mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
106 lines
2.7 KiB
C
106 lines
2.7 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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/* pointer to (x/Q)^i */
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#define Ri(ii) (R + (n-1)*((ii)-1))
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void
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_arb_poly_revert_series_lagrange_fast(arb_ptr Qinv, arb_srcptr Q, slong Qlen, slong n, slong prec)
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{
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slong i, j, m;
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arb_ptr R, S, T, tmp;
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arb_t t;
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if (n <= 2)
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{
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if (n >= 1)
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arb_zero(Qinv);
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if (n == 2)
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arb_inv(Qinv + 1, Q + 1, prec);
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return;
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}
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m = n_sqrt(n);
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arb_init(t);
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R = _arb_vec_init((n - 1) * m);
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S = _arb_vec_init(n - 1);
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T = _arb_vec_init(n - 1);
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arb_zero(Qinv);
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arb_inv(Qinv + 1, Q + 1, prec);
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_arb_poly_inv_series(Ri(1), Q + 1, FLINT_MIN(Qlen, n) - 1, n - 1, prec);
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for (i = 2; i <= m; i++)
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_arb_poly_mullow(Ri(i), Ri((i + 1) / 2), n - 1, Ri(i / 2), n - 1, n - 1, prec);
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for (i = 2; i < m; i++)
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arb_div_ui(Qinv + i, Ri(i) + i - 1, i, prec);
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_arb_vec_set(S, Ri(m), n - 1);
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for (i = m; i < n; i += m)
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{
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arb_div_ui(Qinv + i, S + i - 1, i, prec);
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for (j = 1; j < m && i + j < n; j++)
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{
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arb_dot(t, NULL, 0, S, 1, Ri(j) + i + j - 1, -1, i + j, prec);
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arb_div_ui(Qinv + i + j, t, i + j, prec);
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}
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if (i + 1 < n)
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{
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_arb_poly_mullow(T, S, n - 1, Ri(m), n - 1, n - 1, prec);
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tmp = S; S = T; T = tmp;
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}
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}
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arb_clear(t);
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_arb_vec_clear(R, (n - 1) * m);
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_arb_vec_clear(S, n - 1);
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_arb_vec_clear(T, n - 1);
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}
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void
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arb_poly_revert_series_lagrange_fast(arb_poly_t Qinv,
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const arb_poly_t Q, slong n, slong prec)
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{
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slong Qlen = Q->length;
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if (Qlen < 2 || !arb_is_zero(Q->coeffs)
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|| arb_contains_zero(Q->coeffs + 1))
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{
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flint_printf("Exception (arb_poly_revert_series_lagrange_fast). Input \n"
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"must have zero constant term and nonzero coefficient of x^1.\n");
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flint_abort();
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}
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if (Qinv != Q)
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{
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arb_poly_fit_length(Qinv, n);
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_arb_poly_revert_series_lagrange_fast(Qinv->coeffs, Q->coeffs, Qlen, n, prec);
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}
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else
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{
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arb_poly_t t;
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arb_poly_init2(t, n);
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_arb_poly_revert_series_lagrange_fast(t->coeffs, Q->coeffs, Qlen, n, prec);
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arb_poly_swap(Qinv, t);
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arb_poly_clear(t);
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}
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_arb_poly_set_length(Qinv, n);
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_arb_poly_normalise(Qinv);
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}
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