pqc/external/flint-2.4.3/qadic/teichmuller.c
2014-05-24 23:16:06 +02:00

178 lines
4.9 KiB
C

/*=============================================================================
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 <stdlib.h>
#include "fmpz_mod_poly.h"
#include "qadic.h"
/*
Uses Hensel lifting along the polynomial $X^q - X$, which yields
the formula $z' = z - (z^q - z) / (q z^{q-1} - 1)$.
We observe that the denominator is an approximation to $q - 1$,
which allows us to use the formula $z' = z - (q-1)^{-1} (z^q - z)$
during the iteration.
Supports aliasing between \code{rop} and \code{op}.
*/
void _qadic_teichmuller(fmpz *rop, const fmpz *op, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
if (len == 1)
{
_padic_teichmuller(rop, op, p, N);
_fmpz_vec_zero(rop + 1, d - 1);
}
else if (N == 1)
{
_fmpz_vec_scalar_mod_fmpz(rop, op, len, p);
_fmpz_vec_zero(rop + len, d - len);
}
else /* d, N >= 2 */
{
slong *e, i, n;
fmpz *pow, *u, *t, *w;
fmpz_t inv, q, qm1;
n = FLINT_CLOG2(N) + 1;
e = flint_malloc(n * sizeof(slong));
for (e[i = 0] = N; e[i] > 1; i++)
e[i + 1] = (e[i] + 1) / 2;
w = _fmpz_vec_init(n + n + (2 * d - 1));
pow = w;
u = w + n;
t = w + 2 * n;
fmpz_init(inv);
fmpz_init(q);
fmpz_init(qm1);
fmpz_pow_ui(q, p, d);
fmpz_sub_ui(qm1, q, 1);
/* Compute powers of p */
{
fmpz_one(t);
fmpz_set(pow + i, p);
}
for (i--; i >= 1; i--)
{
if (e[i] & WORD(1))
{
fmpz_mul(pow + i, t, pow + (i + 1));
fmpz_mul(t, t, t);
}
else
{
fmpz_mul(t, t, pow + (i + 1));
fmpz_mul(pow + i, pow + (i + 1), pow + (i + 1));
}
}
{
if (e[i] & WORD(1))
fmpz_mul(pow + i, t, pow + (i + 1));
else
fmpz_mul(pow + i, pow + (i + 1), pow + (i + 1));
}
/* Compute reduced units for (q-1) */
{
fmpz_mod(u + 0, qm1, pow + 0);
}
for (i = 1; i < n; i++)
{
fmpz_mod(u + i, u + (i - 1), pow + i);
}
/* Run Newton iteration */
i = n - 1;
{
_fmpz_vec_scalar_mod_fmpz(rop, op, len, pow + i);
_fmpz_vec_zero(rop + len, d - len);
fmpz_sub_ui(inv, p, 1);
}
for (i--; i >= 0; i--)
{
/* Lift rop */
_qadic_pow(t, rop, d, q, a, j, lena, pow + i);
_fmpz_poly_sub(t, t, d, rop, d);
_fmpz_vec_scalar_submul_fmpz(rop, t, d, inv);
_fmpz_vec_scalar_mod_fmpz(rop, rop, d, pow + i);
/* Lift inv */
if (i > 0)
{
fmpz_mul(t, inv, inv);
fmpz_mul(t + 1, u + i, t);
fmpz_mul_2exp(inv, inv, 1);
fmpz_sub(inv, inv, t + 1);
fmpz_mod(inv, inv, pow + i);
}
}
_fmpz_vec_clear(w, n + n + (2 * d - 1));
fmpz_clear(inv);
fmpz_clear(q);
fmpz_clear(qm1);
flint_free(e);
}
}
void qadic_teichmuller(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
const slong N = qadic_prec(rop);
if (op->val < 0)
{
flint_printf("Exception (qadic_teichmuller). val(op) is negative.\n");
abort();
}
if (qadic_is_zero(op) || op->val > 0 || N <= 0)
{
qadic_zero(rop);
}
else
{
const slong d = qadic_ctx_degree(ctx);
padic_poly_fit_length(rop, d);
_qadic_teichmuller(rop->coeffs, op->coeffs, op->length,
ctx->a, ctx->j, ctx->len, (&ctx->pctx)->p, N);
rop->val = 0;
_padic_poly_set_length(rop, d);
_padic_poly_normalise(rop);
}
}