使用列表将C中的多项式相乘

我正在使用列表来实现多项式的乘法。我的代码是：

typedef struct node *node_ptr;
typedef struct node
{
    unsigned int power;
    int coeff;
    node_ptr next;
}POLY;
typedef node_ptr polynomial; 

void mult_polynomial(polynomial poly1, polynomial poly2, polynomial poly_mult)
{
    assert(!is_null(poly1) && !is_null(poly2) && is_null(poly_mult));
    node_ptr p1 = poly1->next;
    node_ptr p2;
    node_ptr p3;
    node_ptr tmp, cell;

    while (p1) {
        p2 = poly2->next;
        while (p2) {
            p3 = poly_mult;
            cell = p3->next;
            tmp = (node_ptr)malloc(sizeof(struct node));
            tmp->power = p1->power + p2->power;
            tmp->coeff = p1->coeff * p2->coeff;
            tmp->next = NULL;
            if (!cell)
                p3->next = tmp;
            else { 
                if (cell->power == tmp->power) {
                    cell->coeff += tmp->coeff;
                    free(tmp);   
                } else if (cell->power < tmp->power) {
                    p3->next = tmp;
                    tmp->next = cell;
                } else if (cell->power > tmp->power) {
                    while (cell->power > tmp->power) {
                        if(!cell->next || cell->next->power < tmp->power) {
                            cell->next = tmp;
                            break; 
                        } else if (cell->next->power == tmp->power) {
                            cell->next->coeff += tmp->coeff;
                            break;
                        }
                        p3 = cell;
                        cell = p3->next;
                    }
                }
            }
            p2 = p2->next;
        }
        p1 = p1->next;
    }
}

但这似乎太多余了；如何简化呢？