| /* mpfr_atanh -- Inverse Hyperbolic Tangente |
| |
| 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" |
| |
| /* 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 , mp_rnd_t rnd_mode) |
| { |
| int inexact; |
| mpfr_t x, t, te; |
| mp_prec_t Nx, Ny, Nt; |
| mp_exp_t err; |
| MPFR_ZIV_DECL (loop); |
| 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 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_EXP (xt) > 0)) |
| { |
| if (MPFR_EXP (xt) == 1 && mpfr_powerof2_raw (xt)) |
| { |
| MPFR_SET_INF (y); |
| MPFR_SET_SAME_SIGN (y, xt); |
| 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, GMP_RNDU); /* (1-xt)*/ |
| mpfr_add_ui (t, x, 1, GMP_RNDD); /* (xt+1)*/ |
| mpfr_div (t, t, te, GMP_RNDN); /* (1+xt)/(1-xt)*/ |
| mpfr_log (t, t, GMP_RNDN); /* ln((1+xt)/(1-xt))*/ |
| mpfr_div_2ui (t, t, 1, GMP_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); |
| } |
| |