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Diffstat (limited to 'src/tanh.c')
| -rw-r--r-- | src/tanh.c | 153 |
1 files changed, 153 insertions, 0 deletions
diff --git a/src/tanh.c b/src/tanh.c new file mode 100644 index 0000000..b1e9b7d --- /dev/null +++ b/src/tanh.c @@ -0,0 +1,153 @@ +/* mpfr_tanh -- hyperbolic tangent + +Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. +Contributed by the AriC and Caramel 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 3 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.LESSER. If not, see +http://www.gnu.org/licenses/ or 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 , mpfr_rnd_t rnd_mode) +{ + /****** Declaration ******/ + mpfr_t x; + int inexact; + MPFR_SAVE_EXPO_DECL (expo); + + MPFR_LOG_FUNC + (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (xt), mpfr_log_prec, xt, rnd_mode), + ("y[%Pu]=%.*Rg inexact=%d", + mpfr_get_prec (y), mpfr_log_prec, 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; + mpfr_exp_t d; + + /* Declaration of the size variable */ + mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */ + mpfr_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, MPFR_RNDN); /* 2x */ + /* since x > 0, we can only have an overflow */ + mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */ + if (MPFR_UNLIKELY (MPFR_IS_INF (te))) { + set_one: + inexact = MPFR_FROM_SIGN_TO_INT (sign); + mpfr_set4 (y, __gmpfr_one, MPFR_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, MPFR_RNDD); /* exp(2x) + 1*/ + mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1*/ + d = d - MPFR_GET_EXP (te); + mpfr_div (t, te, t, MPFR_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; +} + |