--- /dev/null
+/* mpfr_tanh -- hyperbolic tangent
+
+Copyright 2001, 2002, 2003, 2004, 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. */
+
+#define MPFR_NEED_LONGLONG_H
+#include "mpfr-impl.h"
+
+int
+mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
+{
+ /****** Declaration ******/
+ mpfr_t x;
+ int inexact;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode),
+ ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+ /* Special value checking */
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
+ {
+ if (MPFR_IS_NAN (xt))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ else if (MPFR_IS_INF (xt))
+ {
+ /* tanh(inf) = 1 && tanh(-inf) = -1 */
+ return mpfr_set_si (y, MPFR_INT_SIGN (xt), rnd_mode);
+ }
+ else /* tanh (0) = 0 and xt is zero */
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO(xt));
+ MPFR_SET_ZERO (y);
+ MPFR_SET_SAME_SIGN (y, xt);
+ MPFR_RET (0);
+ }
+ }
+
+ /* tanh(x) = x - x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
+ MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 0,
+ rnd_mode, {});
+
+ MPFR_TMP_INIT_ABS (x, xt);
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ /* General case */
+ {
+ /* Declaration of the intermediary variable */
+ mpfr_t t, te;
+ mp_exp_t d;
+
+ /* Declaration of the size variable */
+ mp_prec_t Ny = MPFR_PREC(y); /* target precision */
+ mp_prec_t Nt; /* working precision */
+ long int err; /* error */
+ int sign = MPFR_SIGN (xt);
+ MPFR_ZIV_DECL (loop);
+ MPFR_GROUP_DECL (group);
+
+ /* First check for BIG overflow of exp(2*x):
+ For x > 0, exp(2*x) > 2^(2*x)
+ If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */
+ if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) {
+ /* initialise of intermediary variables
+ since 'set_one' label assumes the variables have been
+ initialize */
+ MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te);
+ goto set_one;
+ }
+
+ /* Compute the precision of intermediary variable */
+ /* The optimal number of bits: see algorithms.tex */
+ Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 4;
+ /* if x is small, there will be a cancellation in exp(2x)-1 */
+ if (MPFR_GET_EXP (x) < 0)
+ Nt += -MPFR_GET_EXP (x);
+
+ /* initialise of intermediary variable */
+ MPFR_GROUP_INIT_2 (group, Nt, t, te);
+
+ MPFR_ZIV_INIT (loop, Nt);
+ for (;;) {
+ /* tanh = (exp(2x)-1)/(exp(2x)+1) */
+ mpfr_mul_2ui (te, x, 1, GMP_RNDN); /* 2x */
+ /* since x > 0, we can only have an overflow */
+ mpfr_exp (te, te, GMP_RNDN); /* exp(2x) */
+ if (MPFR_UNLIKELY (MPFR_IS_INF (te))) {
+ set_one:
+ inexact = MPFR_FROM_SIGN_TO_INT (sign);
+ mpfr_set4 (y, __gmpfr_one, GMP_RNDN, sign);
+ if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign)))
+ {
+ inexact = -inexact;
+ mpfr_nexttozero (y);
+ }
+ break;
+ }
+ d = MPFR_GET_EXP (te); /* For Error calculation */
+ mpfr_add_ui (t, te, 1, GMP_RNDD); /* exp(2x) + 1*/
+ mpfr_sub_ui (te, te, 1, GMP_RNDU); /* exp(2x) - 1*/
+ d = d - MPFR_GET_EXP (te);
+ mpfr_div (t, te, t, GMP_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/
+
+ /* Calculation of the error */
+ d = MAX(3, d + 1);
+ err = Nt - (d + 1);
+
+ if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
+ {
+ inexact = mpfr_set4 (y, t, rnd_mode, sign);
+ break;
+ }
+
+ /* if t=1, we still can round since |sinh(x)| < 1 */
+ if (MPFR_GET_EXP (t) == 1)
+ goto set_one;
+
+ /* Actualisation of the precision */
+ MPFR_ZIV_NEXT (loop, Nt);
+ MPFR_GROUP_REPREC_2 (group, Nt, t, te);
+ }
+ MPFR_ZIV_FREE (loop);
+ MPFR_GROUP_CLEAR (group);
+ }
+ MPFR_SAVE_EXPO_FREE (expo);
+ inexact = mpfr_check_range (y, inexact, rnd_mode);
+
+ return inexact;
+}
+
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