mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
100 lines
2.4 KiB
C
100 lines
2.4 KiB
C
/*
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Copyright (C) 2016 Pascal Molin
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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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void
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acb_dirichlet_qseries_arb_powers_naive(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_powers_t z, slong len, slong prec)
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{
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slong k;
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arb_t xk2, dx, x2;
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acb_t zk;
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arb_init(xk2);
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arb_init(dx);
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arb_init(x2);
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acb_init(zk);
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arb_set(dx, x);
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arb_set(xk2, dx);
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arb_mul(x2, dx, dx, prec);
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acb_set_arb(res, xk2);
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/* TODO: reduce prec */
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for (k = 2; k < len; k++)
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{
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arb_mul(dx, dx, x2, prec);
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arb_mul(xk2, xk2, dx, prec);
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if (a[k] != DIRICHLET_CHI_NULL)
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{
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acb_dirichlet_power(zk, z, a[k], prec);
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if (parity)
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acb_mul_si(zk, zk, k, prec);
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acb_addmul_arb(res, zk, xk2, prec);
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}
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}
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arb_clear(xk2);
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arb_clear(x2);
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arb_clear(dx);
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acb_clear(zk);
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}
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/* small order, multiply by chi at the end */
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void
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acb_dirichlet_qseries_arb_powers_smallorder(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_powers_t z, slong len, slong prec)
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{
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slong k;
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ulong order = z->order;
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arb_t xk2, kxk2, dx, x2;
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acb_ptr t;
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arb_init(xk2);
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arb_init(dx);
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arb_init(x2);
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arb_init(kxk2);
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arb_set(dx, x);
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arb_set(xk2, x);
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arb_mul(x2, x, x, prec);
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t = _acb_vec_init(order);
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_acb_vec_zero(t, order);
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arb_set(acb_realref(t + 0), xk2);
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/* TODO: reduce precision at each step */
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for (k = 2; k < len; k++)
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{
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arb_mul(dx, dx, x2, prec);
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arb_mul(xk2, xk2, dx, prec);
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if (a[k] != DIRICHLET_CHI_NULL)
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{
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if (parity)
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{
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arb_mul_si(kxk2, xk2, k, prec);
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arb_add(acb_realref(t + a[k]), acb_realref(t + a[k]), kxk2, prec);
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}
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else
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{
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arb_add(acb_realref(t + a[k]), acb_realref(t + a[k]), xk2, prec);
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}
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}
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}
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/* now Hörner */
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_acb_poly_evaluate(res, t, order, z->z, prec);
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_acb_vec_clear(t, order);
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arb_clear(xk2);
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arb_clear(x2);
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arb_clear(dx);
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}
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