* 1/2(exp(x) + 1/exp(x))*/
107
108        /* Estimation of the error */
109        err = Nt - 3;
110        /* Check if we can round */
111        if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
112          {
113            inexact = mpfr_set (y, t, rnd_mode);
114            break;
115          }
116
117        /* Actualisation of the precision */
118        MPFR_ZIV_NEXT (loop, Nt);
119        MPFR_GROUP_REPREC_2 (group, Nt, t, te);
120      }
121    MPFR_ZIV_FREE (loop);
122    MPFR_GROUP_CLEAR (group);
123  }
124
125 end:
126  MPFR_SAVE_EXPO_FREE (expo);
127  return mpfr_check_range (y, inexact, rnd_mode);
128}
129