pqc/external/flint-2.4.3/qadic/exp_balanced.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"
extern slong _padic_exp_bound(slong v, slong N, const fmpz_t p);
static void
_qadic_exp_bsplit_series(fmpz *P, fmpz_t Q, fmpz *T,
const fmpz *x, slong len, slong lo, slong hi,
const fmpz *a, const slong *j, slong lena)
{
const slong d = j[lena - 1];
if (hi - lo == 1)
{
_fmpz_vec_set(P, x, len);
_fmpz_vec_zero(P + len, 2*d - 1 - len);
fmpz_set_si(Q, lo);
_fmpz_vec_set(T, P, 2*d - 1);
}
else if (hi - lo == 2)
{
_fmpz_poly_sqr(P, x, len);
_fmpz_vec_zero(P + (2*len - 1), d - (2*len - 1));
_fmpz_poly_reduce(P, 2*len - 1, a, j, lena);
fmpz_set_si(Q, lo);
fmpz_mul_si(Q, Q, lo + 1);
_fmpz_vec_scalar_mul_si(T, x, len, lo + 1);
_fmpz_vec_zero(T + len, d - len);
_fmpz_vec_add(T, T, P, d);
}
else
{
const slong m = (lo + hi) / 2;
fmpz *PR, *TR, *W;
fmpz_t QR;
PR = _fmpz_vec_init(2*d - 1);
TR = _fmpz_vec_init(2*d - 1);
W = _fmpz_vec_init(2*d - 1);
fmpz_init(QR);
_qadic_exp_bsplit_series(P, Q, T, x, len, lo, m, a, j, lena);
_qadic_exp_bsplit_series(PR, QR, TR, x, len, m, hi, a, j, lena);
_fmpz_poly_mul(W, TR, d, P, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mul_fmpz(T, T, d, QR);
_fmpz_vec_add(T, T, W, d);
_fmpz_poly_mul(W, P, d, PR, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_swap(P, W, d);
fmpz_mul(Q, Q, QR);
_fmpz_vec_clear(PR, 2*d - 1);
_fmpz_vec_clear(TR, 2*d - 1);
_fmpz_vec_clear(W, 2*d - 1);
fmpz_clear(QR);
}
}
static void
_qadic_exp_bsplit(fmpz *y, const fmpz *x, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
const slong n = _padic_exp_bound(v, N, p);
if (n == 1)
{
fmpz_one(y + 0);
_fmpz_vec_zero(y + 1, d - 1);
}
else
{
fmpz *P, *T;
fmpz_t Q, R;
slong f;
P = _fmpz_vec_init(2*d - 1);
T = _fmpz_vec_init(2*d - 1);
fmpz_init(Q);
fmpz_init(R);
_qadic_exp_bsplit_series(P, Q, T, x, len, 1, n, a, j, lena);
fmpz_add(T + 0, T + 0, Q); /* (T,Q) := (T,Q) + 1 */
/* Note exp(x) is a unit so val(T) == val(Q). */
f = fmpz_remove(Q, Q, p);
fmpz_pow_ui(R, p, f);
_fmpz_vec_scalar_divexact_fmpz(T, T, d, R);
_padic_inv(Q, Q, p, N);
_fmpz_vec_scalar_mul_fmpz(y, T, d, Q);
_fmpz_vec_clear(P, 2*d - 1);
_fmpz_vec_clear(T, 2*d - 1);
fmpz_clear(Q);
fmpz_clear(R);
}
}
void _qadic_exp_balanced(fmpz *rop, const fmpz *x, 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];
fmpz_t pw;
fmpz *r, *s, *t;
slong i, w;
r = _fmpz_vec_init(d);
s = _fmpz_vec_init(2*d - 1);
t = _fmpz_vec_init(d);
fmpz_init(pw);
fmpz_pow_ui(pw, p, v);
_fmpz_vec_scalar_mul_fmpz(t, x, len, pw);
_fmpz_vec_scalar_mod_fmpz(t, t, len, pN);
_fmpz_vec_zero(t + len, d - len);
fmpz_set(pw, p);
fmpz_one(rop + 0);
_fmpz_vec_zero(rop + 1, d - 1);
w = 1;
while (!_fmpz_vec_is_zero(t, d))
{
fmpz_mul(pw, pw, pw);
for (i = 0; i < d; i++)
{
fmpz_fdiv_r(r + i, t + i, pw);
fmpz_sub(t + i, t + i, r + i);
}
if (!_fmpz_vec_is_zero(r, d))
{
_qadic_exp_bsplit(r, r, w, d, a, j, lena, p, N);
_fmpz_poly_mul(s, rop, d, r, d);
_fmpz_poly_reduce(s, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mod_fmpz(rop, s, d, pN);
}
w *= 2;
}
_fmpz_vec_clear(r, d);
_fmpz_vec_clear(s, 2*d - 1);
_fmpz_vec_clear(t, d);
fmpz_clear(pw);
}
int qadic_exp_balanced(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 pN;
int alloc;
alloc = _padic_ctx_pow_ui(pN, N, &ctx->pctx);
padic_poly_fit_length(rop, d);
_qadic_exp_balanced(rop->coeffs, op->coeffs, v, op->length,
ctx->a, ctx->j, ctx->len, p, N, pN);
rop->val = 0;
_padic_poly_set_length(rop, d);
_padic_poly_normalise(rop);
if (alloc)
fmpz_clear(pN);
}
else
{
padic_poly_one(rop);
}
return 1;
}
}