[gcc] GCC 4.5.0=>4.5.1

gcc/mpfr/acos.c

-/* mpfr_acos -- arc-cosinus 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_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);
-  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, 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;
-
-  /* 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, 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_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);
-}