1  /* generic inverse of a function.
       2  
       3  Copyright 2005-2023 Free Software Foundation, Inc.
       4  Contributed by the AriC and Caramba 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  https://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  }