// retourne le degré du plus petit facteur
int poly_degppf(poly_t g) {
int i, d, res;
poly_t *u, p, r, s;
d = poly_deg(g);
u = malloc(d * sizeof (poly_t *));
for (i = 0; i < d; ++i)
u[i] = poly_alloc(d + 1);
poly_sqmod_init(g, u);
p = poly_alloc(d - 1);
poly_set_deg(p, 1);
poly_set_coeff(p, 1, gf_unit());
r = poly_alloc(d - 1);
res = d;
for (i = 1; i <= (d / 2) * gf_extd(); ++i) {
poly_sqmod(r, p, u, d);
// r = x^(2^i) mod g
if ((i % gf_extd()) == 0) { // donc 2^i = (2^m)^j (m deg d'extension)
poly_addto_coeff(r, 1, gf_unit());
poly_calcule_deg(r); // le degré peut changer
s = poly_gcd(g, r);
if (poly_deg(s) > 0) {
poly_free(s);
res = i / gf_extd();
break;
}
poly_free(s);
poly_addto_coeff(r, 1, gf_unit());
poly_calcule_deg(r); // le degré peut changer
}
// on se sert de s pour l'échange
s = p;
p = r;
r = s;
}
poly_free(p);
poly_free(r);
for (i = 0; i < d; ++i) {
poly_free(u[i]);
}
free(u);
return res;
}
// Returns the degree of the smallest factor
int poly_degppf(poly_t g) {
int i, d, res;
poly_t *u, p, r, s;
d = poly_deg(g);
u = malloc(d * sizeof (poly_t *));
for (i = 0; i < d; ++i)
u[i] = poly_alloc(d + 1);
poly_sqmod_init(g, u);
p = poly_alloc(d - 1);
poly_set_deg(p, 1);
poly_set_coeff(p, 1, gf_unit());
r = poly_alloc(d - 1);
res = d;
for (i = 1; i <= (d / 2) * gf_extd(); ++i) {
poly_sqmod(r, p, u, d);
// r = x^(2^i) mod g
if ((i % gf_extd()) == 0) { // so 2^i = (2^m)^j (m ext. degree)
poly_addto_coeff(r, 1, gf_unit());
poly_calcule_deg(r); // The degree may change
s = poly_gcd(g, r);
if (poly_deg(s) > 0) {
poly_free(s);
res = i / gf_extd();
break;
}
poly_free(s);
poly_addto_coeff(r, 1, gf_unit());
poly_calcule_deg(r); // The degree may change
}
// No need for the exchange s
s = p;
p = r;
r = s;
}
poly_free(p);
poly_free(r);
for (i = 0; i < d; ++i) {
poly_free(u[i]);
}
free(u);
return res;
}
poly_t poly_mul(poly_t p, poly_t q) {
int i,j,dp,dq;
poly_t r;
poly_calcule_deg(p);
poly_calcule_deg(q);
dp = poly_deg(p);
dq = poly_deg(q);
r=poly_alloc(dp+dq);
for (i = 0; i <= dp; ++i)
for (j = 0; j <= dq; ++j)
poly_addto_coeff(r,i+j,gf_mul(poly_coeff(p,i),poly_coeff(q,j)));
poly_calcule_deg(r);
return(r);
}
// p contiendra son reste modulo g
void poly_rem(poly_t p, poly_t g) {
int i, j, d;
gf_t a, b;
d = poly_deg(p) - poly_deg(g);
if (d >= 0) {
a = gf_inv(poly_tete(g));
for (i = poly_deg(p); d >= 0; --i, --d) {
if (poly_coeff(p, i) != gf_zero()) {
b = gf_mul_fast(a, poly_coeff(p, i));
for (j = 0; j < poly_deg(g); ++j)
poly_addto_coeff(p, j + d, gf_mul_fast(b, poly_coeff(g, j)));
poly_set_coeff(p, i, gf_zero());
}
}
poly_set_deg(p, poly_deg(g) - 1);
while ((poly_deg(p) >= 0) && (poly_coeff(p, poly_deg(p)) == gf_zero()))
poly_set_deg(p, poly_deg(p) - 1);
}
}
// carré de p modulo un certain polynôme g, sq[] contient les carrés
// modulo g de la base canonique des polynômes de degré < d, où d est
// le degré de g. La table sq[] sera calculée par poly_sqmod_init()
void poly_sqmod(poly_t res, poly_t p, poly_t * sq, int d) {
int i, j;
gf_t a;
poly_set_to_zero(res);
// termes de bas degré
for (i = 0; i < d / 2; ++i)
poly_set_coeff(res, i * 2, gf_square(poly_coeff(p, i)));
// termes de haut degré
for (; i < d; ++i) {
if (poly_coeff(p, i) != gf_zero()) {
a = gf_square(poly_coeff(p, i));
for (j = 0; j < d; ++j)
poly_addto_coeff(res, j, gf_mul_fast(a, poly_coeff(sq[i], j)));
}
}
// mise à jour du degré
poly_set_deg(res, d - 1);
while ((poly_deg(res) >= 0) && (poly_coeff(res, poly_deg(res)) == gf_zero()))
poly_set_deg(res, poly_deg(res) - 1);
}
poly_t poly_quo(poly_t p, poly_t d) {
int i, j, dd, dp;
gf_t a, b;
poly_t quo, rem;
dd = poly_calcule_deg(d);
dp = poly_calcule_deg(p);
rem = poly_copy(p);
quo = poly_alloc(dp - dd);
poly_set_deg(quo, dp - dd);
a = gf_inv(poly_coeff(d, dd));
for (i = dp; i >= dd; --i) {
b = gf_mul_fast(a, poly_coeff(rem, i));
poly_set_coeff(quo, i - dd, b);
if (b != gf_zero()) {
poly_set_coeff(rem, i, gf_zero());
for (j = i - 1; j >= i - dd; --j)
poly_addto_coeff(rem, j, gf_mul_fast(b, poly_coeff(d, dd - i + j)));
}
}
poly_free(rem);
return quo;
}
void poly_sqmod(poly_t res, poly_t p, poly_t * sq, int d) {
int i, j;
gf_t a;
poly_set_to_zero(res);
// terms of low degree
for (i = 0; i < d / 2; ++i)
poly_set_coeff(res, i * 2, gf_square(poly_coeff(p, i)));
// terms of high degree
for (; i < d; ++i) {
if (poly_coeff(p, i) != gf_zero()) {
a = gf_square(poly_coeff(p, i));
for (j = 0; j < d; ++j)
poly_addto_coeff(res, j, gf_mul_fast(a, poly_coeff(sq[i], j)));
}
}
// Update degre
poly_set_deg(res, d - 1);
while ((poly_deg(res) >= 0) && (poly_coeff(res, poly_deg(res)) == gf_zero()))
poly_set_deg(res, poly_deg(res) - 1);
}
// On suppose deg(g) >= deg(p)
void poly_eeaux(poly_t * u, poly_t * v, poly_t p, poly_t g, int t) {
int i, j, dr, du, delta;
gf_t a;
poly_t aux, r0, r1, u0, u1;
// initialisation des variables locales
// r0 <- g, r1 <- p, u0 <- 0, u1 <- 1
dr = poly_deg(g);
r0 = poly_alloc(dr);
r1 = poly_alloc(dr - 1);
u0 = poly_alloc(dr - 1);
u1 = poly_alloc(dr - 1);
poly_set(r0, g);
poly_set(r1, p);
poly_set_to_zero(u0);
poly_set_to_zero(u1);
poly_set_coeff(u1, 0, gf_unit());
poly_set_deg(u1, 0);
// invariants:
// r1 = u1 * p + v1 * g
// r0 = u0 * p + v0 * g
// et deg(u1) = deg(g) - deg(r0)
// on s'arrête lorsque deg(r1) < t (et deg(r0) >= t)
// et donc deg(u1) = deg(g) - deg(r0) < deg(g) - t
du = 0;
dr = poly_deg(r1);
delta = poly_deg(r0) - dr;
while (dr >= t) {
for (j = delta; j >= 0; --j) {
a = gf_div(poly_coeff(r0, dr + j), poly_coeff(r1, dr));
if (a != gf_zero()) {
// u0(z) <- u0(z) + a * u1(z) * z^j
for (i = 0; i <= du; ++i) {
poly_addto_coeff(u0, i + j, gf_mul_fast(a, poly_coeff(u1, i)));
}
// r0(z) <- r0(z) + a * r1(z) * z^j
for (i = 0; i <= dr; ++i)
poly_addto_coeff(r0, i + j, gf_mul_fast(a, poly_coeff(r1, i)));
}
}
// échanges
aux = r0;
r0 = r1;
r1 = aux;
aux = u0;
u0 = u1;
u1 = aux;
du = du + delta;
delta = 1;
while (poly_coeff(r1, dr - delta) == gf_zero())
delta++;
dr -= delta;
}
poly_set_deg(u1, du);
poly_set_deg(r1, dr);
//return u1 and r1;
*u=u1;
*v=r1;
poly_free(r0);
poly_free(u0);
}