mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
71 lines
2 KiB
C
71 lines
2 KiB
C
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/*
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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_zeta_rs_f_coeffs(acb_ptr c, const arb_t p, slong N, slong prec)
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{
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arb_ptr R, I, T, X;
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slong i, len;
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R = _arb_vec_init(N);
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I = _arb_vec_init(N);
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T = _arb_vec_init(N);
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X = _arb_vec_init(2);
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arb_set(X, p);
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arb_one(X + 1);
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/* I, R = sin,cos(pi*(X^2/2 + 3/8)) */
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len = FLINT_MIN(N, 3);
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_arb_poly_mullow(T, X, 2, X, 2, len, prec);
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_arb_vec_scalar_mul_2exp_si(T, T, len, -1);
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arb_set_d(R, 0.375);
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arb_add(T, T, R, prec);
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_arb_poly_sin_cos_pi_series(I, R, T, len, N, prec);
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/* I -= cos(pi*x/2) * sqrt(2) */
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_arb_vec_scalar_mul_2exp_si(X, X, 2, -1);
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_arb_poly_cos_pi_series(T, X, 2, N, prec);
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arb_sqrt_ui((arb_ptr) c, 2, prec);
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_arb_vec_scalar_mul(T, T, N, (arb_ptr) c, prec);
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_arb_vec_sub(I, I, T, N, prec);
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_arb_vec_scalar_mul_2exp_si(X, X, 2, 1);
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/* T = 1 / (2 cos(pi*x)) */
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_arb_poly_cos_pi_series(T, X, 2, N, prec);
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_arb_vec_scalar_mul_2exp_si(T, T, N, 1);
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_arb_poly_inv_series((arb_ptr) c, T, N, N, prec);
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_arb_vec_swap(T, (arb_ptr) c, N);
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/* R, I *= T */
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_arb_poly_mullow((arb_ptr) c, R, N, T, N, N, prec);
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_arb_vec_swap(R, (arb_ptr) c, N);
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_arb_poly_mullow((arb_ptr) c, I, N, T, N, N, prec);
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_arb_vec_swap(I, (arb_ptr) c, N);
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for (i = 0; i < N; i++)
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{
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arb_swap(acb_realref(c + i), R + i);
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arb_swap(acb_imagref(c + i), I + i);
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}
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_acb_poly_inv_borel_transform(c, c, N, prec);
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_arb_vec_clear(R, N);
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_arb_vec_clear(I, N);
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_arb_vec_clear(T, N);
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_arb_vec_clear(X, 2);
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}
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