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diff --git a/mpfr/tan.c b/mpfr/tan.c
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--- /dev/null
+++ b/mpfr/tan.c
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+/* mpfr_tan -- tangent 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.
+
+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"
+
+/* computes tan(x) = sign(x)*sqrt(1/cos(x)^2-1) */
+int
+mpfr_tan (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
+{
+  mp_prec_t precy, m;
+  int inexact;
+  mpfr_t s, c;
+  MPFR_ZIV_DECL (loop);
+  MPFR_SAVE_EXPO_DECL (expo);
+  MPFR_GROUP_DECL (group);
+
+  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
+                  ("y[%#R]=%R inexact=%d", y, y, inexact));
+
+  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
+    {
+      if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
+        {
+          MPFR_SET_NAN(y);
+          MPFR_RET_NAN;
+        }
+      else /* x is zero */
+        {
+          MPFR_ASSERTD(MPFR_IS_ZERO(x));
+          MPFR_SET_ZERO(y);
+          MPFR_SET_SAME_SIGN(y, x);
+          MPFR_RET(0);
+        }
+    }
+
+  /* tan(x) = x + x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
+  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 1, 1,
+                                    rnd_mode, {});
+
+  MPFR_SAVE_EXPO_MARK (expo);
+
+  /* Compute initial precision */
+  precy = MPFR_PREC (y);
+  m = precy + MPFR_INT_CEIL_LOG2 (precy) + 13;
+  MPFR_ASSERTD (m >= 2); /* needed for the error analysis in algorithms.tex */
+
+  MPFR_GROUP_INIT_2 (group, m, s, c);
+  MPFR_ZIV_INIT (loop, m);
+  for (;;)
+    {
+      /* The only way to get an overflow is to get ~ Pi/2
+         But the result will be ~ 2^Prec(y). */
+      mpfr_sin_cos (s, c, x, GMP_RNDN); /* err <= 1/2 ulp on s and c */
+      mpfr_div (c, s, c, GMP_RNDN);     /* err <= 4 ulps */
+      MPFR_ASSERTD (!MPFR_IS_SINGULAR (c));
+      if (MPFR_LIKELY (MPFR_CAN_ROUND (c, m - 2, precy, rnd_mode)))
+        break;
+      MPFR_ZIV_NEXT (loop, m);
+      MPFR_GROUP_REPREC_2 (group, m, s, c);
+    }
+  MPFR_ZIV_FREE (loop);
+  inexact = mpfr_set (y, c, rnd_mode);
+  MPFR_GROUP_CLEAR (group);
+
+  MPFR_SAVE_EXPO_FREE (expo);
+  return mpfr_check_range (y, inexact, rnd_mode);
+}