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dev branch for simplification

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2024-05-07 10:56:58 -07:00
parent 8f4ffc7caf
commit 1589e7dafa
6 changed files with 459 additions and 112 deletions
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8
src/math/lp/lp_settings.h
View file

@ -128,8 +128,12 @@ struct statistics {
unsigned m_grobner_conflicts;
unsigned m_offset_eqs;
unsigned m_fixed_eqs;
::statistics m_st;
statistics() { reset(); }
void reset() { memset(this, 0, sizeof(*this)); }
void reset() {
memset(this, 0, sizeof(*this));
m_st.reset();
}
void collect_statistics(::statistics& st) const {
st.update("arith-factorizations", m_num_factorizations);
st.update("arith-make-feasible", m_make_feasible);
@ -157,7 +161,7 @@ struct statistics {
st.update("arith-nla-lemmas", m_nla_lemmas);
st.update("arith-nra-calls", m_nra_calls);
st.update("arith-bounds-improvements", m_nla_bounds_improvements);
st.copy(m_st);
}
};

11
src/math/lp/nra_solver.cpp
View file

@ -34,7 +34,7 @@ struct solver::imp {
scoped_ptr<scoped_anum_vector> m_values; // values provided by LRA solver
scoped_ptr<scoped_anum> m_tmp1, m_tmp2;
nla::core& m_nla_core;
imp(lp::lar_solver& s, reslimit& lim, params_ref const& p, nla::core& nla_core):
lra(s),
m_limit(lim),
@ -180,6 +180,7 @@ struct solver::imp {
}
lbool r = l_undef;
statistics& st = m_nla_core.lp_settings().stats().m_st;
try {
r = m_nlsat->check();
}
@ -188,9 +189,11 @@ struct solver::imp {
r = l_undef;
}
else {
m_nlsat->collect_statistics(st);
throw;
}
}
m_nlsat->collect_statistics(st);
TRACE("nra",
m_nlsat->display(tout << r << "\n");
display(tout);
@ -234,6 +237,7 @@ struct solver::imp {
return r;
}
void add_monic_eq_bound(mon_eq const& m) {
if (!lra.column_has_lower_bound(m.var()) &&
!lra.column_has_upper_bound(m.var()))
@ -374,6 +378,7 @@ struct solver::imp {
}
lbool r = l_undef;
statistics& st = m_nla_core.lp_settings().stats().m_st;
try {
r = m_nlsat->check();
}
@ -382,9 +387,11 @@ struct solver::imp {
r = l_undef;
}
else {
m_nlsat->collect_statistics(st);
throw;
}
}
m_nlsat->collect_statistics(st);
switch (r) {
case l_true:
@ -665,7 +672,7 @@ nlsat::anum_manager& solver::am() {
scoped_anum& solver::tmp1() { return m_imp->tmp1(); }
scoped_anum& solver::tmp2() { return m_imp->tmp2(); }
void solver::updt_params(params_ref& p) {
m_imp->updt_params(p);

114
src/math/polynomial/polynomial.cpp
View file

@ -2504,30 +2504,124 @@ namespace polynomial {
return p;
}
void gcd_simplify(polynomial * p) {
if (m_manager.finite()) return;
void gcd_simplify(polynomial_ref& p, manager::ineq_type t) {
auto& m = m_manager.m();
unsigned sz = p->size();
if (sz == 0)
return;
unsigned g = 0;
for (unsigned i = 0; i < sz; i++) {
for (unsigned i = 0; i < sz; i++) {
if (!m.is_int(p->a(i))) {
gcd_simplify_slow(p, t);
return;
}
if (t != EQ && is_unit(p->m(i)))
continue;
int j = m.get_int(p->a(i));
if (j == INT_MIN || j == 1 || j == -1)
if (j == INT_MIN) {
gcd_simplify_slow(p, t);
return;
}
if (j == 1 || j == -1)
return;
g = u_gcd(abs(j), g);
if (g == 1)
return;
}
scoped_mpz r(m), gg(m);
scoped_mpz gg(m);
m.set(gg, g);
for (unsigned i = 0; i < sz; ++i) {
m.div_gcd(p->a(i), gg, r);
m.set(p->a(i), r);
apply_gcd_simplify(gg, p, t);
}
void apply_gcd_simplify(mpz & g, polynomial_ref& p, manager::ineq_type t) {
auto& m = m_manager.m();
// m.display(verbose_stream() << "gcd ", g);
// p->display(verbose_stream() << "\n", m_manager, false);
char const* tt = "";
switch (t) {
case ineq_type::GT: tt = ">"; break;
case ineq_type::LT: tt = "<"; break;
case ineq_type::EQ: tt = "="; break;
}
// verbose_stream() << " " << tt << " 0\n ->\n";
scoped_mpz r(m);
unsigned sz = p->size();
bool has_zero = false;
for (unsigned i = 0; i < sz; ++i) {
if (t != EQ && is_unit(p->m(i))) {
scoped_mpz one(m);
m.set(one, 1);
if (t == GT) {
// p - 2 - 1 >= 0
// p div 2 + floor((-2 - 1 ) / 2) >= 0
// p div 2 + floor(-3 / 2) >= 0
// p div 2 - 2 >= 0
// p div 2 - 1 > 0
//
// p + k > 0
// p + k - 1 >= 0
// p div g + (k - 1) div g >= 0
// p div g + (k - 1) div g + 1 > 0
m.sub(p->a(i), one, r);
bool is_neg = m.is_neg(r);
if (is_neg) {
m.neg(r);
m.add(r, g, r);
m.sub(r, one, r);
m.div_gcd(r, g, r);
m.neg(r);
}
else {
m.div_gcd(r, g, r);
}
m.add(r, one, r);
}
else {
// p + k < 0
// p + k + 1 <= 0
// p div g + (k + 1 + g - 1) div g <= 0
// p div g + (k + 1 + g - 1) div g - 1 < 0
m.add(p->a(i), g, r);
m.div_gcd(r, g, r);
m.sub(r, one, r);
}
}
else {
m.div_gcd(p->a(i), g, r);
}
m.set(p->a(i), r);
if (m.is_zero(r))
has_zero = true;
}
if (has_zero) {
m_som_buffer.reset();
for (unsigned i = 0; i < sz; ++i)
if (!m.is_zero(p->a(i)))
m_som_buffer.add(p->a(i), p->m(i));
p = m_som_buffer.mk();
}
// p->display(verbose_stream(), m_manager, false);
// verbose_stream() << " " << tt << " 0\n";
}
void gcd_simplify_slow(polynomial_ref& p, manager::ineq_type t) {
auto& m = m_manager.m();
unsigned sz = p->size();
scoped_mpz g(m);
m.set(g, 0);
for (unsigned i = 0; i < sz; i++) {
auto const& a = p->a(i);
if (m.is_one(a) || m.is_minus_one(a))
return;
if (t != EQ && is_unit(p->m(i)))
continue;
m.gcd(a, g, g);
if (m.is_one(g))
return;
}
apply_gcd_simplify(g, p, t);
}
polynomial * mk_zero() {
@ -6971,8 +7065,8 @@ namespace polynomial {
return m_imp->hash(p);
}
void manager::gcd_simplify(polynomial * p) {
m_imp->gcd_simplify(p);
void manager::gcd_simplify(polynomial_ref& p, ineq_type t) {
m_imp->gcd_simplify(p, t);
}
polynomial * manager::coeff(polynomial const * p, var x, unsigned k) {

3
src/math/polynomial/polynomial.h
View file

@ -285,7 +285,8 @@ namespace polynomial {
/**
\brief Normalize coefficients by dividing by their gcd
*/
void gcd_simplify(polynomial* p);
enum ineq_type { EQ, LT, GT };
void gcd_simplify(polynomial_ref& p, ineq_type t);
/**
\brief Return true if \c m is the unit monomial.

8
src/math/polynomial/polynomial_cache.cpp
View file

@ -126,11 +126,8 @@ namespace polynomial {
}
void reset_factor_cache() {
factor_cache::iterator it = m_factor_cache.begin();
factor_cache::iterator end = m_factor_cache.end();
for (; it != end; ++it) {
del_factor_entry(*it);
}
for (auto & e : m_factor_cache)
del_factor_entry(e);
m_factor_cache.reset();
}
@ -139,7 +136,6 @@ namespace polynomial {
polynomial * mk_unique(polynomial * p) {
if (m_in_cache.get(pid(p), false))
return p;
// m.gcd_simplify(p);
polynomial * p_prime = m_poly_table.insert_if_not_there(p);
if (p == p_prime) {
m_cached_polys.push_back(p_prime);

427
src/nlsat/nlsat_solver.cpp
View file

@ -220,12 +220,19 @@ namespace nlsat {
unsigned m_max_conflicts;
unsigned m_lemma_count;
struct stats {
unsigned m_simplifications;
unsigned m_restarts;
unsigned m_conflicts;
unsigned m_propagations;
unsigned m_decisions;
unsigned m_stages;
unsigned m_irrational_assignments; // number of irrational witnesses
void reset() { memset(this, 0, sizeof(*this)); }
stats() { reset(); }
};
// statistics
unsigned m_conflicts;
unsigned m_propagations;
unsigned m_decisions;
unsigned m_stages;
unsigned m_irrational_assignments; // number of irrational witnesses
stats m_stats;
imp(solver& s, ctx& c):
m_ctx(c),
@ -594,7 +601,7 @@ namespace nlsat {
}
ineq_atom* mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool& is_new) {
ineq_atom* mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool& is_new, bool simplify) {
SASSERT(sz >= 1);
SASSERT(k == atom::LT || k == atom::GT || k == atom::EQ);
int sign = 1;
@ -609,6 +616,24 @@ namespace nlsat {
var curr_max = max_var(p.get());
if (curr_max > max || max == null_var)
max = curr_max;
if (sz == 1 && simplify) {
if (sign < 0)
k = atom::flip(k);
sign = 1;
polynomial::manager::ineq_type t;
switch (k) {
case atom::EQ: t = polynomial::manager::ineq_type::EQ; break;
case atom::LT: t = polynomial::manager::ineq_type::LT; break;
case atom::GT: t = polynomial::manager::ineq_type::GT; break;
default: UNREACHABLE(); break;
}
polynomial::var_vector vars;
m_pm.vars(p, vars);
bool all_int = all_of(vars, [&](var x) { return is_int(x); });
if (!all_int)
t = polynomial::manager::ineq_type::EQ;
m_pm.gcd_simplify(p, t);
}
uniq_ps.push_back(m_cache.mk_unique(p));
TRACE("nlsat_table_bug", tout << "p: " << p << ", uniq: " << uniq_ps.back() << "\n";);
}
@ -633,9 +658,9 @@ namespace nlsat {
return atom;
}
bool_var mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even) {
bool_var mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool simplify = false) {
bool is_new = false;
ineq_atom* atom = mk_ineq_atom(k, sz, ps, is_even, is_new);
ineq_atom* atom = mk_ineq_atom(k, sz, ps, is_even, is_new, simplify);
if (!is_new) {
return atom->bvar();
}
@ -648,7 +673,7 @@ namespace nlsat {
}
}
literal mk_ineq_literal(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even) {
literal mk_ineq_literal(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool simplify = false) {
SASSERT(k == atom::LT || k == atom::GT || k == atom::EQ);
bool is_const = true;
polynomial::manager::scoped_numeral cnst(m_pm.m());
@ -676,7 +701,7 @@ namespace nlsat {
if (m_pm.m().is_zero(cnst) && k == atom::EQ) return true_literal;
return false_literal;
}
return literal(mk_ineq_atom(k, sz, ps, is_even), false);
return literal(mk_ineq_atom(k, sz, ps, is_even, simplify), false);
}
bool_var mk_root_atom(atom::kind k, var x, unsigned i, poly * p) {
@ -879,13 +904,13 @@ namespace nlsat {
for (literal lit : *c) {
lits.push_back(literal(tr[lit.var()], lit.sign()));
}
checker.mk_clause(lits.size(), lits.data(), nullptr);
checker.mk_external_clause(lits.size(), lits.data(), nullptr);
}
}
for (unsigned i = 0; i < n; ++i) {
literal lit = cls[i];
literal nlit(tr[lit.var()], !lit.sign());
checker.mk_clause(1, &nlit, nullptr);
checker.mk_external_clause(1, &nlit, nullptr);
}
lbool r = checker.check();
if (r == l_true) {
@ -973,7 +998,7 @@ namespace nlsat {
return cls;
}
void mk_clause(unsigned num_lits, literal const * lits, assumption a) {
void mk_external_clause(unsigned num_lits, literal const * lits, assumption a) {
_assumption_set as = nullptr;
if (a != nullptr)
as = m_asm.mk_leaf(a);
@ -1170,9 +1195,9 @@ namespace nlsat {
SASSERT(j != null_justification);
SASSERT(!j.is_null());
if (j.is_decision())
m_decisions++;
m_stats.m_decisions++;
else
m_propagations++;
m_stats.m_propagations++;
bool_var b = l.var();
m_bvalues[b] = to_lbool(!l.sign());
m_levels[b] = m_scope_lvl;
@ -1472,7 +1497,7 @@ namespace nlsat {
\brief Create a new stage. See Dejan and Leo's paper.
*/
void new_stage() {
m_stages++;
m_stats.m_stages++;
save_new_stage_trail();
if (m_xk == null_var)
m_xk = 0;
@ -1492,7 +1517,7 @@ namespace nlsat {
tout << "assigning "; m_display_var(tout, m_xk) << "(x" << m_xk << ") -> " << w << "\n";);
TRACE("nlsat_root", tout << "value as root object: "; m_am.display_root(tout, w); tout << "\n";);
if (!m_am.is_rational(w))
m_irrational_assignments++;
m_stats.m_irrational_assignments++;
m_assignment.set_core(m_xk, w);
}
@ -1556,7 +1581,7 @@ namespace nlsat {
break;
if (!resolve(*conflict_clause))
return l_false;
if (m_conflicts >= m_max_conflicts)
if (m_stats.m_conflicts >= m_max_conflicts)
return l_undef;
log();
}
@ -1595,20 +1620,27 @@ namespace nlsat {
unsigned m_next_conflict = 100;
void log() {
if (m_conflicts != 1 && m_conflicts < m_next_conflict)
if (m_stats.m_conflicts != 1 && m_stats.m_conflicts < m_next_conflict)
return;
m_next_conflict += 100;
IF_VERBOSE(2, verbose_stream() << "(nlsat :conflicts " << m_conflicts << " :decisions " << m_decisions << " :propagations " << m_propagations << " :clauses " << m_clauses.size() << " :learned " << m_learned.size() << ")\n");
IF_VERBOSE(2, verbose_stream() << "(nlsat :conflicts " << m_stats.m_conflicts
<< " :decisions " << m_stats.m_decisions
<< " :propagations " << m_stats.m_propagations
<< " :clauses " << m_clauses.size()
<< " :learned " << m_learned.size() << ")\n");
}
lbool search_check() {
lbool r = l_undef;
m_conflicts = 0;
m_stats.m_conflicts = 0;
m_stats.m_restarts = 0;
m_next_conflict = 0;
while (true) {
r = search();
if (r != l_true) break;
if (r != l_true)
break;
++m_stats.m_restarts;
vector<std::pair<var, rational>> bounds;
for (var x = 0; x < num_vars(); x++) {
@ -1631,11 +1663,22 @@ namespace nlsat {
bounds.push_back(std::make_pair(x, lo));
}
}
if (bounds.empty()) break;
if (bounds.empty())
break;
gc();
if (m_stats.m_restarts % 10 == 0) {
if (m_reordered)
restore_order();
apply_reorder();
}
init_search();
IF_VERBOSE(2, verbose_stream() << "(nlsat-b&b :conflicts " << m_conflicts << " :decisions " << m_decisions << " :propagations " << m_propagations << " :clauses " << m_clauses.size() << " :learned " << m_learned.size() << ")\n");
IF_VERBOSE(2, verbose_stream() << "(nlsat-b&b :conflicts " << m_stats.m_conflicts
<< " :decisions " << m_stats.m_decisions
<< " :propagations " << m_stats.m_propagations
<< " :clauses " << m_clauses.size()
<< " :learned " << m_learned.size() << ")\n");
for (auto const& b : bounds) {
var x = b.first;
rational lo = b.second;
@ -1653,6 +1696,7 @@ namespace nlsat {
// perform branch and bound
clause * cls = mk_clause(m_lemma.size(), m_lemma.data(), true, nullptr);
IF_VERBOSE(4, display(verbose_stream(), *cls) << "\n");
if (cls) {
TRACE("nlsat", display(tout << "conflict " << lo << " " << hi, *cls); tout << "\n";);
}
@ -1661,35 +1705,40 @@ namespace nlsat {
return r;
}
bool m_reordered = false;
void apply_reorder() {
m_reordered = false;
if (!can_reorder())
;
else if (m_random_order) {
shuffle_vars();
m_reordered = true;
}
else if (m_reorder) {
heuristic_reorder();
m_reordered = true;
}
}
lbool check() {
TRACE("nlsat_smt2", display_smt2(tout););
TRACE("nlsat_fd", tout << "is_full_dimensional: " << is_full_dimensional() << "\n";);
init_search();
m_explain.set_full_dimensional(is_full_dimensional());
bool reordered = false;
apply_reorder();
if (!m_incremental && m_inline_vars) {
if (!simplify())
if (!simplify())
return l_false;
}
if (!can_reorder()) {
}
else if (m_random_order) {
shuffle_vars();
reordered = true;
}
else if (m_reorder) {
heuristic_reorder();
reordered = true;
}
sort_watched_clauses();
lbool r = search_check();
CTRACE("nlsat_model", r == l_true, tout << "model before restore order\n"; display_assignment(tout););
if (reordered) {
restore_order();
}
if (m_reordered)
restore_order();
CTRACE("nlsat_model", r == l_true, tout << "model\n"; display_assignment(tout););
CTRACE("nlsat", r == l_false, display(tout << "unsat\n"););
SASSERT(r != l_true || check_satisfied(m_clauses));
@ -1713,7 +1762,7 @@ namespace nlsat {
unsigned sz = assumptions.size();
literal const* ptr = assumptions.data();
for (unsigned i = 0; i < sz; ++i) {
mk_clause(1, ptr+i, (assumption)(ptr+i));
mk_external_clause(1, ptr+i, (assumption)(ptr+i));
}
display_literal_assumption dla(*this, assumptions);
scoped_display_assumptions _scoped_display(*this, dla);
@ -1910,6 +1959,8 @@ namespace nlsat {
for (unsigned i = 0; i < sz; i++) {
literal l = m_lazy_clause[i];
if (l.var() != b) {
if (value(l) != l_false)
display(verbose_stream() << value(l) << " ", 1, &l);
SASSERT(value(l) == l_false || m_rlimit.is_canceled());
}
else {
@ -2052,7 +2103,7 @@ namespace nlsat {
SASSERT(check_marks());
TRACE("nlsat_proof", tout << "STARTING RESOLUTION\n";);
TRACE("nlsat_proof_sk", tout << "STARTING RESOLUTION\n";);
m_conflicts++;
m_stats.m_conflicts++;
TRACE("nlsat", tout << "resolve, conflicting clause:\n"; display(tout, *conflict_clause) << "\n";
tout << "xk: "; if (m_xk != null_var) m_display_var(tout, m_xk); else tout << "<null>"; tout << "\n";
tout << "scope_lvl: " << scope_lvl() << "\n";
@ -2197,8 +2248,7 @@ namespace nlsat {
VERIFY(process_clause(*conflict_clause, true));
return true;
}
new_cls = mk_clause(sz, m_lemma.data(), true, m_lemma_assumptions.get());
new_cls = mk_clause(sz, m_lemma.data(), true, m_lemma_assumptions.get());
}
NLSAT_VERBOSE(display(verbose_stream(), *new_cls) << "\n";);
if (!process_clause(*new_cls, true)) {
@ -2303,19 +2353,17 @@ namespace nlsat {
// -----------------------
void collect_statistics(statistics & st) {
st.update("nlsat conflicts", m_conflicts);
st.update("nlsat propagations", m_propagations);
st.update("nlsat decisions", m_decisions);
st.update("nlsat stages", m_stages);
st.update("nlsat irrational assignments", m_irrational_assignments);
st.update("nlsat conflicts", m_stats.m_conflicts);
st.update("nlsat propagations", m_stats.m_propagations);
st.update("nlsat decisions", m_stats.m_decisions);
st.update("nlsat restarts", m_stats.m_restarts);
st.update("nlsat stages", m_stats.m_stages);
st.update("nlsat simplifications", m_stats.m_simplifications);
st.update("nlsat irrational assignments", m_stats.m_irrational_assignments);
}
void reset_statistics() {
m_conflicts = 0;
m_propagations = 0;
m_decisions = 0;
m_stages = 0;
m_irrational_assignments = 0;
m_stats.reset();
}
// -----------------------
@ -2327,6 +2375,7 @@ namespace nlsat {
struct var_info_collector {
pmanager & pm;
atom_vector const & m_atoms;
var_vector m_shuffle;
unsigned_vector m_max_degree;
unsigned_vector m_num_occs;
@ -2402,7 +2451,7 @@ namespace nlsat {
return false;
if (m_info.m_num_occs[x] > m_info.m_num_occs[y])
return true;
return x < y;
return m_info.m_shuffle[x] < m_info.m_shuffle[y];
}
};
@ -2412,11 +2461,12 @@ namespace nlsat {
var_info_collector collector(m_pm, m_atoms, num);
collector.collect(m_clauses);
collector.collect(m_learned);
init_shuffle(collector.m_shuffle);
TRACE("nlsat_reorder", collector.display(tout, m_display_var););
var_vector new_order;
for (var x = 0; x < num; x++) {
for (var x = 0; x < num; x++)
new_order.push_back(x);
}
std::sort(new_order.begin(), new_order.end(), reorder_lt(collector));
TRACE("nlsat_reorder",
tout << "new order: "; for (unsigned i = 0; i < num; i++) tout << new_order[i] << " "; tout << "\n";);
@ -2429,20 +2479,23 @@ namespace nlsat {
SASSERT(check_invariant());
}
void shuffle_vars() {
var_vector p;
void init_shuffle(var_vector& p) {
unsigned num = num_vars();
for (var x = 0; x < num; x++) {
for (var x = 0; x < num; x++)
p.push_back(x);
}
random_gen r(++m_random_seed);
shuffle(p.size(), p.data(), r);
}
void shuffle_vars() {
var_vector p;
init_shuffle(p);
reorder(p.size(), p.data());
}
bool can_reorder() const {
return m_bounds.empty()
&& all_of(m_learned, [&](clause* c) { return !has_root_atom(*c); })
return all_of(m_learned, [&](clause* c) { return !has_root_atom(*c); })
&& all_of(m_clauses, [&](clause* c) { return !has_root_atom(*c); });
}
@ -2499,6 +2552,8 @@ namespace nlsat {
}
#endif
m_pm.rename(sz, p);
for (auto& b : m_bounds)
b.x = p[b.x];
TRACE("nlsat_bool_assignment_bug", tout << "before reinit cache\n"; display_bool_assignment(tout););
reinit_cache();
m_assignment.swap(new_assignment);
@ -2740,16 +2795,23 @@ namespace nlsat {
unsigned sz = m_clauses.size();
while (true) {
subsumption_simplify();
while (elim_uncnstr())
;
simplify_literals();
while (fm())
;
if (!solve_eqs())
return false;
subsumption_simplify();
if (m_clauses.size() >= sz)
break;
split_factors();
sz = m_clauses.size();
}
@ -2758,6 +2820,151 @@ namespace nlsat {
return true;
}
//
// Replace unit literals p*q > 0 by clauses.
//
void split_factors() {
auto sz = m_clauses.size();
for (unsigned i = 0; i < sz; ++i) {
auto& c = *m_clauses[i];
if (c.size() != 1)
continue;
auto lit = c[0];
auto a1 = m_atoms[lit.var()];
if (!a1)
continue;
auto& a = *to_ineq_atom(a1);
if (a.size() != 2)
continue;
auto* p = a.p(0);
auto* q = a.p(1);
auto is_evenp = a.is_even(0);
auto is_evenq = a.is_even(1);
auto asum = static_cast<_assumption_set>(c.assumptions());
literal lits[2];
c.set_removed();
++m_stats.m_simplifications;
switch (a.get_kind()) {
case atom::EQ: {
auto l1 = mk_ineq_literal(atom::EQ, 1, &p, &is_evenp, false);
auto l2 = mk_ineq_literal(atom::EQ, 1, &q, &is_evenq, false);
if (lit.sign()) {
lits[0] = ~l1;
mk_clause(1, lits, false, asum);
lits[0] = ~l2;
mk_clause(1, lits, false, asum);
}
else {
lits[0] = l1;
lits[1] = l2;
mk_clause(2, lits, false, asum);
}
break;
}
case atom::LT:
if (lit.sign()) {
// p*q >= 0 <=> (p <= 0 => q <= 0) & (q <= 0 => p <= 0)
// (p > 0 or !(q > 0)) & (q > 0 or !(p > 0))
auto l1 = mk_ineq_literal(atom::GT, 1, &p, &is_evenp, false);
auto l2 = mk_ineq_literal(atom::GT, 1, &q, &is_evenq, false);
lits[0] = l1;
lits[1] = ~l2;
mk_clause(2, lits, false, asum);
lits[0] = ~l1;
lits[1] = l2;
mk_clause(2, lits, false, asum);
}
else {
// p*q < 0
// (p > 0 & q < 0) or (q > 0 & p < 0)
// (p > 0 or q > 0) and (p < 0 or q < 0)
auto pgt = mk_ineq_literal(atom::GT, 1, &p, &is_evenp, false);
auto plt = mk_ineq_literal(atom::LT, 1, &p, &is_evenp, false);
auto qgt = mk_ineq_literal(atom::GT, 1, &q, &is_evenq, false);
auto qlt = mk_ineq_literal(atom::LT, 1, &q, &is_evenq, false);
lits[0] = pgt;
lits[1] = qgt;
mk_clause(2, lits, false, asum);
lits[0] = plt;
lits[1] = qlt;
mk_clause(2, lits, false, asum);
}
break;
case atom::GT: {
auto pgt = mk_ineq_literal(atom::GT, 1, &p, &is_evenp, false);
auto plt = mk_ineq_literal(atom::LT, 1, &p, &is_evenp, false);
auto qgt = mk_ineq_literal(atom::GT, 1, &q, &is_evenq, false);
auto qlt = mk_ineq_literal(atom::LT, 1, &q, &is_evenq, false);
if (lit.sign()) {
// p*q <= 0
// (p >= 0 => q <= 0) &
// (p < 0 or !(q > 0)) & (q < 0 or !(p > 0))
lits[0] = plt;
lits[1] = ~qgt;
mk_clause(2, lits, false, asum);
lits[0] = qlt;
lits[1] = ~plt;
mk_clause(2, lits, false, asum);
}
else {
// p*q > 0
// (p > 0 or q < 0) & (p < 0 or q > 0)
lits[0] = plt;
lits[1] = qgt;
mk_clause(2, lits, false, asum);
lits[0] = qlt;
lits[1] = plt;
mk_clause(2, lits, false, asum);
}
break;
}
}
}
cleanup_removed();
}
//
// Apply gcd simplification to literals
//
void simplify_literals() {
u_map<literal> b2l;
scoped_literal_vector lits(m_solver);
polynomial_ref_vector factors(m_pm);
ptr_buffer<poly> ps;
buffer<bool> is_even;
unsigned num_atoms = m_atoms.size();
for (unsigned j = 0; j < num_atoms; ++j) {
atom* a1 = m_atoms[j];
if (a1 && a1->is_ineq_atom()) {
ineq_atom const& a = *to_ineq_atom(a1);
ps.reset();
is_even.reset();
for (unsigned i = 0; i < a.size(); ++i) {
factors.reset();
m_cache.factor(a.p(i), factors);
for (auto q : factors) {
ps.push_back(q);
is_even.push_back(a.is_even(i));
}
}
literal l = mk_ineq_literal(a.get_kind(), ps.size(), ps.data(), is_even.data(), true);
if (l == null_literal)
continue;
lits.push_back(l);
if (a.m_bool_var != l.var()) {
IF_VERBOSE(3, display(verbose_stream() << "simplify ", l) << "\n");
b2l.insert(a.m_bool_var, l);
}
}
}
update_clauses(b2l, nullptr);
}
//
// Remove unconstrained assertions.
//
@ -2777,6 +2984,7 @@ namespace nlsat {
continue;
if (!is_unconstrained(v, c))
continue;
++m_stats.m_simplifications;
c.set_removed();
to_delete.push_back(&c);
}
@ -2874,16 +3082,17 @@ namespace nlsat {
compute_occurs();
for (unsigned v = m_var_occurs.size(); v-- > 0; )
apply_fm(v, m_var_occurs[v]);
apply_fm(v, m_var_occurs[v]);
return cleanup_removed();
}
// progression of features
// unit literals
// single occurrence of x in C
// (x <= t or x <= s or C) == (x <= max(s, t) or C)
// progression of possible features:
// . Current: unit literals
// . Either lower or upper bound is unit coefficient
// . single occurrence of x in C
// . (x <= t or x <= s or C) == (x <= max(s, t) or C)
//
bool is_invertible(var x, polynomial_ref & A) {
if (!m_pm.is_const(A))
@ -2974,10 +3183,8 @@ namespace nlsat {
break;
case atom::EQ: {
all_solved = false;
continue;
// unsound:
m_display_var(verbose_stream(), x);
display(verbose_stream() << " ", *c) << "\n";
if (!m_pm.is_const(B))
continue;
bound_constraint l(x, A, B, false, c);
A = -A;
B = -B;
@ -3049,16 +3256,16 @@ namespace nlsat {
bool is_even = false;
m_lemma.reset();
if (l.is_strict || h.is_strict)
m_lemma.push_back(mk_ineq_literal(atom::GT, 1, &p, &is_even));
m_lemma.push_back(mk_ineq_literal(atom::GT, 1, &p, &is_even, true));
else
m_lemma.push_back(~mk_ineq_literal(atom::LT, 1, &p, &is_even));
m_lemma.push_back(~mk_ineq_literal(atom::LT, 1, &p, &is_even, true));
if (m_lemma[0] == true_literal)
continue;
auto a1 = static_cast<_assumption_set>(l.c->assumptions());
auto a2 = static_cast<_assumption_set>(h.c->assumptions());
auto cls = mk_clause(m_lemma.size(), m_lemma.data(), false, m_asm.mk_join(a1, a2));
if (cls)
compute_occurs(*cls);
compute_occurs(*cls);
IF_VERBOSE(3, display(verbose_stream() << "add resolvent ", *cls) << "\n");
}
}
@ -3088,6 +3295,7 @@ namespace nlsat {
l.A = -l.A;
l.B = -l.B;
apply_fm_equality(x, clauses, l, h);
++m_stats.m_simplifications;
return true;
}
l.A = -l.A;
@ -3102,7 +3310,6 @@ namespace nlsat {
auto a1 = static_cast<_assumption_set>(l.c->assumptions());
auto a2 = static_cast<_assumption_set>(h.c->assumptions());
a1 = m_asm.mk_join(a1, a2);
m_lemma_assumptions = a1;
polynomial_ref A(l.A), B(l.B);
@ -3142,26 +3349,59 @@ namespace nlsat {
}
// track updates for model reconstruction
m_bounds.push_back(l);
m_bounds.push_back(h);
m_bounds.push_back(h);
++m_stats.m_simplifications;
}
bool unit_subsumption_simplify(clause& src, clause& c) {
if (src.size() != 1)
return false;
auto u = src[0];
for (auto lit : c) {
if (subsumes(u, ~lit)) {
auto a1 = static_cast<_assumption_set>(c.assumptions());
auto a2 = static_cast<_assumption_set>(src.assumptions());
auto a = m_asm.mk_join(a1, a2);
literal_vector lits;
for (auto lit2 : c)
if (lit2 != lit)
lits.push_back(lit2);
auto cls = mk_clause(lits.size(), lits.data(), false, a);
if (cls)
compute_occurs(*cls);
return true;
}
}
return false;
}
//
// Subsumption simplification
//
//
// Remove D if C subsumes D
//
// Unit subsumption resolution
// u is a unit literal (lit or C) is a clause
// u => ~lit, then simplify (lit or C) to C
//
void subsumption_simplify() {
compute_occurs();
for (unsigned v = m_var_occurs.size(); v-- > 0; ) {
auto& clauses = m_var_occurs[v];
for (auto c : clauses) {
unsigned sz = clauses.size();
for (unsigned i = 0; i < sz; ++i) {
auto c = clauses[i];
if (c->is_marked() || c->is_removed())
continue;
c->mark();
for (auto c2 : clauses) {
c->mark();
for (unsigned j = 0; j < sz; ++j) {
auto c2 = clauses[j];
if (c == c2 || c2->is_removed())
continue;
if (subsumes(*c, *c2)) {
if (subsumes(*c, *c2) || unit_subsumption_simplify(*c, *c2)) {
IF_VERBOSE(3, display(verbose_stream() << "subsumes ", *c);
display(verbose_stream() << " ", *c2) << "\n");
++m_stats.m_simplifications;
c2->set_removed();
}
}
@ -3274,6 +3514,7 @@ namespace nlsat {
del_clause(c, m_clauses);
TRACE("nlsat", display(tout << "simplified\n"););
change = true;
++m_stats.m_simplifications;
break;
}
}
@ -3426,7 +3667,7 @@ namespace nlsat {
}
if (!change)
return null_literal;
return mk_ineq_literal(k, ps.size(), ps.data(), even.data());
return mk_ineq_literal(k, ps.size(), ps.data(), even.data(), true);
}
bool substitute_var(var x, poly* p, poly* q, clause& src) {
@ -3446,19 +3687,23 @@ namespace nlsat {
}
}
}
return update_clauses(b2l, src);
return update_clauses(b2l, &src);
}
bool update_clauses(u_map<literal> const& b2l, clause& src) {
bool update_clauses(u_map<literal> const& b2l, clause* src) {
bool is_sat = true;
literal_vector lits;
clause_vector to_delete;
unsigned n = m_clauses.size();
auto a1 = static_cast<_assumption_set>(src.assumptions());
_assumption_set a1 = nullptr;
if (src)
a1 = static_cast<_assumption_set>(src->assumptions());
for (unsigned i = 0; i < n; ++i) {
clause* c = m_clauses[i];
if (c == &src)
if (c == src)
continue;
lits.reset();
bool changed = false;
@ -4501,7 +4746,7 @@ namespace nlsat {
}
void solver::mk_clause(unsigned num_lits, literal * lits, assumption a) {
return m_imp->mk_clause(num_lits, lits, a);
return m_imp->mk_external_clause(num_lits, lits, a);
}
std::ostream& solver::display(std::ostream & out) const {