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/* mpfr_tan -- tangent of a floating-point number
Copyright 2001, 2002, 2003, 2004, 2005 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. */
#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)
{
int precy, m, inexact;
mpfr_t s, c;
MPFR_ZIV_DECL (loop);
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);
}
}
MPFR_LOG_BEGIN (("x[%#R]=%R rnd=%d", x, x, rnd_mode));
precy = MPFR_PREC (y);
m = precy + MPFR_INT_CEIL_LOG2 (precy) + 13;
if (MPFR_GET_EXP (x) > 0)
m += MPFR_GET_EXP (x) / 3;
else
m += -MPFR_GET_EXP (x);
mpfr_init2 (s, m);
mpfr_init2 (c, m);
MPFR_ZIV_INIT (loop, m);
for (;;)
{
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 */
if (MPFR_IS_INF(x) || mpfr_can_round (c, m - 1, GMP_RNDN, GMP_RNDZ,
precy + (rnd_mode == GMP_RNDN)))
break;
MPFR_ZIV_NEXT (loop, m);
mpfr_set_prec (s, m);
mpfr_set_prec (c, m);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, c, rnd_mode);
mpfr_clear (s);
mpfr_clear (c);
MPFR_LOG_END (("y[%#R]=%R inexact=%d", y, y, inexact));
return inexact;
}
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