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/*
Copyright (C) 2016 Pascal Molin
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"
#include "acb_poly.h"
void
acb_dirichlet_qseries_arb_powers_naive(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_roots_t roots, slong len, slong prec)
{
slong k;
arb_t xk2, dx, x2;
acb_t zk;
arb_init(xk2);
arb_init(dx);
arb_init(x2);
acb_init(zk);
arb_set(dx, x);
arb_set(xk2, dx);
arb_mul(x2, dx, dx, prec);
acb_set_arb(res, xk2);
/* TODO: reduce prec */
for (k = 2; k < len; k++)
{
arb_mul(dx, dx, x2, prec);
arb_mul(xk2, xk2, dx, prec);
if (a[k] != DIRICHLET_CHI_NULL)
{
acb_dirichlet_root(zk, roots, a[k], prec);
if (parity)
acb_mul_si(zk, zk, k, prec);
acb_addmul_arb(res, zk, xk2, prec);
}
}
arb_clear(xk2);
arb_clear(x2);
arb_clear(dx);
acb_clear(zk);
}
/* small order, multiply by chi at the end */
void
acb_dirichlet_qseries_arb_powers_smallorder(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_roots_t roots, slong len, slong prec)
{
slong k;
ulong order = roots->order;
arb_t xk2, kxk2, dx, x2;
acb_ptr t;
arb_init(xk2);
arb_init(dx);
arb_init(x2);
arb_init(kxk2);
arb_set(dx, x);
arb_set(xk2, x);
arb_mul(x2, x, x, prec);
t = _acb_vec_init(order);
_acb_vec_zero(t, order);
arb_set(acb_realref(t + 0), xk2);
/* TODO: reduce precision at each step */
for (k = 2; k < len; k++)
{
arb_mul(dx, dx, x2, prec);
arb_mul(xk2, xk2, dx, prec);
if (a[k] != DIRICHLET_CHI_NULL)
{
if (parity)
{
arb_mul_si(kxk2, xk2, k, prec);
arb_add(acb_realref(t + a[k]), acb_realref(t + a[k]), kxk2, prec);
}
else
{
arb_add(acb_realref(t + a[k]), acb_realref(t + a[k]), xk2, prec);
}
}
}
/* now Horner */
acb_dirichlet_root(res, roots, 1, prec);
_acb_poly_evaluate(res, t, order, res, prec);
_acb_vec_clear(t, order);
arb_clear(xk2);
arb_clear(x2);
arb_clear(dx);
arb_clear(kxk2);
}
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