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  }