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/* mpfr_sin -- sine of a floating-point number
Copyright 2001, 2002, 2003, 2004 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 "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;
mp_prec_t m;
mpfr_srcptr y;
K = MPFR_GET_EXP(x);
m = (K < 0) ? 0 : K;
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/Pi): does not have to be exact since
the result is an integer */
mpfr_const_pi (c, GMP_RNDN); /* err <= 1/2*ulp(c) = 2^(1-m) */
/* we need that k is not-to-badly rounded to an integer,
i.e. ulp(k) <= 1, so m >= EXP(k). */
mpfr_div (k, x, c, GMP_RNDN);
mpfr_round (k, k);
sign = 1;
if (MPFR_NOTZERO(k)) /* subtract k*approx(Pi) */
{
/* determine parity of k for sign */
if (MPFR_EXP(k)<=0 || (mpfr_uexp_t) MPFR_EXP(k) <= m)
{
mp_size_t j = BITS_PER_MP_LIMB * MPFR_LIMB_SIZE(k) - MPFR_EXP(k);
mp_size_t l = j / BITS_PER_MP_LIMB;
/* parity bit is j-th bit starting from least significant bits */
if ((MPFR_MANT(k)[l] >> (j % BITS_PER_MP_LIMB)) & 1)
sign = -1; /* k is odd */
}
K = MPFR_GET_EXP (k); /* k is an integer, thus K >= 1, k < 2^K */
mpfr_mul (k, k, c, GMP_RNDN); /* err <= oldk*err(c) + 1/2*ulp(k)
<= 2^(K+2-m) */
mpfr_sub (k, x, k, GMP_RNDN);
/* assuming |k| <= Pi, err <= 2^(1-m)+2^(K+2-m) < 2^(K+3-m) */
MPFR_ASSERTN(MPFR_EXP(k) <= 2);
y = k;
}
else
{
K = 1;
y = x;
}
/* sign of sign(y) is uncertain if |y| <= err < 2^(K+3-m),
thus EXP(y) < K+4-m */
}
while (MPFR_IS_ZERO (y) || (MPFR_GET_EXP (y) < K + 4 - (mp_exp_t) m));
if (MPFR_IS_NEG(y))
sign = -sign;
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_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_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_GET_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_GET_EXP (c)) / 2;
mpfr_sqrt (c, c, GMP_RNDN);
if (MPFR_IS_NEG_SIGN(sign))
MPFR_CHANGE_SIGN(c);
/* the absolute error on c is at most 2^(e-m) = 2^(EXP(c)-err) */
e = MPFR_GET_EXP (c) + m - e;
ok = (e >= 0) && mpfr_can_round (c, e, GMP_RNDN, GMP_RNDZ,
precy + (rnd_mode == GMP_RNDN));
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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