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/* 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, e, inexact;
mpfr_t 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 (c, m);
do
{
mpfr_cos (c, x, GMP_RNDZ);
mpfr_mul (c, c, c, GMP_RNDZ);
mpfr_ui_div (c, 1, c, GMP_RNDU);
e = MPFR_EXP(c);
mpfr_sub_ui (c, c, 1, GMP_RNDN);
e = e - MPFR_EXP(c);
mpfr_sqrt (c, c, GMP_RNDU);
if (mpfr_cmp_ui (x, 0) < 0)
mpfr_neg (c, c, GMP_RNDN);
/* the error on c is at most (2+11*2^e)*ulp(c) <= 2^(e+4)*ulp(c)
= 2^(e+4+EXP(c)-m) = 2^(EXP(c)-err) */
e = m - e - 4;
ok = (e >= 0) && mpfr_can_round (c, e, GMP_RNDN, rnd_mode, precy);
if (ok == 0)
{
m += BITS_PER_MP_LIMB;
mpfr_set_prec (c, m);
}
}
while (!ok);
inexact = mpfr_set (y, c, rnd_mode);
mpfr_clear (c);
return inexact;
}
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