126 lines
3.0 KiB
C
126 lines
3.0 KiB
C
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/*=============================================================================
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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) 2011 Jan Tuitman
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Copyright (C) 2011, 2012 Sebastian Pancratz
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******************************************************************************/
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#include "padic.h"
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#define n (S->n)
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#define pow (S->pow)
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void _padic_inv_precompute(padic_inv_t S, const fmpz_t p, slong N)
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{
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slong *a;
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a = _padic_lifts_exps(&n, N);
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pow = _fmpz_vec_init(2 * n + 2);
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_padic_lifts_pows(pow, a, n, p);
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flint_free(a);
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}
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void _padic_inv_clear(padic_inv_t S)
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{
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_fmpz_vec_clear(pow, 2 * n + 2);
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}
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void _padic_inv_precomp(fmpz_t rop, const fmpz_t op, const padic_inv_t S)
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{
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slong i;
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fmpz *t, *u;
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u = pow + n;
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t = pow + 2 * n;
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/* Compute reduced units */
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{
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fmpz_mod(u + 0, op, pow + 0);
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}
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for (i = 1; i < n; i++)
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{
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fmpz_mod(u + i, u + (i - 1), pow + i);
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}
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/* Run Newton iteration */
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i = n - 1;
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{
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fmpz_invmod(rop, u + i, pow + i);
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}
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for (i--; i >= 0; i--)
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{
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fmpz_mul(t, rop, rop);
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fmpz_mul(t + 1, u + i, t);
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fmpz_mul_2exp(rop, rop, 1);
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fmpz_sub(rop, rop, t + 1);
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fmpz_mod(rop, rop, pow + i);
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}
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}
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#undef n
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#undef pow
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void _padic_inv(fmpz_t rop, const fmpz_t op, const fmpz_t p, slong N)
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{
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if (N == 1)
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{
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fmpz_invmod(rop, op, p);
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}
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else
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{
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padic_inv_t S;
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_padic_inv_precompute(S, p, N);
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_padic_inv_precomp(rop, op, S);
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_padic_inv_clear(S);
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}
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}
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void padic_inv(padic_t rop, const padic_t op, const padic_ctx_t ctx)
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{
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if (padic_is_zero(op))
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{
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flint_printf("Exception (padic_inv). Zero is not invertible.\n");
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abort();
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}
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/*
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If x = u p^v has negative valuation with N <= -v then the
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exact inverse of x is zero when reduced modulo $p^N$
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*/
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if (padic_prec(rop) + padic_val(op) <= 0)
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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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_padic_inv(padic_unit(rop),
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padic_unit(op), ctx->p, padic_prec(rop) + padic_val(op));
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padic_val(rop) = - padic_val(op);
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}
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}
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