mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
107 lines
3 KiB
C
107 lines
3 KiB
C
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/*=============================================================================
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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) 2013 Fredrik Johansson
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******************************************************************************/
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#include "arb_poly.h"
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#define CUTOFF 5
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void
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_arb_poly_revert_series_newton(arb_ptr Qinv, arb_srcptr Q, long Qlen, long n, long prec)
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{
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long i, k, a[FLINT_BITS];
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arb_ptr T, U, V;
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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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T = _arb_vec_init(n);
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U = _arb_vec_init(n);
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V = _arb_vec_init(n);
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k = n;
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for (i = 1; (1L << i) < k; i++);
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a[i = 0] = k;
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while (k >= CUTOFF)
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a[++i] = (k = (k + 1) / 2);
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_arb_poly_revert_series_lagrange(Qinv, Q, Qlen, k, prec);
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_arb_vec_zero(Qinv + k, n - k);
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for (i--; i >= 0; i--)
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{
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k = a[i];
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_arb_poly_compose_series(T, Q, FLINT_MIN(Qlen, k), Qinv, k, k, prec);
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_arb_poly_derivative(U, T, k, prec); arb_zero(U + k - 1);
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arb_zero(T + 1);
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_arb_poly_div_series(V, T, k, U, k, k, prec);
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_arb_poly_derivative(T, Qinv, k, prec);
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_arb_poly_mullow(U, V, k, T, k, k, prec);
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_arb_vec_sub(Qinv, Qinv, U, k, prec);
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}
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_arb_vec_clear(T, n);
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_arb_vec_clear(U, n);
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_arb_vec_clear(V, n);
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}
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void
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arb_poly_revert_series_newton(arb_poly_t Qinv,
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const arb_poly_t Q, long n, long prec)
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{
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long 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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printf("Exception (arb_poly_revert_series_newton). Input must \n"
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"have zero constant term and nonzero coefficient of x^1.\n");
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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_newton(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_newton(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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