1/* mpfr_sech - Hyperbolic secant function = 1/cosh.
2
3Copyright 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
4Contributed by the Arenaire and Cacao projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 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"
41