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diff --git a/mpfr/acosh.c b/mpfr/acosh.c
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+++ b/mpfr/acosh.c
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+/* mpfr_acosh -- inverse hyperbolic cosine
+
+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.
+
+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. */
+
+#define MPFR_NEED_LONGLONG_H
+#include "mpfr-impl.h"
+
+/* The computation of acosh is done by   *
+ *  acosh= ln(x + sqrt(x^2-1))           */
+
+int
+mpfr_acosh (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode)
+{
+  MPFR_SAVE_EXPO_DECL (expo);
+  int inexact;
+  int comp;
+
+  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
+                 ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+  /* Deal with special cases */
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+    {
+      /* Nan, or zero or -Inf */
+      if (MPFR_IS_INF (x) && MPFR_IS_POS (x))
+        {
+          MPFR_SET_INF (y);
+          MPFR_SET_POS (y);
+          MPFR_RET (0);
+        }
+      else /* Nan, or zero or -Inf */
+        {
+          MPFR_SET_NAN (y);
+          MPFR_RET_NAN;
+        }
+    }
+  comp = mpfr_cmp_ui (x, 1);
+  if (MPFR_UNLIKELY (comp < 0))
+    {
+      MPFR_SET_NAN (y);
+      MPFR_RET_NAN;
+    }
+  else if (MPFR_UNLIKELY (comp == 0))
+    {
+      MPFR_SET_ZERO (y); /* acosh(1) = 0 */
+      MPFR_SET_POS (y);
+      MPFR_RET (0);
+    }
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* General case */
+  {
+    /* Declaration of the intermediary variables */
+    mpfr_t t;
+    /* Declaration of the size variables */
+    mp_prec_t Ny = MPFR_PREC(y);   /* Precision of output variable */
+    mp_prec_t Nt;                  /* Precision of the intermediary variable */
+    mp_exp_t  err, exp_te, d;      /* Precision of error */
+    MPFR_ZIV_DECL (loop);
+
+    /* compute the precision of intermediary variable */
+    /* the optimal number of bits : see algorithms.tex */
+    Nt = Ny + 4 + MPFR_INT_CEIL_LOG2 (Ny);
+
+    /* initialization of intermediary variables */
+    mpfr_init2 (t, Nt);
+
+    /* First computation of acosh */
+    MPFR_ZIV_INIT (loop, Nt);
+    for (;;)
+      {
+        MPFR_BLOCK_DECL (flags);
+
+        /* compute acosh */
+        MPFR_BLOCK (flags, mpfr_mul (t, x, x, GMP_RNDD));  /* x^2 */
+        if (MPFR_OVERFLOW (flags))
+          {
+            mpfr_t ln2;
+            mp_prec_t pln2;
+
+            /* As x is very large and the precision is not too large, we
+               assume that we obtain the same result by evaluating ln(2x).
+               We need to compute ln(x) + ln(2) as 2x can overflow. TODO:
+               write a proof and add an MPFR_ASSERTN. */
+            mpfr_log (t, x, GMP_RNDN);  /* err(log) < 1/2 ulp(t) */
+            pln2 = Nt - MPFR_PREC_MIN < MPFR_GET_EXP (t) ?
+              MPFR_PREC_MIN : Nt - MPFR_GET_EXP (t);
+            mpfr_init2 (ln2, pln2);
+            mpfr_const_log2 (ln2, GMP_RNDN);  /* err(ln2) < 1/2 ulp(t) */
+            mpfr_add (t, t, ln2, GMP_RNDN);  /* err <= 3/2 ulp(t) */
+            mpfr_clear (ln2);
+            err = 1;
+          }
+        else
+          {
+            exp_te = MPFR_GET_EXP (t);
+            mpfr_sub_ui (t, t, 1, GMP_RNDD);   /* x^2-1 */
+            if (MPFR_UNLIKELY (MPFR_IS_ZERO (t)))
+              {
+                /* This means that x is very close to 1: x = 1 + t with
+                   t < 2^(-Nt). We have: acosh(x) = sqrt(2t) (1 - eps(t))
+                   with 0 < eps(t) < t / 12. */
+                mpfr_sub_ui (t, x, 1, GMP_RNDD);   /* t = x - 1 */
+                mpfr_mul_2ui (t, t, 1, GMP_RNDN);  /* 2t */
+                mpfr_sqrt (t, t, GMP_RNDN);        /* sqrt(2t) */
+                err = 1;
+              }
+            else
+              {
+                d = exp_te - MPFR_GET_EXP (t);
+                mpfr_sqrt (t, t, GMP_RNDN);        /* sqrt(x^2-1) */
+                mpfr_add (t, t, x, GMP_RNDN);      /* sqrt(x^2-1)+x */
+                mpfr_log (t, t, GMP_RNDN);         /* ln(sqrt(x^2-1)+x) */
+
+                /* error estimate -- see algorithms.tex */
+                err = 3 + MAX (1, d) - MPFR_GET_EXP (t);
+                /* error is bounded by 1/2 + 2^err <= 2^(max(0,1+err)) */
+                err = MAX (0, 1 + err);
+              }
+          }
+
+        if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt - err, Ny, rnd_mode)))
+          break;
+
+        /* reactualisation of the precision */
+        MPFR_ZIV_NEXT (loop, Nt);
+        mpfr_set_prec (t, Nt);
+      }
+    MPFR_ZIV_FREE (loop);
+
+    inexact = mpfr_set (y, t, rnd_mode);
+
+    mpfr_clear (t);
+  }
+
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd_mode);
+}