source/libs/mpfr/mpfr-3.1.3/src/atanh.c

   1 /* mpfr_atanh -- Inverse Hyperbolic Tangente
   2
   3 Copyright 2001-2015 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  /* The computation of atanh is done by
  27        atanh= 1/2*ln(x+1)-1/2*ln(1-x)   */
  28
  29 int
  30 mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
  31 {
  32   int inexact;
  33   mpfr_t x, t, te;
  34   mpfr_prec_t Nx, Ny, Nt;
  35   mpfr_exp_t err;
  36   MPFR_ZIV_DECL (loop);
  37   MPFR_SAVE_EXPO_DECL (expo);
  38
  39   MPFR_LOG_FUNC
  40     (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
  41     ("y[%Pu]=%.*Rg inexact=%d",
  42      mpfr_get_prec (y), mpfr_log_prec, y, inexact));
  43
  44   /* Special cases */
  45   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
  46     {
  47       /* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result
  48          between -1 and 1 */
  49       if (MPFR_IS_NAN (xt) || MPFR_IS_INF (xt))
  50         {
  51           MPFR_SET_NAN (y);
  52           MPFR_RET_NAN;
  53         }
  54       else /* necessarily xt is 0 */
  55         {
  56           MPFR_ASSERTD (MPFR_IS_ZERO (xt));
  57           MPFR_SET_ZERO (y);   /* atanh(0) = 0 */
  58           MPFR_SET_SAME_SIGN (y,xt);
  59           MPFR_RET (0);
  60         }
  61     }
  62
  63   /* atanh (x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */
  64   if (MPFR_UNLIKELY (MPFR_GET_EXP (xt) > 0))
  65     {
  66       if (MPFR_GET_EXP (xt) == 1 && mpfr_powerof2_raw (xt))
  67         {
  68           MPFR_SET_INF (y);
  69           MPFR_SET_SAME_SIGN (y, xt);
  70           mpfr_set_divby0 ();
  71           MPFR_RET (0);
  72         }
  73       MPFR_SET_NAN (y);
  74       MPFR_RET_NAN;
  75     }
  76
  77   /* atanh(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
  78   MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 1,
  79                                     rnd_mode, {});
  80
  81   MPFR_SAVE_EXPO_MARK (expo);
  82
  83   /* Compute initial precision */
  84   Nx = MPFR_PREC (xt);
  85   MPFR_TMP_INIT_ABS (x, xt);
  86   Ny = MPFR_PREC (y);
  87   Nt = MAX (Nx, Ny);
  88   /* the optimal number of bits : see algorithms.ps */
  89   Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
  90
  91   /* initialise of intermediary variable */
  92   mpfr_init2 (t, Nt);
  93   mpfr_init2 (te, Nt);
  94
  95   /* First computation of cosh */
  96   MPFR_ZIV_INIT (loop, Nt);
  97   for (;;)
  98     {
  99       /* compute atanh */
 100       mpfr_ui_sub (te, 1, x, MPFR_RNDU);   /* (1-xt)*/
 101       mpfr_add_ui (t,  x, 1, MPFR_RNDD);   /* (xt+1)*/
 102       mpfr_div (t, t, te, MPFR_RNDN);      /* (1+xt)/(1-xt)*/
 103       mpfr_log (t, t, MPFR_RNDN);          /* ln((1+xt)/(1-xt))*/
 104       mpfr_div_2ui (t, t, 1, MPFR_RNDN);   /* (1/2)*ln((1+xt)/(1-xt))*/
 105
 106       /* error estimate: see algorithms.tex */
 107       /* FIXME: this does not correspond to the value in algorithms.tex!!! */
 108       /* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/
 109       err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
 110
 111       if (MPFR_LIKELY (MPFR_IS_ZERO (t)
 112                        || MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
 113         break;
 114
 115       /* reactualisation of the precision */
 116       MPFR_ZIV_NEXT (loop, Nt);
 117       mpfr_set_prec (t, Nt);
 118       mpfr_set_prec (te, Nt);
 119     }
 120   MPFR_ZIV_FREE (loop);
 121
 122   inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
 123
 124   mpfr_clear(t);
 125   mpfr_clear(te);
 126
 127   MPFR_SAVE_EXPO_FREE (expo);
 128   return mpfr_check_range (y, inexact, rnd_mode);
 129 }
 130