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Diffstat (limited to 'src/acos.c')
| -rw-r--r-- | src/acos.c | 142 |
1 files changed, 142 insertions, 0 deletions
diff --git a/src/acos.c b/src/acos.c new file mode 100644 index 000000000..cf019d439 --- /dev/null +++ b/src/acos.c @@ -0,0 +1,142 @@ +/* mpfr_acos -- arc-cosinus of a floating-point number + +Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. +Contributed by the Arenaire and Caramel 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 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" + +int +mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mpfr_rnd_t rnd_mode) +{ + mpfr_t xp, arcc, tmp; + mpfr_exp_t supplement; + mpfr_prec_t prec; + int sign, compared, inexact; + MPFR_SAVE_EXPO_DECL (expo); + MPFR_ZIV_DECL (loop); + + MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode), + ("acos[%#R]=%R inexact=%d", acos, acos, inexact)); + + /* Singular cases */ + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) + { + if (MPFR_IS_NAN (x) || MPFR_IS_INF (x)) + { + MPFR_SET_NAN (acos); + MPFR_RET_NAN; + } + else /* necessarily x=0 */ + { + MPFR_ASSERTD(MPFR_IS_ZERO(x)); + /* acos(0)=Pi/2 */ + inexact = mpfr_const_pi (acos, rnd_mode); + mpfr_div_2ui (acos, acos, 1, rnd_mode); /* exact */ + MPFR_RET (inexact); + } + } + + /* Set x_p=|x| */ + sign = MPFR_SIGN (x); + mpfr_init2 (xp, MPFR_PREC (x)); + mpfr_abs (xp, x, MPFR_RNDN); /* Exact */ + + compared = mpfr_cmp_ui (xp, 1); + + if (MPFR_UNLIKELY (compared >= 0)) + { + mpfr_clear (xp); + if (compared > 0) /* acos(x) = NaN for x > 1 */ + { + MPFR_SET_NAN(acos); + MPFR_RET_NAN; + } + else + { + if (MPFR_IS_POS_SIGN (sign)) /* acos(+1) = 0 */ + return mpfr_set_ui (acos, 0, rnd_mode); + else /* acos(-1) = Pi */ + return mpfr_const_pi (acos, rnd_mode); + } + } + + MPFR_SAVE_EXPO_MARK (expo); + + /* Compute the supplement */ + mpfr_ui_sub (xp, 1, xp, MPFR_RNDD); + if (MPFR_IS_POS_SIGN (sign)) + supplement = 2 - 2 * MPFR_GET_EXP (xp); + else + supplement = 2 - MPFR_GET_EXP (xp); + mpfr_clear (xp); + + prec = MPFR_PREC (acos); + prec += MPFR_INT_CEIL_LOG2(prec) + 10 + supplement; + + /* VL: The following change concerning prec comes from r3145 + "Optimize mpfr_acos by choosing a better initial precision." + but it doesn't seem to be correct and leads to problems (assertion + failure or very important inefficiency) with tiny arguments. + Therefore, I've disabled it. */ + /* If x ~ 2^-N, acos(x) ~ PI/2 - x - x^3/6 + If Prec < 2*N, we can't round since x^3/6 won't be counted. */ +#if 0 + if (MPFR_PREC (acos) >= MPFR_PREC (x) && MPFR_GET_EXP (x) < 0) + { + mpfr_uexp_t pmin = (mpfr_uexp_t) (-2 * MPFR_GET_EXP (x)) + 5; + MPFR_ASSERTN (pmin <= MPFR_PREC_MAX); + if (prec < pmin) + prec = pmin; + } +#endif + + mpfr_init2 (tmp, prec); + mpfr_init2 (arcc, prec); + + MPFR_ZIV_INIT (loop, prec); + for (;;) + { + /* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */ + mpfr_sqr (tmp, x, MPFR_RNDN); + mpfr_ui_sub (tmp, 1, tmp, MPFR_RNDN); + mpfr_sqrt (tmp, tmp, MPFR_RNDN); + mpfr_div (tmp, x, tmp, MPFR_RNDN); + mpfr_atan (arcc, tmp, MPFR_RNDN); + mpfr_const_pi (tmp, MPFR_RNDN); + mpfr_div_2ui (tmp, tmp, 1, MPFR_RNDN); + mpfr_sub (arcc, tmp, arcc, MPFR_RNDN); + + if (MPFR_LIKELY (MPFR_CAN_ROUND (arcc, prec - supplement, + MPFR_PREC (acos), rnd_mode))) + break; + MPFR_ZIV_NEXT (loop, prec); + mpfr_set_prec (tmp, prec); + mpfr_set_prec (arcc, prec); + } + MPFR_ZIV_FREE (loop); + + inexact = mpfr_set (acos, arcc, rnd_mode); + mpfr_clear (tmp); + mpfr_clear (arcc); + + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (acos, inexact, rnd_mode); +} |