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Diffstat (limited to 'src/atanh.c')
| -rw-r--r-- | src/atanh.c | 130 |
1 files changed, 130 insertions, 0 deletions
diff --git a/src/atanh.c b/src/atanh.c new file mode 100644 index 0000000..078ffc6 --- /dev/null +++ b/src/atanh.c @@ -0,0 +1,130 @@ +/* mpfr_atanh -- Inverse Hyperbolic Tangente + +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" + + /* The computation of atanh is done by + atanh= 1/2*ln(x+1)-1/2*ln(1-x) */ + +int +mpfr_atanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) +{ + int inexact; + mpfr_t x, t, te; + mpfr_prec_t Nx, Ny, Nt; + mpfr_exp_t err; + MPFR_ZIV_DECL (loop); + 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 cases */ + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt))) + { + /* atanh(NaN) = NaN, and atanh(+/-Inf) = NaN since tanh gives a result + between -1 and 1 */ + if (MPFR_IS_NAN (xt) || MPFR_IS_INF (xt)) + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + else /* necessarily xt is 0 */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (xt)); + MPFR_SET_ZERO (y); /* atanh(0) = 0 */ + MPFR_SET_SAME_SIGN (y,xt); + MPFR_RET (0); + } + } + + /* atanh (x) = NaN as soon as |x| > 1, and arctanh(+/-1) = +/-Inf */ + if (MPFR_UNLIKELY (MPFR_GET_EXP (xt) > 0)) + { + if (MPFR_GET_EXP (xt) == 1 && mpfr_powerof2_raw (xt)) + { + MPFR_SET_INF (y); + MPFR_SET_SAME_SIGN (y, xt); + mpfr_set_divby0 (); + MPFR_RET (0); + } + MPFR_SET_NAN (y); + MPFR_RET_NAN; + } + + /* atanh(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, 1, + rnd_mode, {}); + + MPFR_SAVE_EXPO_MARK (expo); + + /* Compute initial precision */ + Nx = MPFR_PREC (xt); + MPFR_TMP_INIT_ABS (x, xt); + Ny = MPFR_PREC (y); + Nt = MAX (Nx, Ny); + /* the optimal number of bits : see algorithms.ps */ + Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4; + + /* initialise of intermediary variable */ + mpfr_init2 (t, Nt); + mpfr_init2 (te, Nt); + + /* First computation of cosh */ + MPFR_ZIV_INIT (loop, Nt); + for (;;) + { + /* compute atanh */ + mpfr_ui_sub (te, 1, x, MPFR_RNDU); /* (1-xt)*/ + mpfr_add_ui (t, x, 1, MPFR_RNDD); /* (xt+1)*/ + mpfr_div (t, t, te, MPFR_RNDN); /* (1+xt)/(1-xt)*/ + mpfr_log (t, t, MPFR_RNDN); /* ln((1+xt)/(1-xt))*/ + mpfr_div_2ui (t, t, 1, MPFR_RNDN); /* (1/2)*ln((1+xt)/(1-xt))*/ + + /* error estimate: see algorithms.tex */ + /* FIXME: this does not correspond to the value in algorithms.tex!!! */ + /* err=Nt-__gmpfr_ceil_log2(1+5*pow(2,1-MPFR_EXP(t)));*/ + err = Nt - (MAX (4 - MPFR_GET_EXP (t), 0) + 1); + + if (MPFR_LIKELY (MPFR_IS_ZERO (t) + || MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) + break; + + /* reactualisation of the precision */ + MPFR_ZIV_NEXT (loop, Nt); + mpfr_set_prec (t, Nt); + mpfr_set_prec (te, Nt); + } + MPFR_ZIV_FREE (loop); + + inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt)); + + mpfr_clear(t); + mpfr_clear(te); + + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd_mode); +} + |