| /* mpfr_asinh -- inverse hyperbolic sine |
| |
| 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 asinh is done by * |
| * asinh = ln(x + sqrt(x^2 + 1)) */ |
| |
| int |
| mpfr_asinh (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) |
| { |
| int inexact; |
| int signx, neg; |
| mp_prec_t Ny, Nt; |
| mpfr_t t; /* auxiliary variables */ |
| mp_exp_t err; |
| MPFR_SAVE_EXPO_DECL (expo); |
| MPFR_ZIV_DECL (loop); |
| |
| MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode), |
| ("y[%#R]=%R inexact=%d", y, y, inexact)); |
| |
| if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) |
| { |
| if (MPFR_IS_NAN (x)) |
| { |
| MPFR_SET_NAN (y); |
| MPFR_RET_NAN; |
| } |
| else if (MPFR_IS_INF (x)) |
| { |
| MPFR_SET_INF (y); |
| MPFR_SET_SAME_SIGN (y, x); |
| MPFR_RET (0); |
| } |
| else /* x is necessarily 0 */ |
| { |
| MPFR_ASSERTD (MPFR_IS_ZERO (x)); |
| MPFR_SET_ZERO (y); /* asinh(0) = 0 */ |
| MPFR_SET_SAME_SIGN (y, x); |
| MPFR_RET (0); |
| } |
| } |
| |
| /* asinh(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */ |
| MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0, |
| rnd_mode, {}); |
| |
| Ny = MPFR_PREC (y); /* Precision of output variable */ |
| |
| signx = MPFR_SIGN (x); |
| neg = MPFR_IS_NEG (x); |
| |
| /* General case */ |
| |
| /* compute the precision of intermediary variable */ |
| /* the optimal number of bits : see algorithms.tex */ |
| Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny); |
| |
| MPFR_SAVE_EXPO_MARK (expo); |
| |
| /* initialize intermediary variables */ |
| mpfr_init2 (t, Nt); |
| |
| /* First computation of asinh */ |
| MPFR_ZIV_INIT (loop, Nt); |
| for (;;) |
| { |
| /* compute asinh */ |
| mpfr_mul (t, x, x, GMP_RNDD); /* x^2 */ |
| mpfr_add_ui (t, t, 1, GMP_RNDD); /* x^2+1 */ |
| mpfr_sqrt (t, t, GMP_RNDN); /* sqrt(x^2+1) */ |
| (neg ? mpfr_sub : mpfr_add) (t, t, x, GMP_RNDN); /* sqrt(x^2+1)+x */ |
| mpfr_log (t, t, GMP_RNDN); /* ln(sqrt(x^2+1)+x)*/ |
| |
| if (MPFR_LIKELY (MPFR_IS_PURE_FP (t))) |
| { |
| /* error estimate -- see algorithms.tex */ |
| 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; |
| } |
| |
| /* actualisation of the precision */ |
| MPFR_ZIV_NEXT (loop, Nt); |
| mpfr_set_prec (t, Nt); |
| } |
| MPFR_ZIV_FREE (loop); |
| |
| inexact = mpfr_set4 (y, t, rnd_mode, signx); |
| |
| mpfr_clear (t); |
| |
| MPFR_SAVE_EXPO_FREE (expo); |
| return mpfr_check_range (y, inexact, rnd_mode); |
| } |