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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.
Contributed by the Arenaire and Cacao projects, INRIA.
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) > 0)
{
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
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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