mirror of
https://github.com/Z3Prover/z3
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Add functionality for BDD vectors (#5198)
* Fix XOR over BDDs * Add operator<< for find_int_t * Add equality assertion macro that prints expression values on failure * Adapt contains_int and find_int to take externally-defined bits * Add more operations on BDD vectors * Remove old functions * Additional bddv functions * Rename some things * Make bddv a class and add operators * Fix find_num/contains_num calls
This commit is contained in:
Jakob Rath
GitHub
parent
981839ee73
commit
4da1b7b03c
8 changed files with 499 additions and 138 deletions
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@ -23,6 +23,19 @@ Revision History:
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namespace dd {
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std::ostream& operator<<(std::ostream& out, find_result x) {
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switch (x) {
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case find_result::empty:
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return out << "empty";
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case find_result::singleton:
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return out << "singleton";
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case find_result::multiple:
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return out << "multiple";
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}
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UNREACHABLE();
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return out;
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}
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bdd_manager::bdd_manager(unsigned num_vars) {
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m_cost_metric = bdd_cost;
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m_cost_bdd = 0;
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@ -142,6 +155,8 @@ namespace dd {
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if (a == b) return false_bdd;
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if (is_false(a)) return b;
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if (is_false(b)) return a;
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if (is_true(a)) return mk_not_rec(b);
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if (is_true(b)) return mk_not_rec(a);
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break;
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default:
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UNREACHABLE();
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@ -896,87 +911,54 @@ namespace dd {
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std::ostream& operator<<(std::ostream& out, bdd const& b) { return b.display(out); }
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// NSB code review:
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// this function should be removed and replaced by functionality where the
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// client maintains what are the variables.
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bdd bdd_manager::mk_int(rational const& val, unsigned w) {
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bdd b = mk_true();
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for (unsigned k = w; k-- > 0;)
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b &= val.get_bit(k) ? mk_var(k) : mk_nvar(k);
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return b;
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}
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bool bdd_manager::contains_int(BDD b, rational const& val, unsigned w) {
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bool bdd_manager::contains_num(BDD b, rational const& val, unsigned_vector const& bits) {
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DEBUG_CODE(for (unsigned i = 1; i < bits.size(); ++i) { SASSERT(bits[i-1] < bits[i]); });
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unsigned var_idx = bits.size();
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while (!is_const(b)) {
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unsigned const var = m_level2var[level(b)];
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if (var >= w)
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b = lo(b);
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else
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b = val.get_bit(var) ? hi(b) : lo(b);
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VERIFY(var_idx-- > 0);
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SASSERT(var(b) <= bits[var_idx]);
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while (var(b) < bits[var_idx]) {
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VERIFY(var_idx-- > 0);
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}
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SASSERT(var(b) == bits[var_idx]);
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b = val.get_bit(var_idx) ? hi(b) : lo(b);
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}
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return is_true(b);
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}
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find_int_t bdd_manager::find_int(BDD b, unsigned w, rational& val) {
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find_result bdd_manager::find_num(BDD b, unsigned_vector bits, rational& val) {
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DEBUG_CODE(for (unsigned i = 1; i < bits.size(); ++i) { SASSERT(bits[i-1] < bits[i]); });
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val = 0;
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if (is_false(b))
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return find_int_t::empty;
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return find_result::empty;
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bool is_unique = true;
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unsigned num_vars = 0;
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unsigned var_idx = bits.size();
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while (!is_true(b)) {
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++num_vars;
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VERIFY(var_idx-- > 0);
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SASSERT(var(b) <= bits[var_idx]);
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while (var(b) < bits[var_idx]) {
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is_unique = false;
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VERIFY(var_idx-- > 0);
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}
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if (!is_false(lo(b)) && !is_false(hi(b)))
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is_unique = false;
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if (is_false(lo(b))) {
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val += rational::power_of_two(var(b));
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SASSERT(var(b) == bits[var_idx]);
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val += rational::power_of_two(var_idx);
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b = hi(b);
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}
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else
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b = lo(b);
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}
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is_unique &= (num_vars == w);
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if (var_idx > 0)
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is_unique = false;
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return is_unique ? find_int_t::singleton : find_int_t::multiple;
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return is_unique ? find_result::singleton : find_result::multiple;
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}
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bdd bdd_manager::mk_affine(rational const& a, rational const& b, unsigned w) {
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if (a.is_zero())
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return b.is_zero() ? mk_true() : mk_false();
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// a*x + b == 0 (mod 2^w)
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unsigned const rank_a = a.trailing_zeros();
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unsigned const rank_b = b.is_zero() ? w : b.trailing_zeros();
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// We have a', b' odd such that:
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// 2^rank(a) * a'* x + 2^rank(b) * b' == 0 (mod 2^w)
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if (rank_a > rank_b) {
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// <=> 2^(rank(a)-rank(b)) * a' * x + b' == 0 (mod 2^(w-rank(b)))
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// LHS is always odd => equation cannot be true
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return mk_false();
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}
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else if (b.is_zero()) {
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// this is just a specialization of the else-branch below
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return mk_int(rational::zero(), w - rank_a);
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}
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else {
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unsigned const j = w - rank_a;
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// Let b'' := 2^(rank(b)-rank(a)) * b', then we have:
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// <=> a' * x + b'' == 0 (mod 2^j)
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// <=> x == -b'' * inverse_j(a') (mod 2^j)
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// Now the question is, for what x in Z_{2^w} does this hold?
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// Answer: for all x where the lower j bits are the same as in the RHS of the last equation,
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// so we just fix those bits and leave the others unconstrained
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// (which we can do simply by encoding the RHS as a j-width integer).
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rational const pow2_rank_a = rational::power_of_two(rank_a);
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rational const aa = a / pow2_rank_a; // a'
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rational const bb = b / pow2_rank_a; // b''
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rational inv_aa;
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VERIFY(aa.mult_inverse(j, inv_aa));
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rational const cc = mod(inv_aa * -bb, rational::power_of_two(j));
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return mk_int(cc, j);
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}
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}
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bdd bdd_manager::mk_eq(bddv const& a, bddv const& b) {
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SASSERT(a.size() == b.size());
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bdd eq = mk_true();
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for (unsigned i = a.size(); i-- > 0; ) {
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eq &= !(a[i] ^ b[i]);
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@ -1014,13 +996,132 @@ namespace dd {
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bdd bdd_manager::mk_ult(bddv const& a, bddv const& b) { return mk_ule(a, b) && !mk_eq(a, b); }
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bdd bdd_manager::mk_ugt(bddv const& a, bddv const& b) { return mk_ult(b, a); }
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bdd_manager::bddv bdd_manager::mk_add(bddv const& a, bddv const& b) {
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bddv bdd_manager::mk_add(bddv const& a, bddv const& b) {
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SASSERT(a.size() == b.size());
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bdd carry = mk_false();
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bddv result;
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bddv result(this);
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#if 0
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for (unsigned i = 0; i < a.size(); ++i) {
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carry = (carry && a[i]) || (carry && b[i]) || (a[i] && b[i]);
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result.push_back(carry ^ a[i] ^ b[i]);
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carry = (carry && a[i]) || (carry && b[i]) || (a[i] && b[i]);
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}
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#else
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if (a.size() > 0) {
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result.push_back(a[0] ^ b[0]);
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}
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for (unsigned i = 1; i < a.size(); ++i) {
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carry = (carry && a[i-1]) || (carry && b[i-1]) || (a[i-1] && b[i-1]);
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result.push_back(carry ^ a[i] ^ b[i]);
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}
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#endif
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return result;
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}
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void bdd_manager::bddv_shl(bddv &a) {
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for (unsigned j = a.size(); j-- > 1; ) {
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a[j] = a[j - 1];
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}
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a[0] = mk_false();
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}
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bddv bdd_manager::mk_mul(bddv const& a, bddv const& b) {
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SASSERT(a.size() == b.size());
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bddv a_shifted = a;
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bddv result = mk_zero(a.size());
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for (unsigned i = 0; i < b.size(); ++i) {
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#if 1
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bddv s = a_shifted;
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for (unsigned j = i; j < b.size(); ++j) {
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s[j] &= b[i];
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}
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result = mk_add(result, s);
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#else
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// From BuDDy's bvec_mul. It seems to compute more intermediate BDDs than the version above?
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bddv added = mk_add(result, a_shifted);
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for (unsigned j = 0; j < result.size(); ++j) {
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result[j] = mk_ite(b[i], added[j], result[j]);
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}
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#endif
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bddv_shl(a_shifted);
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}
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return result;
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}
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template <class GetBitFn>
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bddv bdd_manager::mk_mul(bddv const& a, GetBitFn get_bit) {
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bddv a_shifted = a;
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bddv result = mk_zero(a.size());
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for (unsigned i = 0; i < a.size(); ++i) {
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if (get_bit(i)) {
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result = mk_add(result, a_shifted);
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}
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bddv_shl(a_shifted);
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}
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return result;
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}
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bddv bdd_manager::mk_mul(bddv const& a, rational const& val) {
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SASSERT(val.is_int() && val >= 0 && val < rational::power_of_two(a.size()));
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return mk_mul(a, [val](unsigned i) { return val.get_bit(i); });
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}
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bddv bdd_manager::mk_mul(bddv const& a, bool_vector const& b) {
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SASSERT(a.size() == b.size());
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return mk_mul(a, [b](unsigned i) { return b[i]; });
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}
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bddv bdd_manager::mk_num(rational const& n, unsigned num_bits) {
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SASSERT(n.is_int() && n >= 0 && n < rational::power_of_two(num_bits));
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bddv result(this);
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for (unsigned i = 0; i < num_bits; ++i) {
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result.push_back(n.get_bit(i) ? mk_true() : mk_false());
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}
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return result;
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}
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bddv bdd_manager::mk_ones(unsigned num_bits) {
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bddv result(this);
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for (unsigned i = 0; i < num_bits; ++i) {
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result.push_back(mk_true());
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}
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return result;
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}
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bddv bdd_manager::mk_zero(unsigned num_bits) {
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bddv result(this);
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for (unsigned i = 0; i < num_bits; ++i) {
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result.push_back(mk_false());
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}
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return result;
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}
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bddv bdd_manager::mk_var(unsigned num_bits, unsigned const* vars) {
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bddv result(this);
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for (unsigned i = 0; i < num_bits; ++i) {
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result.push_back(mk_var(vars[i]));
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}
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return result;
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}
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bddv bdd_manager::mk_var(unsigned_vector const& vars) {
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return mk_var(vars.size(), vars.data());
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}
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bool bdd_manager::is_constv(bddv const& a) {
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for (bdd const& bit : a.bits)
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if (!is_const(bit.root))
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return false;
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return true;
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}
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rational bdd_manager::to_val(bddv const& a) {
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rational result = rational::zero();
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for (unsigned i = 0; i < a.size(); ++i) {
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bdd const &bit = a[i];
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SASSERT(is_const(bit.root));
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if (bit.is_true()) {
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result += rational::power_of_two(i);
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}
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}
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return result;
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}
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@ -1030,16 +1131,8 @@ namespace dd {
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bdd bdd_manager::mk_sge(bddv const& a, bddv const& b) { return mk_sle(b, a); }
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bdd bdd_manager::mk_slt(bddv const& a, bddv const& b) { return mk_sle(a, b) && !mk_eq(a, b); }
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bdd bdd_manager::mk_sgt(bddv const& a, bddv const& b) { return mk_slt(b, a); }
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bdd_manager::bddv bdd_manager::mk_num(rational const& n, unsigned num_bits);
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bdd_manager::bddv bdd_manager::mk_ones(unsigned num_bits);
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bdd_manager::bddv bdd_manager::mk_zero(unsigned num_bits);
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bdd_manager::bddv bdd_manager::mk_var(unsigned num_bits, unsigned const* vars);
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bdd_manager::bddv bdd_manager::mk_var(unsigned_vector const& vars);
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bdd_manager::bddv bdd_manager::mk_sub(bddv const& a, bddv const& b);
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bdd_manager::bddv bdd_manager::mk_mul(bddv const& a, bddv const& b);
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bdd_manager::bddv bdd_manager::mk_mul(bddv const& a, bool_vector const& b);
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void bdd_manager::mk_quot_rem(bddv const& a, bddv const& b, bddv& quot, bddv& rem);
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rational bdd_manager::to_val(bddv const& a);
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#endif
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}
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@ -26,13 +26,17 @@ Revision History:
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namespace dd {
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class bdd;
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class bddv;
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enum class find_int_t { empty, singleton, multiple };
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enum class find_result { empty, singleton, multiple };
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std::ostream& operator<<(std::ostream& out, find_result x);
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class bdd_manager {
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friend bdd;
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friend bddv;
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typedef unsigned BDD;
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typedef svector<BDD> BDDV;
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const BDD null_bdd = UINT_MAX;
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@ -192,9 +196,6 @@ namespace dd {
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bdd mk_or(bdd const& a, bdd const& b);
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bdd mk_xor(bdd const& a, bdd const& b);
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bool contains_int(BDD b, rational const& val, unsigned w);
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find_int_t find_int(BDD b, unsigned w, rational& val);
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void reserve_var(unsigned v);
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bool well_formed();
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@ -205,6 +206,12 @@ namespace dd {
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~scoped_push() { m.m_bdd_stack.shrink(m_size); }
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};
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bool contains_num(BDD b, rational const& val, unsigned_vector const& bits);
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find_result find_num(BDD b, unsigned_vector bits, rational& val);
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void bddv_shl(bddv& a);
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template <class GetBitFn> bddv mk_mul(bddv const& a, GetBitFn get_bit);
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public:
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struct mem_out {};
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@ -225,8 +232,10 @@ namespace dd {
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bdd mk_forall(unsigned v, bdd const& b);
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bdd mk_ite(bdd const& c, bdd const& t, bdd const& e);
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/* BDD vector operations */
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typedef vector<bdd> bddv;
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/* BDD vector operations
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* - Fixed-width arithmetic, i.e., modulo 2^size
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* - The lowest index is the LSB
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*/
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bdd mk_ule(bddv const& a, bddv const& b);
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bdd mk_uge(bddv const& a, bddv const& b); // { return mk_ule(b, a); }
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bdd mk_ult(bddv const& a, bddv const& b); // { return mk_ule(a, b) && !mk_eq(a, b); }
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@ -247,23 +256,10 @@ namespace dd {
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bddv mk_sub(bddv const& a, bddv const& b);
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bddv mk_mul(bddv const& a, bddv const& b);
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bddv mk_mul(bddv const& a, bool_vector const& b);
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bddv mk_mul(bddv const& a, rational const& val);
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void mk_quot_rem(bddv const& a, bddv const& b, bddv& quot, bddv& rem);
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rational to_val(bddv const& a);
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/** Encodes the lower w bits of val as BDD, using variable indices 0 to w-1.
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* The least-significant bit is encoded as variable 0.
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* val must be an integer.
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*/
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bdd mk_int(rational const& val, unsigned w);
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/** Encodes the solutions of the affine relation
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*
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* a*x + b == 0 (mod 2^w)
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*
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* as BDD.
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*/
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bdd mk_affine(rational const& a, rational const& b, unsigned w);
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bool is_constv(bddv const& a);
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rational to_val(bddv const& a);
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std::ostream& display(std::ostream& out);
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std::ostream& display(std::ostream& out, bdd const& b);
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@ -303,17 +299,102 @@ namespace dd {
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double dnf_size() const { return m->dnf_size(root); }
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unsigned bdd_size() const { return m->bdd_size(*this); }
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/** Checks whether the integer val is contained in the BDD when viewed as set of integers (see also mk_int). */
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// NSB code review: this API needs to be changed: bit-position to variable mapping is external
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bool contains_int(rational const& val, unsigned w) { return m->contains_int(root, val, w); }
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/** Checks whether the integer val is contained in the BDD when viewed as set of integers.
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*
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* Preconditions:
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* - bits are sorted in ascending order,
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* - the bdd only contains variables from bits.
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*/
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bool contains_num(rational const& val, unsigned_vector const& bits) const { return m->contains_num(root, val, bits); }
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/** Returns an integer contained in the BDD, if any, and whether the BDD is a singleton. */
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// NSB code review: this API needs to be changed: bit-position to variable mapping is external
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find_int_t find_int(unsigned w, rational& val) { return m->find_int(root, w, val); }
|
||||
/** Returns an integer contained in the BDD, if any, and whether the BDD is a singleton.
|
||||
*
|
||||
* Preconditions:
|
||||
* - bits are sorted in ascending order,
|
||||
* - the bdd only contains variables from bits.
|
||||
*/
|
||||
find_result find_num(unsigned_vector const& bits, rational& val) const { return m->find_num(root, bits, val); }
|
||||
};
|
||||
|
||||
std::ostream& operator<<(std::ostream& out, bdd const& b);
|
||||
|
||||
class bddv {
|
||||
friend bdd_manager;
|
||||
|
||||
// TODO: currently we repeat the pointer to the manager in every entry of bits.
|
||||
// Should use BDDV instead (drawback: the functions in bdd_manager aren't as nice and they need to be careful about reference counting if they work with BDD directly).
|
||||
vector<bdd> bits;
|
||||
bdd_manager& m;
|
||||
|
||||
bddv(vector<bdd> bits, bdd_manager* m): bits(bits), m(*m) { inc_bits_ref(); }
|
||||
bddv(vector<bdd>&& bits, bdd_manager* m): bits(std::move(bits)), m(*m) { inc_bits_ref(); }
|
||||
void inc_bits_ref() {
|
||||
// NOTE: necessary if we switch to BDDV as storage
|
||||
// for (BDD b : bits) { m.inc_ref(b); }
|
||||
}
|
||||
|
||||
// NOTE: these should probably be removed if we switch to BDDV
|
||||
bddv(bdd_manager* m): bits(), m(*m) { }
|
||||
bdd const& operator[](unsigned i) const { return bits[i]; }
|
||||
bdd& operator[](unsigned i) { return bits[i]; }
|
||||
void push_back(bdd const& a) { bits.push_back(a); }
|
||||
void push_back(bdd&& a) { bits.push_back(a); }
|
||||
public:
|
||||
bddv(bddv const& other): bits(other.bits), m(other.m) { inc_bits_ref(); }
|
||||
bddv(bddv&& other): bits(), m(other.m) { std::swap(bits, other.bits); }
|
||||
bddv& operator=(bddv const& other) {
|
||||
if (this != &other) {
|
||||
bddv old(std::move(*this));
|
||||
bits = other.bits;
|
||||
inc_bits_ref();
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
bddv& operator=(bddv&& other) {
|
||||
if (this != &other) {
|
||||
bddv old(std::move(*this));
|
||||
SASSERT(bits.empty());
|
||||
std::swap(bits, other.bits);
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
~bddv() {
|
||||
// NOTE: necessary if we switch to BDDV as storage
|
||||
// for (BDD b : bits) { m.dec_ref(b); }
|
||||
}
|
||||
|
||||
unsigned size() const { return bits.size(); }
|
||||
vector<bdd> const& get_bits() const { return bits; }
|
||||
|
||||
bdd operator<=(bddv const& other) const { return m.mk_ule(*this, other); }
|
||||
bdd operator>=(bddv const& other) const { return m.mk_uge(*this, other); }
|
||||
bdd operator<(bddv const& other) const { return m.mk_ult(*this, other); }
|
||||
bdd operator>(bddv const& other) const { return m.mk_ugt(*this, other); }
|
||||
// TODO: what about the signed versions?
|
||||
// bdd mk_sle(bddv const& a, bddv const& b);
|
||||
// bdd mk_sge(bddv const& a, bddv const& b); // { return mk_sle(b, a); }
|
||||
// bdd mk_slt(bddv const& a, bddv const& b); // { return mk_sle(a, b) && !mk_eq(a, b); }
|
||||
// bdd mk_sgt(bddv const& a, bddv const& b); // { return mk_slt(b, a); }
|
||||
|
||||
bdd operator==(bddv const& other) const { return m.mk_eq(*this, other); }
|
||||
bdd operator==(rational const& other) const { return m.mk_eq(*this, other); }
|
||||
bdd operator!=(bddv const& other) const { return !m.mk_eq(*this, other); }
|
||||
bdd operator!=(rational const& other) const { return !m.mk_eq(*this, other); }
|
||||
bddv operator+(bddv const& other) const { return m.mk_add(*this, other); }
|
||||
bddv operator+(rational const& other) const { return m.mk_add(*this, m.mk_num(other, size())); }
|
||||
bddv operator-(bddv const& other) const { return m.mk_sub(*this, other); }
|
||||
bddv operator*(bddv const& other) const { return m.mk_mul(*this, other); }
|
||||
bddv operator*(rational const& other) const { return m.mk_mul(*this, other); }
|
||||
bddv operator*(bool_vector const& other) const { return m.mk_mul(*this, other); }
|
||||
|
||||
// void mk_quot_rem(bddv const& a, bddv const& b, bddv& quot, bddv& rem);
|
||||
|
||||
bool is_const() const { return m.is_constv(*this); }
|
||||
rational to_val() const { return m.to_val(*this); }
|
||||
};
|
||||
|
||||
inline bddv operator*(rational const& r, bddv const& a) { return a * r; }
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue