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