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https://github.com/Z3Prover/z3
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593 lines
19 KiB
C++
593 lines
19 KiB
C++
/*++
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Copyright (c) 2019 Microsoft Corporation
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Module Name:
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sat_ddfw.cpp
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Abstract:
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DDFW Local search module for clauses
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Author:
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Nikolaj Bjorner, Marijn Heule 2019-4-23
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Notes:
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http://www.ict.griffith.edu.au/~johnt/publications/CP2006raouf.pdf
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Todo:
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- rephase strategy
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- experiment with backoff schemes for restarts
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- parallel sync
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--*/
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#include "util/luby.h"
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#include "sat/sat_ddfw.h"
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#include "sat/sat_solver.h"
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#include "sat/sat_params.hpp"
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namespace sat {
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ddfw::~ddfw() {
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for (auto& ci : m_clauses) {
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m_alloc.del_clause(ci.m_clause);
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}
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}
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lbool ddfw::check(unsigned sz, literal const* assumptions, parallel* p) {
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init(sz, assumptions);
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flet<parallel*> _p(m_par, p);
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while (m_limit.inc() && m_min_sz > 0) {
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if (should_reinit_weights()) do_reinit_weights();
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else if (do_flip()) ;
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else if (should_restart()) do_restart();
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else if (should_parallel_sync()) do_parallel_sync();
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else shift_weights();
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}
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return m_min_sz == 0 ? l_true : l_undef;
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}
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void ddfw::log() {
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double sec = m_stopwatch.get_current_seconds();
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double kflips_per_sec = (m_flips - m_last_flips) / (1000.0 * sec);
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if (m_last_flips == 0) {
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IF_VERBOSE(0, verbose_stream() << "(sat.ddfw :unsat :models :kflips/sec :flips :restarts :reinits :unsat_vars :shifts";
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if (m_par) verbose_stream() << " :par";
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verbose_stream() << ")\n");
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}
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IF_VERBOSE(0, verbose_stream() << "(sat.ddfw "
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<< std::setw(07) << m_min_sz
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<< std::setw(07) << m_models.size()
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<< std::setw(10) << kflips_per_sec
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<< std::setw(10) << m_flips
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<< std::setw(10) << m_restart_count
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<< std::setw(10) << m_reinit_count
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<< std::setw(10) << m_unsat_vars.size()
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<< std::setw(10) << m_shifts;
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if (m_par) verbose_stream() << std::setw(10) << m_parsync_count;
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verbose_stream() << ")\n");
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m_stopwatch.start();
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m_last_flips = m_flips;
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}
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bool ddfw::do_flip() {
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bool_var v = pick_var();
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if (reward(v) > 0 || (reward(v) == 0 && m_rand(100) <= m_config.m_use_reward_zero_pct)) {
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flip(v);
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if (m_unsat.size() <= m_min_sz) save_best_values();
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return true;
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}
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return false;
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}
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bool_var ddfw::pick_var() {
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double sum_pos = 0;
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unsigned n = 1;
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bool_var v0 = null_bool_var;
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for (bool_var v : m_unsat_vars) {
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int r = reward(v);
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if (r > 0) {
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sum_pos += score(r);
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}
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else if (r == 0 && sum_pos == 0 && (m_rand() % (n++)) == 0) {
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v0 = v;
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}
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}
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if (sum_pos > 0) {
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double lim_pos = ((double) m_rand() / (1.0 + m_rand.max_value())) * sum_pos;
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for (bool_var v : m_unsat_vars) {
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int r = reward(v);
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if (r > 0) {
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lim_pos -= score(r);
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if (lim_pos <= 0) {
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if (m_par) update_reward_avg(v);
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return v;
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}
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}
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}
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}
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if (v0 != null_bool_var) {
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return v0;
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}
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return m_unsat_vars.elem_at(m_rand(m_unsat_vars.size()));
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}
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/**
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* TBD: map reward value to a score, possibly through an exponential function, such as
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* exp(-tau/r), where tau > 0
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*/
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double ddfw::mk_score(unsigned r) {
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return r;
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}
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void ddfw::add(unsigned n, literal const* c) {
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clause* cls = m_alloc.mk_clause(n, c, false);
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unsigned idx = m_clauses.size();
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m_clauses.push_back(clause_info(cls, m_config.m_init_clause_weight));
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for (literal lit : *cls) {
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m_use_list.reserve(2*(lit.var()+1));
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m_vars.reserve(lit.var()+1);
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m_use_list[lit.index()].push_back(idx);
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}
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}
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void ddfw::add(solver const& s) {
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for (auto& ci : m_clauses) {
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m_alloc.del_clause(ci.m_clause);
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}
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m_clauses.reset();
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m_use_list.reset();
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m_num_non_binary_clauses = 0;
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unsigned trail_sz = s.init_trail_size();
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for (unsigned i = 0; i < trail_sz; ++i) {
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add(1, s.m_trail.data() + i);
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}
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unsigned sz = s.m_watches.size();
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for (unsigned l_idx = 0; l_idx < sz; ++l_idx) {
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literal l1 = ~to_literal(l_idx);
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watch_list const & wlist = s.m_watches[l_idx];
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for (watched const& w : wlist) {
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if (!w.is_binary_non_learned_clause())
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continue;
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literal l2 = w.get_literal();
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if (l1.index() > l2.index())
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continue;
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literal ls[2] = { l1, l2 };
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add(2, ls);
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}
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}
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for (clause* c : s.m_clauses) {
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add(c->size(), c->begin());
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}
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m_num_non_binary_clauses = s.m_clauses.size();
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}
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void ddfw::add_assumptions() {
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for (unsigned i = 0; i < m_assumptions.size(); ++i) {
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add(1, m_assumptions.data() + i);
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}
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}
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void ddfw::init(unsigned sz, literal const* assumptions) {
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m_assumptions.reset();
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m_assumptions.append(sz, assumptions);
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add_assumptions();
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for (unsigned v = 0; v < num_vars(); ++v) {
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literal lit(v, false), nlit(v, true);
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value(v) = (m_rand() % 2) == 0; // m_use_list[lit.index()].size() >= m_use_list[nlit.index()].size();
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}
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init_clause_data();
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flatten_use_list();
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m_reinit_count = 0;
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m_reinit_next = m_config.m_reinit_base;
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m_restart_count = 0;
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m_restart_next = m_config.m_restart_base*2;
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m_parsync_count = 0;
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m_parsync_next = m_config.m_parsync_base;
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m_min_sz = m_unsat.size();
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m_flips = 0;
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m_last_flips = 0;
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m_shifts = 0;
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m_stopwatch.start();
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}
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void ddfw::reinit(solver& s) {
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add(s);
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add_assumptions();
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if (s.m_best_phase_size > 0) {
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for (unsigned v = 0; v < num_vars(); ++v) {
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value(v) = s.m_best_phase[v];
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reward(v) = 0;
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make_count(v) = 0;
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}
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}
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init_clause_data();
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flatten_use_list();
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}
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void ddfw::flatten_use_list() {
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m_use_list_index.reset();
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m_flat_use_list.reset();
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for (auto const& ul : m_use_list) {
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m_use_list_index.push_back(m_flat_use_list.size());
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m_flat_use_list.append(ul);
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}
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m_use_list_index.push_back(m_flat_use_list.size());
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}
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void ddfw::flip(bool_var v) {
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++m_flips;
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literal lit = literal(v, !value(v));
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literal nlit = ~lit;
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SASSERT(is_true(lit));
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for (unsigned cls_idx : use_list(*this, lit)) {
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clause_info& ci = m_clauses[cls_idx];
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ci.del(lit);
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unsigned w = ci.m_weight;
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// cls becomes false: flip any variable in clause to receive reward w
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switch (ci.m_num_trues) {
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case 0: {
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m_unsat.insert(cls_idx);
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clause const& c = get_clause(cls_idx);
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for (literal l : c) {
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inc_reward(l, w);
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inc_make(l);
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}
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inc_reward(lit, w);
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break;
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}
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case 1:
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dec_reward(to_literal(ci.m_trues), w);
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break;
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default:
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break;
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}
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}
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for (unsigned cls_idx : use_list(*this, nlit)) {
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clause_info& ci = m_clauses[cls_idx];
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unsigned w = ci.m_weight;
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// the clause used to have a single true (pivot) literal, now it has two.
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// Then the previous pivot is no longer penalized for flipping.
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switch (ci.m_num_trues) {
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case 0: {
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m_unsat.remove(cls_idx);
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clause const& c = get_clause(cls_idx);
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for (literal l : c) {
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dec_reward(l, w);
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dec_make(l);
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}
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dec_reward(nlit, w);
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break;
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}
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case 1:
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inc_reward(to_literal(ci.m_trues), w);
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break;
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default:
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break;
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}
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ci.add(nlit);
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}
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value(v) = !value(v);
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}
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bool ddfw::should_reinit_weights() {
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return m_flips >= m_reinit_next;
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}
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void ddfw::do_reinit_weights() {
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log();
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if (m_reinit_count % 2 == 0) {
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for (auto& ci : m_clauses) {
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ci.m_weight += 1;
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}
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}
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else {
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for (auto& ci : m_clauses) {
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if (ci.is_true()) {
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ci.m_weight = m_config.m_init_clause_weight;
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}
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else {
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ci.m_weight = m_config.m_init_clause_weight + 1;
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}
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}
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}
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init_clause_data();
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++m_reinit_count;
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m_reinit_next += m_reinit_count * m_config.m_reinit_base;
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}
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void ddfw::init_clause_data() {
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for (unsigned v = 0; v < num_vars(); ++v) {
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make_count(v) = 0;
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reward(v) = 0;
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}
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m_unsat_vars.reset();
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m_unsat.reset();
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unsigned sz = m_clauses.size();
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for (unsigned i = 0; i < sz; ++i) {
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auto& ci = m_clauses[i];
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clause const& c = get_clause(i);
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ci.m_trues = 0;
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ci.m_num_trues = 0;
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for (literal lit : c) {
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if (is_true(lit)) {
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ci.add(lit);
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}
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}
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switch (ci.m_num_trues) {
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case 0:
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for (literal lit : c) {
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inc_reward(lit, ci.m_weight);
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inc_make(lit);
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}
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m_unsat.insert(i);
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break;
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case 1:
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dec_reward(to_literal(ci.m_trues), ci.m_weight);
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break;
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default:
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break;
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}
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}
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}
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bool ddfw::should_restart() {
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return m_flips >= m_restart_next;
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}
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void ddfw::do_restart() {
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reinit_values();
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init_clause_data();
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m_restart_next += m_config.m_restart_base*get_luby(++m_restart_count);
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}
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/**
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\brief the higher the bias, the lower the probability to deviate from the value of the bias
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during a restart.
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bias = 0 -> flip truth value with 50%
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|bias| = 1 -> toss coin with 25% probability
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|bias| = 2 -> toss coin with 12.5% probability
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etc
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*/
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void ddfw::reinit_values() {
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for (unsigned i = 0; i < num_vars(); ++i) {
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int b = bias(i);
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if (0 == (m_rand() % (1 + abs(b)))) {
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value(i) = (m_rand() % 2) == 0;
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}
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else {
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value(i) = bias(i) > 0;
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}
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}
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}
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bool ddfw::should_parallel_sync() {
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return m_par != nullptr && m_flips >= m_parsync_next;
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}
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void ddfw::do_parallel_sync() {
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if (m_par->from_solver(*this)) {
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// Sum exp(xi) / exp(a) = Sum exp(xi - a)
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double max_avg = 0;
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for (unsigned v = 0; v < num_vars(); ++v) {
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max_avg = std::max(max_avg, (double)m_vars[v].m_reward_avg);
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}
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double sum = 0;
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for (unsigned v = 0; v < num_vars(); ++v) {
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sum += exp(m_config.m_itau * (m_vars[v].m_reward_avg - max_avg));
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}
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if (sum == 0) {
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sum = 0.01;
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}
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m_probs.reset();
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for (unsigned v = 0; v < num_vars(); ++v) {
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m_probs.push_back(exp(m_config.m_itau * (m_vars[v].m_reward_avg - max_avg)) / sum);
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}
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m_par->to_solver(*this);
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}
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++m_parsync_count;
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m_parsync_next *= 3;
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m_parsync_next /= 2;
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}
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void ddfw::save_best_values() {
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if (m_unsat.empty()) {
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m_model.reserve(num_vars());
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for (unsigned i = 0; i < num_vars(); ++i) {
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m_model[i] = to_lbool(value(i));
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}
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}
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if (m_unsat.size() < m_min_sz) {
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m_models.reset();
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// skip saving the first model.
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for (unsigned v = 0; v < num_vars(); ++v) {
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int& b = bias(v);
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if (abs(b) > 3) {
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b = b > 0 ? 3 : -3;
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}
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}
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}
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unsigned h = value_hash();
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if (!m_models.contains(h)) {
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for (unsigned v = 0; v < num_vars(); ++v) {
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bias(v) += value(v) ? 1 : -1;
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}
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m_models.insert(h);
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if (m_models.size() > m_config.m_max_num_models) {
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m_models.erase(*m_models.begin());
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}
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}
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m_min_sz = m_unsat.size();
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}
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unsigned ddfw::value_hash() const {
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unsigned s0 = 0, s1 = 0;
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for (auto const& vi : m_vars) {
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s0 += vi.m_value;
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s1 += s0;
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}
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return s1;
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}
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/**
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\brief Filter on whether to select a satisfied clause
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1. with some probability prefer higher weight to lesser weight.
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2. take into account number of trues ?
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3. select multiple clauses instead of just one per clause in unsat.
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*/
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bool ddfw::select_clause(unsigned max_weight, unsigned max_trues, clause_info const& cn, unsigned& n) {
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if (cn.m_num_trues == 0 || cn.m_weight < max_weight) {
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return false;
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}
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if (cn.m_weight > max_weight) {
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n = 2;
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return true;
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}
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return (m_rand() % (n++)) == 0;
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}
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unsigned ddfw::select_max_same_sign(unsigned cf_idx) {
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clause const& c = get_clause(cf_idx);
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unsigned max_weight = 2;
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unsigned max_trues = 0;
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unsigned cl = UINT_MAX; // clause pointer to same sign, max weight satisfied clause.
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unsigned n = 1;
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for (literal lit : c) {
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for (unsigned cn_idx : use_list(*this, lit)) {
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auto& cn = m_clauses[cn_idx];
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if (select_clause(max_weight, max_trues, cn, n)) {
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cl = cn_idx;
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max_weight = cn.m_weight;
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max_trues = cn.m_num_trues;
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}
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}
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}
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return cl;
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}
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void ddfw::shift_weights() {
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++m_shifts;
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for (unsigned cf_idx : m_unsat) {
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auto& cf = m_clauses[cf_idx];
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SASSERT(!cf.is_true());
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unsigned cn_idx = select_max_same_sign(cf_idx);
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while (cn_idx == UINT_MAX) {
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unsigned idx = (m_rand() * m_rand()) % m_clauses.size();
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auto & cn = m_clauses[idx];
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if (cn.is_true() && cn.m_weight >= 2) {
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cn_idx = idx;
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}
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}
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auto & cn = m_clauses[cn_idx];
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SASSERT(cn.is_true());
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unsigned wn = cn.m_weight;
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SASSERT(wn >= 2);
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unsigned inc = (wn > 2) ? 2 : 1;
|
|
SASSERT(wn - inc >= 1);
|
|
cf.m_weight += inc;
|
|
cn.m_weight -= inc;
|
|
for (literal lit : get_clause(cf_idx)) {
|
|
inc_reward(lit, inc);
|
|
}
|
|
if (cn.m_num_trues == 1) {
|
|
inc_reward(to_literal(cn.m_trues), inc);
|
|
}
|
|
}
|
|
// DEBUG_CODE(invariant(););
|
|
}
|
|
|
|
std::ostream& ddfw::display(std::ostream& out) const {
|
|
unsigned num_cls = m_clauses.size();
|
|
for (unsigned i = 0; i < num_cls; ++i) {
|
|
out << get_clause(i) << " ";
|
|
auto const& ci = m_clauses[i];
|
|
out << ci.m_num_trues << " " << ci.m_weight << "\n";
|
|
}
|
|
for (unsigned v = 0; v < num_vars(); ++v) {
|
|
out << v << ": " << reward(v) << "\n";
|
|
}
|
|
out << "unsat vars: ";
|
|
for (bool_var v : m_unsat_vars) {
|
|
out << v << " ";
|
|
}
|
|
out << "\n";
|
|
return out;
|
|
}
|
|
|
|
void ddfw::invariant() {
|
|
// every variable in unsat vars is in a false clause.
|
|
for (bool_var v : m_unsat_vars) {
|
|
bool found = false;
|
|
for (unsigned cl : m_unsat) {
|
|
for (literal lit : get_clause(cl)) {
|
|
if (lit.var() == v) { found = true; break; }
|
|
}
|
|
if (found) break;
|
|
}
|
|
if (!found) IF_VERBOSE(0, verbose_stream() << "unsat var not found: " << v << "\n"; );
|
|
VERIFY(found);
|
|
}
|
|
for (unsigned v = 0; v < num_vars(); ++v) {
|
|
int v_reward = 0;
|
|
literal lit(v, !value(v));
|
|
for (unsigned j : m_use_list[lit.index()]) {
|
|
clause_info const& ci = m_clauses[j];
|
|
if (ci.m_num_trues == 1) {
|
|
SASSERT(lit == to_literal(ci.m_trues));
|
|
v_reward -= ci.m_weight;
|
|
}
|
|
}
|
|
for (unsigned j : m_use_list[(~lit).index()]) {
|
|
clause_info const& ci = m_clauses[j];
|
|
if (ci.m_num_trues == 0) {
|
|
v_reward += ci.m_weight;
|
|
}
|
|
}
|
|
IF_VERBOSE(0, if (v_reward != reward(v)) verbose_stream() << v << " " << v_reward << " " << reward(v) << "\n");
|
|
SASSERT(reward(v) == v_reward);
|
|
}
|
|
DEBUG_CODE(
|
|
for (auto const& ci : m_clauses) {
|
|
SASSERT(ci.m_weight > 0);
|
|
}
|
|
for (unsigned i = 0; i < m_clauses.size(); ++i) {
|
|
bool found = false;
|
|
for (literal lit : get_clause(i)) {
|
|
if (is_true(lit)) found = true;
|
|
}
|
|
SASSERT(found == !m_unsat.contains(i));
|
|
}
|
|
// every variable in a false clause is in unsat vars
|
|
for (unsigned cl : m_unsat) {
|
|
for (literal lit : get_clause(cl)) {
|
|
SASSERT(m_unsat_vars.contains(lit.var()));
|
|
}
|
|
});
|
|
}
|
|
|
|
void ddfw::updt_params(params_ref const& _p) {
|
|
sat_params p(_p);
|
|
m_config.m_init_clause_weight = p.ddfw_init_clause_weight();
|
|
m_config.m_use_reward_zero_pct = p.ddfw_use_reward_pct();
|
|
m_config.m_reinit_base = p.ddfw_reinit_base();
|
|
m_config.m_restart_base = p.ddfw_restart_base();
|
|
}
|
|
|
|
}
|
|
|