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      1 /* mpfr_cosh -- hyperbolic cosine
      2 
      3 Copyright 2001-2002, 2004-2023 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 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[%Pd]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode),
     38     ("y[%Pd]=%.*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     /* initialize 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 }
    129