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

   1 /* mpfr_sech - Hyperbolic secant function = 1/cosh.
   2
   3 Copyright 2005-2015 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 /* 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"