poly_t poly_gcd(poly_t p1, poly_t p2) {
poly_t a, b, c;
a = poly_copy(p1);
b = poly_copy(p2);
if (poly_deg(a) < poly_deg(b))
c = poly_copy(poly_gcd_aux(b, a));
else
c = poly_copy(poly_gcd_aux(a, b));
poly_free(a);
poly_free(b);
return c;
}
void poly_mul_inp(Poly** lhs, const Poly* rhs)
{
Poly* p1;
Poly* res = NULL;
const Poly* p2;
//think about the situation that: lhs and rhs are the same poly ?
Poly* origin_lhs = poly_copy(*lhs);
//we append {-1, 0} to rhs to balance out the origin lhs
for (p2 = rhs; NULL != p2; p2 = p2->next) {
Poly* tmp = poly_copy(origin_lhs);
for (p1 = tmp; NULL != p1; p1 = p1->next) {
p1->coeff *= p2->coeff;
p1->index += p2->index;
}
poly_add_inp(&res, tmp);
}
destroy_poly(lhs);
*lhs = res;
destroy_poly(&origin_lhs);
}
void poly_pow_inp(Poly** poly, int n)
{
int i;
Poly* origin;
if (0 == n) {
*poly = create_poly(1, 0);
return;
}
origin = poly_copy(*poly);
for (i = 0; i < n - 1; i++)
poly_mul_inp(poly, origin);
destroy_poly(&origin);
}
/**
*negative index is not allowed
*@return: stored quotient in plhs
*/
void poly_div_inp(Poly** plhs, const Poly* rhs)
{
Poly* lhs = *plhs;
Poly odd = {.next = lhs};
Poly* res = NULL;
if (NULL == lhs || NULL == rhs)
return;
if (*plhs == rhs) { //lhs and rhs are the same poly
destroy_poly(plhs);
*plhs = create_poly(1, 0);
return;
}
for (; NULL != lhs && lhs->index >= rhs->index;) {
Poly *p1, *q1;
const Poly* p2;
Poly* item = create_poly(lhs->coeff / rhs->coeff,
lhs->index - rhs->index);
poly_add_inp(&res, poly_copy(item));
//printf("res: \n");
//print_poly(res);
for (p1 = lhs, q1 = &odd, p2 = rhs; NULL != p1 && NULL != p2;) {
//print_poly(p2);
if (p1->index - p2->index == item->index) {
p1->coeff -= p2->coeff * item->coeff; //coeff may be zero
if (DOUBLE_EQUAL(p1->coeff, 0)) {
destroy_poly_head(&p1); //move forward
q1->next = p1;
}
p2 = p2->next;
} else if (p1->index - p2->index > item->index) {
q1 = p1;
p1 = p1->next;
} else
p2 = p2->next;
}
lhs = odd.next;
//printf("lhs: \n");
//print_poly(lhs);
}
*plhs = odd.next;
destroy_poly(plhs);
*plhs = res;
}
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;
}
