source/libs/mpfr/mpfr-src/src/cosh.c

   1 /* mpfr_cosh -- hyperbolic cosine
   2
   3 Copyright 2001-2002, 2004-2016 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 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 cosh is done by    *
  27  *  cosh= 1/2[e^(x)+e^(-x)]              */
  28
  29 int
  30 mpfr_cosh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
  31 {
  32   mpfr_t x;
  33   int inexact;
  34   MPFR_SAVE_EXPO_DECL (expo);
  35
  36   MPFR_LOG_FUNC (
  37     ("x[%Pu]=%*.Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
  38     ("y[%Pu]=%*.Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
  39      inexact));
  40
  41   if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(xt)))
  42     {
  43       if (MPFR_IS_NAN(xt))
  44         {
  45           MPFR_SET_NAN(y);
  46           MPFR_RET_NAN;
  47         }
  48       else if (MPFR_IS_INF(xt))
  49         {
  50           MPFR_SET_INF(y);
  51           MPFR_SET_POS(y);
  52           MPFR_RET(0);
  53         }
  54       else
  55         {
  56           MPFR_ASSERTD(MPFR_IS_ZERO(xt));
  57           return mpfr_set_ui (y, 1, rnd_mode); /* cosh(0) = 1 */
  58         }
  59     }
  60
  61   MPFR_SAVE_EXPO_MARK (expo);
  62
  63   /* cosh(x) = 1+x^2/2 + ... <= 1+x^2 for x <= 2.9828...,
  64      thus the error < 2^(2*EXP(x)). If x >= 1, then EXP(x) >= 1,
  65      thus the following will always fail. */
  66   MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, -2 * MPFR_GET_EXP (xt), 0,
  67                                     1, rnd_mode, inexact = _inexact; goto end);
  68
  69   MPFR_TMP_INIT_ABS(x, xt);
  70   /* General case */
  71   {
  72     /* Declaration of the intermediary variable */
  73     mpfr_t t, te;
  74     /* Declaration of the size variable */
  75     mpfr_prec_t Ny = MPFR_PREC(y);   /* Precision of output variable */
  76     mpfr_prec_t Nt;                  /* Precision of the intermediary variable */
  77     long int err;                  /* Precision of error */
  78     MPFR_ZIV_DECL (loop);
  79     MPFR_GROUP_DECL (group);
  80
  81     /* compute the precision of intermediary variable */
  82     /* The optimal number of bits : see algorithms.tex */
  83     Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
  84
  85     /* initialise of intermediary variables */
  86     MPFR_GROUP_INIT_2 (group, Nt, t, te);
  87
  88     /* First computation of cosh */
  89     MPFR_ZIV_INIT (loop, Nt);
  90     for (;;)
  91       {
  92         MPFR_BLOCK_DECL (flags);
  93
  94         /* Compute cosh */
  95         MPFR_BLOCK (flags, mpfr_exp (te, x, MPFR_RNDD));  /* exp(x) */
  96         /* exp can overflow (but not underflow since x>0) */
  97         if (MPFR_OVERFLOW (flags))
  98           /* cosh(x) > exp(x), cosh(x) underflows too */
  99           {
 100             inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
 101             MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
 102             break;
 103           }
 104         mpfr_ui_div (t, 1, te, MPFR_RNDU);   /* 1/exp(x) */
 105         mpfr_add (t, te, t, MPFR_RNDU);      /* exp(x) + 1/exp(x)*/
 106         mpfr_div_2ui (t, t, 1, MPFR_RNDN);   /* 1/2(exp(x) + 1/exp(x))*/
 107
 108         /* Estimation of the error */
 109         err = Nt - 3;
 110         /* Check if we can round */
 111         if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
 112           {
 113             inexact = mpfr_set (y, t, rnd_mode);
 114             break;
 115           }
 116
 117         /* Actualisation of the precision */
 118         MPFR_ZIV_NEXT (loop, Nt);
 119         MPFR_GROUP_REPREC_2 (group, Nt, t, te);
 120       }
 121     MPFR_ZIV_FREE (loop);
 122     MPFR_GROUP_CLEAR (group);
 123   }
 124
 125  end:
 126   MPFR_SAVE_EXPO_FREE (expo);
 127   return mpfr_check_range (y, inexact, rnd_mode);
 128 }