mirror of
https://github.com/vale981/arb
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95 lines
2.3 KiB
C
95 lines
2.3 KiB
C
/*
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Copyright (C) 2012 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 "acb_poly.h"
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static void
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_acb_poly_exp_series_basecase_rec(acb_ptr f, acb_ptr a,
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acb_srcptr h, slong hlen, slong n, slong prec)
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{
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slong k;
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acb_t s;
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acb_init(s);
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acb_exp(f, h, prec);
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for (k = 1; k < hlen; k++)
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acb_mul_ui(a + k, h + k, k, prec);
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for (k = 1; k < n; k++)
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{
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acb_dot(s, NULL, 0, a + 1, 1, f + k - 1, -1, FLINT_MIN(k, hlen - 1), prec);
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acb_div_ui(f + k, s, k, prec);
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}
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acb_clear(s);
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}
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void
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_acb_poly_exp_series_basecase(acb_ptr f,
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acb_srcptr h, slong hlen, slong n, slong prec)
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{
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hlen = FLINT_MIN(n, hlen);
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if (n < 20 || hlen < 0.9 * n || prec <= 2 * FLINT_BITS || n < 1000.0 / log(prec + 10) - 70)
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{
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acb_ptr t = _acb_vec_init(hlen);
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_acb_poly_exp_series_basecase_rec(f, t, h, hlen, n, prec);
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_acb_vec_clear(t, hlen);
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}
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else
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{
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slong m, v;
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acb_ptr t, u;
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m = (n + 2) / 3;
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v = m * 2;
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t = _acb_vec_init(n);
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u = _acb_vec_init(n - m);
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_acb_poly_mullow(t, h + m, hlen - m, h + m, hlen - m, n - v, prec);
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_acb_vec_scalar_mul_2exp_si(t, t, n - v, -1);
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_acb_vec_set(u, h + m, v - m);
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_acb_poly_add(u + v - m, t, n - v, h + v, hlen - v, prec);
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_acb_poly_exp_series_basecase_rec(f, t, h, m, n, prec);
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_acb_poly_mullow(t, f, n, u, n - m, n - m, prec);
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_acb_poly_add(f + m, f + m, n - m, t, n - m, prec);
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_acb_vec_clear(t, n);
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_acb_vec_clear(u, n - m);
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}
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}
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void
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acb_poly_exp_series_basecase(acb_poly_t f, const acb_poly_t h, slong n, slong prec)
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{
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slong hlen = h->length;
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if (n == 0)
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{
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acb_poly_zero(f);
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return;
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}
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if (hlen == 0)
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{
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acb_poly_one(f);
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return;
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}
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acb_poly_fit_length(f, n);
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_acb_poly_exp_series_basecase(f->coeffs, h->coeffs, hlen, n, prec);
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_acb_poly_set_length(f, n);
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_acb_poly_normalise(f);
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}
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