mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
114 lines
2.8 KiB
C
114 lines
2.8 KiB
C
/*
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Copyright (C) 2012, 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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#define MULLOW(z, x, xn, y, yn, nn, prec) \
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if ((xn) >= (yn)) \
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_arb_poly_mullow(z, x, xn, y, yn, nn, prec); \
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else \
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_arb_poly_mullow(z, y, yn, x, xn, nn, prec); \
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void
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_arb_poly_inv_series(arb_ptr Qinv,
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arb_srcptr Q, slong Qlen, slong len, slong prec)
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{
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Qlen = FLINT_MIN(Qlen, len);
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arb_inv(Qinv, Q, prec);
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if (Qlen == 1)
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{
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_arb_vec_zero(Qinv + 1, len - 1);
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}
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else if (len == 2)
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{
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arb_mul(Qinv + 1, Qinv, Qinv, prec);
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arb_mul(Qinv + 1, Qinv + 1, Q + 1, prec);
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arb_neg(Qinv + 1, Qinv + 1);
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}
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else
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{
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slong i, blen;
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/* The basecase algorithm is faster for much larger Qlen or len than
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this, but unfortunately also much less numerically stable. */
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if (Qlen == 2 || len <= 8)
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blen = len;
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else
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blen = FLINT_MIN(len, 4);
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for (i = 1; i < blen; i++)
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{
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arb_dot(Qinv + i, NULL, 1,
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Q + 1, 1, Qinv + i - 1, -1, FLINT_MIN(i, Qlen - 1), prec);
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if (!arb_is_one(Qinv))
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arb_mul(Qinv + i, Qinv + i, Qinv, prec);
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}
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if (len > blen)
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{
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slong Qnlen, Wlen, W2len;
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arb_ptr W;
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W = _arb_vec_init(len);
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NEWTON_INIT(blen, len)
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NEWTON_LOOP(m, n)
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Qnlen = FLINT_MIN(Qlen, n);
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Wlen = FLINT_MIN(Qnlen + m - 1, n);
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W2len = Wlen - m;
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MULLOW(W, Q, Qnlen, Qinv, m, Wlen, prec);
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MULLOW(Qinv + m, Qinv, m, W + m, W2len, n - m, prec);
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_arb_vec_neg(Qinv + m, Qinv + m, n - m);
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NEWTON_END_LOOP
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NEWTON_END
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_arb_vec_clear(W, len);
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}
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}
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}
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void
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arb_poly_inv_series(arb_poly_t Qinv, const arb_poly_t Q, slong n, slong prec)
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{
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if (n == 0)
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{
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arb_poly_zero(Qinv);
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return;
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}
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if (Q->length == 0)
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{
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arb_poly_fit_length(Qinv, n);
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_arb_vec_indeterminate(Qinv->coeffs, n);
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_arb_poly_set_length(Qinv, n);
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return;
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}
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if (Qinv == Q)
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{
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arb_poly_t t;
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arb_poly_init(t);
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arb_poly_inv_series(t, Q, n, prec);
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arb_poly_swap(Qinv, t);
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arb_poly_clear(t);
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return;
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}
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arb_poly_fit_length(Qinv, n);
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_arb_poly_inv_series(Qinv->coeffs, Q->coeffs, Q->length, n, prec);
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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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