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/* mpfr_sin_cos -- sine and cosine of a floating-point number
Copyright 2002, 2003, 2004, 2005, 2006, 2007 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., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"
/* (y, z) <- (sin(x), cos(x)), return value is 0 iff both results are exact
ie, iff x = 0 */
int
mpfr_sin_cos (mpfr_ptr y, mpfr_ptr z, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mp_prec_t prec, m;
int neg;
mpfr_t c, k;
mp_exp_t e;
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_SET_NAN (z);
MPFR_RET_NAN;
}
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
mpfr_set_ui (z, 1, GMP_RNDN);
MPFR_RET (0);
}
}
MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode),
("sin[%#R]=%R cos[%#R]=%R", y, y, z, z));
prec = MAX (MPFR_PREC (y), MPFR_PREC (z));
m = prec + MPFR_INT_CEIL_LOG2 (prec) + 13;
e = MPFR_GET_EXP (x);
m += (e < 0) ? -2*e : e;
mpfr_init2 (c, m);
/* first determine sign of sinus */
if (MPFR_GET_EXP (x) > 1) /* |x| >= 2 */
{
/* FIXME: we can start with a small precision,
and increase until we can decide the sign. */
mpfr_init2 (k, m);
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); /* PI is cached */
neg = mpfr_cmp (k, c) > 0;
mpfr_clear (k);
}
else /* if EXP(x) <= 1, then |x| < 2, thus sign(sin(x)) = sign(x) */
neg = MPFR_IS_NEG (x);
MPFR_ZIV_INIT (loop, m);
for (;;)
{
mpfr_cos (c, x, GMP_RNDZ);
if (!mpfr_can_round (c, m, GMP_RNDZ, rnd_mode, MPFR_PREC (z)))
goto next_step;
mpfr_set (z, c, rnd_mode);
mpfr_sqr (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 (neg)
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;
if (mpfr_can_round (c, e, GMP_RNDN, rnd_mode, MPFR_PREC (y)))
break;
/* check for huge cancellation */
if (e < (mp_exp_t) MPFR_PREC (y))
m += MPFR_PREC (y) - e;
/* Check if near 1 */
if (MPFR_GET_EXP (c) == 1
&& MPFR_MANT (c)[MPFR_LIMB_SIZE (c)-1] == MPFR_LIMB_HIGHBIT)
m = 2*m;
next_step:
MPFR_ZIV_NEXT (loop, m);
mpfr_set_prec (c, m);
}
MPFR_ZIV_FREE (loop);
mpfr_set (y, c, rnd_mode);
mpfr_clear (c);
MPFR_RET (1); /* Always inexact */
}
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