/*
* Expanded form for a product c * p
* - c is a normalized bitvector constant
* - p is a power product stored in a pp_buffer object
* - n = bitsize of p
* - the expansion is returned in a bvarith_buffer or bvarith64_buffer object
* - the result is normalized
*/
void expand_bvpprod64(bvexp_table_t *table, bvarith64_buffer_t *buffer, pp_buffer_t *p, uint32_t n, uint64_t c) {
bv_vartable_t *vtbl;
bvmlist64_t *q;
pp_buffer_t *aux;
pprod_t *r;
uint64_t a;
uint32_t i, m, e, d;
thvar_t x;
assert(buffer->store == &table->store64 && buffer->ptbl == &table->pprods);
bvarith64_buffer_prepare(buffer, n);
bvarith64_buffer_set_one(buffer);
aux = p;
vtbl = table->vtbl;
if (total_degree_test64(table, vtbl, p)) {
/*
* Expansion of c * x_1^d_1 ... x_n^ d_n:
* - for a constant x_i, update c to c * a^d_i (where a = value of c)
* - if x_i is expanded to q_i, update buffer to buffer * q_i ^ d_i
* - otherwise, x_i^d_i is copied into the aux buffer
*/
aux = &table->pp;
pp_buffer_reset(aux);
m = p->len;
for (i=0; i<m; i++) {
x = p->prod[i].var;
d = p->prod[i].exp;
if (bvvar_is_const64(vtbl, x)) {
a = bvvar_val64(vtbl, x);
c *= upower64(a, d);
} else {
q = bvexp_def64(table, x);
if (q != NULL && mlist64_is_short(q, &e) && d * e <= BVEXP_DEGREE_LIMIT) {
// replace x^d by q^d in buffer
bvarith64_buffer_mul_mlist_power(buffer, q, d, &table->aux64);
} else {
// copy x^d into aux
pp_buffer_mul_varexp(aux, x, d);
}
}
}
c = norm64(c, n);
pp_buffer_normalize(aux);
}
/*
* The result is c * aux * buffer
*/
r = pprod_from_buffer(&table->pprods, aux);
bvarith64_buffer_mul_mono(buffer, c, r);
bvarith64_buffer_normalize(buffer);
}
/*
* Expanded form of a bitvector polynomial p
* - p is stored in a bvpoly_buffer object
* - the expansion is returned in a bvarith_buffer or bvarith64_buffer object
* - the result is normalized
*/
void expand_bvpoly64(bvexp_table_t *table, bvarith64_buffer_t *buffer, bvpoly_buffer_t *p) {
bv_vartable_t *vtbl;
bvmlist64_t *q;
uint64_t c;
uint32_t i, n;
thvar_t x;
assert(buffer->store == &table->store64 && buffer->ptbl == &table->pprods);
bvarith64_buffer_prepare(buffer, bvpoly_buffer_bitsize(p));
n = bvpoly_buffer_num_terms(p);
if (n > 0) {
vtbl = table->vtbl;
i = 0;
// deal with the constant term if any
if (bvpoly_buffer_var(p, 0) == const_idx) {
bvarith64_buffer_add_const(buffer, bvpoly_buffer_coeff64(p, 0));
i ++;
}
/*
* non-constant terms of p are of the form a * x
* we replace x by its value if x has tag BVTAG_CONST64
* we replace x by its definition if x has a definition in table
* otherwise, we keep x as is
*/
while (i < n) {
x = bvpoly_buffer_var(p, i);
c = bvpoly_buffer_coeff64(p, i);
i ++;
if (bvvar_is_const64(vtbl, x)) {
c *= bvvar_val64(vtbl, x);
bvarith64_buffer_add_const(buffer, c);
} else {
q = bvexp_def64(table, x);
if (q != NULL) {
bvarith64_buffer_add_const_times_mlist(buffer, q, c);
} else {
bvarith64_buffer_add_varmono(buffer, c, x);
}
}
}
bvarith64_buffer_normalize(buffer);
}
}
int main(void) {
thvar_t x, y, z;
init_bvconstants();
init_bv_vartable(&vtbl);
init_bvexp_table(&table, &vtbl);
bvexp_init_buffer64(&table, &b1);
bvexp_init_buffer64(&table, &b2);
bvexp_init_buffer(&table, &c1);
bvexp_init_buffer(&table, &c2);
printf("=== Initial table ===\n");
print_bvexp_table(stdout, &table);
printf("\n");
x = make_bvvar(&vtbl, 10);
y = make_bvvar(&vtbl, 10);
z = make_bvvar(&vtbl, 10);
// 2 + x + y
bvarith64_buffer_prepare(&b1, 10);
bvarith64_buffer_add_const(&b1, 2);
bvarith64_buffer_add_var(&b1, x);
bvarith64_buffer_add_var(&b1, y);
bvarith64_buffer_normalize(&b1);
test_buffer64(&table, &b1);
bvarith64_buffer_prepare(&b1, 10);
bvarith64_buffer_add_const(&b1, 2);
bvarith64_buffer_add_var(&b1, x);
bvarith64_buffer_add_var(&b1, y);
bvarith64_buffer_normalize(&b1);
test_buffer64(&table, &b1);
// (x + z) * (y - z)
bvarith64_buffer_prepare(&b1, 10);
bvarith64_buffer_add_var(&b1, x);
bvarith64_buffer_add_var(&b1, z);
bvarith64_buffer_prepare(&b2, 10);
bvarith64_buffer_add_var(&b2, y);
bvarith64_buffer_sub_var(&b2, z);
bvarith64_buffer_mul_buffer(&b1, &b2);
bvarith64_buffer_normalize(&b1);
test_buffer64(&table, &b1);
bvarith64_buffer_prepare(&b1, 10);
bvarith64_buffer_add_var(&b1, x);
bvarith64_buffer_add_var(&b1, z);
bvarith64_buffer_prepare(&b2, 10);
bvarith64_buffer_add_var(&b2, y);
bvarith64_buffer_sub_var(&b2, z);
bvarith64_buffer_mul_buffer(&b1, &b2);
bvarith64_buffer_normalize(&b1);
test_buffer64(&table, &b1);
// x * y * z^2
bvarith64_buffer_prepare(&b1, 10);
bvarith64_buffer_add_var(&b1, z);
bvarith64_buffer_square(&b1);
bvarith64_buffer_mul_var(&b1, y);
bvarith64_buffer_mul_var(&b1, x);
bvarith64_buffer_normalize(&b1);
test_buffer64(&table, &b1);
bvarith64_buffer_prepare(&b1, 10);
bvarith64_buffer_add_var(&b1, z);
bvarith64_buffer_square(&b1);
bvarith64_buffer_mul_var(&b1, y);
bvarith64_buffer_mul_var(&b1, x);
bvarith64_buffer_normalize(&b1);
test_buffer64(&table, &b1);
// Large coefficients
x = make_bvvar(&vtbl, 100);
y = make_bvvar(&vtbl, 100);
z = make_bvvar(&vtbl, 100);
// 1 + x + y
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_set_one(&c1);
bvarith_buffer_add_var(&c1, x);
bvarith_buffer_add_var(&c1, y);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_set_one(&c1);
bvarith_buffer_add_var(&c1, x);
bvarith_buffer_add_var(&c1, y);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
// (x + z) * (y - z)
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_add_var(&c1, x);
bvarith_buffer_add_var(&c1, z);
bvarith_buffer_prepare(&c2, 100);
bvarith_buffer_add_var(&c2, y);
bvarith_buffer_sub_var(&c2, z);
bvarith_buffer_mul_buffer(&c1, &c2);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_add_var(&c1, x);
bvarith_buffer_add_var(&c1, z);
bvarith_buffer_prepare(&c2, 100);
bvarith_buffer_add_var(&c2, y);
bvarith_buffer_sub_var(&c2, z);
bvarith_buffer_mul_buffer(&c1, &c2);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
// x * y * z^2
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_add_var(&c1, z);
bvarith_buffer_square(&c1);
bvarith_buffer_mul_var(&c1, y);
bvarith_buffer_mul_var(&c1, x);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_add_var(&c1, z);
bvarith_buffer_square(&c1);
bvarith_buffer_mul_var(&c1, y);
bvarith_buffer_mul_var(&c1, x);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
printf("=== Final table ===\n");
print_bvexp_table(stdout, &table);
printf("\n");
// remove two variables
bvexp_table_remove_vars(&table, 11);
printf("=== After removing two variables ===\n");
print_bvexp_table(stdout, &table);
printf("\n");
// recheck: 1 + x + y
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_set_one(&c1);
bvarith_buffer_add_var(&c1, x);
bvarith_buffer_add_var(&c1, y);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
// recheck: (x + z) * (y - z)
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_add_var(&c1, x);
bvarith_buffer_add_var(&c1, z);
bvarith_buffer_prepare(&c2, 100);
bvarith_buffer_add_var(&c2, y);
bvarith_buffer_sub_var(&c2, z);
bvarith_buffer_mul_buffer(&c1, &c2);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
bvarith_buffer_prepare(&c1, 100);
bvarith_buffer_add_var(&c1, x);
bvarith_buffer_add_var(&c1, z);
bvarith_buffer_prepare(&c2, 100);
bvarith_buffer_add_var(&c2, y);
bvarith_buffer_sub_var(&c2, z);
bvarith_buffer_mul_buffer(&c1, &c2);
bvarith_buffer_normalize(&c1);
test_buffer(&table, &c1);
printf("=== Final table ===\n");
print_bvexp_table(stdout, &table);
printf("\n");
// cleanup
delete_bvarith64_buffer(&b1);
delete_bvarith64_buffer(&b2);
delete_bvarith_buffer(&c1);
delete_bvarith_buffer(&c2);
delete_bvexp_table(&table);
delete_bv_vartable(&vtbl);
cleanup_bvconstants();
return 0;
}
