contrib/mpfr/src/tanh.c

   1 /* mpfr_tanh -- hyperbolic tangent
   2
   3 Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 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 int
  27 mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
  28 {
  29   /****** Declaration ******/
  30   mpfr_t x;
  31   int inexact;
  32   MPFR_SAVE_EXPO_DECL (expo);
  33
  34   MPFR_LOG_FUNC
  35     (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
  36      ("y[%Pu]=%.*Rg inexact=%d",
  37       mpfr_get_prec (y), mpfr_log_prec, y, inexact));
  38
  39   /* Special value checking */
  40   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
  41     {
  42       if (MPFR_IS_NAN (xt))
  43         {
  44           MPFR_SET_NAN (y);
  45           MPFR_RET_NAN;
  46         }
  47       else if (MPFR_IS_INF (xt))
  48         {
  49           /* tanh(inf) = 1 && tanh(-inf) = -1 */
  50           return mpfr_set_si (y, MPFR_INT_SIGN (xt), rnd_mode);
  51         }
  52       else /* tanh (0) = 0 and xt is zero */
  53         {
  54           MPFR_ASSERTD (MPFR_IS_ZERO(xt));
  55           MPFR_SET_ZERO (y);
  56           MPFR_SET_SAME_SIGN (y, xt);
  57           MPFR_RET (0);
  58         }
  59     }
  60
  61   /* tanh(x) = x - x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
  62   MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 0,
  63                                     rnd_mode, {});
  64
  65   MPFR_TMP_INIT_ABS (x, xt);
  66
  67   MPFR_SAVE_EXPO_MARK (expo);
  68
  69   /* General case */
  70   {
  71     /* Declaration of the intermediary variable */
  72     mpfr_t t, te;
  73     mpfr_exp_t d;
  74
  75     /* Declaration of the size variable */
  76     mpfr_prec_t Ny = MPFR_PREC(y);   /* target precision */
  77     mpfr_prec_t Nt;                  /* working precision */
  78     long int err;                  /* error */
  79     int sign = MPFR_SIGN (xt);
  80     MPFR_ZIV_DECL (loop);
  81     MPFR_GROUP_DECL (group);
  82
  83     /* First check for BIG overflow of exp(2*x):
  84        For x > 0, exp(2*x) > 2^(2*x)
  85        If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */
  86     if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) {
  87       /* initialise of intermediary variables
  88          since 'set_one' label assumes the variables have been
  89          initialize */
  90       MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te);
  91       goto set_one;
  92     }
  93
  94     /* Compute the precision of intermediary variable */
  95     /* The optimal number of bits: see algorithms.tex */
  96     Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 4;
  97     /* if x is small, there will be a cancellation in exp(2x)-1 */
  98     if (MPFR_GET_EXP (x) < 0)
  99       Nt += -MPFR_GET_EXP (x);
 100
 101     /* initialise of intermediary variable */
 102     MPFR_GROUP_INIT_2 (group, Nt, t, te);
 103
 104     MPFR_ZIV_INIT (loop, Nt);
 105     for (;;) {
 106       /* tanh = (exp(2x)-1)/(exp(2x)+1) */
 107       mpfr_mul_2ui (te, x, 1, MPFR_RNDN);  /* 2x */
 108       /* since x > 0, we can only have an overflow */
 109       mpfr_exp (te, te, MPFR_RNDN);        /* exp(2x) */
 110       if (MPFR_UNLIKELY (MPFR_IS_INF (te))) {
 111       set_one:
 112         inexact = MPFR_FROM_SIGN_TO_INT (sign);
 113         mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign);
 114         if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign)))
 115           {
 116             inexact = -inexact;
 117             mpfr_nexttozero (y);
 118           }
 119         break;
 120       }
 121       d = MPFR_GET_EXP (te);              /* For Error calculation */
 122       mpfr_add_ui (t, te, 1, MPFR_RNDD);   /* exp(2x) + 1*/
 123       mpfr_sub_ui (te, te, 1, MPFR_RNDU);  /* exp(2x) - 1*/
 124       d = d - MPFR_GET_EXP (te);
 125       mpfr_div (t, te, t, MPFR_RNDN);      /* (exp(2x)-1)/(exp(2x)+1)*/
 126
 127       /* Calculation of the error */
 128       d = MAX(3, d + 1);
 129       err = Nt - (d + 1);
 130
 131       if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
 132         {
 133           inexact = mpfr_set4 (y, t, rnd_mode, sign);
 134           break;
 135         }
 136
 137       /* if t=1, we still can round since |sinh(x)| < 1 */
 138       if (MPFR_GET_EXP (t) == 1)
 139         goto set_one;
 140
 141       /* Actualisation of the precision */
 142       MPFR_ZIV_NEXT (loop, Nt);
 143       MPFR_GROUP_REPREC_2 (group, Nt, t, te);
 144     }
 145     MPFR_ZIV_FREE (loop);
 146     MPFR_GROUP_CLEAR (group);
 147   }
 148   MPFR_SAVE_EXPO_FREE (expo);
 149   inexact = mpfr_check_range (y, inexact, rnd_mode);
 150
 151   return inexact;
 152 }
 153