| /* mpfr_asin -- arc-sinus of a floating-point number |
| |
| 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, and was contributed by Mathieu Dutour. |
| |
| 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. */ |
| |
| #include "mpfr-impl.h" |
| |
| int |
| mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mp_rnd_t rnd_mode) |
| { |
| mpfr_t xp; |
| int compared, inexact; |
| mp_prec_t prec; |
| mp_exp_t xp_exp; |
| MPFR_SAVE_EXPO_DECL (expo); |
| MPFR_ZIV_DECL (loop); |
| |
| MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode), |
| ("asin[%#R]=%R inexact=%d", asin, asin, inexact)); |
| |
| /* Special cases */ |
| if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) |
| { |
| if (MPFR_IS_NAN (x) || MPFR_IS_INF (x)) |
| { |
| MPFR_SET_NAN (asin); |
| MPFR_RET_NAN; |
| } |
| else /* x = 0 */ |
| { |
| MPFR_ASSERTD (MPFR_IS_ZERO (x)); |
| MPFR_SET_ZERO (asin); |
| MPFR_SET_SAME_SIGN (asin, x); |
| MPFR_RET (0); /* exact result */ |
| } |
| } |
| |
| /* asin(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */ |
| MPFR_FAST_COMPUTE_IF_SMALL_INPUT (asin, x, -2 * MPFR_GET_EXP (x), 2, 1, |
| rnd_mode, {}); |
| |
| /* Set x_p=|x| (x is a normal number) */ |
| mpfr_init2 (xp, MPFR_PREC (x)); |
| inexact = mpfr_abs (xp, x, GMP_RNDN); |
| MPFR_ASSERTD (inexact == 0); |
| |
| compared = mpfr_cmp_ui (xp, 1); |
| |
| if (MPFR_UNLIKELY (compared >= 0)) |
| { |
| mpfr_clear (xp); |
| if (compared > 0) /* asin(x) = NaN for |x| > 1 */ |
| { |
| MPFR_SET_NAN (asin); |
| MPFR_RET_NAN; |
| } |
| else /* x = 1 or x = -1 */ |
| { |
| if (MPFR_IS_POS (x)) /* asin(+1) = Pi/2 */ |
| inexact = mpfr_const_pi (asin, rnd_mode); |
| else /* asin(-1) = -Pi/2 */ |
| { |
| inexact = -mpfr_const_pi (asin, MPFR_INVERT_RND(rnd_mode)); |
| MPFR_CHANGE_SIGN (asin); |
| } |
| mpfr_div_2ui (asin, asin, 1, rnd_mode); /* May underflow */ |
| return inexact; |
| } |
| } |
| |
| MPFR_SAVE_EXPO_MARK (expo); |
| |
| /* Compute exponent of 1 - ABS(x) */ |
| mpfr_ui_sub (xp, 1, xp, GMP_RNDD); |
| MPFR_ASSERTD (MPFR_GET_EXP (xp) <= 0); |
| MPFR_ASSERTD (MPFR_GET_EXP (x) <= 0); |
| xp_exp = 2 - MPFR_GET_EXP (xp); |
| |
| /* Set up initial prec */ |
| prec = MPFR_PREC (asin) + 10 + xp_exp; |
| |
| /* use asin(x) = atan(x/sqrt(1-x^2)) */ |
| MPFR_ZIV_INIT (loop, prec); |
| for (;;) |
| { |
| mpfr_set_prec (xp, prec); |
| mpfr_sqr (xp, x, GMP_RNDN); |
| mpfr_ui_sub (xp, 1, xp, GMP_RNDN); |
| mpfr_sqrt (xp, xp, GMP_RNDN); |
| mpfr_div (xp, x, xp, GMP_RNDN); |
| mpfr_atan (xp, xp, GMP_RNDN); |
| if (MPFR_LIKELY (MPFR_CAN_ROUND (xp, prec - xp_exp, |
| MPFR_PREC (asin), rnd_mode))) |
| break; |
| MPFR_ZIV_NEXT (loop, prec); |
| } |
| MPFR_ZIV_FREE (loop); |
| inexact = mpfr_set (asin, xp, rnd_mode); |
| |
| mpfr_clear (xp); |
| |
| MPFR_SAVE_EXPO_FREE (expo); |
| return mpfr_check_range (asin, inexact, rnd_mode); |
| } |