// check whether the subtree rooted at x is ordered
static bool is_ordered(rba_buffer_t *b, uint32_t x) {
uint32_t i, j;
pprod_t *r, *s, *t;
assert(x < b->num_nodes);
if (x == 0) return true;
i = b->child[x][0]; // left child
j = b->child[x][1]; // right child
r = b->mono[x].prod;
s = b->mono[i].prod;
t = b->mono[j].prod;
// the expected order is s < r < t
if (i != 0 && !pprod_precedes(s, r)) {
printf("tree not ordered at node %"PRIu32" (for left child %"PRIu32")\n", x, i);
fflush(stdout);
return false;
}
if (j != 0 && !pprod_precedes(r, t)) {
printf("tree not ordered at node %"PRIu32" (for right child = %"PRIu32")\n", x, j);
fflush(stdout);
return false;
}
return is_ordered(b, i) && is_ordered(b, j);
}
/*
* Add a * r * b1 to b
*/
void arith_buffer_add_mono_times_buffer(arith_buffer_t *b, arith_buffer_t *b1, rational_t *a, pprod_t *r) {
mlist_t *p, *aux, *p1;
mlist_t **q;
pprod_t *r1;
q = &b->list;
p = *q;
p1 = b1->list;
while (p1->next != NULL) {
r1 = pprod_mul(b->ptbl, p1->prod, r);
while (pprod_precedes(p->prod, r1)) {
q = &p->next;
p = *q;
}
if (p->prod == r1) {
q_addmul(&p->coeff, &p1->coeff, a);
q = &p->next;
p = *q;
} else {
assert(pprod_precedes(r1, p->prod));
aux = alloc_list_elem(b->store);
aux->next = p;
q_addmul(&aux->coeff, &p1->coeff, a); // since aux->coeff is 0 initially
aux->prod = r1;
*q = aux;
q = &aux->next;
b->nterms ++;
}
p1 = p1->next;
}
}
/*
* Add -r to b
*/
void arith_buffer_sub_pp(arith_buffer_t *b, pprod_t *r) {
mlist_t *p, *aux;
mlist_t **q;
q = &b->list;
p = *q;
assert(p == b->list);
while (pprod_precedes(p->prod, r)) {
q = &p->next;
p = *q;
}
// p points to a monomial with p->prod >= r
// q is either &p->list or &p0->next where p0 is p's predecessor
if (p->prod == r) {
q_sub_one(&p->coeff);
} else {
assert(pprod_precedes(r, p->prod));
aux = alloc_list_elem(b->store);
aux->next = p;
q_set_minus_one(&aux->coeff);
aux->prod = r;
*q = aux;
b->nterms ++;
}
}
/*
* Add - r * b1 to b
*/
void arith_buffer_sub_pp_times_buffer(arith_buffer_t *b, arith_buffer_t *b1, pprod_t *r) {
mlist_t *p, *aux, *p1;
mlist_t **q;
pprod_t *r1;
q = &b->list;
p = *q;
p1 = b1->list;
while (p1->next != NULL) {
r1 = pprod_mul(b->ptbl, p1->prod, r);
while (pprod_precedes(p->prod, r1)) {
q = &p->next;
p = *q;
}
if (p->prod == r1) {
q_sub(&p->coeff, &p1->coeff);
q = &p->next;
p = *q;
} else {
assert(pprod_precedes(r1, p->prod));
aux = alloc_list_elem(b->store);
aux->next = p;
q_set_neg(&aux->coeff, &p1->coeff);
aux->prod = r1;
*q = aux;
q = &aux->next;
b->nterms ++;
}
p1 = p1->next;
}
}
/*
* Add -a * r to b
*/
void arith_buffer_sub_mono(arith_buffer_t *b, rational_t *a, pprod_t *r) {
mlist_t *p, *aux;
mlist_t **q;
if (q_is_zero(a)) return;
q = &b->list;
p = *q;
assert(p == b->list);
while (pprod_precedes(p->prod, r)) {
q = &p->next;
p = *q;
}
// p points to a monomial with p->prod >= r
// q is &b->list if p is first in the list
// q is &p0->next where p0 = predecessor of p otherwise.
if (p->prod == r) {
q_sub(&p->coeff, a);
} else {
assert(pprod_precedes(r, p->prod));
aux = alloc_list_elem(b->store);
aux->next = p;
q_set_neg(&aux->coeff, a);
aux->prod = r;
*q = aux;
b->nterms ++;
}
}
/*
* Monomial of p whose pp equals r (or NULL)
*/
mlist_t *arith_buffer_get_mono(arith_buffer_t *b, pprod_t *r) {
mlist_t *p;
p = b->list;
while (pprod_precedes(p->prod, r)) {
p = p->next;
}
if (p->prod == r) {
return p;
} else {
assert(pprod_precedes(r, p->prod));
return NULL;
}
}
/*
* Add poly to buffer b
*/
void arith_buffer_add_monarray(arith_buffer_t *b, monomial_t *poly, pprod_t **pp) {
mlist_t *p, *aux;
mlist_t **q;
pprod_t *r1;
assert(good_pprod_array(poly, pp));
q = &b->list;
p = *q;
while (poly->var < max_idx) {
// poly points to a pair (coeff, x_i)
// r1 = power product for x_i
r1 = *pp;
while (pprod_precedes(p->prod, r1)) {
q = &p->next;
p = *q;
}
// p points to monomial whose prod is >= r1 in the deg-lex order
// q is either &b->list or &p0->next where p0 is the predecessor
// of p in the list
if (p->prod == r1) {
q_add(&p->coeff, &poly->coeff);
q = &p->next;
p = *q;
} else {
assert(pprod_precedes(r1, p->prod));
aux = alloc_list_elem(b->store);
aux->next = p;
q_set(&aux->coeff, &poly->coeff);
aux->prod = r1;
*q = aux;
q = &aux->next;
b->nterms ++;
}
// move to the next monomial of poly
poly ++;
pp ++;
}
}
/*
* Subtract a * poly from b
*/
void arith_buffer_sub_mono_times_monarray(arith_buffer_t *b, monomial_t *poly, pprod_t **pp, rational_t *a, pprod_t *r) {
mlist_t *p, *aux;
mlist_t **q;
pprod_t *r1;
assert(good_pprod_array(poly, pp));
q = &b->list;
p = *q;
while (poly->var < max_idx) {
// poly points to a pair (coeff, x_i)
// r1 = r * power product for x_i
r1 = pprod_mul(b->ptbl, *pp, r);
while (pprod_precedes(p->prod, r1)) {
q = &p->next;
p = *q;
}
// p points to monomial whose prod is >= r1 in the deg-lex order
// q points to the predecessor of p in the list
if (p->prod == r1) {
q_submul(&p->coeff, &poly->coeff, a);
q = &p->next;
p = *q;
} else {
assert(pprod_precedes(r1, p->prod));
aux = alloc_list_elem(b->store);
aux->next = p;
q_submul(&aux->coeff, &poly->coeff, a); // aux->coeff is initialized to 0 in alloc_list_elem
aux->prod = r1;
*q = aux;
q = &aux->next;
b->nterms ++;
}
// move to the next monomial of poly
poly ++;
pp ++;
}
}
/*
* Add b1 to b
*/
void arith_buffer_add_buffer(arith_buffer_t *b, arith_buffer_t *b1) {
mlist_t *p, *aux, *p1;
mlist_t **q;
pprod_t *r1;
assert(b->ptbl == b1->ptbl);
q = &b->list;
p = *q;
p1 = b1->list;
while (p1->next != NULL) {
r1 = p1->prod;
while (pprod_precedes(p->prod, r1)) {
q = &p->next;
p = *q;
}
if (p->prod == r1) {
q_add(&p->coeff, &p1->coeff);
q = &p->next;
p = *q;
} else {
assert(pprod_precedes(r1, p->prod));
aux = alloc_list_elem(b->store);
aux->next = p;
q_set(&aux->coeff, &p1->coeff);
aux->prod = r1;
*q = aux;
q = &aux->next;
b->nterms ++;
}
p1 = p1->next;
}
}
/*
* Add (-a) * b1 to b
*/
void arith_buffer_sub_const_times_buffer(arith_buffer_t *b, arith_buffer_t *b1, rational_t *a) {
mlist_t *p, *aux, *p1;
mlist_t **q;
pprod_t *r1;
q = &b->list;
p = *q;
p1 = b1->list;
while (p1->next != NULL) {
r1 = p1->prod;
while (pprod_precedes(p->prod, r1)) {
q = &p->next;
p = *q;
}
if (p->prod == r1) {
q_submul(&p->coeff, &p1->coeff, a);
q = &p->next;
p = *q;
} else {
assert(pprod_precedes(r1, p->prod));
// aux->coeff is initialized to 0 in alloc_list_elem
aux = alloc_list_elem(b->store);
aux->next = p;
q_submul(&aux->coeff, &p1->coeff, a);
aux->prod = r1;
*q = aux;
q = &aux->next;
b->nterms ++;
}
p1 = p1->next;
}
}
/*
* For debugging: check that q contains valid power products
* sorted in increasing deg-lex ordering.
*/
static bool good_pprod_array(monomial_t *poly, pprod_t **pp) {
pprod_t *r;
if (poly->var < max_idx) {
r = *pp;
poly ++;
pp ++;
while (poly->var < max_idx) {
if (! pprod_precedes(r, *pp)) return false;
r = *pp;
pp ++;
poly ++;
}
}
return true;
}
int main() {
pprod_t *p1, *p2;
uint32_t i, j;
int32_t cmp;
p[0] = empty_pp;
p[1] = var_pp(0);
p[2] = var_pp(1);
p[3] = var_pp(0x3fffffff);
init_pp_buffer(&buffer, 0);
p[4] = pp_buffer_getprod(&buffer); // empty
pp_buffer_reset(&buffer);
pp_buffer_mul_var(&buffer, 0);
p[5] = pp_buffer_getprod(&buffer); // x_0
pp_buffer_reset(&buffer);
pp_buffer_mul_var(&buffer, 0);
pp_buffer_mul_var(&buffer, 1);
pp_buffer_mul_var(&buffer, 0);
p[6] = pp_buffer_getprod(&buffer); // x_0^2 x_1
pp_buffer_reset(&buffer);
pp_buffer_mul_varexp(&buffer, 1, 2);
pp_buffer_mul_varexp(&buffer, 4, 3);
p[7] = pp_buffer_getprod(&buffer); // x_1^2 x_4^3
pp_buffer_set_varexp(&buffer, 3, 2);
pp_buffer_mul_varexp(&buffer, 1, 4);
p[8] = pp_buffer_getprod(&buffer); // x_3^2 x_1^4
pp_buffer_set_pprod(&buffer, p[7]);
pp_buffer_mul_pprod(&buffer, p[1]);
pp_buffer_mul_pprod(&buffer, p[8]);
p[9] = pp_buffer_getprod(&buffer);
for (i=0; i<NUM_PRODS; i++) {
printf("p[%"PRIu32"] = ", i);
print_pprod(stdout, p[i]);
printf(" total degree = %"PRIu32"\n", pprod_degree(p[i]));
for (j=0; j<5; j++) {
printf(" degree of x_%"PRIu32" = %"PRIu32"\n", j, pprod_var_degree(p[i], j));
}
printf("----\n");
}
printf("\n");
for (i=0; i<NUM_PRODS; i++) {
p1 = p[i];
for (j=0; j<NUM_PRODS; j++) {
p2 = p[j];
printf("p1: ");
print_pprod0(stdout, p1);
printf("p2: ");
print_pprod0(stdout, p2);
if (pprod_equal(p1, p2)) {
printf("equal products\n");
}
if (pprod_divides(p1, p2)) {
printf("p1 divides p2\n");
}
if (pprod_divisor(&buffer, p1, p2)) {
printf("p2/p1: ");
print_pp_buffer0(stdout, &buffer);
}
if (pprod_divides(p2, p1)) {
printf("p2 divides p1\n");
}
if (pprod_divisor(&buffer, p2, p1)) {
printf("p1/p2: ");
print_pp_buffer0(stdout, &buffer);
}
cmp = pprod_lex_cmp(p1, p2);
if (cmp < 0) {
printf("p1 < p2 in lex order\n");
} else if (cmp > 0) {
printf("p1 > p2 in lex order\n");
} else {
printf("p1 = p2 in lex order\n");
}
if (pprod_precedes(p1, p2)) {
printf("p1 < p2 in deglex ordering\n");
}
if (pprod_precedes(p2, p1)) {
printf("p2 < p1 in deglex ordering\n");
}
printf("----\n");
}
}
for (i=0; i<10; i++) {
free_pprod(p[i]);
}
delete_pp_buffer(&buffer);
return 0;
}