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

198 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
Copyright (C) 2012 Fredrik Johansson
******************************************************************************/
#include "padic.h"
/*
Computes the sum $1 + x + x^2 / 2$ reduced modulo $p^N$,
where $x = p^v u$.
Supports aliasing between \code{rop} and $u$.
*/
static void _padic_exp_small(fmpz_t rop, const fmpz_t u, slong v, slong n,
const fmpz_t p, const fmpz_t pN)
{
if (n == 1) /* rop = 1 */
{
fmpz_one(rop);
}
else if (n == 2) /* rop = 1 + x */
{
fmpz_t f;
fmpz_init(f);
fmpz_pow_ui(f, p, v);
fmpz_mul(rop, f, u);
fmpz_add_ui(rop, rop, 1);
fmpz_mod(rop, rop, pN);
fmpz_clear(f);
}
else /* n == 3, rop = 1 + x + x^2 / 2 */
{
fmpz_t f;
fmpz_init(f);
fmpz_pow_ui(f, p, v);
fmpz_mul(rop, f, u);
fmpz_mul(f, rop, rop);
if (fmpz_is_odd(f))
fmpz_add(f, f, pN);
fmpz_fdiv_q_2exp(f, f, 1);
fmpz_add(rop, rop, f);
fmpz_add_ui(rop, rop, 1);
fmpz_clear(f);
}
}
void _padic_exp_rectangular(fmpz_t rop, const fmpz_t u, slong v,
const fmpz_t p, slong N)
{
const slong n = _padic_exp_bound(v, N, p);
fmpz_t pN;
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
if (n <= 3)
{
_padic_exp_small(rop, u, v, n, p, pN);
}
else
{
const slong k = fmpz_fits_si(p) ?
(n - 1 - 1) / (fmpz_get_si(p) - 1) : 0;
slong i, npows, nsums;
fmpz_t c, f, s, t, sum, pNk;
fmpz *pows;
fmpz_init(pNk);
fmpz_pow_ui(pNk, p, N + k);
npows = n_sqrt(n);
nsums = (n + npows - 1) / npows;
fmpz_init(c);
fmpz_init(f);
fmpz_init(s);
fmpz_init(t);
fmpz_init(sum);
/* Compute pows; pows[i] = x^i. */
pows = _fmpz_vec_init(npows + 1);
fmpz_one(pows + 0);
fmpz_pow_ui(f, p, v);
fmpz_mul(pows + 1, f, u);
for (i = 2; i <= npows; i++)
{
fmpz_mul(pows + i, pows + i - 1, pows + 1);
fmpz_mod(pows + i, pows + i, pNk);
}
fmpz_zero(sum);
fmpz_one(f);
for (i = nsums - 1; i >= 0; i--)
{
slong lo = i * npows;
slong hi = FLINT_MIN(n - 1, lo + npows - 1);
fmpz_zero(s);
fmpz_one(c);
for ( ; hi >= lo; hi--)
{
fmpz_addmul(s, pows + hi - lo, c);
if (hi != 0)
fmpz_mul_ui(c, c, hi);
}
fmpz_mul(t, pows + npows, sum);
fmpz_mul(sum, s, f);
fmpz_add(sum, sum, t);
fmpz_mod(sum, sum, pNk);
fmpz_mul(f, f, c);
}
/* Divide by factorial, TODO: Improve */
/* Note exp(x) is a unit so val(sum) == val(f) */
if (fmpz_remove(sum, sum, p))
fmpz_remove(f, f, p);
_padic_inv(f, f, p, N);
fmpz_mul(rop, sum, f);
_fmpz_vec_clear(pows, npows + 1);
fmpz_clear(c);
fmpz_clear(f);
fmpz_clear(s);
fmpz_clear(t);
fmpz_clear(sum);
fmpz_clear(pNk);
}
fmpz_mod(rop, rop, pN);
fmpz_clear(pN);
}
int padic_exp_rectangular(padic_t rop, const padic_t op, const padic_ctx_t ctx)
{
const slong N = padic_prec(rop);
const slong v = padic_val(op);
const fmpz *p = ctx->p;
if (padic_is_zero(op))
{
padic_one(rop);
return 1;
}
if ((fmpz_equal_ui(p, 2) && v <= 1) || (v <= 0))
{
return 0;
}
else
{
if (v < N)
{
_padic_exp_rectangular(padic_unit(rop),
padic_unit(op), padic_val(op), p, N);
padic_val(rop) = 0;
}
else
{
padic_one(rop);
}
return 1;
}
}