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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"
/* determine the sign of sin(x) using argument reduction.
Assumes x is not an exact multiple of Pi (this excludes x=0). */
static int
mpfr_sin_sign (mpfr_srcptr x)
{
mpfr_t c, k;
mp_exp_t K;
int sign = 0;
mp_prec_t m;
mpfr_srcptr y;
m = MPFR_PREC(x);
mpfr_init2 (c, 2);
mpfr_init2 (k, 2);
do
{
m += BITS_PER_MP_LIMB;
mpfr_set_prec (c, m);
mpfr_set_prec (k, m);
/* first determine round(x/(2*Pi)): does not have to be exact since
the result is an integer */
mpfr_const_pi (c, GMP_RNDN); /* err <= ulp(c) = 2^(2-m) */
mpfr_div (k, x, c, GMP_RNDN);
MPFR_EXP(k) --; /* x/(2Pi) = 1/2*(x/Pi) */
mpfr_rint (k, k, GMP_RNDN);
if (MPFR_NOTZERO(k))
{
K = MPFR_EXP(k); /* k is an integer, thus K >= 1 */
mpfr_mul (k, k, c, GMP_RNDN); /* err <= 2^(K+3-m) */
MPFR_EXP(k) ++;
mpfr_sub (k, x, k, GMP_RNDN); /* err<=2^(4-m)+2^(K+3-m)<=2^(K+4-m) */
y = k;
}
else
{
K = 1;
y = x;
}
if (mpfr_cmp (y, c) >= 0)
{
mpfr_sub (k, y, c, GMP_RNDN); /* err <= 2^(2-m)+2^(K+4-m)+2^(2-m)
= 2^(3-m) + 2^(K+4-m) */
y = k;
}
}
while (MPFR_IS_ZERO(y) || (MPFR_EXP(y) < K + 5 - (mp_exp_t) m));
sign = MPFR_SIGN(y);
mpfr_clear (k);
mpfr_clear (c);
return sign;
}
int
mpfr_sin (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
int precy, m, ok, e, inexact, sign;
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 + __gmpfr_ceil_log2 ((double) precy) + MAX(0,MPFR_EXP(x)) + 13;
sign = mpfr_sin_sign (x);
mpfr_init2 (c, m);
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 (sign < 0)
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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