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https://github.com/Z3Prover/z3
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na
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
2c6e6b1fdb
commit
914856b9ba
5 changed files with 216 additions and 63 deletions
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@ -23,13 +23,13 @@ Revision History:
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namespace dd {
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pdd_manager::pdd_manager(unsigned num_vars) {
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pdd_manager::pdd_manager(unsigned num_vars, semantics s) {
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m_spare_entry = nullptr;
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m_max_num_nodes = 1 << 24; // up to 16M nodes
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m_mark_level = 0;
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m_disable_gc = false;
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m_is_new_node = false;
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m_mod2_semantics = false;
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m_semantics = s;
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// add dummy nodes for operations, and 0, 1 pdds.
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for (unsigned i = 0; i < pdd_no_op; ++i) {
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@ -61,7 +61,7 @@ namespace dd {
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}
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pdd pdd_manager::add(pdd const& a, pdd const& b) { return pdd(apply(a.root, b.root, pdd_add_op), this); }
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pdd pdd_manager::sub(pdd const& a, pdd const& b) { pdd m(minus(b)); return pdd(apply(a.root, m.root, pdd_add_op), this); }
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pdd pdd_manager::sub(pdd const& a, pdd const& b) { return pdd(apply(a.root, b.root, pdd_sub_op), this); }
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pdd pdd_manager::mul(pdd const& a, pdd const& b) { return pdd(apply(a.root, b.root, pdd_mul_op), this); }
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pdd pdd_manager::reduce(pdd const& a, pdd const& b) { return pdd(apply(a.root, b.root, pdd_reduce_op), this); }
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pdd pdd_manager::mk_val(rational const& r) { return pdd(imk_val(r), this); }
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@ -71,6 +71,8 @@ namespace dd {
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pdd pdd_manager::one() { return pdd(one_pdd, this); }
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pdd pdd_manager::mk_or(pdd const& p, pdd const& q) { return p + q - (p*q); }
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pdd pdd_manager::mk_xor(pdd const& p, pdd const& q) { return (p*q*2) - p - q; }
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pdd pdd_manager::mk_not(pdd const& p) { return 1 - p; }
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pdd_manager::PDD pdd_manager::apply(PDD arg1, PDD arg2, pdd_op op) {
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bool first = true;
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@ -108,6 +110,11 @@ namespace dd {
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pdd_manager::PDD pdd_manager::apply_rec(PDD p, PDD q, pdd_op op) {
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switch (op) {
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case pdd_sub_op:
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if (is_zero(q)) return p;
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if (is_val(p) && is_val(q)) return imk_val(val(p) - val(q));
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if (m_semantics != mod2_e) break;
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op = pdd_add_op;
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case pdd_add_op:
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if (is_zero(p)) return q;
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if (is_zero(q)) return p;
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@ -163,6 +170,35 @@ namespace dd {
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npop = 1;
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}
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break;
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case pdd_sub_op:
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if (is_val(p)) {
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push(apply_rec(p, lo(q), op));
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r = make_node(level_q, read(1), hi(q));
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npop = 1;
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}
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else if (is_val(q)) {
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push(apply_rec(lo(p), q, op));
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r = make_node(level_p, read(1), hi(p));
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npop = 1;
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}
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else if (level_p == level_q) {
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push(apply_rec(lo(p), lo(q), op));
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push(apply_rec(hi(p), hi(q), op));
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r = make_node(level_p, read(2), read(1));
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}
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else if (level_p > level_q) {
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// x*hi(p) + (lo(p) - q)
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push(apply_rec(lo(p), q, op));
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r = make_node(level_p, read(1), hi(p));
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npop = 1;
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}
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else {
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// x*hi(q) + (p - lo(q))
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push(apply_rec(p, lo(q), op));
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r = make_node(level_q, read(1), hi(q));
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npop = 1;
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}
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break;
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case pdd_mul_op:
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SASSERT(!is_val(p));
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if (is_val(q)) {
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@ -171,17 +207,18 @@ namespace dd {
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r = make_node(level_p, read(2), read(1));
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}
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else if (level_p == level_q) {
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if (m_mod2_semantics) {
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if (m_semantics != free_e) {
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//
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// (xa+b)*(xc+d) mod2 == x(ac+bc+ad) + bd
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// == x((a+b)(c+d)+bd) + bd
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// (xa+b)*(xc+d) == x(ac+bc+ad) + bd
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// == x((a+b)(c+d)-bd) + bd
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// because x*x = x
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//
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push(apply_rec(lo(p), lo(q), pdd_mul_op));
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unsigned bd = read(1);
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push(apply_rec(hi(p), lo(p), pdd_add_op));
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push(apply_rec(hi(q), lo(q), pdd_add_op));
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push(apply_rec(read(1), read(2), pdd_mul_op));
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push(apply_rec(read(1), bd, pdd_add_op));
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push(apply_rec(read(1), bd, pdd_sub_op));
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r = make_node(level_p, bd, read(1));
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npop = 5;
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}
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@ -243,7 +280,7 @@ namespace dd {
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}
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pdd pdd_manager::minus(pdd const& a) {
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if (m_mod2_semantics) {
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if (m_semantics == mod2_e) {
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return a;
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}
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bool first = true;
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@ -264,7 +301,7 @@ namespace dd {
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}
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pdd_manager::PDD pdd_manager::minus_rec(PDD a) {
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SASSERT(!m_mod2_semantics);
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SASSERT(m_semantics != mod2_e);
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if (is_zero(a)) return zero_pdd;
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if (is_val(a)) return imk_val(-val(a));
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op_entry* e1 = pop_entry(a, a, pdd_minus_op);
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@ -358,7 +395,7 @@ namespace dd {
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while (!is_val(x)) p.push_back(var(x)), x = hi(x);
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pc = val(x);
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qc = val(y);
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if (!m_mod2_semantics && pc.is_int() && qc.is_int()) {
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if (m_semantics != mod2_e && pc.is_int() && qc.is_int()) {
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rational g = gcd(pc, qc);
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pc /= g;
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qc /= g;
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@ -461,6 +498,17 @@ namespace dd {
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return is_binary(p.root);
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}
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/**
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Determine if p is a monomial.
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*/
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bool pdd_manager::is_monomial(PDD p) {
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while (true) {
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if (is_val(p)) return true;
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if (!is_zero(lo(p))) return false;
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p = hi(p);
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}
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}
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/*
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\brief determine if v occurs as a leaf variable.
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*/
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@ -522,7 +570,7 @@ namespace dd {
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pdd_manager::PDD pdd_manager::imk_val(rational const& r) {
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if (r.is_zero()) return zero_pdd;
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if (r.is_one()) return one_pdd;
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if (m_mod2_semantics) return imk_val(mod(r, rational(2)));
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if (m_semantics == mod2_e) return imk_val(mod(r, rational(2)));
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const_info info;
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if (!m_mpq_table.find(r, info)) {
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init_value(info, r);
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@ -41,6 +41,9 @@ namespace dd {
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class pdd;
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class pdd_manager {
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public:
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enum semantics { free_e, mod2_e, zero_one_vars_e };
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private:
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friend pdd;
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typedef unsigned PDD;
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@ -52,10 +55,11 @@ namespace dd {
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enum pdd_op {
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pdd_add_op = 2,
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pdd_minus_op = 3,
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pdd_mul_op = 4,
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pdd_reduce_op = 5,
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pdd_no_op = 6
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pdd_sub_op = 3,
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pdd_minus_op = 4,
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pdd_mul_op = 5,
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pdd_reduce_op = 6,
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pdd_no_op = 7
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};
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struct node {
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@ -151,7 +155,7 @@ namespace dd {
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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_nodes;
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bool m_mod2_semantics;
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semantics m_semantics;
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unsigned_vector m_free_vars;
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unsigned_vector m_free_values;
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rational m_freeze_value;
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@ -230,10 +234,9 @@ namespace dd {
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struct mem_out {};
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pdd_manager(unsigned nodes);
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pdd_manager(unsigned nodes, semantics s = free_e);
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~pdd_manager();
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void set_mod2_semantics() { m_mod2_semantics = true; }
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void set_max_num_nodes(unsigned n) { m_max_num_nodes = n; }
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void set_level2var(unsigned_vector const& level2var);
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unsigned_vector const& get_level2var() const { return m_level2var; }
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@ -249,6 +252,8 @@ namespace dd {
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pdd mul(pdd const& a, pdd const& b);
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pdd mul(rational const& c, pdd const& b);
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pdd mk_or(pdd const& p, pdd const& q);
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pdd mk_xor(pdd const& p, pdd const& q);
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pdd mk_not(pdd const& p);
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pdd reduce(pdd const& a, pdd const& b);
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bool is_linear(PDD p);
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@ -257,6 +262,8 @@ namespace dd {
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bool is_binary(PDD p);
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bool is_binary(pdd const& p);
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bool is_monomial(PDD p);
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// create an spoly r if leading monomials of a and b overlap
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bool try_spoly(pdd const& a, pdd const& b, pdd& r);
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@ -293,22 +300,28 @@ namespace dd {
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bool is_zero() const { return m.is_zero(root); }
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bool is_linear() const { return m.is_linear(root); }
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bool is_binary() const { return m.is_binary(root); }
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bool is_monomial() const { return m.is_monomial(root); }
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bool var_is_leaf(unsigned v) const { return m.var_is_leaf(root, v); }
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pdd minus() const { return m.minus(*this); }
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pdd operator-() const { return m.minus(*this); }
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pdd operator+(pdd const& other) const { return m.add(*this, other); }
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pdd operator-(pdd const& other) const { return m.sub(*this, other); }
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pdd operator*(pdd const& other) const { return m.mul(*this, other); }
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pdd operator&(pdd const& other) const { return m.mul(*this, other); }
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pdd operator|(pdd const& other) const { return m.mk_or(*this, other); }
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pdd operator^(pdd const& other) const { return m.mk_xor(*this, other); }
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pdd operator*(rational const& other) const { return m.mul(other, *this); }
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pdd operator+(rational const& other) const { return m.add(other, *this); }
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pdd operator|(pdd const& other) const { return m.mk_or(*this, other); }
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pdd operator~() const { return m.mk_not(*this); }
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pdd rev_sub(rational const& r) const { return m.sub(m.mk_val(r), *this); }
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pdd reduce(pdd const& other) const { return m.reduce(*this, other); }
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bool different_leading_term(pdd const& other) const { return m.different_leading_term(*this, other); }
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std::ostream& display(std::ostream& out) const { return m.display(out, *this); }
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bool operator==(pdd const& other) const { return root == other.root; }
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bool operator!=(pdd const& other) const { return root != other.root; }
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bool operator<(pdd const& b) const { return m.lt(*this, b); }
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bool operator<(pdd const& other) const { return m.lt(*this, other); }
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unsigned dag_size() const { return m.dag_size(*this); }
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double tree_size() const { return m.tree_size(*this); }
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@ -323,16 +336,17 @@ namespace dd {
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inline pdd operator+(int x, pdd const& b) { return b + rational(x); }
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inline pdd operator+(pdd const& b, int x) { return b + rational(x); }
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inline pdd operator-(rational const& r, pdd const& b) { return r + b.minus(); }
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inline pdd operator-(rational const& r, pdd const& b) { return b.rev_sub(r); }
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inline pdd operator-(int x, pdd const& b) { return rational(x) - b; }
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inline pdd operator-(pdd const& b, int x) { return b + (-rational(x)); }
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inline pdd& operator&=(pdd & p, pdd const& q) { p = p & q; return p; }
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inline pdd& operator^=(pdd & p, pdd const& q) { p = p ^ q; return p; }
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inline pdd& operator*=(pdd & p, pdd const& q) { p = p * q; return p; }
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inline pdd& operator|=(pdd & p, pdd const& q) { p = p | q; return p; }
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inline pdd& operator-=(pdd & p, pdd const& q) { p = p - q; return p; }
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inline pdd& operator+=(pdd & p, pdd const& q) { p = p + q; return p; }
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std::ostream& operator<<(std::ostream& out, pdd const& b);
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}
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