mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
120 lines
3.3 KiB
C
120 lines
3.3 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2013 Fredrik Johansson
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******************************************************************************/
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#include "fmprb_poly.h"
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#include "fmpcb_poly.h"
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void
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_fmprb_poly_riemann_siegel_z_series(fmprb_ptr res, fmprb_srcptr h, long hlen, long len, long prec)
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{
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long i, alloc;
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fmprb_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 = _fmprb_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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fmpcb_ptr sx, z;
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fmpcb_t a;
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long slen = FLINT_MIN(len, 2);
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z = _fmpcb_vec_init(len);
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sx = _fmpcb_vec_init(slen);
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fmpcb_init(a);
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fmpcb_one(a);
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fmpcb_one(sx);
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fmpcb_mul_2exp_si(sx, sx, -1);
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fmprb_set(fmpcb_imagref(sx), h);
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if (slen > 1)
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fmprb_one(fmpcb_imagref(sx + 1));
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_fmpcb_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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fmprb_set(v + i, fmpcb_realref(z + i));
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fmprb_set(w + i, fmpcb_imagref(z + i));
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}
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fmpcb_clear(a);
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_fmpcb_vec_clear(z, len);
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_fmpcb_vec_clear(sx, slen);
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}
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/* (t + ui) = exp(i theta(s+x)) */
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fmprb_set(u, h);
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if (len > 1)
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fmprb_one(u + 1);
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_fmprb_poly_riemann_siegel_theta_series(t, u, 2, len, prec);
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_fmprb_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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_fmprb_poly_mullow(q, t, len, v, len, len, prec);
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_fmprb_poly_mullow(t, u, len, w, len, len, prec);
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_fmprb_vec_sub(t, q, t, len, prec);
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/* compose with nonconstant part */
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fmprb_zero(u);
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_fmprb_vec_set(u + 1, h + 1, hlen - 1);
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_fmprb_poly_compose_series(res, t, len, u, hlen, len, prec);
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_fmprb_vec_clear(t, alloc);
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}
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void
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fmprb_poly_riemann_siegel_z_series(fmprb_poly_t res, const fmprb_poly_t f, long n, long prec)
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{
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if (n == 0)
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{
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fmprb_poly_zero(res);
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return;
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}
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fmprb_poly_fit_length(res, n);
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if (f->length == 0)
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{
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fmprb_t t;
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fmprb_init(t);
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_fmprb_poly_riemann_siegel_z_series(res->coeffs, t, 1, n, prec);
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fmprb_clear(t);
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}
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else
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{
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_fmprb_poly_riemann_siegel_z_series(res->coeffs, f->coeffs, f->length, n, prec);
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}
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_fmprb_poly_set_length(res, n);
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_fmprb_poly_normalise(res);
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}
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