/*
* Add -a * r * b1 to b
*/
void arith_buffer_sub_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_submul(&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_submul(&aux->coeff, &p1->coeff, a); // since aux->coeff is 0 initially
aux->prod = r1;
*q = aux;
q = &aux->next;
b->nterms ++;
}
p1 = p1->next;
}
}
/*
* 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 ++;
}
}
/*
* Phase and period of p
* - p is c + (a_1/b_1) x_1 + ... + (a_n/b_n) x_n where
* a_i/b_i is an irreducible fraction
* - let D = gcd(a_1,..., a_n) and L = lcm(b_1,...,b_n)
* then period = D/L and phase = c - floor(c/period) * period
*/
void monarray_period_and_phase(monomial_t *p, rational_t *period, rational_t *phase) {
rational_t aux;
monomial_t *c;
int32_t v;
/*
* c := the constant monomial of p or NULL if p's constant is zero
*/
c = NULL;
v = p->var;
if (v == const_idx) {
c = p;
p ++;
v = p->var;
}
if (v < max_idx) {
/*
* p is not a constant: compute D and L
* we use period for D and phase for L
*/
q_get_num(period, &p->coeff); // D := |a_1|
if (q_is_neg(period)) {
q_neg(period);
}
q_get_den(phase, &p->coeff); // L := b_1
q_init(&aux);
for (;;) {
p ++;
v = p->var;
if (v >= max_idx) break;
q_get_num(&aux, &p->coeff);
q_gcd(period, &aux); // D := gcd(D, a_i)
q_get_den(&aux, &p->coeff);
q_lcm(phase, &aux); // L := lcm(L, b_i)
}
assert(q_is_pos(period) && q_is_pos(phase));
q_div(period, phase); // period := D/L
/*
* Phase: constant modulo D/L
*/
if (c == NULL) {
q_clear(phase); // no constant: phase = 0
} else {
q_set(&aux, &c->coeff);
q_div(&aux, period);
q_floor(&aux); // aux = floor(c/period)
q_set(phase, &c->coeff);
q_submul(phase, &aux, period); // phase = c - aux * period
assert(q_is_nonneg(phase) && q_lt(phase, period));
}
q_clear(&aux);
} else {
/*
* p is constant: period := 0, phase = constant coeff
*/
q_clear(period);
if (c == NULL) {
q_clear(phase);
} else {
q_set(phase, &c->coeff);
}
}
}
