--- /dev/null
+/* mpfr_coth - Hyperbolic cotangent function.
+
+Copyright 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU 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 GNU 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 GNU 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, rnd_mode)
+#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; \
+ } \
+ }
+
+/* The analysis is adapted from that for mpfr_csc:
+ near x=0, coth(x) = 1/x + x/3 + ..., more precisely we have
+ |coth(x) - 1/x| <= 0.32 for |x| <= 1. Like for csc, the error term has
+ the same sign as 1/x, thus |coth(x)| >= |1/x|. Then:
+ (i) either x is a power of two, then 1/x is exactly representable, and
+ as long as 1/2*ulp(1/x) > 0.32, we can conclude;
+ (ii) otherwise assume x has <= n bits, and y has <= n+1 bits, then
+ |y - 1/x| >= 2^(-2n) ufp(y), where ufp means unit in first place.
+ Since |coth(x) - 1/x| <= 0.32, if 2^(-2n) ufp(y) >= 0.64, then
+ |y - coth(x)| >= 2^(-2n-1) ufp(y), and rounding 1/x gives the correct
+ result. If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1).
+ A sufficient condition is thus EXP(x) + 1 <= -2 MAX(PREC(x),PREC(Y)). */
+#define ACTION_TINY(y,x,r) \
+ if (MPFR_EXP(x) + 1 <= -2 * (mp_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y))) \
+ { \
+ int signx = MPFR_SIGN(x); \
+ inexact = mpfr_ui_div (y, 1, x, r); \
+ if (inexact == 0) /* x is a power of two */ \
+ { /* result always 1/x, except when rounding away from zero */ \
+ if (rnd_mode == GMP_RNDU) \
+ { \
+ if (signx > 0) \
+ mpfr_nextabove (y); /* 2^k + epsilon */ \
+ inexact = 1; \
+ } \
+ else if (rnd_mode == GMP_RNDD) \
+ { \
+ if (signx < 0) \
+ mpfr_nextbelow (y); /* -2^k - epsilon */ \
+ inexact = -1; \
+ } \
+ else /* round to zero, or nearest */ \
+ inexact = -signx; \
+ } \
+ MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); \
+ goto end; \
+ }
+
+#include "gen_inverse.h"
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