z3-z3-4.13.0.src.math.lp.var_eqs.h Maven / Gradle / Ivy
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/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
Abstract:
Author:
Nikolaj Bjorner (nbjorner)
Lev Nachmanson (levnach)
Revision History:
--*/
#pragma once
#include "util/union_find.h"
#include "math/lp/nla_defs.h"
#include "util/rational.h"
#include "math/lp/explanation.h"
#include "math/lp/incremental_vector.h"
namespace nla {
class eq_justification {
u_dependency* m_cs[4];
public:
eq_justification(std::initializer_list cs) {
int i = 0;
for (auto c: cs) {
m_cs[i++] = c;
}
for (; i < 4; i++) {
m_cs[i] = nullptr;
}
}
u_dependency* const* begin() const { return m_cs; }
u_dependency* const* end() const {
unsigned i = 0;
for (; i < 4 && m_cs[i]; ++i)
;
return m_cs + i;
}
};
template
class var_eqs {
struct eq_edge {
signed_var m_var;
eq_justification m_just;
eq_edge(signed_var v, eq_justification const& j): m_var(v), m_just(j) {}
};
struct var_frame {
signed_var m_var;
unsigned m_index;
var_frame(signed_var v, unsigned i): m_var(v), m_index(i) {}
};
struct stats {
unsigned m_num_explain_calls;
unsigned m_num_explains;
stats() { memset(this, 0, sizeof(*this)); }
};
T* m_merge_handler;
union_find m_uf;
lp::incremental_vector> m_trail;
vector> m_eqs; // signed_var.index() -> the edges adjacent to signed_var.index()
trail_stack m_stack;
mutable svector m_todo;
mutable bool_vector m_marked;
mutable unsigned_vector m_marked_trail;
mutable svector m_justtrail;
mutable stats m_stats;
public:
var_eqs(): m_merge_handler(nullptr), m_uf(*this), m_stack() {}
/**
\brief push a scope */
void push() {
m_trail.push_scope();
m_stack.push_scope();
}
/**
\brief pop n scopes
*/
void pop(unsigned n) {
unsigned old_sz = m_trail.peek_size(n);
for (unsigned i = m_trail.size(); i-- > old_sz; ) {
auto const& sv = m_trail[i];
m_eqs[sv.first.index()].pop_back();
m_eqs[sv.second.index()].pop_back();
m_eqs[(~sv.first).index()].pop_back();
m_eqs[(~sv.second).index()].pop_back();
}
m_trail.pop_scope(n);
m_stack.pop_scope(n); // this cass takes care of unmerging through union_find m_uf
}
/**
\brief merge equivalence classes for v1, v2 with justification j
*/
void merge(signed_var v1, signed_var v2, eq_justification const& j) {
if (v1 == v2)
return;
if (find(v1).var() == find(v2).var())
return;
unsigned max_i = std::max(v1.index(), v2.index()) + 2;
m_eqs.reserve(max_i);
while (m_uf.get_num_vars() <= max_i) m_uf.mk_var();
TRACE("nla_solver_mons", tout << v1 << " == " << v2 << " " << m_uf.find(v1.index()) << " == " << m_uf.find(v2.index()) << "\n";);
m_trail.push_back(std::make_pair(v1, v2));
m_uf.merge(v1.index(), v2.index());
m_uf.merge((~v1).index(), (~v2).index());
m_eqs[v1.index()].push_back(eq_edge(v2, j));
m_eqs[v2.index()].push_back(eq_edge(v1, j));
m_eqs[(~v1).index()].push_back(eq_edge(~v2, j));
m_eqs[(~v2).index()].push_back(eq_edge(~v1, j));
}
void merge_plus(lpvar v1, lpvar v2, eq_justification const& j) { merge(signed_var(v1, false), signed_var(v2, false), j); }
void merge_minus(lpvar v1, lpvar v2, eq_justification const& j) { merge(signed_var(v1, false), signed_var(v2, true), j); }
/**
\brief find equivalence class representative for v
*/
signed_var find(signed_var v) const {
if (v.index() >= m_uf.get_num_vars()) {
return v;
}
unsigned idx = m_uf.find(v.index());
return signed_var(idx);
}
inline signed_var find(lpvar j) const {
return find(signed_var(j, false));
}
inline bool is_root(lpvar j) const {
signed_var sv = find(signed_var(j, false));
return sv.var() == j;
}
inline bool is_root(svector v) const {
for (lpvar j : v)
if (!is_root(j))
return false;
return true;
}
bool vars_are_equiv(lpvar j, lpvar k) const {
signed_var sj = find(signed_var(j, false));
signed_var sk = find(signed_var(k, false));
return sj.var() == sk.var();
}
/**
\brief Returns eq_justifications for
\pre find(v1) == find(v2)
*/
void explain_dfs(signed_var v1, signed_var v2, lp::explanation& e) const {
SASSERT(find(v1) == find(v2));
if (v1 == v2) {
return;
}
m_todo.push_back(var_frame(v1, 0));
m_justtrail.reset();
m_marked.reserve(m_eqs.size(), false);
SASSERT(m_marked_trail.empty());
m_marked[v1.index()] = true;
m_marked_trail.push_back(v1.index());
while (true) {
SASSERT(!m_todo.empty());
var_frame& f = m_todo.back();
signed_var v = f.m_var;
if (v == v2) {
break;
}
auto const& next = m_eqs[v.index()];
bool seen_all = true;
unsigned sz = next.size();
for (unsigned i = f.m_index; seen_all && i < sz; ++i) {
eq_edge const& jv = next[i];
signed_var v3 = jv.m_var;
if (!m_marked[v3.index()]) {
seen_all = false;
f.m_index = i + 1;
m_todo.push_back(var_frame(v3, 0));
m_justtrail.push_back(jv.m_just);
m_marked_trail.push_back(v3.index());
m_marked[v3.index()] = true;
}
}
if (seen_all) {
m_todo.pop_back();
m_justtrail.pop_back();
}
}
for (eq_justification const& j : m_justtrail) {
explain_eq(j, e);
}
m_stats.m_num_explains += m_justtrail.size();
m_stats.m_num_explain_calls++;
m_todo.reset();
m_justtrail.reset();
for (unsigned idx : m_marked_trail) {
m_marked[idx] = false;
}
m_marked_trail.reset();
// IF_VERBOSE(2, verbose_stream() << (double)m_stats.m_num_explains / m_stats.m_num_explain_calls << "\n");
}
void explain_eq(eq_justification const& eq, lp::explanation& e) const {
u_dependency_manager dm;
unsigned_vector deps;
for (auto* dep : eq) {
deps.reset();
dm.linearize(dep, deps);
for (auto ci : deps)
e.push_back(ci);
}
}
void explain_bfs(signed_var v1, signed_var v2, lp::explanation& e) const {
SASSERT(find(v1) == find(v2));
if (v1 == v2) {
return;
}
m_todo.push_back(var_frame(v1, 0));
m_justtrail.push_back(eq_justification({}));
m_marked.reserve(m_eqs.size(), false);
SASSERT(m_marked_trail.empty());
m_marked[v1.index()] = true;
m_marked_trail.push_back(v1.index());
unsigned head = 0;
for (; ; ++head) {
var_frame& f = m_todo[head];
signed_var v = f.m_var;
if (v == v2) {
break;
}
auto const& next = m_eqs[v.index()];
unsigned sz = next.size();
for (unsigned i = sz; i-- > 0; ) {
eq_edge const& jv = next[i];
signed_var v3 = jv.m_var;
if (!m_marked[v3.index()]) {
m_todo.push_back(var_frame(v3, head));
m_justtrail.push_back(jv.m_just);
m_marked_trail.push_back(v3.index());
m_marked[v3.index()] = true;
}
}
}
while (head != 0) {
explain_eq(m_justtrail[head], e);
head = m_todo[head].m_index;
++m_stats.m_num_explains;
}
++m_stats.m_num_explain_calls;
m_todo.reset();
m_justtrail.reset();
for (unsigned idx : m_marked_trail) {
m_marked[idx] = false;
}
m_marked_trail.reset();
// IF_VERBOSE(2, verbose_stream() << (double)m_stats.m_num_explains / m_stats.m_num_explain_calls << "\n");
}
inline void explain(signed_var v1, signed_var v2, lp::explanation& e) const {
explain_bfs(v1, v2, e);
}
inline void explain(lpvar v1, lpvar v2, lp::explanation & e) const {
return explain(signed_var(v1, false), signed_var(v2, false), e);
}
inline void explain(lpvar j, lp::explanation& e) const {
signed_var s(j, false);
return explain(find(s), s, e);
}
// iterates over the class of lpvar(m_idx)
class iterator {
var_eqs& m_ve; // context.
unsigned m_idx; // index into a signed variable, same as union-find index
bool m_touched; // toggle between initial and final state
public:
iterator(var_eqs& ve, unsigned idx, bool t) : m_ve(ve), m_idx(idx), m_touched(t) {}
signed_var operator*() const {
return signed_var(m_idx);
}
iterator& operator++() { m_idx = m_ve.m_uf.next(m_idx); m_touched = true; return *this; }
bool operator==(iterator const& other) const { return m_idx == other.m_idx && m_touched == other.m_touched; }
bool operator!=(iterator const& other) const { return m_idx != other.m_idx || m_touched != other.m_touched; }
};
class eq_class {
var_eqs& m_ve;
signed_var m_v;
public:
eq_class(var_eqs& ve, signed_var v) : m_ve(ve), m_v(v) {}
iterator begin() { return iterator(m_ve, m_v.index(), false); }
iterator end() { return iterator(m_ve, m_v.index(), true); }
};
eq_class equiv_class(signed_var v) { return eq_class(*this, v); }
eq_class equiv_class(lpvar v) { return equiv_class(signed_var(v, false)); }
std::ostream& display(std::ostream& out) const {
m_uf.display(out);
unsigned idx = 0;
for (auto const& edges : m_eqs) {
if (!edges.empty()) {
auto v = signed_var(idx);
out << v << " root: " << find(v) << " : ";
for (auto const& jv : edges) {
out << jv.m_var << " ";
}
out << "\n";
}
++idx;
}
return out;
}
// union find event handlers
void set_merge_handler(T* mh) { m_merge_handler = mh; }
// this method is required by union_find
trail_stack & get_trail_stack() { return m_stack; }
void unmerge_eh(unsigned i, unsigned j) {
if (m_merge_handler) {
m_merge_handler->unmerge_eh(signed_var(i), signed_var(j));
}
}
void merge_eh(unsigned r2, unsigned r1, unsigned v2, unsigned v1) {
if (m_merge_handler) {
m_merge_handler->merge_eh(signed_var(r2), signed_var(r1),
signed_var(v2), signed_var(v1));
}
}
void after_merge_eh(unsigned r2, unsigned r1, unsigned v2, unsigned v1) {
if (m_merge_handler) {
m_merge_handler->after_merge_eh(signed_var(r2), signed_var(r1),
signed_var(v2), signed_var(v1));
}
}
}; // end of var_eqs
}