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Diffstat (limited to 'src/asin.c')
| -rw-r--r-- | src/asin.c | 125 |
1 files changed, 125 insertions, 0 deletions
diff --git a/src/asin.c b/src/asin.c new file mode 100644 index 0000000..e243dcd --- /dev/null +++ b/src/asin.c @@ -0,0 +1,125 @@ +/* mpfr_asin -- arc-sinus of a floating-point number + +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. */ + +#include "mpfr-impl.h" + +int +mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mpfr_rnd_t rnd_mode) +{ + mpfr_t xp; + int compared, inexact; + mpfr_prec_t prec; + mpfr_exp_t xp_exp; + MPFR_SAVE_EXPO_DECL (expo); + MPFR_ZIV_DECL (loop); + + MPFR_LOG_FUNC ( + ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), + ("asin[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (asin), mpfr_log_prec, 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, MPFR_RNDN); + MPFR_ASSERTD (inexact == 0); + + compared = mpfr_cmp_ui (xp, 1); + + MPFR_SAVE_EXPO_MARK (expo); + + if (MPFR_UNLIKELY (compared >= 0)) + { + mpfr_clear (xp); + if (compared > 0) /* asin(x) = NaN for |x| > 1 */ + { + MPFR_SAVE_EXPO_FREE (expo); + 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); + } + } + else + { + /* Compute exponent of 1 - ABS(x) */ + mpfr_ui_sub (xp, 1, xp, MPFR_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, MPFR_RNDN); + mpfr_ui_sub (xp, 1, xp, MPFR_RNDN); + mpfr_sqrt (xp, xp, MPFR_RNDN); + mpfr_div (xp, x, xp, MPFR_RNDN); + mpfr_atan (xp, xp, MPFR_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); +} |