mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
119 lines
3 KiB
C
119 lines
3 KiB
C
/*
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Copyright (C) 2016 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_dirichlet.h"
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#include "acb_poly.h"
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#define POWER(_k) (powers + (((_k)-1)/2) * (len))
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#define DIVISOR(_k) (divisors[((_k)-1)/2])
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void
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acb_dirichlet_powsum_sieved(acb_ptr z, const acb_t s, ulong n, slong len, slong prec)
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{
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slong * divisors;
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slong powers_alloc;
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slong i, j, k, ibound, power_of_two, horner_point;
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ulong kprev;
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int critical_line, integer;
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acb_ptr powers;
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acb_ptr t, u, x;
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acb_ptr p1, p2;
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arb_t logk, v, w;
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if (n <= 1)
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{
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acb_set_ui(z, n);
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_acb_vec_zero(z + 1, len - 1);
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return;
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}
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critical_line = arb_is_exact(acb_realref(s)) &&
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(arf_cmp_2exp_si(arb_midref(acb_realref(s)), -1) == 0);
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integer = arb_is_zero(acb_imagref(s)) && arb_is_int(acb_realref(s));
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divisors = flint_calloc(n / 2 + 1, sizeof(slong));
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powers_alloc = (n / 6 + 1) * len;
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powers = _acb_vec_init(powers_alloc);
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ibound = n_sqrt(n);
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for (i = 3; i <= ibound; i += 2)
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if (DIVISOR(i) == 0)
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for (j = i * i; j <= n; j += 2 * i)
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DIVISOR(j) = i;
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t = _acb_vec_init(len);
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u = _acb_vec_init(len);
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x = _acb_vec_init(len);
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arb_init(logk);
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arb_init(v);
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arb_init(w);
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power_of_two = 1;
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while (power_of_two * 2 <= n)
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power_of_two *= 2;
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horner_point = n / power_of_two;
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_acb_vec_zero(z, len);
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kprev = 1;
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acb_dirichlet_powsum_term(x, logk, &kprev, s, 2,
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integer, critical_line, len, prec);
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for (k = 1; k <= n; k += 2)
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{
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/* t = k^(-s) */
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if (DIVISOR(k) == 0)
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{
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acb_dirichlet_powsum_term(t, logk, &kprev, s, k,
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integer, critical_line, len, prec);
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}
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else
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{
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p1 = POWER(DIVISOR(k));
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p2 = POWER(k / DIVISOR(k));
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if (len == 1)
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acb_mul(t, p1, p2, prec);
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else
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_acb_poly_mullow(t, p1, len, p2, len, len, prec);
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}
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if (k * 3 <= n)
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_acb_vec_set(POWER(k), t, len);
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_acb_vec_add(u, u, t, len, prec);
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while (k == horner_point && power_of_two != 1)
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{
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_acb_poly_mullow(t, z, len, x, len, len, prec);
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_acb_vec_add(z, t, u, len, prec);
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power_of_two /= 2;
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horner_point = n / power_of_two;
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horner_point -= (horner_point % 2 == 0);
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}
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}
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_acb_poly_mullow(t, z, len, x, len, len, prec);
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_acb_vec_add(z, t, u, len, prec);
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flint_free(divisors);
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_acb_vec_clear(powers, powers_alloc);
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_acb_vec_clear(t, len);
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_acb_vec_clear(u, len);
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_acb_vec_clear(x, len);
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arb_clear(logk);
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arb_clear(v);
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arb_clear(w);
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}
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