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/* mpfr_sinu -- sinu(x) = sin(2*pi*x/u)
Copyright 2020 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 3 of the License, or (at your
option) any later version.
The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see
https://www.gnu.org/licenses/ or 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"
/* FIXME[VL]: Implement the range reduction in this function.
That's the whole point of sinu compared to sin. */
/* put in y the corrected-rounded value of sin(2*pi*x/u) */
int
mpfr_sinu (mpfr_ptr y, mpfr_srcptr x, unsigned long u, mpfr_rnd_t rnd_mode)
{
mpfr_prec_t precy, prec;
mpfr_exp_t expx, expt, err;
mpfr_t t;
int inexact = 0, nloops = 0, underflow = 0;
MPFR_ZIV_DECL (loop);
MPFR_SAVE_EXPO_DECL (expo);
if (u == 0 || MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
/* for u=0, return NaN */
if (u == 0 || 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_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0);
}
}
MPFR_SAVE_EXPO_MARK (expo);
precy = MPFR_PREC (y);
expx = MPFR_GET_EXP (x);
/* for x large, since argument reduction is expensive, we want to avoid
any failure in Ziv's strategy, thus we take into account expx too */
prec = precy + MPFR_INT_CEIL_LOG2 (MAX(precy,expx)) + 8;
MPFR_ASSERTD(prec >= 2);
mpfr_init (t);
MPFR_ZIV_INIT (loop, prec);
for (;;)
{
nloops ++;
/* We first compute an approximation t of 2*pi*x/u, then call sin(t).
If t = 2*pi*x/u + s, then |sin(t) - sin(2*pi*x/u)| <= |s|. */
mpfr_set_prec (t, prec);
mpfr_const_pi (t, MPFR_RNDN); /* t = pi * (1 + theta1) where
|theta1| <= 2^-prec */
mpfr_mul_2ui (t, t, 1, MPFR_RNDN); /* t = 2*pi * (1 + theta1) */
mpfr_mul (t, t, x, MPFR_RNDN); /* t = 2*pi*x * (1 + theta2)^2 where
|theta2| <= 2^-prec */
mpfr_div_ui (t, t, u, MPFR_RNDN); /* t = 2*pi*x/u * (1 + theta3)^3 where
|theta2| <= 2^-prec */
/* if t is zero here, it means the division by u underflows, then
sin(t) also underflows, since |sin(x)| <= |x| for say |x| < 1. */
if (MPFR_IS_ZERO (t))
{
inexact = mpfr_underflow (y, rnd_mode, MPFR_SIGN(t));
underflow = 1;
goto end;
}
/* since prec >= 2, |(1 + theta3)^3 - 1| <= 4*theta3 <= 2^(2-prec) */
expt = MPFR_GET_EXP (t);
/* we have |s| <= 2^(expt + 2 - prec) */
mpfr_sin (t, t, MPFR_RNDN);
err = MPFR_GET_EXP (t) + prec - expt - 2;
if (MPFR_CAN_ROUND (t, err, precy, rnd_mode))
break;
/* check exact cases: this can only occur if 2*pi*x/u is a multiple
of pi/2, i.e., if x/u is a multiple of 1/4 */
if (nloops == 1)
{
inexact = mpfr_div_ui (t, x, u, MPFR_RNDN);
mpfr_mul_2ui (t, t, 2, MPFR_RNDN);
if (inexact == 0 && mpfr_integer_p (t))
{
if (!mpfr_odd_p (t))
/* t is even: we have a multiple of pi, thus sinu = 0,
for the sign, we follow IEEE 754-2019: sinPi(+n) is +0
and sinPi(-n) is -0 for positive integers n, so that the
function is odd. */
mpfr_set_zero (y, MPFR_IS_POS(t) ? +1 : -1);
else /* t is odd */
{
inexact = mpfr_sub_ui (t, t, 1, MPFR_RNDZ);
MPFR_ASSERTD(inexact == 0);
inexact = mpfr_div_2ui (t, t, 1, MPFR_RNDZ);
MPFR_ASSERTD(inexact == 0);
if (!mpfr_odd_p (t)) /* case pi/4: sinu = 1 */
mpfr_set_ui (y, 1, MPFR_RNDZ);
else
mpfr_set_si (y, -1, MPFR_RNDZ);
}
goto end;
}
}
MPFR_ZIV_NEXT (loop, prec);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (y, t, rnd_mode);
end:
mpfr_clear (t);
MPFR_SAVE_EXPO_FREE (expo);
return (underflow == 0) ? mpfr_check_range (y, inexact, rnd_mode) : inexact;
}
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