138 lines
4.2 KiB
C
138 lines
4.2 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT 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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FLINT 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 FLINT; 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) 2010, 2011 Sebastian Pancratz
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Copyright (C) 2013 Mike Hansen
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******************************************************************************/
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#ifdef T
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#include "templates.h"
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#define FQ_POLY_INV_NEWTON_CUTOFF 64
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void
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_TEMPLATE(T, poly_inv_series_newton) (TEMPLATE(T, struct) * Qinv,
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const TEMPLATE(T, struct) * Q, slong n,
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const TEMPLATE(T, t) cinv,
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const TEMPLATE(T, ctx_t) ctx)
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{
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if (n == 1) /* {Q,1} x* cinv == 1 mod (x) */
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{
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TEMPLATE(T, set) (Qinv, cinv, ctx);
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}
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else
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{
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const slong alloc = FLINT_MAX(n, 3 * FQ_POLY_INV_NEWTON_CUTOFF);
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slong *a, i, m;
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TEMPLATE(T, struct) * W;
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W = _TEMPLATE(T, vec_init) (alloc, ctx);
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for (i = 1; (WORD(1) << i) < n; i++) ;
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a = (slong *) flint_malloc(i * sizeof(slong));
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a[i = 0] = n;
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while (n >= FQ_POLY_INV_NEWTON_CUTOFF)
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a[++i] = (n = (n + 1) / 2);
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/* Base case */
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{
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TEMPLATE(T, struct) * Qrev = W + 2 * FQ_POLY_INV_NEWTON_CUTOFF;
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_TEMPLATE(T, poly_reverse) (Qrev, Q, n, n, ctx);
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_TEMPLATE(T, vec_zero) (W, 2 * n - 2, ctx);
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TEMPLATE(T, one) (W + (2 * n - 2), ctx);
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_TEMPLATE(T, poly_div_basecase) (Qinv, W, W, 2 * n - 1, Qrev, n,
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cinv, ctx);
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_TEMPLATE(T, poly_reverse) (Qinv, Qinv, n, n, ctx);
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}
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for (i--; i >= 0; i--)
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{
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m = n;
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n = a[i];
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_TEMPLATE(T, poly_mullow) (W, Q, n, Qinv, m, n, ctx);
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_TEMPLATE(T, poly_mullow) (Qinv + m, Qinv, m, W + m, n - m, n - m,
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ctx);
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_TEMPLATE(T, poly_neg) (Qinv + m, Qinv + m, n - m, ctx);
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}
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_TEMPLATE(T, vec_clear) (W, alloc, ctx);
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flint_free(a);
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}
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}
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void
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TEMPLATE(T, poly_inv_series_newton) (TEMPLATE(T, poly_t) Qinv,
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const TEMPLATE(T, poly_t) Q, slong n,
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const TEMPLATE(T, ctx_t) ctx)
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{
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TEMPLATE(T, t) cinv;
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TEMPLATE(T, struct) * Qcopy;
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int Qalloc;
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if (Q->length >= n)
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{
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Qcopy = Q->coeffs;
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Qalloc = 0;
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}
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else
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{
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Qcopy = _TEMPLATE(T, vec_init) (n, ctx);
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_TEMPLATE(T, vec_set) (Qcopy, Q->coeffs, Q->length, ctx);
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Qalloc = 1;
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}
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TEMPLATE(T, init) (cinv, ctx);
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TEMPLATE(T, inv) (cinv, Q->coeffs, ctx);
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if (Qinv != Q)
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{
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TEMPLATE(T, poly_fit_length) (Qinv, n, ctx);
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_TEMPLATE(T, poly_inv_series_newton) (Qinv->coeffs, Qcopy, n, cinv,
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ctx);
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}
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else
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{
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TEMPLATE(T, struct) * t = _TEMPLATE(T, vec_init) (n, ctx);
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_TEMPLATE(T, poly_inv_series_newton) (t, Qcopy, n, cinv, ctx);
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_TEMPLATE(T, vec_clear) (Qinv->coeffs, Qinv->alloc, ctx);
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Qinv->coeffs = t;
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Qinv->alloc = n;
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Qinv->length = n;
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}
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_TEMPLATE(T, poly_set_length) (Qinv, n, ctx);
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_TEMPLATE(T, poly_normalise) (Qinv, ctx);
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if (Qalloc)
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_TEMPLATE(T, vec_clear) (Qcopy, n, ctx);
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TEMPLATE(T, clear) (cinv, ctx);
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}
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#endif
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