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

227 lines
6.5 KiB
C
Raw Normal View History

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 "fmpz_mod_poly.h"
#include "qadic.h"
extern slong _padic_exp_bound(slong v, slong N, const fmpz_t p);
void _qadic_exp_rectangular(fmpz *rop, const fmpz *op, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N, const fmpz_t pN)
{
const slong d = j[lena - 1];
const slong n = _padic_exp_bound(v, N, p);
if (n < 4)
{
if (n == 1) /* y := 1 */
{
fmpz_one(rop);
_fmpz_vec_zero(rop + 1, d - 1);
}
else if (n == 2) /* y := 1 + x */
{
fmpz_t f;
fmpz_init(f);
fmpz_pow_ui(f, p, v);
_fmpz_vec_scalar_mul_fmpz(rop, op, len, f);
_fmpz_vec_zero(rop + len, d - len);
fmpz_add_ui(rop, rop, 1);
_fmpz_vec_scalar_mod_fmpz(rop, rop, len, pN);
fmpz_clear(f);
}
else /* y := 1 + x + x^2/2 */
{
slong i;
fmpz *x = _fmpz_vec_init(len + 1);
fmpz_pow_ui(x + len, p, v);
_fmpz_vec_scalar_mul_fmpz(x, op, len, x + len);
_fmpz_poly_sqr(rop, x, len);
if (*p != WORD(2))
{
for (i = 0; i < 2 * len - 1; i++)
if (fmpz_is_odd(rop + i))
fmpz_add(rop + i, rop + i, pN);
}
_fmpz_vec_scalar_fdiv_q_2exp(rop, rop, 2 * len - 1, 1);
_fmpz_mod_poly_reduce(rop, 2 * len - 1, a, j, lena, pN);
_fmpz_vec_zero(rop + (2 * len - 1), d - (2 * len - 1));
_fmpz_mod_poly_add(rop, rop, d, x, len, pN);
fmpz_add_ui(rop, rop, 1);
if (fmpz_equal(rop, pN))
fmpz_zero(rop);
_fmpz_vec_clear(x, len + 1);
}
}
else /* n >= 4 */
{
const slong k = fmpz_fits_si(p) ?
(n - 1 - 1) / (fmpz_get_si(p) - 1) : 0;
const slong b = n_sqrt(n);
slong i;
fmpz_t c, f, pNk;
fmpz *s, *t, *x;
fmpz_init(c);
fmpz_init(f);
fmpz_init(pNk);
s = _fmpz_vec_init(2 * d - 1);
t = _fmpz_vec_init(2 * d - 1);
x = _fmpz_vec_init(d * (b + 1) + d - 1);
fmpz_pow_ui(f, p, v);
fmpz_pow_ui(pNk, p, N + k);
/* Compute powers x^i of the argument */
fmpz_one(x);
_fmpz_vec_scalar_mul_fmpz(x + d, op, len, f);
_fmpz_vec_zero(x + d + len, d - len);
for (i = 2; i <= b; i++)
{
_fmpz_mod_poly_mul(x + i * d, x + (i - 1) * d, d, x + d, d, pNk);
_fmpz_mod_poly_reduce(x + i * d, 2 * d - 1, a, j, lena, pNk);
}
_fmpz_vec_zero(rop, d);
fmpz_one(f);
for (i = (n + b - 1) / b - 1; i >= 0; i--)
{
slong lo = i * b;
slong hi = FLINT_MIN(n - 1, lo + b - 1);
_fmpz_vec_zero(s, d);
fmpz_one(c);
for ( ; hi >= lo; hi--)
{
_fmpz_vec_scalar_addmul_fmpz(s, x + (hi - lo) * d, d, c);
if (hi != 0)
fmpz_mul_ui(c, c, hi);
}
_fmpz_poly_mul(t, x + b * d, d, rop, d);
_fmpz_mod_poly_reduce(t, 2 * d - 1, a, j, lena, pNk);
_fmpz_vec_scalar_mul_fmpz(rop, s, d, f);
_fmpz_vec_add(rop, rop, t, d);
_fmpz_vec_scalar_mod_fmpz(rop, rop, d, pNk);
fmpz_mul(f, f, c);
}
/* Note exp(x) is a unit so val(sum) == val(f). */
i = fmpz_remove(f, f, p);
if (i)
{
fmpz_pow_ui(c, p, i);
_fmpz_vec_scalar_divexact_fmpz(rop, rop, d, c);
}
_padic_inv(f, f, p, N);
_fmpz_vec_scalar_mul_fmpz(rop, rop, d, f);
_fmpz_vec_scalar_mod_fmpz(rop, rop, d, pN);
_fmpz_vec_clear(s, 2 * d - 1);
_fmpz_vec_clear(t, 2 * d - 1);
_fmpz_vec_clear(x, d * (b + 1) + d - 1);
fmpz_clear(c);
fmpz_clear(f);
fmpz_clear(pNk);
}
}
int qadic_exp_rectangular(qadic_t rop, const qadic_t op, const qadic_ctx_t ctx)
{
const slong N = qadic_prec(rop);
const slong v = op->val;
const fmpz *p = (&ctx->pctx)->p;
if (padic_poly_is_zero(op))
{
padic_poly_one(rop);
return 1;
}
if ((*p == WORD(2) && v <= 1) || (v <= 0))
{
return 0;
}
else
{
if (v < N)
{
const slong d = qadic_ctx_degree(ctx);
fmpz *t;
fmpz_t pN;
int alloc;
alloc = _padic_ctx_pow_ui(pN, N, &ctx->pctx);
if (rop == op)
{
t = _fmpz_vec_init(2 * d - 1);
}
else
{
padic_poly_fit_length(rop, 2 * d - 1);
t = rop->coeffs;
}
_qadic_exp_rectangular(t, op->coeffs, v, op->length,
ctx->a, ctx->j, ctx->len, p, N, pN);
rop->val = 0;
if (rop == op)
{
_fmpz_vec_clear(rop->coeffs, rop->alloc);
rop->coeffs = t;
rop->alloc = 2 * d - 1;
rop->length = d;
}
_padic_poly_set_length(rop, d);
_padic_poly_normalise(rop);
if (alloc)
fmpz_clear(pN);
}
else
{
padic_poly_one(rop);
}
return 1;
}
}