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

264 lines
5.8 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
\begin{equation*}
(a-1)! x^{1-a} \sum_{i=a}^{b-1} \frac{x^i}{i!}.
\end{equation*}
in the rational $(T, Q)$.
Assumes that $1 \leq a < b$.
If $a + 1 = b$, sets $P = x$, $Q = a$, and $T = x$.
If $a + 2 = b$, sets $P = x^2$, $Q = a (a + 1)$, $T = x (a + 1) + x^2$.
In general, sets
\begin{align*}
P & = x^{b-a}, \\
Q & = \frac{(b-1)!}{(a-1)!}, \\
T & = (b-1)! x^{1-a} \sum_{i=a}^{b-1} \frac{x^i}{i!}.
\end{align*}
*/
static void
_padic_exp_bsplit_series(fmpz_t P, fmpz_t Q, fmpz_t T,
const fmpz_t x, slong a, slong b)
{
if (b - a == 1)
{
fmpz_set(P, x);
fmpz_set_ui(Q, a);
fmpz_set(T, x);
}
else if (b - a == 2)
{
fmpz_mul(P, x, x);
fmpz_set_ui(Q, a);
fmpz_mul_ui(Q, Q, a + 1);
fmpz_mul_ui(T, x, a + 1);
fmpz_add(T, T, P);
}
else
{
const slong m = (a + b) / 2;
fmpz_t PR, QR, TR;
fmpz_init(PR);
fmpz_init(QR);
fmpz_init(TR);
_padic_exp_bsplit_series(P, Q, T, x, a, m);
_padic_exp_bsplit_series(PR, QR, TR, x, m, b);
fmpz_mul(T, T, QR);
fmpz_addmul(T, P, TR);
fmpz_mul(P, P, PR);
fmpz_mul(Q, Q, QR);
fmpz_clear(PR);
fmpz_clear(QR);
fmpz_clear(TR);
}
}
/*
Assumes that $x$ is such that $\exp(x)$ converges.
Assumes that $v = \ord_p(x)$ with $v < N$,
which also forces $N$ to positive.
The result $y$ might not be reduced modulo $p^N$.
Supports aliasing between $x$ and $y$.
*/
static void
_padic_exp_bsplit(fmpz_t y, const fmpz_t x, slong v, const fmpz_t p, slong N)
{
const slong n = _padic_exp_bound(v, N, p);
if (n == 1)
{
fmpz_one(y);
}
else
{
fmpz_t P, Q, T;
fmpz_init(P);
fmpz_init(Q);
fmpz_init(T);
_padic_exp_bsplit_series(P, Q, T, x, 1, n);
fmpz_add(T, T, Q); /* (T,Q) := (T,Q) + 1 */
/* Note exp(x) is a unit so val(T) == val(Q). */
if (fmpz_remove(T, T, p))
fmpz_remove(Q, Q, p);
_padic_inv(Q, Q, p, N);
fmpz_mul(y, T, Q);
fmpz_clear(P);
fmpz_clear(Q);
fmpz_clear(T);
}
}
void _padic_exp_balanced_2(fmpz_t rop, const fmpz_t xu, slong xv, slong N)
{
const fmpz_t p = {WORD(2)};
fmpz_t r, t;
slong w;
fmpz_init(r);
fmpz_init(t);
w = 1;
fmpz_mul_2exp(t, xu, xv);
fmpz_fdiv_r_2exp(t, t, N);
fmpz_one(rop);
while (!fmpz_is_zero(t))
{
fmpz_fdiv_r_2exp(r, t, 2*w);
fmpz_sub(t, t, r);
if (!fmpz_is_zero(r))
{
_padic_exp_bsplit(r, r, w, p, N);
fmpz_mul(rop, rop, r);
fmpz_fdiv_r_2exp(rop, rop, N);
}
w *= 2;
}
fmpz_clear(r);
fmpz_clear(t);
}
void _padic_exp_balanced_p(fmpz_t rop, const fmpz_t xu, slong xv,
const fmpz_t p, slong N)
{
fmpz_t r, t, pw, pN;
slong w;
fmpz_init(r);
fmpz_init(t);
fmpz_init(pw);
fmpz_init(pN);
fmpz_set(pw, p);
fmpz_pow_ui(pN, p, N);
w = 1;
fmpz_pow_ui(t, p, xv);
fmpz_mul(t, t, xu);
fmpz_mod(t, t, pN);
fmpz_one(rop);
while (!fmpz_is_zero(t))
{
fmpz_mul(pw, pw, pw);
fmpz_fdiv_r(r, t, pw);
fmpz_sub(t, t, r);
if (!fmpz_is_zero(r))
{
_padic_exp_bsplit(r, r, w, p, N);
fmpz_mul(rop, rop, r);
fmpz_mod(rop, rop, pN);
}
w *= 2;
}
fmpz_clear(r);
fmpz_clear(t);
fmpz_clear(pw);
fmpz_clear(pN);
}
/*
Assumes that the exponential series converges at $x \neq 0$,
and that $\ord_p(x) < N$.
Supports aliasing between $x$ and $y$.
TODO: Take advantage of additional factors of $p$ in $x$.
*/
void _padic_exp_balanced(fmpz_t rop, const fmpz_t u, slong v,
const fmpz_t p, slong N)
{
if (fmpz_equal_ui(p, 2))
_padic_exp_balanced_2(rop, u, v, N);
else
_padic_exp_balanced_p(rop, u, v, p, N);
}
int padic_exp_balanced(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_balanced(padic_unit(rop),
padic_unit(op), padic_val(op), p, N);
padic_val(rop) = 0;
}
else
{
padic_one(rop);
}
return 1;
}
}