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);
}
// 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;
}
// copie q dans p
void poly_set(poly_t p, poly_t q) {
int d = p->size - q->size;
if (d < 0) {
memcpy(p->coeff, q->coeff, p->size * sizeof (gf_t));
poly_calcule_deg(p);
}
else {
memcpy(p->coeff, q->coeff, q->size * sizeof (gf_t));
memset(p->coeff + q->size, 0, d * sizeof (gf_t));
p->deg = q->deg;
}
}
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;
}
