pqc/external/flint-2.4.3/qadic/norm_analytic.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2012 Sebastian Pancratz
******************************************************************************/
#include "qadic.h"
/*
Computes the norm of an element $x$ of $\mathbf{Z}_q$ via the identity
$\Norm(x) = \exp \Trace \log (x)$
whenever $y = 1-x$ has valuation $v$ greater than $(p-1)^{-1}$.
Assumes that $y$ is non-zero.
*/
void _qadic_norm_analytic(fmpz_t rop, const fmpz *y, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
fmpz_t pN, tru;
slong trv;
fmpz *lg;
fmpz_init(pN);
fmpz_init(tru);
lg = _fmpz_vec_init(d);
fmpz_pow_ui(pN, p, N);
_qadic_log(lg, y, v, len, a, j, lena, p, N, pN);
_qadic_trace(tru, lg, d, a, j, lena, pN);
if (!fmpz_is_zero(tru))
{
trv = fmpz_remove(tru, tru, p);
_padic_exp(rop, tru, trv, p, N);
fmpz_mod(rop, rop, pN);
}
else
{
fmpz_one(rop);
}
fmpz_clear(pN);
fmpz_clear(tru);
_fmpz_vec_clear(lg, d);
}
void qadic_norm_analytic(padic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
const slong N = padic_prec(rop);
const slong d = qadic_ctx_degree(ctx);
const fmpz *p = (&ctx->pctx)->p;
/* N(p^v u) = p^{dv} N(u) */
if (qadic_is_zero(op) || d * op->val >= N)
{
padic_zero(rop);
}
else if (op->length == 1)
{
fmpz_t pN;
int alloc;
alloc = _padic_ctx_pow_ui(pN, N - d * op->val, (&ctx->pctx));
fmpz_powm_ui(padic_unit(rop), op->coeffs + 0, d, pN);
padic_val(rop) = d * op->val;
if (alloc)
fmpz_clear(pN);
}
else /* len >= 2 */
{
fmpz *y;
slong w;
y = _fmpz_vec_init(op->length);
_fmpz_vec_neg(y, op->coeffs, op->length);
fmpz_add_ui(y + 0, y + 0, 1);
w = _fmpz_vec_ord_p(y, op->length, p);
if ((w < 2 && *p == WORD(2)) || w < 1)
{
flint_printf("ERROR (qadic_norm_analytic). w = %wd.\n", w);
abort();
}
_qadic_norm_analytic(padic_unit(rop), y, w, op->length,
ctx->a, ctx->j, ctx->len, p, N - d * op->val);
padic_val(rop) = d * op->val;
_fmpz_vec_clear(y, op->length);
}
}