mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
98 lines
2.6 KiB
C
98 lines
2.6 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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void
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acb_dirichlet_hurwitz_precomp_init(acb_dirichlet_hurwitz_precomp_t pre,
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const acb_t s, int deflate, slong A, slong K, slong N, slong prec)
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{
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slong i, k;
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pre->deflate = deflate;
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pre->A = A;
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pre->K = K;
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pre->N = N;
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acb_init(&pre->s);
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acb_set(&pre->s, s);
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if (A == 0)
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return;
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if (A < 1 || K < 1 || N < 1)
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{
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flint_printf("hurwitz_precomp_init: require A, K, N >= 1 (unless A == 0)\n");
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flint_abort();
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}
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pre->coeffs = _acb_vec_init(N * K);
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mag_init(&pre->err);
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acb_dirichlet_hurwitz_precomp_bound(&pre->err, s, A, K, N);
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if (mag_is_finite(&pre->err))
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{
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acb_t t, a;
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acb_init(t);
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acb_init(a);
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/* (-1)^k (s)_k / k! */
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acb_one(pre->coeffs + 0);
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for (k = 1; k < K; k++)
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{
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acb_add_ui(pre->coeffs + k, s, k - 1, prec);
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acb_mul(pre->coeffs + k, pre->coeffs + k, pre->coeffs + k - 1, prec);
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acb_div_ui(pre->coeffs + k, pre->coeffs + k, k, prec);
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acb_neg(pre->coeffs + k, pre->coeffs + k);
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}
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for (i = 1; i < N; i++)
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_acb_vec_set(pre->coeffs + i * K, pre->coeffs, K);
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/* zeta(s+k,a) where a = A + (2*i+1)/(2*N) */
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for (i = 0; i < N; i++)
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{
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acb_set_ui(a, 2 * i + 1);
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acb_div_ui(a, a, 2 * N, prec);
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acb_add_ui(a, a, A, prec);
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for (k = 0; k < K; k++)
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{
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acb_add_ui(t, s, k, prec);
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if (deflate && k == 0)
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_acb_poly_zeta_cpx_series(t, t, a, 1, 1, prec);
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else
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acb_hurwitz_zeta(t, t, a, prec);
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acb_mul(pre->coeffs + i * K + k,
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pre->coeffs + i * K + k, t, prec);
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}
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}
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acb_clear(t);
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acb_clear(a);
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}
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}
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void
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acb_dirichlet_hurwitz_precomp_init_num(acb_dirichlet_hurwitz_precomp_t pre,
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const acb_t s, int deflate, double num_eval, slong prec)
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{
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ulong A, K, N;
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acb_dirichlet_hurwitz_precomp_choose_param(&A, &K, &N, s, num_eval, prec);
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acb_dirichlet_hurwitz_precomp_init(pre, s, deflate, A, K, N, prec);
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}
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