mirror of
https://github.com/vale981/arb
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92 lines
2.6 KiB
C
92 lines
2.6 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) 2012 Fredrik Johansson
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******************************************************************************/
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#include "fmprb.h"
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#include "fmprb_poly.h"
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void
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fmprb_rfac_ui_multipoint(fmprb_t f, const fmprb_t c, ulong n, long prec)
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{
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long i, m, wp;
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fmprb_struct *t, *u, *v;
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fmprb_t r, w;
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ulong s;
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if (n <= 1)
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{
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if (n == 0)
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fmprb_one(f);
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else
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fmprb_set(f, c);
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return;
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}
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/* TODO: this is useless if the input isn't as precise as the working
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precision to begin with. We rather want to convert to an exact input
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within the evaluation, and add the propagated error afterwards. */
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wp = FMPR_PREC_ADD(prec, n);
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fmprb_init(r);
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fmprb_init(w);
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m = n_sqrt(n);
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t = _fmprb_vec_init(m + 1);
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u = _fmprb_vec_init(m + 1);
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v = _fmprb_vec_init(m + 1);
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/* the polynomial is x(x+1)(x+2)... */
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for (i = 0; i < m; i++)
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fmprb_set_si(t + i, -i);
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_fmprb_poly_product_roots(u, t, m, wp);
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/* the evaluation points are c, c+m, ... */
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for (i = 0; i < m; i++)
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fmprb_add_ui(t + i, c, i * m, wp);
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_fmprb_poly_evaluate_vec_fast(v, u, m + 1, t, m, wp);
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fmprb_one(r);
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for (i = 0; i < m; i++)
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fmprb_mul(r, r, v + i, wp);
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/* remaining part of product (todo: this should use binary
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splitting as well, to minimize numerical error) */
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for (s = m * m; s < n; s++)
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{
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fmprb_add_ui(w, c, s, wp);
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fmprb_mul(r, r, w, wp);
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}
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fmprb_set(f, r);
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_fmprb_vec_clear(t, m + 1);
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_fmprb_vec_clear(u, m + 1);
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_fmprb_vec_clear(v, m + 1);
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fmprb_clear(r);
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fmprb_clear(w);
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}
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