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/* mpfr_sin -- sine 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"
int
mpfr_sin (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int precy, m, ok, e, inexact, neg;
mpfr_t c, k;
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);
mpfr_init2 (k, m);
/* first determine sign */
mpfr_const_pi (c, GMP_RNDN);
mpfr_mul_2ui (c, c, 1, GMP_RNDN); /* 2*Pi */
mpfr_div (k, x, c, GMP_RNDN); /* x/(2*Pi) */
mpfr_floor (k, k); /* floor(x/(2*Pi)) */
mpfr_mul (c, k, c, GMP_RNDN);
mpfr_sub (k, x, c, GMP_RNDN); /* 0 <= k < 2*Pi */
mpfr_const_pi (c, GMP_RNDN); /* cached */
neg = mpfr_cmp (k, c) > 0;
mpfr_clear (k);
do
{
mpfr_cos (c, x, GMP_RNDZ);
mpfr_mul (c, c, c, GMP_RNDU);
mpfr_ui_sub (c, 1, c, GMP_RNDN);
e = 2 + (-MPFR_EXP(c)) / 2;
mpfr_sqrt (c, c, GMP_RNDN);
if (neg)
mpfr_neg (c, c, GMP_RNDN);
/* the absolute error on c is at most 2^(e-m) = 2^(EXP(c)-err) */
e = MPFR_EXP(c) + m - e;
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; /* inexact */
}
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