mirror of
https://github.com/vale981/arb
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127 lines
2.6 KiB
C
127 lines
2.6 KiB
C
/*
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Copyright (C) 2015 Jonathan Bober
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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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/* todo: modular arithmetic */
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static ulong
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chi_odd_exponent(const acb_dirichlet_group_t G, ulong m, ulong n)
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{
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ulong x, k, pk, gk, logm, logn;
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x = 0;
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for (k = 0; k < G->num; k++)
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{
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pk = n_pow(G->primes[k], G->exponents[k]);
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gk = G->generators[k] % pk;
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logm = n_discrete_log_bsgs(m % pk, gk, pk);
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logn = n_discrete_log_bsgs(n % pk, gk, pk);
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x = (x + G->PHI[k] * logm * logn) % G->phi_q_odd;
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}
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return x;
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}
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static ulong
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chi_even_exponent(const acb_dirichlet_group_t G, ulong m, ulong n)
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{
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ulong x;
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ulong q_even = G->q_even;
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if (q_even <= 2)
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return 0;
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x = 0;
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if ((m % 4 == 3) && (n % 4 == 3))
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x = q_even / 8;
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if (q_even > 4)
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{
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ulong g2, logm, logn;
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g2 = 5;
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if (m % 4 == 3)
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{
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m = n_negmod(m, q_even);
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}
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if (n % 4 == 3)
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{
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n = n_negmod(n, q_even);
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}
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logm = n_discrete_log_bsgs(m % q_even, g2, q_even);
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logn = n_discrete_log_bsgs(n % q_even, g2, q_even);
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x += logm * logn;
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}
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return x % (q_even / 4);
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}
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void
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acb_dirichlet_chi(acb_t res, const acb_dirichlet_group_t G, ulong m, ulong n, slong prec)
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{
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fmpq_t t, u;
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ulong odd_part, even_part;
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ulong q_even = G->q_even;
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ulong q_odd = G->q_odd;
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if ((q_even > 1 && (n % 2 == 0)) || (q_odd > 1 && (n_gcd(q_odd, n) != 1)))
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{
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acb_zero(res);
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return;
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}
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if (q_even > 2)
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{
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if (q_even == 4)
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{
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if (m % 4 == 3 && n % 4 == 3)
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even_part = q_even / 2; /* -1 */
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else
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even_part = 0; /* 1 */
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}
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else
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{
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even_part = 4 * chi_even_exponent(G, m % q_even, n % q_even);
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}
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}
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else
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{
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even_part = 0;
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}
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if (q_odd > 1)
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odd_part = chi_odd_exponent(G, m % q_odd, n % q_odd);
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else
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odd_part = 0;
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fmpq_init(t);
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fmpq_init(u);
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fmpq_set_si(t, 2 * even_part, q_even);
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fmpq_set_si(u, 2 * odd_part, G->phi_q_odd);
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fmpq_add(t, t, u);
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arb_sin_cos_pi_fmpq(acb_imagref(res), acb_realref(res), t, prec);
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fmpq_clear(t);
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fmpq_clear(u);
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}
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