source/libs/mpfr/mpfr-3.1.3/src/gen_inverse.h

   1 /* generic inverse of a function.
   2
   3 Copyright 2005-2015 Free Software Foundation, Inc.
   4 Contributed by the AriC and Caramel projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 3 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
  20 http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
  21 51 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
  43 int
  44 FUNCTION (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 }