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      1 /* mpfr_asinh -- inverse hyperbolic sine
      2 
      3 Copyright 2001-2023 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 /* The computation of asinh is done by  *
     27  *    asinh = ln(x + sqrt(x^2 + 1))     */
     28 
     29 int
     30 mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
     31 {
     32   int inexact;
     33   int signx, neg;
     34   mpfr_prec_t Ny, Nt;
     35   mpfr_t t; /* auxiliary variables */
     36   mpfr_exp_t err;
     37   MPFR_SAVE_EXPO_DECL (expo);
     38   MPFR_ZIV_DECL (loop);
     39 
     40   MPFR_LOG_FUNC (
     41     ("x[%Pd]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
     42     ("y[%Pd]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
     43      inexact));
     44 
     45   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
     46     {
     47       if (MPFR_IS_NAN (x))
     48         {
     49           MPFR_SET_NAN (y);
     50           MPFR_RET_NAN;
     51         }
     52       else if (MPFR_IS_INF (x))
     53         {
     54           MPFR_SET_INF (y);
     55           MPFR_SET_SAME_SIGN (y, x);
     56           MPFR_RET (0);
     57         }
     58       else /* x is necessarily 0 */
     59         {
     60           MPFR_ASSERTD (MPFR_IS_ZERO (x));
     61           MPFR_SET_ZERO (y);   /* asinh(0) = 0 */
     62           MPFR_SET_SAME_SIGN (y, x);
     63           MPFR_RET (0);
     64         }
     65     }
     66 
     67   /* asinh(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
     68   MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0,
     69                                     rnd_mode, {});
     70 
     71   Ny = MPFR_PREC (y);   /* Precision of output variable */
     72 
     73   signx = MPFR_SIGN (x);
     74   neg = MPFR_IS_NEG (x);
     75 
     76   /* General case */
     77 
     78   /* compute the precision of intermediary variable */
     79   /* the optimal number of bits : see algorithms.tex */
     80   Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);
     81 
     82   MPFR_SAVE_EXPO_MARK (expo);
     83 
     84   /* initialize intermediary variables */
     85   mpfr_init2 (t, Nt);
     86 
     87   /* First computation of asinh */
     88   MPFR_ZIV_INIT (loop, Nt);
     89   for (;;)
     90     {
     91       /* compute asinh */
     92       mpfr_sqr (t, x, MPFR_RNDD);                       /* x^2 */
     93       mpfr_add_ui (t, t, 1, MPFR_RNDD);                 /* x^2+1 */
     94       mpfr_sqrt (t, t, MPFR_RNDN);                      /* sqrt(x^2+1) */
     95       (neg ? mpfr_sub : mpfr_add) (t, t, x, MPFR_RNDN); /* sqrt(x^2+1)+x */
     96       mpfr_log (t, t, MPFR_RNDN);                       /* ln(sqrt(x^2+1)+x)*/
     97 
     98       if (MPFR_LIKELY (MPFR_IS_PURE_FP (t)))
     99         {
    100           /* error estimate -- see algorithms.tex */
    101           err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1);
    102           if (MPFR_LIKELY (MPFR_IS_ZERO (t)
    103                            || MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
    104             break;
    105         }
    106 
    107       /* actualization of the precision */
    108       MPFR_ZIV_NEXT (loop, Nt);
    109       mpfr_set_prec (t, Nt);
    110     }
    111   MPFR_ZIV_FREE (loop);
    112 
    113   inexact = mpfr_set4 (y, t, rnd_mode, signx);
    114 
    115   mpfr_clear (t);
    116 
    117   MPFR_SAVE_EXPO_FREE (expo);
    118   return mpfr_check_range (y, inexact, rnd_mode);
    119 }
    120