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Initial revision

/* mpfr_tan -- tangent of a floating-point number

Copyright 2001, 2002 Free Software Foundation, Inc.

This file is part of the MPFR Library.

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 "gmp.h"
#include "gmp-impl.h"
#include "mpfr.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)
{
  int precy, m, ok, inexact;
  mpfr_t s, c;

  if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
    {
      MPFR_SET_NAN(y);
      MPFR_RET_NAN;
    }

  if (MPFR_IS_ZERO(x))
    {
      MPFR_CLEAR_FLAGS(y);
      MPFR_SET_ZERO(y);
      MPFR_SET_SAME_SIGN(y, x);
      MPFR_RET(0);
    }

  precy = MPFR_PREC(y);
  m = precy + _mpfr_ceil_log2 ((double) precy) + ABS(MPFR_EXP(x)) + 13;

  mpfr_init2 (s, m);
  mpfr_init2 (c, m);

  do
    {
      mpfr_sin_cos (s, c, x, GMP_RNDN); /* err <= 1/2 ulp on s and c */
      mpfr_div (c, s, c, GMP_RNDN);     /* err <= 2 ulps */
      ok = mpfr_can_round (c, m - 1, GMP_RNDN, rnd_mode, precy);

      if (ok == 0)
	{
	  m += BITS_PER_MP_LIMB;
	  mpfr_set_prec (s, m);
	  mpfr_set_prec (c, m);
	}
    }
  while (!ok);

  inexact = mpfr_set (y, c, rnd_mode);

  mpfr_clear (s);
  mpfr_clear (c);

  return inexact;
}