mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
131 lines
3.6 KiB
C
131 lines
3.6 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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/* x(t) = exp(-Pi / q * t^2) */
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static void
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acb_dirichlet_arb_theta_xt(arb_t xt, ulong q, const arb_t t, slong prec)
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{
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arb_const_pi(xt, prec);
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arb_div_ui(xt, xt, q, prec);
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arb_mul(xt, xt, t, prec);
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arb_mul(xt, xt, t, prec);
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arb_neg(xt, xt);
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arb_exp(xt, xt, prec);
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}
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void
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acb_dirichlet_chi_theta_arb_smallorder(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, const arb_t xt, slong len, slong prec)
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{
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ulong * a;
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acb_dirichlet_powers_t z;
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a = flint_malloc(len * sizeof(ulong));
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acb_dirichlet_ui_chi_vec(a, G, chi, len);
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_acb_dirichlet_powers_init(z, chi->order.n, 0, 0, prec);
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acb_dirichlet_arb_theta_smallorder(res, xt, chi->parity, a, z, len, prec);
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acb_dirichlet_powers_clear(z);
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flint_free(a);
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}
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void
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acb_dirichlet_chi_theta_arb_series(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, const arb_t xt, slong len, slong prec)
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{
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acb_ptr a;
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a = _acb_vec_init(len);
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acb_dirichlet_chi_vec(a, G, chi, len, prec);
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if (chi->parity)
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{
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slong k;
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for (k = 2; k < len; k++)
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acb_mul_si(a + k, a + k, k, prec);
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}
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acb_dirichlet_qseries_eval_arb(res, a, xt, len, prec);
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_acb_vec_clear(a, len);
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}
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void
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acb_dirichlet_vec_mellin_series(acb_ptr res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, slong len, const arb_t t, slong n, slong prec)
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{
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slong k;
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arb_t tk, xt, stk, st;
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acb_ptr a;
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a = _acb_vec_init(len);
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acb_dirichlet_chi_vec(a, G, chi, len, prec);
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if (chi->parity)
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{
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for (k = 2; k < len; k++)
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acb_mul_si(a + k, a + k, k, prec);
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}
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arb_init(tk);
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arb_init(xt);
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arb_init(st);
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arb_init(stk);
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arb_sqrt(st, t, prec);
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arb_one(tk);
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arb_one(stk);
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for (k = 0; k < n; k++)
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{
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acb_dirichlet_arb_theta_xt(xt, G->q, tk, prec);
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/* TODO: reduce len */
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acb_dirichlet_qseries_eval_arb(res + k, a, xt, len, prec);
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acb_mul_arb(res + k, res + k, stk, prec);
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arb_mul(tk, tk, t, prec);
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arb_mul(stk, stk, st, prec);
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}
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arb_clear(xt);
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arb_clear(tk);
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arb_clear(stk);
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arb_clear(st);
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_acb_vec_clear(a, len);
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}
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void
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acb_dirichlet_chi_theta_arb_naive(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, const arb_t xt, slong len, slong prec)
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{
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ulong * a;
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acb_dirichlet_powers_t z;
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a = flint_malloc(len * sizeof(ulong));
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acb_dirichlet_ui_chi_vec(a, G, chi, len);
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acb_dirichlet_powers_init(z, chi->order.n, len, prec);
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acb_dirichlet_arb_theta_naive(res, xt, chi->parity, a, z, len, prec);
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acb_dirichlet_powers_clear(z);
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flint_free(a);
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}
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void
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acb_dirichlet_chi_theta_arb(acb_t res, const acb_dirichlet_group_t G, const acb_dirichlet_char_t chi, const arb_t t, slong prec)
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{
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slong len;
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arb_t xt;
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len = acb_dirichlet_theta_length(G->q, t, prec);
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arb_init(xt);
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acb_dirichlet_arb_theta_xt(xt, G->q, t, prec);
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/* TODO: tune this limit */
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if (chi->order.n < 30)
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acb_dirichlet_chi_theta_arb_smallorder(res, G, chi, xt, len, prec);
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else
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acb_dirichlet_chi_theta_arb_naive(res, G, chi, xt, len, prec);
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arb_clear(xt);
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}
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