mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
115 lines
2.4 KiB
C
115 lines
2.4 KiB
C
/*
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Copyright (C) 2014 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 "flint/fmpz_poly.h"
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#include "acb.h"
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void rising_difference_polynomial(fmpz * s, fmpz * c, ulong m);
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void
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acb_rising_ui_rs(acb_t y, const acb_t x, ulong n, ulong m, slong prec)
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{
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acb_ptr xs;
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acb_t t, u, v;
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ulong i, k, rem;
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fmpz_t c, h;
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fmpz *s, *d;
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slong wp;
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if (n == 0)
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{
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acb_one(y);
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return;
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}
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if (n == 1)
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{
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acb_set_round(y, x, prec);
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return;
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}
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wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
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acb_init(t);
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acb_init(u);
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acb_init(v);
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fmpz_init(c);
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fmpz_init(h);
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if (m == 0)
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{
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ulong m1, m2;
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m1 = 0.2 * pow(2.0 * wp, 0.4);
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m2 = n_sqrt(n);
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m = FLINT_MIN(m1, m2);
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}
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m = FLINT_MIN(m, n);
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m = FLINT_MAX(m, 1);
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xs = _acb_vec_init(m + 1);
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d = _fmpz_vec_init(m * m);
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s = _fmpz_vec_init(m + 1);
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_acb_vec_set_powers(xs, x, m + 1, wp);
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rising_difference_polynomial(s, d, m);
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/* tail */
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rem = m;
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while (rem + m <= n)
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rem += m;
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acb_one(y);
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for (k = rem; k < n; k++)
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{
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acb_add_ui(t, xs + 1, k, wp);
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acb_mul(y, y, t, wp);
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}
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/* initial rising factorial */
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acb_zero(t);
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for (i = 1; i <= m; i++)
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acb_addmul_fmpz(t, xs + i, s + i, wp);
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acb_mul(y, y, t, wp);
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/* the leading coefficient is always the same */
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acb_mul_fmpz(xs + m - 1, xs + m - 1, d + m - 1 + 0, wp);
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for (k = 0; k + 2 * m <= n; k += m)
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{
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for (i = 0; i < m - 1; i++)
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{
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fmpz_set_ui(h, k);
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_fmpz_poly_evaluate_horner_fmpz(c, d + i * m, m - i, h);
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if (i == 0)
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acb_add_fmpz(t, t, c, wp);
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else
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acb_addmul_fmpz(t, xs + i, c, wp);
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}
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acb_add(t, t, xs + m - 1, wp);
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acb_mul(y, y, t, wp);
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}
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acb_set_round(y, y, prec);
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acb_clear(t);
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acb_clear(u);
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acb_clear(v);
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_acb_vec_clear(xs, m + 1);
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_fmpz_vec_clear(d, m * m);
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_fmpz_vec_clear(s, m + 1);
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fmpz_clear(c);
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fmpz_clear(h);
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}
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