1  /* mpfr_sech - Hyperbolic secant function = 1/cosh.
       2  
       3  Copyright 2005-2023 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  /* The hyperbolic secant function is defined by sech(x)=1/cosh(x):
      24      csc (NaN) = NaN.
      25      csc (+Inf) = csc (-Inf) = 0+.
      26      csc (+0) = csc (-0) = 1.
      27   */
      28  
      29  #define FUNCTION mpfr_sech
      30  #define INVERSE  mpfr_cosh
      31  #define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1)
      32  #define ACTION_INF(y) return mpfr_set_ui (y, 0, MPFR_RNDN)
      33  #define ACTION_ZERO(y,x) return mpfr_set_ui (y, 1, rnd_mode)
      34  /* for x near 0, sech(x) = 1 - x^2/2 + ..., more precisely |sech(x)-1| <= x^2/2
      35     for |x| <= 1. The tiny action is the same as for cos(x). */
      36  #define ACTION_TINY(y,x,r) \
      37    MPFR_FAST_COMPUTE_IF_SMALL_INPUT(y, __gmpfr_one, -2 * MPFR_GET_EXP (x), 1, \
      38                                     0, r, inexact = _inexact; goto end)
      39  
      40  #include "gen_inverse.h"