152 lines
4.8 KiB
C
152 lines
4.8 KiB
C
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/* mpfr_tanh -- hyperbolic tangent
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Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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int
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mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode)
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{
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/****** Declaration ******/
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mpfr_t x;
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int inexact;
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode),
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("y[%#R]=%R inexact=%d", y, y, inexact));
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/* Special value checking */
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if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
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{
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if (MPFR_IS_NAN (xt))
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{
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MPFR_SET_NAN (y);
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MPFR_RET_NAN;
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}
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else if (MPFR_IS_INF (xt))
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{
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/* tanh(inf) = 1 && tanh(-inf) = -1 */
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return mpfr_set_si (y, MPFR_INT_SIGN (xt), rnd_mode);
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}
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else /* tanh (0) = 0 and xt is zero */
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{
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MPFR_ASSERTD (MPFR_IS_ZERO(xt));
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MPFR_SET_ZERO (y);
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MPFR_SET_SAME_SIGN (y, xt);
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MPFR_RET (0);
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}
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}
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/* tanh(x) = x - x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
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MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 0,
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rnd_mode, {});
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MPFR_TMP_INIT_ABS (x, xt);
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MPFR_SAVE_EXPO_MARK (expo);
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/* General case */
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{
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/* Declaration of the intermediary variable */
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mpfr_t t, te;
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mpfr_exp_t d;
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/* Declaration of the size variable */
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mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */
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mpfr_prec_t Nt; /* working precision */
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long int err; /* error */
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int sign = MPFR_SIGN (xt);
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MPFR_ZIV_DECL (loop);
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MPFR_GROUP_DECL (group);
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/* First check for BIG overflow of exp(2*x):
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For x > 0, exp(2*x) > 2^(2*x)
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If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */
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if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) {
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/* initialise of intermediary variables
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since 'set_one' label assumes the variables have been
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initialize */
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MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te);
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goto set_one;
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}
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/* Compute the precision of intermediary variable */
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/* The optimal number of bits: see algorithms.tex */
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Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 4;
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/* if x is small, there will be a cancellation in exp(2x)-1 */
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if (MPFR_GET_EXP (x) < 0)
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Nt += -MPFR_GET_EXP (x);
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/* initialise of intermediary variable */
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MPFR_GROUP_INIT_2 (group, Nt, t, te);
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MPFR_ZIV_INIT (loop, Nt);
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for (;;) {
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/* tanh = (exp(2x)-1)/(exp(2x)+1) */
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mpfr_mul_2ui (te, x, 1, MPFR_RNDN); /* 2x */
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/* since x > 0, we can only have an overflow */
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mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */
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if (MPFR_UNLIKELY (MPFR_IS_INF (te))) {
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set_one:
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inexact = MPFR_FROM_SIGN_TO_INT (sign);
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mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign);
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if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign)))
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{
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inexact = -inexact;
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mpfr_nexttozero (y);
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}
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break;
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}
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d = MPFR_GET_EXP (te); /* For Error calculation */
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mpfr_add_ui (t, te, 1, MPFR_RNDD); /* exp(2x) + 1*/
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mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1*/
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d = d - MPFR_GET_EXP (te);
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mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/
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/* Calculation of the error */
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d = MAX(3, d + 1);
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err = Nt - (d + 1);
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if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
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{
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inexact = mpfr_set4 (y, t, rnd_mode, sign);
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break;
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}
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/* if t=1, we still can round since |sinh(x)| < 1 */
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if (MPFR_GET_EXP (t) == 1)
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goto set_one;
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/* Actualisation of the precision */
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MPFR_ZIV_NEXT (loop, Nt);
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MPFR_GROUP_REPREC_2 (group, Nt, t, te);
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}
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MPFR_ZIV_FREE (loop);
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MPFR_GROUP_CLEAR (group);
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}
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MPFR_SAVE_EXPO_FREE (expo);
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inexact = mpfr_check_range (y, inexact, rnd_mode);
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return inexact;
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}
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