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

   1 /* mpfr_asinh -- inverse hyperbolic sine
   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 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[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
  42     ("y[%Pu]=%.*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_mul (t, x, 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       /* actualisation 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 }