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/*
Copyright (C) 2016 Pascal Molin
Copyright (C) 2016 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_dirichlet.h"
void
acb_dirichlet_root(acb_t z, const acb_dirichlet_roots_t t, ulong k, slong prec)
{
ulong n = t->order;
int swap, flip, conjugate;
slong wp;
if (k > n)
k %= n;
swap = flip = conjugate = 0;
if (k > n / 2)
{
conjugate = 1;
k = n - k;
}
if (n % 2 == 0 && k > n / 4)
{
flip = 1;
k = n / 2 - k;
}
if (n % 4 == 0 && k > n / 8)
{
swap = 1;
k = n / 4 - k;
}
wp = prec + 6 + 2 * FLINT_BIT_COUNT(t->reduced_order);
if (k == 0)
{
acb_one(z);
}
else if (t->depth == 0)
{
if (t->use_pow)
{
acb_pow_ui(z, t->z, k, wp);
acb_set_round(z, z, prec);
}
else
{
ulong r;
fmpq_t t;
fmpq_init(t);
r = n_gcd(n, 2 * k); /* no overflow since since k <= n / 2 */
fmpz_set_ui(fmpq_numref(t), (2 * k) / r);
fmpz_set_ui(fmpq_denref(t), n / r);
arb_sin_cos_pi_fmpq(acb_imagref(z), acb_realref(z), t, prec);
fmpq_clear(t);
}
}
else if (t->depth == 1)
{
acb_set_round(z, t->Z[0] + k, prec);
}
else
{
slong j;
ulong r;
r = k % t->size;
k = k / t->size;
acb_set(z, t->Z[0] + r);
for (j = 1; j < t->depth && k != 0; j++)
{
r = k % t->size;
k = k / t->size;
acb_mul(z, z, t->Z[j] + r, wp);
}
if (k != 0)
flint_abort();
acb_set_round(z, z, prec);
}
if (swap)
arb_swap(acb_realref(z), acb_imagref(z));
if (flip)
arb_neg(acb_realref(z), acb_realref(z));
if (conjugate)
arb_neg(acb_imagref(z), acb_imagref(z));
}
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