mirror of
https://github.com/Z3Prover/z3
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BDD vectors: add subtract and quot_rem, move finite domain abstraction out of bdd_manager (#5201)
* Coding style * Simplify bddv class * mk_eq: run loop from below * Add unit test for bddv unsigned comparison * Add test that shows contains_num/find_num fail after reordering * Add BDD vector subtraction * Call apply_rec in mk_ite_rec instead of apply * Question about mk_quant * Implement quot_rem over BDD vectors * Move shl/shr to bddv * Make unit test smaller * Add class dd::fdd to manage association between BDDs and numbers * Remove contains_num/find_num from bdd_manager
This commit is contained in:
Jakob Rath
GitHub
parent
bc695a5a97
commit
77350d97da
10 changed files with 494 additions and 301 deletions
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@ -1,6 +1,7 @@
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z3_add_component(dd
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SOURCES
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dd_bdd.cpp
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dd_fdd.cpp
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dd_pdd.cpp
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COMPONENT_DEPENDENCIES
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util
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@ -23,19 +23,6 @@ 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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@ -606,10 +593,10 @@ namespace dd {
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if (is_true(a)) return b;
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if (is_false(a)) return c;
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if (b == c) return b;
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if (is_true(b)) return apply(a, c, bdd_or_op);
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if (is_false(c)) return apply(a, b, bdd_and_op);
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if (is_false(b)) return apply(mk_not_rec(a), c, bdd_and_op);
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if (is_true(c)) return apply(mk_not_rec(a), b, bdd_or_op);
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if (is_true(b)) return apply_rec(a, c, bdd_or_op);
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if (is_false(c)) return apply_rec(a, b, bdd_and_op);
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if (is_false(b)) return apply_rec(mk_not_rec(a), c, bdd_and_op);
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if (is_true(c)) return apply_rec(mk_not_rec(a), b, bdd_or_op);
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SASSERT(!is_const(a) && !is_const(b) && !is_const(c));
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op_entry * e1 = pop_entry(a, b, c);
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op_entry const* e2 = m_op_cache.insert_if_not_there(e1);
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@ -659,6 +646,7 @@ namespace dd {
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bdd_manager::BDD bdd_manager::mk_quant(unsigned n, unsigned const* vars, BDD b, bdd_op op) {
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BDD result = b;
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// TODO: should this method catch mem_out like the other non-rec mk_ methods?
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for (unsigned i = 0; i < n; ++i) {
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result = mk_quant_rec(m_var2level[vars[i]], result, op);
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}
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@ -911,65 +899,18 @@ namespace dd {
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std::ostream& operator<<(std::ostream& out, bdd const& b) { return b.display(out); }
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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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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_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_result::empty;
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bool is_unique = true;
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unsigned var_idx = bits.size();
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while (!is_true(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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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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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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if (var_idx > 0)
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is_unique = false;
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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_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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for (unsigned i = 0; i < a.size(); ++i)
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eq &= !(a[i] ^ b[i]);
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}
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return eq;
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}
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bdd bdd_manager::mk_eq(bddv const& a, rational const& n) {
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SASSERT(n.is_int() && n >= 0 && n < rational(2).expt(a.size()));
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bdd b = mk_true();
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for (unsigned i = a.size(); i-- > 0; )
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for (unsigned i = 0; i < a.size(); ++i)
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b &= n.get_bit(i) ? a[i] : !a[i];
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return b;
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}
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@ -977,7 +918,7 @@ namespace dd {
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bdd bdd_manager::mk_eq(unsigned_vector const& vars, rational const& n) {
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SASSERT(n.is_int() && n >= 0 && n < rational(2).expt(vars.size()));
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bdd b = mk_true();
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for (unsigned i = vars.size(); i-- > 0; )
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for (unsigned i = 0; i < vars.size(); ++i)
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b &= n.get_bit(i) ? mk_var(vars[i]) : mk_nvar(vars[i]);
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return b;
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}
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@ -1006,9 +947,8 @@ namespace dd {
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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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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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@ -1017,11 +957,18 @@ namespace dd {
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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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bddv bdd_manager::mk_sub(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(this);
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if (a.size() > 0)
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result.push_back(a[0] ^ b[0]);
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for (unsigned i = 1; i < a.size(); ++i) {
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// carry = (a[i-1] && b[i-1] && carry) || (!a[i-1] && (b[i-1] || carry));
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carry = mk_ite(a[i-1], b[i-1] && carry, b[i-1] || carry);
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result.push_back(carry ^ a[i] ^ b[i]);
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}
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a[0] = mk_false();
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return result;
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}
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bddv bdd_manager::mk_mul(bddv const& a, bddv const& b) {
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@ -1031,18 +978,16 @@ namespace dd {
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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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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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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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a_shifted.shl();
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}
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return result;
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}
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@ -1052,10 +997,9 @@ namespace dd {
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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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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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a_shifted.shl();
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}
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return result;
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}
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@ -1070,36 +1014,63 @@ namespace dd {
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return mk_mul(a, [b](unsigned i) { return b[i]; });
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}
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void bdd_manager::mk_quot_rem(bddv const& a, bddv const& b, bddv& quot, bddv& rem) {
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SASSERT(a.size() == b.size());
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quot = mk_zero(a.size());
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// We work with double-size vectors
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unsigned worksize = a.size() + b.size();
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// Extend dividend to worksize
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rem = a;
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for (unsigned i = b.size(); i-- > 0; )
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rem.push_back(mk_false());
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// Shift divisor to the left
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bddv div(this);
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for (unsigned i = a.size(); i-- > 0; )
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div.push_back(mk_false());
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div.m_bits.append(b.m_bits);
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// Keep shifting divisor to the right and subtract whenever it is
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// smaller than the remaining value
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for (int i = 0; i <= b.size(); ++i) {
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bdd divLteRem = div <= rem;
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bddv remSubDiv = rem - div;
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for (int j = 0; j < worksize; ++j)
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rem[j] = mk_ite(divLteRem, remSubDiv[j], rem[j]);
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if (i > 0)
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quot[b.size()-i] = divLteRem;
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div.shr();
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}
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rem.m_bits.shrink(b.size());
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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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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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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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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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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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@ -1108,7 +1079,7 @@ namespace dd {
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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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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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@ -1119,9 +1090,8 @@ namespace dd {
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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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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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@ -1131,8 +1101,18 @@ 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_sub(bddv const& a, bddv 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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#endif
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void bddv::shl() {
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for (unsigned j = size(); j-- > 1;)
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m_bits[j] = m_bits[j-1];
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m_bits[0] = m->mk_false();
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}
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void bddv::shr() {
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for (unsigned j = 1; j < size(); ++j)
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m_bits[j-1] = m_bits[j];
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m_bits[size()-1] = m->mk_false();
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}
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}
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@ -27,16 +27,14 @@ namespace dd {
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class bdd;
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class bddv;
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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 test_bdd;
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class bdd_manager {
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friend bdd;
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friend bddv;
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friend test_bdd;
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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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@ -206,10 +204,6 @@ 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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@ -284,7 +278,8 @@ namespace dd {
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unsigned var() const { return m->var(root); }
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bool is_true() const { return root == bdd_manager::true_bdd; }
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bool is_false() const { return root == bdd_manager::false_bdd; }
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bool is_false() const { return root == bdd_manager::false_bdd; }
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bool is_const() const { return is_false() || is_true(); }
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bdd operator!() const { return m->mk_not(*this); }
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bdd operator&&(bdd const& other) const { return m->mk_and(*this, other); }
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@ -298,22 +293,6 @@ namespace dd {
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double cnf_size() const { return m->cnf_size(root); }
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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.
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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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*
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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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find_result find_num(unsigned_vector const& bits, rational& val) const { return m->find_num(root, bits, val); }
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};
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std::ostream& operator<<(std::ostream& out, bdd const& b);
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@ -321,79 +300,69 @@ namespace dd {
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class bddv {
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friend bdd_manager;
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// TODO: currently we repeat the pointer to the manager in every entry of bits.
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// 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).
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vector<bdd> bits;
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bdd_manager& m;
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vector<bdd> m_bits;
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bdd_manager* m;
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bddv(vector<bdd> bits, bdd_manager* m): bits(bits), m(*m) { inc_bits_ref(); }
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bddv(vector<bdd>&& bits, bdd_manager* m): bits(std::move(bits)), m(*m) { inc_bits_ref(); }
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void inc_bits_ref() {
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// NOTE: necessary if we switch to BDDV as storage
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// for (BDD b : bits) { m.inc_ref(b); }
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}
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bddv(vector<bdd> bits, bdd_manager* m): m_bits(bits), m(m) { SASSERT(m); }
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bddv(vector<bdd>&& bits, bdd_manager* m): m_bits(std::move(bits)), m(m) { SASSERT(m); }
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bddv(bdd_manager* m): m_bits(), m(m) { SASSERT(m); }
|
||||
bdd const& operator[](unsigned i) const { return m_bits[i]; }
|
||||
bdd& operator[](unsigned i) { return m_bits[i]; }
|
||||
void push_back(bdd const& a) { m_bits.push_back(a); }
|
||||
void push_back(bdd&& a) { m_bits.push_back(std::move(a)); }
|
||||
void shl();
|
||||
void shr();
|
||||
|
||||
// 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 m_bits.size(); }
|
||||
vector<bdd> const& bits() const { return m_bits; }
|
||||
|
||||
unsigned size() const { return bits.size(); }
|
||||
vector<bdd> const& get_bits() const { return bits; }
|
||||
/* unsigned comparison operators */
|
||||
bdd operator<=(bddv const& other) const { return m->mk_ule(*this, other); } ///< unsigned comparison
|
||||
bdd operator>=(bddv const& other) const { return m->mk_uge(*this, other); } ///< unsigned comparison
|
||||
bdd operator< (bddv const& other) const { return m->mk_ult(*this, other); } ///< unsigned comparison
|
||||
bdd operator> (bddv const& other) const { return m->mk_ugt(*this, other); } ///< unsigned comparison
|
||||
bdd operator<=(rational const& other) const { return m->mk_ule(*this, m->mk_num(other, size())); } ///< unsigned comparison
|
||||
bdd operator>=(rational const& other) const { return m->mk_uge(*this, m->mk_num(other, size())); } ///< unsigned comparison
|
||||
bdd operator< (rational const& other) const { return m->mk_ult(*this, m->mk_num(other, size())); } ///< unsigned comparison
|
||||
bdd operator> (rational const& other) const { return m->mk_ugt(*this, m->mk_num(other, size())); } ///< unsigned comparison
|
||||
|
||||
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); }
|
||||
/* signed comparison operators */
|
||||
bdd sle(bddv const& other) const { return m->mk_sle(*this, other); }
|
||||
bdd sge(bddv const& other) const { return m->mk_sge(*this, other); }
|
||||
bdd slt(bddv const& other) const { return m->mk_slt(*this, other); }
|
||||
bdd sgt(bddv const& other) const { return m->mk_sgt(*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); }
|
||||
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); }
|
||||
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); }
|
||||
|
||||
// void mk_quot_rem(bddv const& a, bddv const& b, bddv& quot, bddv& rem);
|
||||
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-(rational const& other) const { return m->mk_sub(*this, m->mk_num(other, size())); }
|
||||
bddv rev_sub(rational const& other) const { return m->mk_sub(m->mk_num(other, size()), *this); }
|
||||
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); }
|
||||
|
||||
bool is_const() const { return m.is_constv(*this); }
|
||||
rational to_val() const { return m.to_val(*this); }
|
||||
void quot_rem(bddv const& divisor, bddv& quot, bddv& rem) const { m->mk_quot_rem(*this, divisor, quot, rem); }
|
||||
|
||||
bool is_const() const { return m->is_constv(*this); }
|
||||
rational to_val() const { return m->to_val(*this); }
|
||||
};
|
||||
|
||||
inline bdd operator<=(rational const& r, bddv const& a) { return a >= r; } ///< unsigned comparison
|
||||
inline bdd operator>=(rational const& r, bddv const& a) { return a <= r; } ///< unsigned comparison
|
||||
inline bdd operator< (rational const& r, bddv const& a) { return a > r; } ///< unsigned comparison
|
||||
inline bdd operator> (rational const& r, bddv const& a) { return a < r; } ///< unsigned comparison
|
||||
inline bdd operator==(rational const& r, bddv const& a) { return a == r; }
|
||||
inline bdd operator!=(rational const& r, bddv const& a) { return a != r; }
|
||||
inline bddv operator*(rational const& r, bddv const& a) { return a * r; }
|
||||
inline bddv operator+(rational const& r, bddv const& a) { return a + r; }
|
||||
inline bddv operator-(rational const& r, bddv const& a) { return a.rev_sub(r); }
|
||||
|
||||
}
|
||||
|
||||
|
|
|
|||
88
src/math/dd/dd_fdd.cpp
Normal file
88
src/math/dd/dd_fdd.cpp
Normal file
|
|
@ -0,0 +1,88 @@
|
|||
/*++
|
||||
Copyright (c) 2021 Microsoft Corporation
|
||||
|
||||
Module Name:
|
||||
|
||||
dd_fdd
|
||||
|
||||
Abstract:
|
||||
|
||||
Finite domain abstraction for using BDDs as sets of integers, inspired by BuDDy's fdd module.
|
||||
|
||||
Author:
|
||||
|
||||
Nikolaj Bjorner (nbjorner) 2021-04-20
|
||||
Jakob Rath 2021-04-20
|
||||
|
||||
--*/
|
||||
|
||||
#include "math/dd/dd_fdd.h"
|
||||
|
||||
namespace dd {
|
||||
|
||||
fdd::fdd(bdd_manager& manager, unsigned_vector&& vars)
|
||||
: m_pos2var(std::move(vars))
|
||||
, m_var2pos()
|
||||
// , m(&manager)
|
||||
, m_var(manager.mk_var(m_pos2var))
|
||||
{
|
||||
for (unsigned pos = 0; pos < m_pos2var.size(); ++pos) {
|
||||
unsigned const var = m_pos2var[pos];
|
||||
while (var >= m_var2pos.size())
|
||||
m_var2pos.push_back(UINT_MAX);
|
||||
m_var2pos[var] = pos;
|
||||
}
|
||||
}
|
||||
|
||||
unsigned fdd::var2pos(unsigned var) const {
|
||||
return var < m_var2pos.size() ? m_var2pos[var] : UINT_MAX;
|
||||
}
|
||||
|
||||
bool fdd::contains(bdd b, rational const& val) const {
|
||||
while (!b.is_const()) {
|
||||
unsigned const pos = var2pos(b.var());
|
||||
SASSERT(pos != UINT_MAX && "Unexpected BDD variable");
|
||||
b = val.get_bit(pos) ? b.hi() : b.lo();
|
||||
}
|
||||
return b.is_true();
|
||||
}
|
||||
|
||||
find_t fdd::find(bdd b, rational& out_val) const {
|
||||
out_val = 0;
|
||||
if (b.is_false())
|
||||
return find_t::empty;
|
||||
bool is_unique = true;
|
||||
unsigned num_vars = 0;
|
||||
while (!b.is_true()) {
|
||||
++num_vars;
|
||||
unsigned const pos = var2pos(b.var());
|
||||
SASSERT(pos != UINT_MAX && "Unexpected BDD variable");
|
||||
if (b.lo().is_false()) {
|
||||
out_val += rational::power_of_two(pos);
|
||||
b = b.hi();
|
||||
}
|
||||
else {
|
||||
if (!b.hi().is_false())
|
||||
is_unique = false;
|
||||
b = b.lo();
|
||||
}
|
||||
}
|
||||
if (num_vars != num_bits())
|
||||
is_unique = false;
|
||||
return is_unique ? find_t::singleton : find_t::multiple;
|
||||
}
|
||||
|
||||
std::ostream& operator<<(std::ostream& out, find_t x) {
|
||||
switch (x) {
|
||||
case find_t::empty:
|
||||
return out << "empty";
|
||||
case find_t::singleton:
|
||||
return out << "singleton";
|
||||
case find_t::multiple:
|
||||
return out << "multiple";
|
||||
}
|
||||
UNREACHABLE();
|
||||
return out;
|
||||
}
|
||||
|
||||
}
|
||||
69
src/math/dd/dd_fdd.h
Normal file
69
src/math/dd/dd_fdd.h
Normal file
|
|
@ -0,0 +1,69 @@
|
|||
/*++
|
||||
Copyright (c) 2021 Microsoft Corporation
|
||||
|
||||
Module Name:
|
||||
|
||||
dd_fdd
|
||||
|
||||
Abstract:
|
||||
|
||||
Finite domain abstraction for using BDDs as sets of integers, inspired by BuDDy's fdd module.
|
||||
|
||||
Author:
|
||||
|
||||
Nikolaj Bjorner (nbjorner) 2021-04-20
|
||||
Jakob Rath 2021-04-20
|
||||
|
||||
--*/
|
||||
#pragma once
|
||||
|
||||
#include "math/dd/dd_bdd.h"
|
||||
#include "util/vector.h"
|
||||
#include "util/rational.h"
|
||||
|
||||
namespace dd {
|
||||
|
||||
enum class find_t { empty, singleton, multiple };
|
||||
std::ostream& operator<<(std::ostream& out, find_t x);
|
||||
|
||||
/**
|
||||
* Finite domain abstraction over BDDs.
|
||||
*/
|
||||
class fdd {
|
||||
unsigned_vector m_pos2var; // pos -> BDD var
|
||||
unsigned_vector m_var2pos; // var -> pos (pos = place number in the bit representation, 0 is LSB's place)
|
||||
// bdd_manager* m; // NOTE: currently unused
|
||||
bddv m_var;
|
||||
|
||||
static unsigned_vector seq(unsigned count) {
|
||||
unsigned_vector result;
|
||||
for (unsigned i = 0; i < count; ++i)
|
||||
result.push_back(i);
|
||||
return result;
|
||||
}
|
||||
|
||||
unsigned var2pos(unsigned var) const;
|
||||
|
||||
public:
|
||||
/** Initialize FDD using BDD variables from 0 to num_bits-1. */
|
||||
fdd(bdd_manager& manager, unsigned num_bits) : fdd(manager, seq(num_bits)) { }
|
||||
fdd(bdd_manager& manager, unsigned_vector const& vars) : fdd(manager, unsigned_vector(vars)) { }
|
||||
fdd(bdd_manager& manager, unsigned_vector&& vars);
|
||||
|
||||
unsigned num_bits() const { return m_pos2var.size(); }
|
||||
unsigned_vector const& bdd_vars() const { return m_pos2var; }
|
||||
|
||||
bddv const& var() const { return m_var; }
|
||||
|
||||
/** Checks whether the integer val is contained in the BDD when viewed as set of integers.
|
||||
* Precondition: the bdd only contains variables managed by this fdd.
|
||||
*/
|
||||
bool contains(bdd b, rational const& val) const;
|
||||
|
||||
/** Returns an integer contained in the BDD, if any, and whether the BDD is a singleton.
|
||||
* Precondition: the bdd only contains variables managed by this fdd.
|
||||
*/
|
||||
find_t find(bdd b, rational& out_val) const;
|
||||
};
|
||||
|
||||
}
|
||||
|
|
@ -57,13 +57,13 @@ namespace polysat {
|
|||
if (try_narrow_with(q, s)) {
|
||||
rational val;
|
||||
switch (s.find_viable(other_var, val)) {
|
||||
case dd::find_result::empty:
|
||||
case dd::find_t::empty:
|
||||
s.set_conflict(*this);
|
||||
return false;
|
||||
case dd::find_result::singleton:
|
||||
case dd::find_t::singleton:
|
||||
s.propagate(other_var, val, *this);
|
||||
return false;
|
||||
case dd::find_result::multiple:
|
||||
case dd::find_t::multiple:
|
||||
/* do nothing */
|
||||
break;
|
||||
}
|
||||
|
|
@ -95,7 +95,7 @@ namespace polysat {
|
|||
pvar v = q.var();
|
||||
rational a = q.hi().val();
|
||||
rational b = q.lo().val();
|
||||
bddv const& x = s.m_bdd.mk_var(s.sz2bits(s.size(v)));
|
||||
bddv const& x = s.sz2bits(s.size(v)).var();
|
||||
bdd xs = (a * x + b == rational(0));
|
||||
s.intersect_viable(v, xs);
|
||||
s.push_cjust(v, this);
|
||||
|
|
|
|||
|
|
@ -29,20 +29,18 @@ namespace polysat {
|
|||
return *m_pdd[sz];
|
||||
}
|
||||
|
||||
unsigned_vector const& solver::sz2bits(unsigned sz) {
|
||||
dd::fdd const& solver::sz2bits(unsigned sz) {
|
||||
m_bits.reserve(sz + 1);
|
||||
auto* bits = m_bits[sz];
|
||||
if (!bits) {
|
||||
m_bits.set(sz, alloc(unsigned_vector));
|
||||
m_bits.set(sz, alloc(dd::fdd, m_bdd, sz));
|
||||
bits = m_bits[sz];
|
||||
for (unsigned i = 0; i < sz; ++i)
|
||||
bits->push_back(i);
|
||||
}
|
||||
return *bits;
|
||||
}
|
||||
|
||||
bool solver::is_viable(pvar v, rational const& val) {
|
||||
return m_viable[v].contains_num(val, sz2bits(size(v)));
|
||||
return sz2bits(size(v)).contains(m_viable[v], val);
|
||||
}
|
||||
|
||||
void solver::add_non_viable(pvar v, rational const& val) {
|
||||
|
|
@ -50,7 +48,7 @@ namespace polysat {
|
|||
TRACE("polysat", tout << "v" << v << " /= " << val << "\n";);
|
||||
SASSERT(is_viable(v, val));
|
||||
auto& bits = sz2bits(size(v));
|
||||
intersect_viable(v, !m_bdd.mk_eq(bits, val));
|
||||
intersect_viable(v, bits.var() != val);
|
||||
}
|
||||
|
||||
void solver::intersect_viable(pvar v, bdd vals) {
|
||||
|
|
@ -60,8 +58,8 @@ namespace polysat {
|
|||
set_conflict(v);
|
||||
}
|
||||
|
||||
dd::find_result solver::find_viable(pvar v, rational & val) {
|
||||
return m_viable[v].find_num(sz2bits(size(v)), val);
|
||||
dd::find_t solver::find_viable(pvar v, rational & val) {
|
||||
return sz2bits(size(v)).find(m_viable[v], val);
|
||||
}
|
||||
|
||||
solver::solver(reslimit& lim):
|
||||
|
|
@ -323,15 +321,15 @@ namespace polysat {
|
|||
IF_LOGGING(log_viable(v));
|
||||
rational val;
|
||||
switch (find_viable(v, val)) {
|
||||
case dd::find_result::empty:
|
||||
case dd::find_t::empty:
|
||||
LOG("Conflict: no value for pvar " << v);
|
||||
set_conflict(v);
|
||||
break;
|
||||
case dd::find_result::singleton:
|
||||
case dd::find_t::singleton:
|
||||
LOG("Propagation: pvar " << v << " := " << val << " (due to unique value)");
|
||||
assign_core(v, val, justification::propagation(m_level));
|
||||
break;
|
||||
case dd::find_result::multiple:
|
||||
case dd::find_t::multiple:
|
||||
LOG("Decision: pvar " << v << " := " << val);
|
||||
push_level();
|
||||
assign_core(v, val, justification::decision(m_level));
|
||||
|
|
|
|||
|
|
@ -45,7 +45,7 @@ namespace polysat {
|
|||
|
||||
reslimit& m_lim;
|
||||
scoped_ptr_vector<dd::pdd_manager> m_pdd;
|
||||
scoped_ptr_vector<unsigned_vector> m_bits;
|
||||
scoped_ptr_vector<dd::fdd> m_bits;
|
||||
dd::bdd_manager m_bdd;
|
||||
dep_value_manager m_value_manager;
|
||||
small_object_allocator m_alloc;
|
||||
|
|
@ -132,7 +132,7 @@ namespace polysat {
|
|||
/**
|
||||
* Find a next viable value for variable.
|
||||
*/
|
||||
dd::find_result find_viable(pvar v, rational & val);
|
||||
dd::find_t find_viable(pvar v, rational & val);
|
||||
|
||||
/** Log all viable values for the given variable.
|
||||
* (Inefficient, but useful for debugging small instances.)
|
||||
|
|
@ -147,7 +147,7 @@ namespace polysat {
|
|||
void del_var();
|
||||
|
||||
dd::pdd_manager& sz2pdd(unsigned sz);
|
||||
unsigned_vector const& sz2bits(unsigned sz);
|
||||
dd::fdd const& sz2bits(unsigned sz);
|
||||
|
||||
void push_level();
|
||||
void pop_levels(unsigned num_levels);
|
||||
|
|
|
|||
|
|
@ -20,6 +20,7 @@ Author:
|
|||
#include "util/ref_vector.h"
|
||||
#include "math/dd/dd_pdd.h"
|
||||
#include "math/dd/dd_bdd.h"
|
||||
#include "math/dd/dd_fdd.h"
|
||||
|
||||
namespace polysat {
|
||||
|
||||
|
|
|
|||
291
src/test/bdd.cpp
291
src/test/bdd.cpp
|
|
@ -1,6 +1,11 @@
|
|||
#include "math/dd/dd_bdd.h"
|
||||
#include "math/dd/dd_fdd.h"
|
||||
|
||||
namespace dd {
|
||||
|
||||
class test_bdd {
|
||||
public:
|
||||
|
||||
static void test1() {
|
||||
bdd_manager m(20);
|
||||
bdd v0 = m.mk_var(0);
|
||||
|
|
@ -86,52 +91,65 @@ namespace dd {
|
|||
}
|
||||
|
||||
static void test_bddv_ops_on_constants() {
|
||||
unsigned const num_bits = 4;
|
||||
std::cout << "test_bddv_ops_on_constants\n";
|
||||
unsigned const num_bits = 3;
|
||||
rational const modulus = rational::power_of_two(num_bits);
|
||||
bdd_manager m(num_bits);
|
||||
|
||||
SASSERT_EQ(m.to_val(m.mk_zero(num_bits)), rational(0));
|
||||
SASSERT_EQ(m.to_val(m.mk_ones(num_bits)), modulus - 1);
|
||||
|
||||
for (unsigned n = 0; n < 16; ++n) {
|
||||
for (unsigned n = 0; n < 8; ++n) {
|
||||
rational const nr(n);
|
||||
SASSERT_EQ(m.to_val(m.mk_num(nr, num_bits)), nr);
|
||||
}
|
||||
|
||||
for (unsigned n = 0; n < 16; ++n) {
|
||||
for (unsigned k = 0; k < 16; ++k) {
|
||||
for (unsigned n = 0; n < 8; ++n) {
|
||||
for (unsigned k = 0; k < 8; ++k) {
|
||||
rational const nr(n);
|
||||
rational const kr(k);
|
||||
bddv const nv = m.mk_num(nr, num_bits);
|
||||
bddv const kv = m.mk_num(kr, num_bits);
|
||||
SASSERT_EQ((nv + kv).to_val(), (nr + kr) % modulus);
|
||||
SASSERT_EQ((nv - kv).to_val(), (nr - kr + modulus) % modulus);
|
||||
SASSERT_EQ((nv * kr).to_val(), (nr * kr) % modulus);
|
||||
SASSERT_EQ((nv * kv).to_val(), (nr * kr) % modulus);
|
||||
bdd eq = m.mk_eq(nv, kv);
|
||||
SASSERT((eq.is_true() || eq.is_false()) && (eq.is_true() == (n == k)));
|
||||
SASSERT(eq.is_const() && (eq.is_true() == (n == k)));
|
||||
eq = m.mk_eq(nv, kr);
|
||||
SASSERT((eq.is_true() || eq.is_false()) && (eq.is_true() == (n == k)));
|
||||
SASSERT(eq.is_const() && (eq.is_true() == (n == k)));
|
||||
|
||||
bddv quotv = m.mk_zero(num_bits);
|
||||
bddv remv = m.mk_zero(num_bits);
|
||||
nv.quot_rem(kv, quotv, remv);
|
||||
if (k != 0) {
|
||||
SASSERT_EQ(quotv.to_val(), rational(n / k));
|
||||
SASSERT_EQ(remv.to_val(), rational(n % k));
|
||||
} else {
|
||||
// std::cout << "n=" << n << " k=" << k << "\n";
|
||||
// std::cout << " quot: " << quotv.to_val() << "\n";
|
||||
// std::cout << " rem: " << remv.to_val() << "\n";
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
static void test_bddv_eqfind_small() {
|
||||
std::cout << "test_bddv_eqfind_small\n";
|
||||
bdd_manager m(4);
|
||||
unsigned_vector bits;
|
||||
bits.push_back(0);
|
||||
bddv const x = m.mk_var(bits);
|
||||
bddv const one = m.mk_num(rational(1), bits.size());
|
||||
bdd x_is_one = m.mk_eq(x, one);
|
||||
fdd const x_dom(m, 1);
|
||||
bddv const x = x_dom.var();
|
||||
bdd x_is_one = (x == rational(1));
|
||||
std::cout << "x_is_one:\n" << x_is_one << "\n";
|
||||
rational r;
|
||||
auto res = x_is_one.find_num(bits, r);
|
||||
SASSERT_EQ(res, find_result::singleton);
|
||||
auto res = x_dom.find(x_is_one, r);
|
||||
SASSERT_EQ(res, find_t::singleton);
|
||||
SASSERT_EQ(r, rational(1));
|
||||
}
|
||||
|
||||
static void test_bddv_eqfind() {
|
||||
unsigned const num_bits = 4;
|
||||
bdd_manager m(num_bits);
|
||||
std::cout << "test_bddv_eqfind\n";
|
||||
bdd_manager m(4);
|
||||
|
||||
unsigned_vector bits;
|
||||
bits.push_back(0);
|
||||
|
|
@ -139,43 +157,60 @@ namespace dd {
|
|||
bits.push_back(4);
|
||||
bits.push_back(27);
|
||||
|
||||
bddv const x = m.mk_var(bits);
|
||||
bddv const zero = m.mk_zero(num_bits);
|
||||
bddv const one = m.mk_num(rational(1), num_bits);
|
||||
bddv const five = m.mk_num(rational(5), num_bits);
|
||||
fdd const x_dom(m, bits);
|
||||
bddv const x = x_dom.var();
|
||||
bddv const zero = m.mk_zero(x_dom.num_bits());
|
||||
bddv const one = m.mk_num(rational(1), x_dom.num_bits());
|
||||
bddv const five = m.mk_num(rational(5), x_dom.num_bits());
|
||||
|
||||
SASSERT(m.mk_eq(one, rational(1)).is_true());
|
||||
SASSERT(m.mk_eq(five, rational(5)).is_true());
|
||||
SASSERT(m.mk_eq(five, rational(4)).is_false());
|
||||
SASSERT(m.mk_eq(five, five).is_true());
|
||||
SASSERT(m.mk_eq(five, one).is_false());
|
||||
SASSERT((one == rational(1)).is_true());
|
||||
SASSERT((five == rational(5)).is_true());
|
||||
SASSERT((five == rational(4)).is_false());
|
||||
SASSERT((five == five).is_true());
|
||||
SASSERT((five == one).is_false());
|
||||
|
||||
// Test the three different mk_eq overloads
|
||||
{
|
||||
bdd const x_is_five = m.mk_eq(x, rational(5));
|
||||
rational r;
|
||||
auto res = x_is_five.find_num(bits, r);
|
||||
SASSERT_EQ(res, find_result::singleton);
|
||||
SASSERT_EQ(r, rational(5));
|
||||
auto res = x_dom.find(x_is_five, r);
|
||||
SASSERT_EQ(res, find_t::singleton);
|
||||
SASSERT_EQ(r, 5);
|
||||
}
|
||||
|
||||
{
|
||||
bdd const x_is_five = m.mk_eq(bits, rational(5));
|
||||
rational r;
|
||||
auto res = x_is_five.find_num(bits, r);
|
||||
SASSERT_EQ(res, find_result::singleton);
|
||||
SASSERT_EQ(r, rational(5));
|
||||
auto res = x_dom.find(x_is_five, r);
|
||||
SASSERT_EQ(res, find_t::singleton);
|
||||
SASSERT_EQ(r, 5);
|
||||
}
|
||||
|
||||
{
|
||||
bdd const x_is_five = m.mk_eq(x, five);
|
||||
rational r;
|
||||
auto res = x_is_five.find_num(bits, r);
|
||||
SASSERT_EQ(res, find_result::singleton);
|
||||
SASSERT_EQ(r, rational(5));
|
||||
auto res = x_dom.find(x_is_five, r);
|
||||
SASSERT_EQ(res, find_t::singleton);
|
||||
SASSERT_EQ(r, 5);
|
||||
}
|
||||
}
|
||||
|
||||
static void test_bddv_addsub() {
|
||||
std::cout << "test_bddv_addsub\n";
|
||||
unsigned_vector bits;
|
||||
bits.push_back(0);
|
||||
bits.push_back(1);
|
||||
bits.push_back(2);
|
||||
bdd_manager m(bits.size());
|
||||
bddv const x = m.mk_var(bits);
|
||||
SASSERT_EQ(x - rational(3) == rational(2), x == rational(5));
|
||||
SASSERT_EQ(x + rational(3) == rational(5), x == rational(2));
|
||||
SASSERT_EQ(x - rational(3) == rational(6), x == rational(1));
|
||||
SASSERT_EQ(x + rational(3) == rational(2), x == rational(7));
|
||||
}
|
||||
|
||||
static void test_bddv_mul() {
|
||||
std::cout << "test_bddv_mul\n";
|
||||
unsigned const num_bits = 4;
|
||||
bdd_manager m(num_bits);
|
||||
|
||||
|
|
@ -191,112 +226,164 @@ namespace dd {
|
|||
bddv const five = m.mk_num(rational(5), num_bits);
|
||||
bddv const six = m.mk_num(rational(6), num_bits);
|
||||
|
||||
{
|
||||
// 5*x == 1 (mod 16) => x == 13 (mod 16)
|
||||
bdd const five_inv = x * five == one;
|
||||
rational r;
|
||||
auto res = five_inv.find_num(bits, r);
|
||||
SASSERT_EQ(res, find_result::singleton);
|
||||
SASSERT_EQ(r, rational(13));
|
||||
}
|
||||
// 5*x == 1 (mod 16) => x == 13 (mod 16)
|
||||
bdd const five_inv = x * five == one;
|
||||
SASSERT_EQ(five_inv, x == rational(13));
|
||||
|
||||
{
|
||||
// 6*x == 1 (mod 16) => no solution for x
|
||||
bdd const six_inv = x * six == one;
|
||||
rational r;
|
||||
auto res = six_inv.find_num(bits, r);
|
||||
SASSERT_EQ(res, find_result::empty);
|
||||
SASSERT(six_inv.is_false());
|
||||
}
|
||||
// 6*x == 1 (mod 16) => no solution for x
|
||||
bdd const six_inv = x * six == one;
|
||||
SASSERT(six_inv.is_false());
|
||||
|
||||
{
|
||||
// 6*x == 0 (mod 16) => x is either 0 or 8 (mod 16)
|
||||
bdd const b = six * x == zero;
|
||||
rational r;
|
||||
SASSERT(b.contains_num(rational(0), bits));
|
||||
SASSERT(b.contains_num(rational(8), bits));
|
||||
SASSERT((b && (x != rational(0)) && (x != rational(8))).is_false());
|
||||
SASSERT((b && (x != rational(0))) == (x == rational(8)));
|
||||
}
|
||||
// 6*x == 0 (mod 16) => x is either 0 or 8 (mod 16)
|
||||
bdd const b = six * x == zero;
|
||||
SASSERT_EQ(b, x == rational(0) || x == rational(8));
|
||||
SASSERT((b && (x != rational(0)) && (x != rational(8))).is_false());
|
||||
SASSERT_EQ(b && (x != rational(0)), x == rational(8));
|
||||
|
||||
SASSERT_EQ((x * zero).get_bits(), (x * rational(0)).get_bits());
|
||||
SASSERT_EQ((x * one).get_bits(), (x * rational(1)).get_bits());
|
||||
SASSERT_EQ((x * five).get_bits(), (x * rational(5)).get_bits());
|
||||
SASSERT_EQ((x * six).get_bits(), (x * rational(6)).get_bits());
|
||||
SASSERT_EQ((x * zero).bits(), (x * rational(0)).bits());
|
||||
SASSERT_EQ((x * one).bits(), (x * rational(1)).bits());
|
||||
SASSERT_EQ((x * five).bits(), (x * rational(5)).bits());
|
||||
SASSERT_EQ((x * six).bits(), (x * rational(6)).bits());
|
||||
}
|
||||
|
||||
static void test_int() {
|
||||
unsigned const w = 3; // bit width
|
||||
static void test_bddv_ule() {
|
||||
std::cout << "test_bddv_ule\n";
|
||||
unsigned const num_bits = 4;
|
||||
bdd_manager m(num_bits);
|
||||
|
||||
unsigned_vector bits;
|
||||
bits.push_back(0);
|
||||
bits.push_back(1);
|
||||
bits.push_back(2);
|
||||
bdd_manager m(w);
|
||||
bits.push_back(3);
|
||||
|
||||
bddv const x = m.mk_var(bits);
|
||||
bddv const three = m.mk_num(rational(3), num_bits);
|
||||
bddv const four = m.mk_num(rational(4), num_bits);
|
||||
bddv const five = m.mk_num(rational(5), num_bits);
|
||||
|
||||
SASSERT_EQ(x >= four && x < five, x == four);
|
||||
SASSERT_EQ(four <= x && x < five, x == four);
|
||||
SASSERT_EQ(three < x && x < five, x == four);
|
||||
SASSERT_EQ(three < x && x <= four, x == four);
|
||||
SASSERT_EQ(three <= x && x < five, x == four || x == three);
|
||||
}
|
||||
|
||||
static void test_fdd3() {
|
||||
std::cout << "test_fdd3\n";
|
||||
unsigned const w = 3; // bit width
|
||||
bdd_manager m(w);
|
||||
|
||||
fdd const x_dom(m, w);
|
||||
bddv const& x = x_dom.var();
|
||||
|
||||
// Encodes the values x satisfying a*x + b == 0 (mod 2^w) as BDD.
|
||||
auto mk_affine = [] (rational const& a, bddv const& x, rational const& b) {
|
||||
return (a*x + b == rational(0));
|
||||
auto mk_affine = [] (unsigned a, bddv const& x, unsigned b) {
|
||||
return (rational(a)*x + rational(b) == rational(0));
|
||||
};
|
||||
|
||||
vector<bdd> num;
|
||||
for (unsigned n = 0; n < (1<<w); ++n)
|
||||
num.push_back(m.mk_eq(x, rational(n)));
|
||||
num.push_back(x == rational(n));
|
||||
|
||||
for (unsigned k = 0; k < (1 << w); ++k) {
|
||||
for (unsigned n = 0; n < (1 << w); ++n) {
|
||||
SASSERT(num[k].contains_num(rational(n), bits) == (n == k));
|
||||
SASSERT(x_dom.contains(num[k], rational(n)) == (n == k));
|
||||
rational r;
|
||||
SASSERT_EQ((num[n] || num[k]).find_num(bits, r), (n == k) ? find_result::singleton : find_result::multiple);
|
||||
SASSERT_EQ(x_dom.find(num[n] || num[k], r), (n == k) ? find_t::singleton : find_t::multiple);
|
||||
SASSERT(r == n || r == k);
|
||||
}
|
||||
}
|
||||
|
||||
bdd s0127 = num[0] || num[1] || num[2] || num[7];
|
||||
SASSERT(s0127.contains_num(rational(0), bits));
|
||||
SASSERT(s0127.contains_num(rational(1), bits));
|
||||
SASSERT(s0127.contains_num(rational(2), bits));
|
||||
SASSERT(!s0127.contains_num(rational(3), bits));
|
||||
SASSERT(!s0127.contains_num(rational(4), bits));
|
||||
SASSERT(!s0127.contains_num(rational(5), bits));
|
||||
SASSERT(!s0127.contains_num(rational(6), bits));
|
||||
SASSERT(s0127.contains_num(rational(7), bits));
|
||||
SASSERT( x_dom.contains(s0127, rational(0)));
|
||||
SASSERT( x_dom.contains(s0127, rational(1)));
|
||||
SASSERT( x_dom.contains(s0127, rational(2)));
|
||||
SASSERT(!x_dom.contains(s0127, rational(3)));
|
||||
SASSERT(!x_dom.contains(s0127, rational(4)));
|
||||
SASSERT(!x_dom.contains(s0127, rational(5)));
|
||||
SASSERT(!x_dom.contains(s0127, rational(6)));
|
||||
SASSERT( x_dom.contains(s0127, rational(7)));
|
||||
|
||||
bdd s123 = num[1] || num[2] || num[3];
|
||||
SASSERT((s0127 && s123) == (num[1] || num[2]));
|
||||
|
||||
SASSERT(mk_affine(rational(0), x, rational(0)).is_true());
|
||||
SASSERT(mk_affine(rational(0), x, rational(1)).is_false());
|
||||
SASSERT(mk_affine(0, x, 0).is_true());
|
||||
SASSERT(mk_affine(0, x, 1).is_false());
|
||||
// 2*x == 0 (mod 2^3) has the solutions 0, 4
|
||||
SASSERT(mk_affine(rational(2), x, rational(0)) == (num[0] || num[4]));
|
||||
SASSERT(mk_affine(2, x, 0) == (num[0] || num[4]));
|
||||
|
||||
// 4*x + 2 == 0 (mod 2^3) has no solutions
|
||||
SASSERT(mk_affine(rational(4), x, rational(2)).is_false());
|
||||
SASSERT(mk_affine(4, x, 2).is_false());
|
||||
// 3*x + 2 == 0 (mod 2^3) has the unique solution 2
|
||||
SASSERT(mk_affine(rational(3), x, rational(2)) == num[2]);
|
||||
SASSERT(mk_affine(3, x, 2) == num[2]);
|
||||
// 2*x + 2 == 0 (mod 2^3) has the solutions 3, 7
|
||||
SASSERT(mk_affine(rational(2), x, rational(2)) == (num[3] || num[7]));
|
||||
|
||||
unsigned_vector bits4 = bits;
|
||||
bits4.push_back(10);
|
||||
bddv const x4 = m.mk_var(bits4);
|
||||
|
||||
// 12*x + 8 == 0 (mod 2^4) has the solutions 2, 6, 10, 14
|
||||
bdd expected = m.mk_eq(x4, rational(2)) || m.mk_eq(x4, rational(6)) || m.mk_eq(x4, rational(10)) || m.mk_eq(x4, rational(14));
|
||||
SASSERT(mk_affine(rational(12), x4, rational(8)) == expected);
|
||||
SASSERT(mk_affine(2, x, 2) == (num[3] || num[7]));
|
||||
}
|
||||
|
||||
static void test_fdd4() {
|
||||
std::cout << "test_fdd4\n";
|
||||
bdd_manager m(4);
|
||||
fdd const y_dom(m, 4);
|
||||
bddv const& y = y_dom.var();
|
||||
// 12*y + 8 == 0 (mod 2^4) has the solutions 2, 6, 10, 14
|
||||
bdd equation = rational(12) * y + rational(8) == rational(0);
|
||||
bdd expected = (y == rational(2)) || (y == rational(6)) || (y == rational(10)) || (y == rational(14));
|
||||
SASSERT(equation == expected);
|
||||
}
|
||||
|
||||
static void test_fdd_reorder() {
|
||||
std::cout << "test_fdd_reorder\n";
|
||||
bdd_manager m(4);
|
||||
fdd const x_dom(m, 4);
|
||||
bddv const& x = x_dom.var();
|
||||
|
||||
vector<bdd> num;
|
||||
for (unsigned n = 0; n < (1 << x_dom.num_bits()); ++n) {
|
||||
num.push_back(x == rational(n));
|
||||
SASSERT(x_dom.contains(num[n], rational(n)));
|
||||
rational r;
|
||||
SASSERT_EQ(x_dom.find(num[n], r), find_t::singleton);
|
||||
SASSERT_EQ(r, n);
|
||||
}
|
||||
|
||||
// need something extra to skew costs and trigger a reorder
|
||||
bdd atleast3 = (x >= rational(3));
|
||||
SASSERT(x_dom.contains(atleast3, rational(3)));
|
||||
|
||||
auto const old_levels = m.m_var2level;
|
||||
std::cout << "old levels: " << old_levels << "\n";
|
||||
m.gc();
|
||||
m.try_reorder();
|
||||
std::cout << "new levels: " << m.m_var2level << "\n";
|
||||
SASSERT(old_levels != m.m_var2level); // ensure that reorder actually did something.
|
||||
|
||||
// Should still give the correct answer after reordering
|
||||
for (unsigned n = 0; n < (1 << x_dom.num_bits()); ++n) {
|
||||
SASSERT(x_dom.contains(num[n], rational(n)));
|
||||
rational r;
|
||||
SASSERT_EQ(x_dom.find(num[n], r), find_t::singleton);
|
||||
SASSERT_EQ(r, n);
|
||||
}
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
}
|
||||
|
||||
void tst_bdd() {
|
||||
dd::test1();
|
||||
dd::test2();
|
||||
dd::test3();
|
||||
dd::test4();
|
||||
dd::test_xor();
|
||||
dd::test_bddv_ops_on_constants();
|
||||
dd::test_bddv_eqfind_small();
|
||||
dd::test_bddv_eqfind();
|
||||
dd::test_bddv_mul();
|
||||
dd::test_int();
|
||||
dd::test_bdd::test1();
|
||||
dd::test_bdd::test2();
|
||||
dd::test_bdd::test3();
|
||||
dd::test_bdd::test4();
|
||||
dd::test_bdd::test_xor();
|
||||
dd::test_bdd::test_bddv_ops_on_constants();
|
||||
dd::test_bdd::test_bddv_eqfind_small();
|
||||
dd::test_bdd::test_bddv_eqfind();
|
||||
dd::test_bdd::test_bddv_addsub();
|
||||
dd::test_bdd::test_bddv_mul();
|
||||
dd::test_bdd::test_bddv_ule();
|
||||
dd::test_bdd::test_fdd3();
|
||||
dd::test_bdd::test_fdd4();
|
||||
dd::test_bdd::test_fdd_reorder();
|
||||
}
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue