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/* mpc_rootofunity -- primitive root of unity.
Copyright (C) 2012 INRIA
This file is part of GNU MPC.
GNU MPC 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.
GNU MPC 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 this program. If not, see http://www.gnu.org/licenses/ .
*/
#include "mpc-impl.h"
int
mpc_rootofunity (mpc_ptr rop, unsigned long int n, mpc_rnd_t rnd)
{
mpfr_t t, s, c;
mpfr_prec_t prec;
int inex_re, inex_im;
/* We assume that only n=1, 2, 3, 4, 6, 12 yield exact results and
treat them separately. */
if (n == 1)
return mpc_set_ui_ui (rop, 1, 0, rnd);
else if (n == 2)
return mpc_set_si_si (rop, -1, 0, rnd);
else if (n == 4)
return mpc_set_ui_ui (rop, 0, 1, rnd);
else if (n == 3 || n == 6) {
inex_re = mpfr_set_si (mpc_realref (rop), (n == 3 ? -1 : 1),
MPC_RND_RE (rnd));
inex_im = mpfr_sqrt_ui (mpc_imagref (rop), 3, MPC_RND_IM (rnd));
mpc_div_2exp (rop, rop, 1, MPC_RNDNN);
return MPC_INEX (inex_re, inex_im);
}
else if (n == 12) {
inex_re = mpfr_sqrt_ui (mpc_imagref (rop), 3, MPC_RND_IM (rnd));
inex_im = mpfr_set_ui (mpc_imagref (rop), 1, MPC_RND_RE (rnd));
mpc_div_2exp (rop, rop, 1u, MPC_RNDNN);
return MPC_INEX (inex_re, inex_im);
}
prec = MPC_MAX_PREC(rop);
mpfr_init2 (t, 2);
mpfr_init2 (s, 2);
mpfr_init2 (c, 2);
do {
prec += mpc_ceil_log2 (prec) + 5;
mpfr_set_prec (t, prec);
mpfr_set_prec (s, prec);
mpfr_set_prec (c, prec);
mpfr_const_pi (t, GMP_RNDN); /* error 0.5 ulp */
mpfr_mul_2ui (t, t, 1u, GMP_RNDN);
mpfr_div_ui (t, t, n, GMP_RNDN); /* error 2*0.5+0.5=1.5 ulp */
mpfr_sin_cos (s, c, t, GMP_RNDN);
/* error (1.5*2^{Exp (t) - Exp (s resp.c)} + 0.5) ulp
<= 6.5 ulp for n>=3 */
}
while ( !mpfr_can_round (c, prec - 3, GMP_RNDN, GMP_RNDZ,
MPC_PREC_RE(rop) + (MPC_RND_RE(rnd) == GMP_RNDN))
|| !mpfr_can_round (s, prec - 3, GMP_RNDN, GMP_RNDZ,
MPC_PREC_IM(rop) + (MPC_RND_IM(rnd) == GMP_RNDN)));
inex_re = mpfr_set (mpc_realref(rop), c, MPC_RND_RE(rnd));
inex_im = mpfr_set (mpc_imagref(rop), s, MPC_RND_IM(rnd));
mpfr_clear (t);
mpfr_clear (s);
mpfr_clear (c);
return MPC_INEX(inex_re, inex_im);
}
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