114 lines
3.3 KiB
C
114 lines
3.3 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) 2012 Sebastian Pancratz
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******************************************************************************/
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#include "qadic.h"
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/*
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Discussion on the choice of the norm algorithm.
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When the logarithm function does not converge for x,
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the only choice is the resultant method.
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However, when the logarithm function converges, we
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can choose between the analytic method and the resultant
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method. Roughly speaking, we postulate that the analytic
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method has runtime A (log N)^2 mu(p,d,N), where mu(p,d,N)
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is (d log d) M(N log p). The resultant method has runtime
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B d^4 M(N log p). Experimentally, we find that A/B is
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somewhere around 4.
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TODO: Repeat the experiments with p=2, which is an
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important special case.
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*/
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void _qadic_norm(fmpz_t rop, const fmpz *op, slong len,
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const fmpz *a, const slong *j, slong lena,
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const fmpz_t p, slong N)
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{
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const slong d = j[lena - 1];
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if (len == 1)
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{
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fmpz_t pN;
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fmpz_init(pN);
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fmpz_pow_ui(pN, p, N);
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fmpz_powm_ui(rop, op + 0, d, pN);
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fmpz_clear(pN);
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}
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else
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{
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fmpz *y;
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slong w;
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y = _fmpz_vec_init(len);
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/* (y,len) := 1 - (op,len) */
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_fmpz_vec_neg(y, op, len);
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fmpz_add_ui(y + 0, y + 0, 1);
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w = _fmpz_vec_ord_p(y, len, p);
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if (w >= 2 || (*p != WORD(2) && w >= 1))
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{
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if (4 * FLINT_FLOG2(N) * FLINT_FLOG2(N) * FLINT_FLOG2(d) < d*d*d)
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{
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_qadic_norm_analytic(rop, y, w, len, a, j, lena, p, N);
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}
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else
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{
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_qadic_norm_resultant(rop, op, len, a, j, lena, p, N);
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}
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}
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else
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{
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_qadic_norm_resultant(rop, op, len, a, j, lena, p, N);
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}
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_fmpz_vec_clear(y, len);
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}
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}
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void qadic_norm(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
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{
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const slong N = padic_prec(rop);
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const slong d = qadic_ctx_degree(ctx);
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const fmpz *p = (&ctx->pctx)->p;
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/* N(p^v u) = p^{dv} N(u) */
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if (qadic_is_zero(op) || d * op->val >= N)
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{
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padic_zero(rop);
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}
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else
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{
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_qadic_norm(padic_unit(rop), op->coeffs, op->length,
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ctx->a, ctx->j, ctx->len, p, N - d * op->val);
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padic_val(rop) = d * op->val;
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}
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}
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