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pqc/external/flint-2.4.3/qadic/frobenius.c
hasufell d51d8e3652
ALL: Add flint
2014-05-24 23:16:06 +02:00

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/*=============================================================================
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 "ulong_extras.h"
#include "qadic.h"
/*
Assumes that \code{len1} and \code{len2} are positive but at
most~$d$, and also that \code{len1} is at least $6$.
The latter assumption guarantees that $\ceil{n/B} \geq 2$,
i.e.\ $n \geq 2B$ so $n \geq 2 \ceil{\sqrt{n}}$.
*/
static void
_fmpz_mod_poly_compose_smod_rectangular(fmpz *rop,
const fmpz *op1, slong len1,
const fmpz *op2, slong len2,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p)
{
const slong d = j[lena - 1];
if (len2 == 1)
{
_fmpz_mod_poly_evaluate_fmpz(rop, op1, len1, op2, p);
_fmpz_vec_zero(rop + 1, d - 1);
}
else
{
const slong B = n_sqrt(len1);
slong i, k;
fmpz *pows, *t;
pows = _fmpz_vec_init((B + 2) * d);
t = _fmpz_vec_init(2 * d - 1);
fmpz_one(pows + 0 * d + 0);
_fmpz_vec_set(pows + 1 * d, op2, len2);
for (i = 2; i <= B; i++)
{
_fmpz_poly_mul(pows + i * d, pows + (i - 1) * d, d, op2, len2);
_fmpz_poly_reduce(pows + i * d, d + len2 - 1, a, j, lena);
_fmpz_vec_scalar_mod_fmpz(pows + i * d, pows + i * d, d, p);
}
_fmpz_vec_zero(rop, d);
for (i = (len1 + B - 1) / B - 1; i >= 0; i--)
{
_fmpz_poly_mul(t, rop, d, pows + B * d, d);
_fmpz_poly_reduce(t, 2 * d - 1, a, j, lena);
_fmpz_vec_set(rop, t, d);
fmpz_add(rop + 0, rop + 0, op1 + i*B);
for (k = FLINT_MIN(B, len1 - i*B) - 1; k > 0; k--)
{
_fmpz_vec_scalar_addmul_fmpz(rop, pows + k * d, d, op1 + (i*B + k));
}
_fmpz_vec_scalar_mod_fmpz(rop, rop, d, p);
}
_fmpz_vec_clear(pows, (B + 2) * d);
_fmpz_vec_clear(t, 2 * d - 1);
}
}
static void
_fmpz_mod_poly_compose_smod_horner(fmpz *rop,
const fmpz *op1, slong len1,
const fmpz *op2, slong len2,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p)
{
const slong d = j[lena - 1];
if (len1 == 1)
{
fmpz_set(rop, op1);
_fmpz_vec_zero(rop + 1, d - 1);
}
else if (len2 == 1)
{
_fmpz_mod_poly_evaluate_fmpz(rop, op1, len1, op2, p);
_fmpz_vec_zero(rop + 1, d - 1);
}
else
{
slong i;
fmpz *t;
t = _fmpz_vec_init(2*d - 1);
_fmpz_vec_zero(rop, d);
for (i = len1 - 1; i >= 0; i--)
{
_fmpz_poly_mul(t, rop, d, op2, len2);
_fmpz_poly_reduce(t, d + len2 - 1, a, j, lena);
_fmpz_poly_add(rop, t, d, op1 + i, 1);
_fmpz_vec_scalar_mod_fmpz(rop, rop, d, p);
}
_fmpz_vec_clear(t, 2*d - 1);
}
}
/*
Computes the composition $f(g(X))$ modulo the sparse polynomial
given by the data \code{(a, j, lena)}, which is assumed to be
of degree~$d \geq 2$.
Sets the vector \code{(rop, d)}.
Assumes that \code{len1} and \code{len2} are positive but at
most~$d$.
Does not support aliasing.
*/
void
_fmpz_mod_poly_compose_smod(fmpz *rop,
const fmpz *op1, slong len1,
const fmpz *op2, slong len2,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p)
{
if (len1 < 6)
{
_fmpz_mod_poly_compose_smod_horner(rop, op1, len1, op2, len2, a, j, lena, p);
}
else
{
_fmpz_mod_poly_compose_smod_rectangular(rop, op1, len1, op2, len2, a, j, lena, p);
}
}
void _qadic_frobenius_a(fmpz *rop, slong exp,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
slong *e, i, n;
fmpz *pow, *f1, *f2, *inv, *s, *t;
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;
pow = _fmpz_vec_init(n);
f1 = _fmpz_vec_init(d + 1);
f2 = _fmpz_vec_init(d);
inv = _fmpz_vec_init(2*d - 1);
s = _fmpz_vec_init(2*d - 1);
t = _fmpz_vec_init(2*d - 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));
}
/* Dense representation of f and f' */
{
slong k;
for (k = 0; k < lena; k++)
fmpz_set(f1 + j[k], a + k);
for (k = 1; k < lena; k++)
fmpz_mul_ui(f2 + (j[k] - 1), a + k, j[k]);
}
/* Run Newton iteration */
i = n - 1;
{
fmpz op[2] = {WORD(0), WORD(1)};
fmpz_pow_ui(t, p, exp);
_qadic_pow(rop, op, 2, t, a, j, lena, pow + i);
_fmpz_mod_poly_compose_smod(t, f2, d, rop, d, a, j, lena, pow + i);
_qadic_inv(inv, t, d, a, j, lena, p, 1);
}
for (i--; i >= 0; i--)
{
_fmpz_mod_poly_compose_smod(s, f1, d + 1, rop, d, a, j, lena, pow + i);
_fmpz_mod_poly_mul(t, s, d, inv, d, pow + i);
_fmpz_mod_poly_reduce(t, 2*d - 1, a, j, lena, pow + i);
_fmpz_mod_poly_sub(rop, rop, d, t, d, pow + i);
if (i > 0)
{
_fmpz_mod_poly_compose_smod(s, f2, d, rop, d, a, j, lena, pow + i);
_fmpz_mod_poly_mul(t, inv, d, s, d, pow + i);
_fmpz_mod_poly_reduce(t, 2*d - 1, a, j, lena, pow + i);
fmpz_sub_ui(t, t, 2);
if (fmpz_sgn(t) < 0)
fmpz_add(t, t, pow + i);
_fmpz_mod_poly_neg(t, t, d, pow + i);
_fmpz_mod_poly_mul(s, inv, d, t, d, pow + i);
_fmpz_mod_poly_reduce(s, 2*d - 1, a, j, lena, pow + i);
/* SWAP(inv, s). Requires the arrays to be of the same size. */
{
fmpz *__t;
__t = inv;
inv = s;
s = __t;
}
}
}
_fmpz_vec_clear(pow, n);
_fmpz_vec_clear(f1, d + 1);
_fmpz_vec_clear(f2, d);
_fmpz_vec_clear(inv, 2*d - 1);
_fmpz_vec_clear(s, 2*d - 1);
_fmpz_vec_clear(t, 2*d - 1);
flint_free(e);
}
/*
Sets (rop, 2d-1) to the image of (op, len) under the Frobenius operator
raised to the e-th power.
*/
void _qadic_frobenius(fmpz *rop, const fmpz *op, slong len, slong e,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
if (len == 1) /* op is in Zp, not just Zq */
{
_fmpz_vec_set(rop, op, len);
_fmpz_vec_zero(rop + len, (2*d - 1) - len);
}
else if (N == 1)
{
fmpz_t t;
fmpz_init(t);
fmpz_pow_ui(t, p, e);
_qadic_pow(rop, op, len, t, a, j, lena, p);
fmpz_clear(t);
}
else
{
fmpz *t;
fmpz_t pow;
t = _fmpz_vec_init(2*d - 1);
fmpz_init(pow);
fmpz_pow_ui(pow, p, N);
_qadic_frobenius_a(t, e, a, j, lena, p, N);
_fmpz_mod_poly_compose_smod(rop, op, len, t, d, a, j, lena, pow);
_fmpz_vec_zero(rop + d, d - 1);
_fmpz_vec_clear(t, 2*d - 1);
fmpz_clear(pow);
}
}
void qadic_frobenius(qadic_t rop, const qadic_t op, slong e, const qadic_ctx_t ctx)
{
const slong N = qadic_prec(rop);
const slong d = qadic_ctx_degree(ctx);
e = e % d;
if (e < 0)
e += d;
if (qadic_is_zero(op) || op->val >= N)
{
qadic_zero(rop);
}
else if (e == 0)
{
padic_poly_set(rop, op, &ctx->pctx);
}
else
{
fmpz *t;
if (rop == op)
{
t = _fmpz_vec_init(2 * d - 1);
}
else
{
padic_poly_fit_length(rop, 2 * d - 1);
t = rop->coeffs;
}
_qadic_frobenius(t, op->coeffs, op->length, e,
ctx->a, ctx->j, ctx->len, (&ctx->pctx)->p, N - op->val);
if (rop == op)
{
_fmpz_vec_clear(rop->coeffs, rop->alloc);
rop->coeffs = t;
rop->alloc = 2 * d - 1;
rop->length = d;
}
else
{
rop->val = op->val;
_padic_poly_set_length(rop, d);
}
_padic_poly_normalise(rop);
}
}
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