/* mpfr_acos -- arc-cosinus of a floating-point number Copyright 2001, 2002, 2003, 2004, 2005 Free Software Foundation. This file is part of the MPFR Library, and was contributed by Mathieu Dutour. The 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 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 MPFR Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ #include "mpfr-impl.h" int mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mp_rnd_t rnd_mode) { mpfr_t xp, arcc, tmp; mp_exp_t supplement; mp_prec_t prec; int sign, compared, inexact; MPFR_SAVE_EXPO_DECL (expo); /* 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, GMP_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, GMP_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) + 10 + supplement; /* 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 (MPFR_PREC (acos) >= MPFR_PREC (x) && prec <= -2*MPFR_GET_EXP (x) + 5) prec = -2*MPFR_GET_EXP (x) + 5; mpfr_init2 (tmp, prec); mpfr_init2 (arcc, prec); for (;;) { /* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */ mpfr_sqr (tmp, x, GMP_RNDN); mpfr_ui_sub (tmp, 1, tmp, GMP_RNDN); mpfr_sqrt (tmp, tmp, GMP_RNDN); mpfr_div (tmp, x, tmp, GMP_RNDN); mpfr_atan (arcc, tmp, GMP_RNDN); mpfr_const_pi (tmp, GMP_RNDN); mpfr_div_2ui (tmp, tmp, 1, GMP_RNDN); mpfr_sub (arcc, tmp, arcc, GMP_RNDN); if (mpfr_can_round (arcc, prec-supplement, GMP_RNDN, GMP_RNDZ, MPFR_PREC (acos) + (rnd_mode == GMP_RNDN))) break; prec += BITS_PER_MP_LIMB; mpfr_set_prec (tmp, prec); mpfr_set_prec (arcc, prec); } 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); }