#include <cmath>
#include "ast/ast_pp.h"
#include "ast/ast_ll_pp.h"
#include "ast/sls/sls_arith_lookahead.h"
#include "ast/sls/sls_arith_base.h"
namespace sls {
template<typename num_t>
arith_lookahead<num_t>::arith_lookahead(arith_base<num_t>& a) :
ctx(a.ctx),
m(a.m),
a(a),
autil(m) {
}
template<typename num_t>
typename arith_lookahead<num_t>::bool_info& arith_lookahead<num_t>::get_bool_info(expr* e) {
unsigned id = e->get_id();
if (id >= m_bool_info.size())
m_bool_info.reserve(id + 1);
if (!m_bool_info[id])
m_bool_info.set(id, alloc(bool_info, a.m_config.paws_init));
return *m_bool_info[id];
}
template<typename num_t>
bool arith_lookahead<num_t>::get_bool_value_rec(expr* e) {
if (!is_app(e))
return ctx.get_value(e) == l_true;
if (is_uninterp(e))
return ctx.get_value(e) == l_true;
app* ap = to_app(e);
bool is_arith_eq = m.is_eq(e) && autil.is_int_real(ap->get_arg(0));
if (ap->get_family_id() == basic_family_id && !is_arith_eq)
return get_basic_bool_value(ap);
auto v = ctx.atom2bool_var(e);
if (v == sat::null_bool_var)
return false;
auto const* ineq = a.get_ineq(v);
if (!ineq)
return false;
return ineq->is_true();
}
template<typename num_t>
bool arith_lookahead<num_t>::get_bool_value(expr* e) {
auto& info = get_bool_info(e);
if (info.value != l_undef)
return info.value == l_true;
auto r = get_bool_value_rec(e);
info.value = to_lbool(r);
return r;
}
template<typename num_t>
bool arith_lookahead<num_t>::get_basic_bool_value(app* e) {
switch (e->get_decl_kind()) {
case OP_TRUE:
return true;
case OP_FALSE:
return false;
case OP_NOT:
return !get_bool_value(e->get_arg(0));
case OP_AND:
return all_of(*e, [&](expr* arg) { return get_bool_value(arg); });
case OP_OR:
return any_of(*e, [&](expr* arg) { return get_bool_value(arg); });
case OP_XOR:
return xor_of(*e, [&](expr* arg) { return get_bool_value(arg); });
case OP_IMPLIES:
return !get_bool_value(e->get_arg(0)) || get_bool_value(e->get_arg(1));
case OP_EQ:
if (m.is_bool(e->get_arg(0)))
return get_bool_value(e->get_arg(0)) == get_bool_value(e->get_arg(1));
return ctx.get_value(e->get_arg(0)) == ctx.get_value(e->get_arg(1));
case OP_DISTINCT:
return false;
case OP_ITE:
return get_bool_value(e->get_arg(0)) ? get_bool_value(e->get_arg(1)) : get_bool_value(e->get_arg(2));
default:
verbose_stream() << mk_pp(e, m) << "\n";
NOT_IMPLEMENTED_YET();
}
return false;
}
template<typename num_t>
double arith_lookahead<num_t>::new_score(expr* e) {
return new_score(e, true);
}
template<typename num_t>
double arith_lookahead<num_t>::new_score(expr* e, bool is_true) {
bool is_true_new = get_bool_value(e);
if (is_true == is_true_new)
return 1;
if (is_uninterp(e))
return 0;
if (m.is_true(e))
return is_true ? 1 : 0;
if (m.is_false(e))
return is_true ? 0 : 1;
expr* x, * y, * z;
if (m.is_not(e, x))
return new_score(x, !is_true);
if ((m.is_and(e) && is_true) || (m.is_or(e) && !is_true)) {
double score = 1;
for (auto arg : *to_app(e))
score = std::min(score, new_score(arg, is_true));
return score;
}
if ((m.is_and(e) && !is_true) || (m.is_or(e) && is_true)) {
double score = 0;
for (auto arg : *to_app(e))
score = std::max(score, new_score(arg, is_true));
return score;
}
if (m.is_iff(e, x, y)) {
auto v0 = get_bool_value(x);
auto v1 = get_bool_value(y);
return (is_true == (v0 == v1)) ? 1 : 0;
}
if (m.is_ite(e, x, y, z))
return get_bool_value(x) ? new_score(y, is_true) : new_score(z, is_true);
auto v = ctx.atom2bool_var(e);
if (v == sat::null_bool_var)
return 0;
auto const* ineq = a.get_ineq(v);
if (!ineq)
return 0;
auto const& args = ineq->m_args_value;
auto const& coeff = ineq->m_coeff;
auto value = args + coeff;
switch (ineq->m_op) {
case arith_base<num_t>::ineq_kind::LE:
if (is_true) {
if (value <= 0)
return 1.0;
}
else {
if (value > 0)
return 1.0;
value = -value + 1;
}
break;
case arith_base<num_t>::ineq_kind::LT:
if (is_true) {
if (value < 0)
return 1.0;
}
else {
if (value >= 0)
return 1.0;
value = -value;
}
break;
case arith_base<num_t>::ineq_kind::EQ:
if (is_true) {
if (value == 0)
return 1.0;
if (value < 0)
value = -value;
}
else {
if (value != 0)
return 1.0;
return 0.0;
}
break;
}
SASSERT(value > 0);
unsigned max_value = 1000;
if (value > max_value)
return 0.0;
auto d = value.get_double();
double score = 1.0 - ((d * d) / ((double)max_value * (double)max_value));
return score;
}
template<typename num_t>
void arith_lookahead<num_t>::rescore() {
m_top_score = 0;
m_is_root.reset();
for (auto a : ctx.input_assertions()) {
double score = new_score(a);
set_score(a, score);
m_top_score += score;
m_is_root.mark(a);
}
}
template<typename num_t>
void arith_lookahead<num_t>::recalibrate_weights() {
for (auto f : ctx.input_assertions()) {
if (ctx.rand(2047) < a.m_config.paws_sp) {
if (get_bool_value(f))
dec_weight(f);
}
else if (!get_bool_value(f))
inc_weight(f);
}
}
template<typename num_t>
void arith_lookahead<num_t>::dec_weight(expr* e) {
auto& i = get_bool_info(e);
i.weight = i.weight > a.m_config.paws_init ? i.weight - 1 : a.m_config.paws_init;
}
template<typename num_t>
void arith_lookahead<num_t>::insert_update_stack_rec(expr* t) {
m_min_depth = m_max_depth = get_depth(t);
insert_update_stack(t);
for (unsigned depth = m_max_depth; depth <= m_max_depth; ++depth) {
for (unsigned i = 0; i < m_update_stack[depth].size(); ++i) {
auto a = m_update_stack[depth][i];
for (auto p : ctx.parents(a)) {
insert_update_stack(p);
m_max_depth = std::max(m_max_depth, get_depth(p));
}
}
}
m_update_stack.reserve(m_max_depth + 1);
}
template<typename num_t>
double arith_lookahead<num_t>::lookahead(expr* t, bool update_score) {
ctx.rlimit().inc();
SASSERT(autil.is_int_real(t) || m.is_bool(t));
double score = m_top_score;
for (unsigned depth = m_min_depth; depth <= m_max_depth; ++depth) {
for (unsigned i = 0; i < m_update_stack[depth].size(); ++i) {
auto* a = m_update_stack[depth][i];
TRACE(arith_verbose, tout << "update " << mk_bounded_pp(a, m) << " depth: " << depth << "\n";);
if (t != a)
set_bool_value(a, get_bool_value_rec(a));
if (m_is_root.is_marked(a)) {
auto nscore = new_score(a);
score += get_weight(a) * (nscore - old_score(a));
if (update_score)
set_score(a, nscore);
}
}
}
return score;
}
template<typename num_t>
void arith_lookahead<num_t>::insert_update_stack(expr* t) {
unsigned depth = get_depth(t);
m_update_stack.reserve(depth + 1);
if (!m_in_update_stack.is_marked(t) && is_app(t)) {
m_in_update_stack.mark(t);
m_update_stack[depth].push_back(to_app(t));
}
}
template<typename num_t>
void arith_lookahead<num_t>::clear_update_stack() {
m_in_update_stack.reset();
m_update_stack.reserve(m_max_depth + 1);
for (unsigned i = m_min_depth; i <= m_max_depth; ++i)
m_update_stack[i].reset();
}
template<typename num_t>
void arith_lookahead<num_t>::lookahead_num(var_t v, num_t const& delta) {
num_t old_value = a.value(v);
expr* e = a.m_vars[v].m_expr;
if (m_last_expr != e) {
if (m_last_expr)
lookahead(m_last_expr, false);
clear_update_stack();
insert_update_stack_rec(e);
m_last_expr = e;
}
else if (a.m_last_delta == delta)
return;
a.m_last_delta = delta;
num_t new_value = old_value + delta;
if (!a.update_num(v, delta))
return;
auto score = lookahead(e, false);
TRACE(arith_verbose, tout << "lookahead " << v << " " << mk_bounded_pp(e, m) << " := " << delta + old_value << " " << score << " (" << m_best_score << ")\n";);
if (score > m_best_score) {
m_tabu_set = 0;
m_best_score = score;
m_best_value = new_value;
m_best_expr = e;
}
else if (a.m_config.allow_plateau && score == m_best_score && !in_tabu_set(e, new_value)) {
m_best_score = score;
m_best_expr = e;
m_best_value = new_value;
insert_tabu_set(e, new_value);
}
a.update_unchecked(v, old_value);
}
template<typename num_t>
bool arith_lookahead<num_t>::in_tabu_set(expr* e, num_t const& n) {
uint64_t h = hash_u_u(e->get_id(), n.hash());
return (m_tabu_set & (1ull << (h & 63ull))) != 0;
}
template<typename num_t>
void arith_lookahead<num_t>::insert_tabu_set(expr* e, num_t const& n) {
uint64_t h = hash_u_u(e->get_id(), n.hash());
m_tabu_set |= (1ull << (h & 63ull));
}
template<typename num_t>
void arith_lookahead<num_t>::lookahead_bool(expr* e) {
bool b = get_bool_value(e);
set_bool_value(e, !b);
insert_update_stack_rec(e);
auto score = lookahead(e, false);
if (score > m_best_score) {
m_tabu_set = 0;
m_best_score = score;
m_best_expr = e;
}
else if (a.m_config.allow_plateau && score == m_best_score && !in_tabu_set(e, num_t(1))) {
m_best_score = score;
m_best_expr = e;
insert_tabu_set(e, num_t(1));
}
set_bool_value(e, b);
lookahead(e, false);
clear_update_stack();
m_last_expr = nullptr;
}
template<typename num_t>
void arith_lookahead<num_t>::add_lookahead(bool_info& i, sat::bool_var bv) {
if (!i.fixable_atoms.contains(bv))
return;
if (m_fixed_atoms.contains(bv))
return;
auto* ineq = a.get_ineq(bv);
if (!ineq)
return;
num_t na, nb;
for (auto const& [x, nl] : ineq->m_nonlinear) {
if (!i.fixable_vars.contains(x))
continue;
if (a.is_fixed(x))
continue;
if (a.is_linear(x, nl, nb))
a.find_linear_moves(*ineq, x, nb);
else if (a.is_quadratic(x, nl, na, nb))
a.find_quadratic_moves(*ineq, x, na, nb, ineq->m_args_value);
else
;
}
m_fixed_atoms.insert(bv);
}
template<typename num_t>
void arith_lookahead<num_t>::add_lookahead(bool_info& i, expr* e) {
auto add_finite_domain = [&](var_t v) {
auto old_value = a.value(v);
for (auto const& n : a.m_vars[v].m_finite_domain)
a.add_update(v, n - old_value);
};
if (m.is_bool(e)) {
auto bv = ctx.atom2bool_var(e);
if (i.fixable_atoms.contains(bv))
lookahead_bool(e);
}
else if (autil.is_int_real(e)) {
auto v = a.mk_term(e);
auto& vi = a.m_vars[v];
if (false && !vi.m_finite_domain.empty()) {
add_finite_domain(v);
return;
}
for (auto bv : vi.m_bool_vars_of)
add_lookahead(i, bv);
}
}
template<typename num_t>
ptr_vector<expr> const& arith_lookahead<num_t>::get_fixable_exprs(expr* e) {
auto& i = get_bool_info(e);
if (!i.fixable_exprs.empty())
return i.fixable_exprs;
expr_mark visited;
ptr_buffer<expr> todo;
auto& tmp_set = a.m_tmp_set;
tmp_set.reset();
todo.push_back(e);
while (!todo.empty()) {
auto e = todo.back();
todo.pop_back();
if (visited.is_marked(e))
continue;
visited.mark(e);
if (m.is_xor(e) || m.is_and(e) || m.is_or(e) || m.is_implies(e) || m.is_iff(e) || m.is_ite(e) || m.is_not(e)) {
for (auto arg : *to_app(e))
todo.push_back(arg);
}
else {
auto bv = ctx.atom2bool_var(e);
if (bv == sat::null_bool_var)
continue;
if (is_uninterp(e)) {
if (!i.fixable_atoms.contains(bv)) {
i.fixable_atoms.push_back(bv);
i.fixable_exprs.push_back(e);
}
continue;
}
auto* ineq = a.get_ineq(bv);
if (!ineq)
continue;
i.fixable_atoms.push_back(bv);
buffer<var_t> vars;
for (auto& [v, occ] : ineq->m_nonlinear)
vars.push_back(v);
for (unsigned j = 0; j < vars.size(); ++j) {
auto v = vars[j];
if (tmp_set.contains(v))
continue;
if (a.is_add(v)) {
for (auto [c, w] : a.get_add(v).m_args)
vars.push_back(w);
}
else if (a.is_mul(v)) {
for (auto [w, p] : a.get_mul(v).m_monomial)
vars.push_back(w);
}
else {
i.fixable_exprs.push_back(a.m_vars[v].m_expr);
tmp_set.insert(v);
}
}
}
}
for (auto v : tmp_set)
i.fixable_vars.push_back(v);
return i.fixable_exprs;
}
template<typename num_t>
bool arith_lookahead<num_t>::apply_move(expr* f, ptr_vector<expr> const& vars, arith_move_type t) {
if (vars.empty())
return false;
auto& info = get_bool_info(f);
m_best_expr = nullptr;
m_best_score = m_top_score;
unsigned sz = vars.size();
unsigned start = ctx.rand();
a.m_updates.reset();
m_fixed_atoms.reset();
switch (t) {
case arith_move_type::random_update: {
for (unsigned i = 0; i < sz; ++i)
add_lookahead(info, vars[(start + i) % sz]);
if (a.m_updates.empty())
return false;
unsigned idx = ctx.rand(a.m_updates.size());
auto& [v, delta, score] = a.m_updates[idx];
m_best_expr = a.m_vars[v].m_expr;
if (false && !a.m_vars[v].m_finite_domain.empty())
m_best_value = a.m_vars[v].m_finite_domain[ctx.rand() % a.m_vars[v].m_finite_domain.size()];
else
m_best_value = a.value(v) + delta;
m_tabu_set = 0;
break;
}
case arith_move_type::hillclimb_plateau:
case arith_move_type::hillclimb: {
for (unsigned i = 0; i < sz; ++i)
add_lookahead(info, vars[(start + i) % sz]);
if (a.m_updates.empty())
return false;
std::stable_sort(a.m_updates.begin(), a.m_updates.end(), [](auto const& a, auto const& b) { return a.m_var < b.m_var || (a.m_var == b.m_var && a.m_delta < b.m_delta); });
m_last_expr = nullptr;
sz = a.m_updates.size();
flet<bool> _allow_plateau(a.m_config.allow_plateau, a.m_config.allow_plateau || t == arith_move_type::hillclimb_plateau);
for (unsigned i = 0; i < sz; ++i) {
auto const& [v, delta, score] = a.m_updates[(start + i) % a.m_updates.size()];
lookahead_num(v, delta);
}
if (m_last_expr) {
lookahead(m_last_expr, false);
clear_update_stack();
}
break;
}
case arith_move_type::random_inc_dec: {
auto e = vars[ctx.rand() % sz];
m_best_expr = e;
if (autil.is_int_real(e)) {
var_t v = a.mk_term(e);
auto& vi = a.m_vars[v];
if (!vi.m_finite_domain.empty())
m_best_value = vi.m_finite_domain[ctx.rand() % vi.m_finite_domain.size()];
else if (ctx.rand(2) == 0)
m_best_value = a.value(v) + 1;
else
m_best_value = a.value(v) - 1;
}
m_tabu_set = 0;
break;
}
}
if (m_best_expr) {
if (m.is_bool(m_best_expr))
set_bool_value(m_best_expr, !get_bool_value(m_best_expr));
else {
var_t v = a.mk_term(m_best_expr);
if (!a.update_num(v, m_best_value - a.value(v))) {
TRACE(arith,
tout << "could not move v" << v << " " << t << " " << mk_bounded_pp(m_best_expr, m) << " := " << a.value(v) << " " << m_top_score << "\n";
);
return false;
}
}
insert_update_stack_rec(m_best_expr);
m_top_score = lookahead(m_best_expr, true);
clear_update_stack();
}
CTRACE(arith, !m_best_expr, tout << "no move " << t << "\n";);
CTRACE(arith, m_best_expr && autil.is_int_real(m_best_expr), {
var_t v = a.mk_term(m_best_expr);
tout << t << " v" << v << " " << mk_bounded_pp(m_best_expr, m) << " := " << a.value(v) << " " << m_top_score << "\n";
});
return !!m_best_expr;
}
std::ostream& operator<<(std::ostream& out, arith_move_type mt) {
switch (mt) {
case arith_move_type::random_update: out << "random-update"; break;
case arith_move_type::hillclimb: out << "hillclimb"; break;
case arith_move_type::random_inc_dec: out << "random-inc-dec"; break;
case arith_move_type::hillclimb_plateau: out << "hillclimb-plateau"; break;
}
return out;
}
template<typename num_t>
void arith_lookahead<num_t>::check_restart() {
if (a.m_stats.m_steps % a.m_config.restart_base == 0) {
ucb_forget();
rescore();
}
if (a.m_stats.m_steps < a.m_config.restart_next)
return;
++a.m_stats.m_restarts;
a.m_config.restart_next = std::max(a.m_config.restart_next, a.m_stats.m_steps);
if (0x1 == (a.m_stats.m_restarts & 0x1))
a.m_config.restart_next += a.m_config.restart_base;
else
a.m_config.restart_next += (2 * (a.m_stats.m_restarts >> 1)) * a.m_config.restart_base;
rescore();
}
template<typename num_t>
void arith_lookahead<num_t>::ucb_forget() {
if (a.m_config.ucb_forget >= 1.0)
return;
for (auto f : ctx.input_assertions()) {
auto touched_old = get_touched(f);
auto touched_new = static_cast<unsigned>((touched_old - 1) * a.m_config.ucb_forget + 1);
set_touched(f, touched_new);
m_touched += touched_new - touched_old;
}
}
template<typename num_t>
void arith_lookahead<num_t>::initialize_bool_assignment() {
for (auto t : ctx.subterms())
if (m.is_bool(t))
set_bool_value(t, get_bool_value_rec(t));
#if 0#endif
}
template<typename num_t>
void arith_lookahead<num_t>::finalize_bool_assignment() {
for (unsigned v = ctx.num_bool_vars(); v-- > 0; ) {
auto a = ctx.atom(v);
if (!a)
continue;
if (get_bool_value(a) != ctx.is_true(v))
ctx.flip(v);
}
#if 0#endif
}
template<typename num_t>
void arith_lookahead<num_t>::search() {
initialize_bool_assignment();
rescore();
a.m_config.max_moves = a.m_stats.m_steps + a.m_config.max_moves_base;
TRACE(arith, tout << "search " << a.m_stats.m_steps << " " << a.m_config.max_moves << "\n";);
IF_VERBOSE(3, verbose_stream() << "lookahead-search steps:" << a.m_stats.m_steps << " max-moves:" << a.m_config.max_moves << "\n");
TRACE(arith, a.display(tout));
while (ctx.rlimit().inc() && a.m_stats.m_steps < a.m_config.max_moves) {
a.m_stats.m_steps++;
check_restart();
auto t = get_candidate_unsat();
if (!t)
break;
auto& vars = get_fixable_exprs(t);
if (vars.empty())
break;
if (ctx.rand(2047) < a.m_config.wp && apply_move(t, vars, arith_move_type::random_inc_dec))
continue;
if (apply_move(t, vars, arith_move_type::hillclimb))
continue;
if (apply_move(t, vars, arith_move_type::random_update))
recalibrate_weights();
}
if (a.m_stats.m_steps >= a.m_config.max_moves)
a.m_config.max_moves_base += 100;
finalize_bool_assignment();
}
template<typename num_t>
expr* arith_lookahead<num_t>::get_candidate_unsat() {
expr* e = nullptr;
if (a.m_config.ucb) {
double max = -1.0;
for (auto f : ctx.input_assertions()) {
if (get_bool_value(f))
continue;
auto const& vars = get_fixable_exprs(f);
if (vars.empty())
continue;
auto score = old_score(f);
auto q = score
+ a.m_config.ucb_constant * ::sqrt(log((double)m_touched) / get_touched(f))
+ a.m_config.ucb_noise * ctx.rand(512);
if (q > max)
max = q, e = f;
}
if (e) {
m_touched++;
inc_touched(e);
}
}
else {
unsigned n = 0;
for (auto a : ctx.input_assertions())
if (!get_bool_value(a) && !get_fixable_exprs(a).empty() && ctx.rand() % ++n == 0)
e = a;
}
m_last_atom = e;
CTRACE(arith, !e, tout << "no unsatisfiable candidate\n";);
CTRACE(arith, e,
tout << "select " << mk_bounded_pp(e, m) << " ";
for (auto v : get_fixable_exprs(e))
tout << mk_bounded_pp(v, m) << " ";
tout << "\n");
return e;
}
}
template class sls::arith_lookahead<checked_int64<true>>;
template class sls::arith_lookahead<rational>;