mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
106 lines
2.5 KiB
C
106 lines
2.5 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_z_series(arb_ptr res, arb_srcptr h, slong hlen, slong len, slong prec)
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{
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slong i, alloc;
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arb_ptr t, u, v, w, q;
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hlen = FLINT_MIN(hlen, len);
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alloc = 5 * len;
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t = _arb_vec_init(alloc);
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u = t + len;
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v = u + len;
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w = v + len;
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q = w + len;
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/* (v + wi) = zeta(1/2 + i (s+x)) */
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{
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acb_ptr sx, z;
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acb_t a;
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slong slen = FLINT_MIN(len, 2);
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z = _acb_vec_init(len);
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sx = _acb_vec_init(slen);
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acb_init(a);
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acb_one(a);
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acb_one(sx);
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acb_mul_2exp_si(sx, sx, -1);
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arb_set(acb_imagref(sx), h);
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if (slen > 1)
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arb_one(acb_imagref(sx + 1));
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_acb_poly_zeta_series(z, sx, slen, a, 0, len, prec);
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for (i = 0; i < len; i++)
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{
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arb_set(v + i, acb_realref(z + i));
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arb_set(w + i, acb_imagref(z + i));
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}
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acb_clear(a);
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_acb_vec_clear(z, len);
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_acb_vec_clear(sx, slen);
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}
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/* (t + ui) = exp(i theta(s+x)) */
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arb_set(u, h);
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if (len > 1)
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arb_one(u + 1);
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_arb_poly_riemann_siegel_theta_series(t, u, 2, len, prec);
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_arb_poly_sin_cos_series(u, t, t, len, len, prec);
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/* (t+ui)(v+wi) = (tv-uw) + (tw+uv)i */
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_arb_poly_mullow(q, t, len, v, len, len, prec);
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_arb_poly_mullow(t, u, len, w, len, len, prec);
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_arb_vec_sub(t, q, t, len, prec);
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/* compose with nonconstant part */
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arb_zero(u);
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_arb_vec_set(u + 1, h + 1, hlen - 1);
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_arb_poly_compose_series(res, t, len, u, hlen, len, prec);
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_arb_vec_clear(t, alloc);
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}
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void
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arb_poly_riemann_siegel_z_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)
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{
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if (n == 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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arb_poly_fit_length(res, n);
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if (f->length == 0)
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{
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arb_t t;
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arb_init(t);
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_arb_poly_riemann_siegel_z_series(res->coeffs, t, 1, n, prec);
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arb_clear(t);
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}
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else
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{
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_arb_poly_riemann_siegel_z_series(res->coeffs, 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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