1/* generic inverse of a function.
2
3Copyright 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#ifndef ACTION_SPECIAL
27#define ACTION_SPECIAL
28#endif
29
30#ifndef ACTION_TINY
31#define ACTION_TINY
32#endif
33
34/* example of use:
35#define FUNCTION mpfr_sec
36#define INVERSE  mpfr_cos
37#define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1)
38#define ACTION_INF(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1)
39#define ACTION_ZERO(y) return mpfr_set_ui (y, 1, MPFR_RNDN)
40#include "gen_inverse.h"
41*/
42
43int
44FUNCTION (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
45{
46  mpfr_prec_t precy; /* target precision */
47  mpfr_prec_t m;     /* working precision */
48  mpfr_t z;        /* temporary variable to store INVERSE(x) */
49  int inexact;     /* inexact flag */
50  MPFR_ZIV_DECL (loop);
51  MPFR_SAVE_EXPO_DECL (expo);
52
53  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
54    {
55      if (MPFR_IS_NAN(x))
56        ACTION_NAN(y);
57      else if (MPFR_IS_INF(x))
58        ACTION_INF(y);
59      else /* x = 0 */
60        ACTION_ZERO(y,x);
61    }
62
63  /* x is neither NaN, Inf nor zero */
64  MPFR_SAVE_EXPO_MARK (expo);
65  ACTION_TINY (y, x, rnd_mode); /* special case for very small input x */
66  precy = MPFR_PREC(y);
67  m = precy + MPFR_INT_CEIL_LOG2 (precy) + 3;
68  mpfr_init2 (z, m);
69
70  MPFR_ZIV_INIT (loop, m);
71  for(;;)
72    {
73      MPFR_BLOCK_DECL (flags);
74
75      MPFR_BLOCK (flags, INVERSE (z, x, MPFR_RNDZ)); /* error k_u < 1 ulp */
76      /* FIXME: the following assumes that if an overflow happens with
77         MPFR_EMAX_MAX, then necessarily an underflow happens with
78         __gmpfr_emin */
79      if (MPFR_OVERFLOW (flags))
80        {
81          int s = MPFR_SIGN(z);
82          MPFR_ZIV_FREE (loop);
83          mpfr_clear (z);
84          MPFR_SAVE_EXPO_FREE (expo);
85          return mpfr_underflow (y, (rnd_mode == MPFR_RNDN) ?
86                                 MPFR_RNDZ : rnd_mode, s);
87        }
88      mpfr_ui_div (z, 1, z, MPFR_RNDN);
89      /* the error is less than c_w + 2*c_u*k_u (see algorithms.tex),
90         where c_w = 1/2, c_u = 1 since z was rounded toward zero,
91         thus 1/2 + 2 < 4 */
92      if (MPFR_LIKELY (MPFR_CAN_ROUND (z, m - 2, precy, rnd_mode)))
93        break;
94      ACTION_SPECIAL;
95      MPFR_ZIV_NEXT (loop, m);
96      mpfr_set_prec (z, m);
97    }
98  MPFR_ZIV_FREE (loop);
99
100  inexact = mpfr_set (y, z, rnd_mode);
101  mpfr_clear (z);
102
103 end:
104  MPFR_SAVE_EXPO_FREE (expo);
105  return mpfr_check_range (y, inexact, rnd_mode);
106}
107