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diff --git a/mpfr/acos.c b/mpfr/acos.c
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--- /dev/null
+++ b/mpfr/acos.c
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+/* 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);
+}