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/* mpfr_coth - Hyperbolic cotangent function.
Copyright 2005, 2006 Free Software Foundation, Inc.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.
The MPFR Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
/* the hyperbolic cotangent is defined by coth(x) = 1/tanh(x)
coth (NaN) = NaN.
coth (+Inf) = 1
coth (-Inf) = -1
coth (+0) = +0.
coth (-0) = -0.
*/
#define FUNCTION mpfr_coth
#define INVERSE mpfr_tanh
#define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1)
#define ACTION_INF(y) return mpfr_set_si (y, MPFR_IS_POS(x) ? 1 : -1, GMP_RNDN)
#define ACTION_ZERO(y,x) do { MPFR_SET_SAME_SIGN(y,x); MPFR_SET_ZERO(y); \
MPFR_RET(0); } while (1)
/* We know |coth(x)| > 1, thus if the approximation z is such that
1 <= z <= 1 + 2^(-p) where p is the target precision, then the
result is either 1 or nextabove(1) = 1 + 2^(1-p). */
#define ACTION_SPECIAL \
if (MPFR_GET_EXP(z) == 1) /* 1 <= |z| < 2 */ \
{ \
/* the following is exact by Sterbenz theorem */ \
mpfr_sub_si (z, z, MPFR_SIGN(z) > 0 ? 1 : -1, GMP_RNDN); \
if (MPFR_IS_ZERO(z) || MPFR_GET_EXP(z) <= - (mp_exp_t) precy) \
{ \
mpfr_add_si (z, z, MPFR_SIGN(z) > 0 ? 1 : -1, GMP_RNDN); \
break; \
} \
}
#include "gen_inverse.h"
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