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

   1 /* mpfr_sinh_cosh -- hyperbolic sine and cosine
   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 #define INEXPOS(y) ((y) == 0 ? 0 : (((y) > 0) ? 1 : 2))
  27 #define INEX(y,z) (INEXPOS(y) | (INEXPOS(z) << 2))
  28
  29  /* The computations are done by
  30     cosh(x) = 1/2 [e^(x)+e^(-x)]
  31     sinh(x) = 1/2 [e^(x)-e^(-x)]
  32     Adapted from mpfr_sinh.c     */
  33
  34 int
  35 mpfr_sinh_cosh (mpfr_ptr sh, mpfr_ptr ch, mpfr_srcptr xt, mpfr_rnd_t rnd_mode)
  36 {
  37   mpfr_t x;
  38   int inexact_sh, inexact_ch;
  39
  40   MPFR_ASSERTN (sh != ch);
  41
  42   MPFR_LOG_FUNC
  43     (("x[%Pu]=%.*Rg rnd=%d",
  44       mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
  45      ("sh[%Pu]=%.*Rg ch[%Pu]=%.*Rg",
  46       mpfr_get_prec (sh), mpfr_log_prec, sh,
  47       mpfr_get_prec (ch), mpfr_log_prec, ch));
  48
  49   if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
  50     {
  51       if (MPFR_IS_NAN (xt))
  52         {
  53           MPFR_SET_NAN (ch);
  54           MPFR_SET_NAN (sh);
  55           MPFR_RET_NAN;
  56         }
  57       else if (MPFR_IS_INF (xt))
  58         {
  59           MPFR_SET_INF (sh);
  60           MPFR_SET_SAME_SIGN (sh, xt);
  61           MPFR_SET_INF (ch);
  62           MPFR_SET_POS (ch);
  63           MPFR_RET (0);
  64         }
  65       else /* xt is zero */
  66         {
  67           MPFR_ASSERTD (MPFR_IS_ZERO (xt));
  68           MPFR_SET_ZERO (sh);                   /* sinh(0) = 0 */
  69           MPFR_SET_SAME_SIGN (sh, xt);
  70           inexact_sh = 0;
  71           inexact_ch = mpfr_set_ui (ch, 1, rnd_mode); /* cosh(0) = 1 */
  72           return INEX(inexact_sh,inexact_ch);
  73         }
  74     }
  75
  76   /* Warning: if we use MPFR_FAST_COMPUTE_IF_SMALL_INPUT here, make sure
  77      that the code also works in case of overlap (see sin_cos.c) */
  78
  79   MPFR_TMP_INIT_ABS (x, xt);
  80
  81   {
  82     mpfr_t s, c, ti;
  83     mpfr_exp_t d;
  84     mpfr_prec_t N;    /* Precision of the intermediary variables */
  85     long int err;    /* Precision of error */
  86     MPFR_ZIV_DECL (loop);
  87     MPFR_SAVE_EXPO_DECL (expo);
  88     MPFR_GROUP_DECL (group);
  89
  90     MPFR_SAVE_EXPO_MARK (expo);
  91
  92     /* compute the precision of intermediary variable */
  93     N = MPFR_PREC (ch);
  94     N = MAX (N, MPFR_PREC (sh));
  95     /* the optimal number of bits : see algorithms.ps */
  96     N = N + MPFR_INT_CEIL_LOG2 (N) + 4;
  97
  98     /* initialise of intermediary variables */
  99     MPFR_GROUP_INIT_3 (group, N, s, c, ti);
 100
 101     /* First computation of sinh_cosh */
 102     MPFR_ZIV_INIT (loop, N);
 103     for (;;)
 104       {
 105         MPFR_BLOCK_DECL (flags);
 106
 107         /* compute sinh_cosh */
 108         MPFR_BLOCK (flags, mpfr_exp (s, x, MPFR_RNDD));
 109         if (MPFR_OVERFLOW (flags))
 110           /* exp(x) does overflow */
 111           {
 112             /* since cosh(x) >= exp(x), cosh(x) overflows too */
 113             inexact_ch = mpfr_overflow (ch, rnd_mode, MPFR_SIGN_POS);
 114             /* sinh(x) may be representable */
 115             inexact_sh = mpfr_sinh (sh, xt, rnd_mode);
 116             MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
 117             break;
 118           }
 119         d = MPFR_GET_EXP (s);
 120         mpfr_ui_div (ti, 1, s, MPFR_RNDU);  /* 1/exp(x) */
 121         mpfr_add (c, s, ti, MPFR_RNDU);     /* exp(x) + 1/exp(x) */
 122         mpfr_sub (s, s, ti, MPFR_RNDN);     /* exp(x) - 1/exp(x) */
 123         mpfr_div_2ui (c, c, 1, MPFR_RNDN);  /* 1/2(exp(x) + 1/exp(x)) */
 124         mpfr_div_2ui (s, s, 1, MPFR_RNDN);  /* 1/2(exp(x) - 1/exp(x)) */
 125
 126         /* it may be that s is zero (in fact, it can only occur when exp(x)=1,
 127            and thus ti=1 too) */
 128         if (MPFR_IS_ZERO (s))
 129           err = N; /* double the precision */
 130         else
 131           {
 132             /* calculation of the error */
 133             d = d - MPFR_GET_EXP (s) + 2;
 134             /* error estimate: err = N-(__gmpfr_ceil_log2(1+pow(2,d)));*/
 135             err = N - (MAX (d, 0) + 1);
 136             if (MPFR_LIKELY (MPFR_CAN_ROUND (s, err, MPFR_PREC (sh),
 137                                              rnd_mode) &&               \
 138                              MPFR_CAN_ROUND (c, err, MPFR_PREC (ch),
 139                                              rnd_mode)))
 140               {
 141                 inexact_sh = mpfr_set4 (sh, s, rnd_mode, MPFR_SIGN (xt));
 142                 inexact_ch = mpfr_set (ch, c, rnd_mode);
 143                 break;
 144               }
 145           }
 146         /* actualisation of the precision */
 147         N += err;
 148         MPFR_ZIV_NEXT (loop, N);
 149         MPFR_GROUP_REPREC_3 (group, N, s, c, ti);
 150       }
 151     MPFR_ZIV_FREE (loop);
 152     MPFR_GROUP_CLEAR (group);
 153     MPFR_SAVE_EXPO_FREE (expo);
 154   }
 155
 156   /* now, let's raise the flags if needed */
 157   inexact_sh = mpfr_check_range (sh, inexact_sh, rnd_mode);
 158   inexact_ch = mpfr_check_range (ch, inexact_ch, rnd_mode);
 159
 160   return INEX(inexact_sh,inexact_ch);
 161 }