mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
84 lines
1.9 KiB
C
84 lines
1.9 KiB
C
/*
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Copyright (C) 2013 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 "arb_poly.h"
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#include "acb_poly.h"
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void
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_arb_poly_riemann_siegel_theta_series(arb_ptr res,
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arb_srcptr h, slong hlen, slong len, slong prec)
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{
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acb_ptr s;
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arb_t u;
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slong i;
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hlen = FLINT_MIN(hlen, len);
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s = _acb_vec_init(len);
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arb_init(u);
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/* s = 1/4 + (1/2) i h */
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for (i = 0; i < hlen; i++)
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arb_mul_2exp_si(acb_imagref(s + i), h + i, -1);
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arb_one(u);
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arb_mul_2exp_si(u, u, -2);
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arb_add(acb_realref(s), acb_realref(s), u, prec);
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/* log gamma */
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_acb_poly_lgamma_series(s, s, hlen, len, prec);
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/* imaginary part */
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for (i = 0; i < len; i++)
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arb_set(res + i, acb_imagref(s + i));
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/* subtract log(pi)/2 * h */
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arb_const_pi(u, prec);
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arb_log(u, u, prec);
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arb_mul_2exp_si(u, u, -1);
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arb_neg(u, u);
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_arb_vec_scalar_addmul(res, h, hlen, u, prec);
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_acb_vec_clear(s, len);
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arb_clear(u);
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}
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void
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arb_poly_riemann_siegel_theta_series(arb_poly_t res,
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const arb_poly_t f, slong n, slong prec)
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{
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if (n == 0 || f->length == 0)
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{
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arb_poly_zero(res);
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return;
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}
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if (res == f)
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{
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arb_poly_t tmp;
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arb_poly_init2(tmp, n);
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_arb_poly_riemann_siegel_theta_series(tmp->coeffs,
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f->coeffs, f->length, n, prec);
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arb_poly_swap(res, tmp);
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arb_poly_clear(tmp);
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}
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else
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{
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arb_poly_fit_length(res, n);
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_arb_poly_riemann_siegel_theta_series(res->coeffs,
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f->coeffs, f->length, n, prec);
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}
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_arb_poly_set_length(res, n);
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_arb_poly_normalise(res);
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}
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