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/*
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"
#include "acb_poly.h"
#define POWER(_k) (powers + (((_k)-1)/2) * (len))
#define DIVISOR(_k) (divisors[((_k)-1)/2])
void
acb_dirichlet_powsum_sieved(acb_ptr z, const acb_t s, ulong n, slong len, slong prec)
{
slong * divisors;
slong powers_alloc;
slong i, j, k, ibound, power_of_two, horner_point;
ulong kprev;
int critical_line, integer;
acb_ptr powers;
acb_ptr t, u, x;
acb_ptr p1, p2;
arb_t logk, v, w;
if (n <= 1)
{
acb_set_ui(z, n);
_acb_vec_zero(z + 1, len - 1);
return;
}
critical_line = arb_is_exact(acb_realref(s)) &&
(arf_cmp_2exp_si(arb_midref(acb_realref(s)), -1) == 0);
integer = arb_is_zero(acb_imagref(s)) && arb_is_int(acb_realref(s));
divisors = flint_calloc(n / 2 + 1, sizeof(slong));
powers_alloc = (n / 6 + 1) * len;
powers = _acb_vec_init(powers_alloc);
ibound = n_sqrt(n);
for (i = 3; i <= ibound; i += 2)
if (DIVISOR(i) == 0)
for (j = i * i; j <= n; j += 2 * i)
DIVISOR(j) = i;
t = _acb_vec_init(len);
u = _acb_vec_init(len);
x = _acb_vec_init(len);
arb_init(logk);
arb_init(v);
arb_init(w);
power_of_two = 1;
while (power_of_two * 2 <= n)
power_of_two *= 2;
horner_point = n / power_of_two;
_acb_vec_zero(z, len);
kprev = 1;
acb_dirichlet_powsum_term(x, logk, &kprev, s, 2,
integer, critical_line, len, prec);
for (k = 1; k <= n; k += 2)
{
/* t = k^(-s) */
if (DIVISOR(k) == 0)
{
acb_dirichlet_powsum_term(t, logk, &kprev, s, k,
integer, critical_line, len, prec);
}
else
{
p1 = POWER(DIVISOR(k));
p2 = POWER(k / DIVISOR(k));
if (len == 1)
acb_mul(t, p1, p2, prec);
else
_acb_poly_mullow(t, p1, len, p2, len, len, prec);
}
if (k * 3 <= n)
_acb_vec_set(POWER(k), t, len);
_acb_vec_add(u, u, t, len, prec);
while (k == horner_point && power_of_two != 1)
{
_acb_poly_mullow(t, z, len, x, len, len, prec);
_acb_vec_add(z, t, u, len, prec);
power_of_two /= 2;
horner_point = n / power_of_two;
horner_point -= (horner_point % 2 == 0);
}
}
_acb_poly_mullow(t, z, len, x, len, len, prec);
_acb_vec_add(z, t, u, len, prec);
flint_free(divisors);
_acb_vec_clear(powers, powers_alloc);
_acb_vec_clear(t, len);
_acb_vec_clear(u, len);
_acb_vec_clear(x, len);
arb_clear(logk);
arb_clear(v);
arb_clear(w);
}
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