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https://github.com/Z3Prover/z3
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384 lines
16 KiB
C++
384 lines
16 KiB
C++
/*++
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Copyright (c) 2017 Microsoft Corporation
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Module Name:
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dd_bdd
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Abstract:
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Simple BDD package modeled after BuDDy, which is modeled after CUDD.
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Author:
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Nikolaj Bjorner (nbjorner) 2017-10-13
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Revision History:
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--*/
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#pragma once
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#include "util/vector.h"
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#include "util/map.h"
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#include "util/small_object_allocator.h"
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#include "util/rational.h"
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namespace dd {
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class bdd;
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class bddv;
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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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const BDD null_bdd = UINT_MAX;
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enum bdd_op {
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bdd_and_op = 2,
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bdd_or_op = 3,
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bdd_xor_op = 4,
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bdd_not_op = 5,
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bdd_and_proj_op = 6,
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bdd_or_proj_op = 7,
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bdd_cofactor_op = 8,
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bdd_no_op = 9,
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};
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struct bdd_node {
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bdd_node(unsigned level, BDD lo, BDD hi):
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m_refcount(0),
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m_level(level),
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m_lo(lo),
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m_hi(hi),
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m_index(0)
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{}
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bdd_node(): m_refcount(0), m_level(0), m_lo(0), m_hi(0), m_index(0) {}
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unsigned m_refcount : 10;
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unsigned m_level : 22;
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BDD m_lo;
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BDD m_hi;
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unsigned m_index;
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unsigned hash() const { return mk_mix(m_level, m_lo, m_hi); }
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bool is_internal() const { return m_lo == 0 && m_hi == 0; }
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void set_internal() { m_lo = 0; m_hi = 0; }
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};
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enum cost_metric {
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cnf_cost,
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dnf_cost,
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bdd_cost
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};
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struct hash_node {
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unsigned operator()(bdd_node const& n) const { return n.hash(); }
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};
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struct eq_node {
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bool operator()(bdd_node const& a, bdd_node const& b) const {
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return a.m_lo == b.m_lo && a.m_hi == b.m_hi && a.m_level == b.m_level;
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}
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};
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typedef hashtable<bdd_node, hash_node, eq_node> node_table;
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struct op_entry {
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op_entry(BDD l, BDD r, BDD op):
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m_bdd1(l),
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m_bdd2(r),
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m_op(op),
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m_result(0)
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{}
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BDD m_bdd1;
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BDD m_bdd2;
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BDD m_op;
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BDD m_result;
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unsigned hash() const { return mk_mix(m_bdd1, m_bdd2, m_op); }
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};
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struct hash_entry {
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unsigned operator()(op_entry* e) const { return e->hash(); }
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};
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struct eq_entry {
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bool operator()(op_entry * a, op_entry * b) const {
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return a->m_bdd1 == b->m_bdd2 && a->m_bdd2 == b->m_bdd2 && a->m_op == b->m_op;
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}
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};
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typedef ptr_hashtable<op_entry, hash_entry, eq_entry> op_table;
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svector<bdd_node> m_nodes;
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op_table m_op_cache;
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node_table m_node_table;
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unsigned_vector m_apply_const;
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svector<BDD> m_bdd_stack;
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op_entry* m_spare_entry;
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svector<BDD> m_var2bdd;
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unsigned_vector m_var2level, m_level2var;
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unsigned_vector m_free_nodes;
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small_object_allocator m_alloc;
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mutable svector<unsigned> m_mark;
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mutable unsigned m_mark_level;
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mutable svector<double> m_count;
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mutable svector<BDD> m_todo;
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bool m_disable_gc;
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bool m_is_new_node;
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unsigned m_max_num_bdd_nodes;
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unsigned_vector m_S, m_T, m_to_free; // used for reordering
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vector<unsigned_vector> m_level2nodes;
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unsigned_vector m_reorder_rc;
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cost_metric m_cost_metric;
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BDD m_cost_bdd;
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BDD make_node(unsigned level, BDD l, BDD r);
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bool is_new_node() const { return m_is_new_node; }
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BDD apply_const(BDD a, BDD b, bdd_op op);
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BDD apply(BDD arg1, BDD arg2, bdd_op op);
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BDD mk_quant(unsigned n, unsigned const* vars, BDD b, bdd_op op);
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BDD apply_rec(BDD arg1, BDD arg2, bdd_op op);
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BDD mk_not_rec(BDD b);
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BDD mk_ite_rec(BDD a, BDD b, BDD c);
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BDD mk_quant_rec(unsigned lvl, BDD b, bdd_op op);
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BDD mk_cofactor_rec(BDD a, BDD b);
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void push(BDD b);
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void pop(unsigned num_scopes);
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BDD read(unsigned index);
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op_entry* pop_entry(BDD l, BDD r, BDD op);
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void push_entry(op_entry* e);
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bool check_result(op_entry*& e1, op_entry const* e2, BDD a, BDD b, BDD c);
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double count(BDD b, unsigned z);
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void alloc_free_nodes(unsigned n);
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void init_mark();
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void set_mark(unsigned i) { m_mark[i] = m_mark_level; }
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bool is_marked(unsigned i) { return m_mark[i] == m_mark_level; }
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void init_reorder();
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void reorder_incref(unsigned n);
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void reorder_decref(unsigned n);
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void sift_up(unsigned level);
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void sift_var(unsigned v);
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double current_cost();
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bool is_bad_cost(double new_cost, double best_cost) const;
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static const BDD false_bdd = 0;
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static const BDD true_bdd = 1;
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static const unsigned max_rc = (1 << 10) - 1;
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inline bool is_true(BDD b) const { return b == true_bdd; }
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inline bool is_false(BDD b) const { return b == false_bdd; }
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inline bool is_const(BDD b) const { return b <= 1; }
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inline unsigned level(BDD b) const { return m_nodes[b].m_level; }
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inline unsigned var(BDD b) const { return m_level2var[level(b)]; }
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inline BDD lo(BDD b) const { return m_nodes[b].m_lo; }
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inline BDD hi(BDD b) const { return m_nodes[b].m_hi; }
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inline void inc_ref(BDD b) { if (m_nodes[b].m_refcount != max_rc) m_nodes[b].m_refcount++; VERIFY(!m_free_nodes.contains(b)); }
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inline void dec_ref(BDD b) { if (m_nodes[b].m_refcount != max_rc) m_nodes[b].m_refcount--; VERIFY(!m_free_nodes.contains(b)); }
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inline BDD level2bdd(unsigned l) const { return m_var2bdd[m_level2var[l]]; }
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double dnf_size(BDD b) { return count(b, 0); }
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double cnf_size(BDD b) { return count(b, 1); }
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unsigned bdd_size(bdd const& b);
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bdd mk_not(bdd b);
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bdd mk_and(bdd const& a, bdd const& b);
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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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bdd mk_cofactor(bdd const& a, bdd const& b);
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void reserve_var(unsigned v);
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bool well_formed();
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struct scoped_push {
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bdd_manager& m;
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unsigned m_size;
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scoped_push(bdd_manager& m) :m(m), m_size(m.m_bdd_stack.size()) {}
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~scoped_push() { m.m_bdd_stack.shrink(m_size); }
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};
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bool_vector mk_usub(bool_vector const& b);
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public:
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struct mem_out {};
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bdd_manager(unsigned num_vars);
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~bdd_manager();
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void set_max_num_nodes(unsigned n) { m_max_num_bdd_nodes = n; }
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bdd mk_var(unsigned i);
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bdd mk_nvar(unsigned i);
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bdd mk_true();
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bdd mk_false();
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bdd mk_exists(unsigned n, unsigned const* vars, bdd const & b);
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bdd mk_forall(unsigned n, unsigned const* vars, bdd const & b);
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bdd mk_exists(unsigned v, bdd const& b);
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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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* - 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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bdd mk_ugt(bddv const& a, bddv const& b); // { return mk_ult(b, a); }
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bdd mk_sle(bddv const& a, bddv const& b);
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bdd mk_sge(bddv const& a, bddv const& b); // { return mk_sle(b, a); }
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bdd mk_slt(bddv const& a, bddv const& b); // { return mk_sle(a, b) && !mk_eq(a, b); }
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bdd mk_sgt(bddv const& a, bddv const& b); // { return mk_slt(b, a); }
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bdd mk_eq(bddv const& a, bddv const& b);
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bdd mk_eq(bddv const& a, rational const& v);
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bdd mk_eq(unsigned_vector const& vars, rational const& v);
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bddv mk_num(rational const& n, unsigned num_bits);
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bddv mk_ones(unsigned num_bits);
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bddv mk_zero(unsigned num_bits);
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bddv mk_var(unsigned num_bits, unsigned const* vars);
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bddv mk_var(unsigned_vector const& vars);
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bddv mk_add(bddv const& a, bddv const& b);
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bddv mk_add(bddv const& a, std::function<bdd(unsigned)>& get_bit);
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bddv mk_sub(bddv const& a, bddv const& b);
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bddv mk_usub(bddv const& a);
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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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bddv mk_concat(bddv const& a, bddv const& b);
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void mk_quot_rem(bddv const& a, bddv const& b, bddv& quot, bddv& rem);
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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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void gc();
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void try_reorder();
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void try_cnf_reorder(bdd const& b);
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};
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class bdd {
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friend class bdd_manager;
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unsigned root;
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bdd_manager* m;
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bdd(unsigned root, bdd_manager* m): root(root), m(m) { m->inc_ref(root); }
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public:
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bdd(bdd const & other): root(other.root), m(other.m) { m->inc_ref(root); }
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bdd(bdd && other) noexcept : root(0), m(other.m) { std::swap(root, other.root); }
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bdd& operator=(bdd const& other);
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~bdd() { m->dec_ref(root); }
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bdd lo() const { return bdd(m->lo(root), m); }
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bdd hi() const { return bdd(m->hi(root), m); }
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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_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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bdd operator||(bdd const& other) const { return m->mk_or(*this, other); }
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bdd operator^(bdd const& other) const { return m->mk_xor(*this, other); }
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bdd operator|=(bdd const& other) { return *this = *this || other; }
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bdd operator&=(bdd const& other) { return *this = *this && other; }
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bdd cofactor(bdd const& cube) { return m->mk_cofactor(*this, cube); }
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std::ostream& display(std::ostream& out) const { return m->display(out, *this); }
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bool operator==(bdd const& other) const { return root == other.root; }
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bool operator!=(bdd const& other) const { return root != other.root; }
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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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};
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std::ostream& operator<<(std::ostream& out, bdd const& b);
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class bddv {
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friend bdd_manager;
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vector<bdd> m_bits;
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bdd_manager* m;
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bddv(vector<bdd> const& 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); }
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bdd const& operator[](unsigned i) const { return m_bits[i]; }
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bdd& operator[](unsigned i) { return m_bits[i]; }
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void push_back(bdd const& a) { m_bits.push_back(a); }
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void push_back(bdd&& a) { m_bits.push_back(std::move(a)); }
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void shl();
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void shr();
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public:
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unsigned size() const { return m_bits.size(); }
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vector<bdd> const& bits() const { return m_bits; }
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/* unsigned comparison operators */
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bdd operator<=(bddv const& other) const { return m->mk_ule(*this, other); } ///< unsigned comparison
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bdd operator>=(bddv const& other) const { return m->mk_uge(*this, other); } ///< unsigned comparison
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bdd operator< (bddv const& other) const { return m->mk_ult(*this, other); } ///< unsigned comparison
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bdd operator> (bddv const& other) const { return m->mk_ugt(*this, other); } ///< unsigned comparison
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bdd operator<=(rational const& other) const { return m->mk_ule(*this, m->mk_num(other, size())); } ///< unsigned comparison
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bdd operator>=(rational const& other) const { return m->mk_uge(*this, m->mk_num(other, size())); } ///< unsigned comparison
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bdd operator< (rational const& other) const { return m->mk_ult(*this, m->mk_num(other, size())); } ///< unsigned comparison
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bdd operator> (rational const& other) const { return m->mk_ugt(*this, m->mk_num(other, size())); } ///< unsigned comparison
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/* signed comparison operators */
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bdd sle(bddv const& other) const { return m->mk_sle(*this, other); }
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bdd sge(bddv const& other) const { return m->mk_sge(*this, other); }
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bdd slt(bddv const& other) const { return m->mk_slt(*this, other); }
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bdd sgt(bddv const& other) const { return m->mk_sgt(*this, other); }
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bdd all0() const;
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bdd all1() const;
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bdd operator==(bddv const& other) const { return m->mk_eq(*this, other); }
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bdd operator==(rational const& other) const { return m->mk_eq(*this, other); }
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bdd operator!=(bddv const& other) const { return !m->mk_eq(*this, other); }
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bdd operator!=(rational const& other) const { return !m->mk_eq(*this, other); }
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bddv operator+(bddv const& other) const { return m->mk_add(*this, other); }
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bddv operator+(rational const& other) const { return m->mk_add(*this, m->mk_num(other, size())); }
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bddv operator-(bddv const& other) const { return m->mk_sub(*this, other); }
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bddv operator-(rational const& other) const { return m->mk_sub(*this, m->mk_num(other, size())); }
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bddv rev_sub(rational const& other) const { return m->mk_sub(m->mk_num(other, size()), *this); }
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bddv operator*(bddv const& other) const { return m->mk_mul(*this, other); }
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bddv operator*(rational const& other) const { return m->mk_mul(*this, other); }
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bddv operator*(bool_vector const& other) const { return m->mk_mul(*this, other); }
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bddv append(bddv const& other) const { return m->mk_concat(*this, other); }
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void quot_rem(bddv const& divisor, bddv& quot, bddv& rem) const { m->mk_quot_rem(*this, divisor, quot, rem); }
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bool is_const() const { return m->is_constv(*this); }
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rational to_val() const { return m->to_val(*this); }
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};
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inline bdd operator<=(rational const& r, bddv const& a) { return a >= r; } ///< unsigned comparison
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inline bdd operator>=(rational const& r, bddv const& a) { return a <= r; } ///< unsigned comparison
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inline bdd operator< (rational const& r, bddv const& a) { return a > r; } ///< unsigned comparison
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inline bdd operator> (rational const& r, bddv const& a) { return a < r; } ///< unsigned comparison
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inline bdd operator==(rational const& r, bddv const& a) { return a == r; }
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inline bdd operator!=(rational const& r, bddv const& a) { return a != r; }
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inline bddv operator*(rational const& r, bddv const& a) { return a * r; }
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inline bddv operator+(rational const& r, bddv const& a) { return a + r; }
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inline bddv operator-(rational const& r, bddv const& a) { return a.rev_sub(r); }
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inline bdd operator<=(int i, bddv const& a) { return a >= rational(i); }
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inline bdd operator<=(bddv const& a, int i) { return a <= rational(i); }
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}
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