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https://github.com/vale981/arb
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77 lines
2.3 KiB
C
77 lines
2.3 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2016 Pascal Molin
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******************************************************************************/
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#include "acb_dirichlet.h"
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#include "acb_poly.h"
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/* small order, multiply by chi at the end */
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void
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acb_dirichlet_arb_theta_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] != ACB_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 + 1, 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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