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cleanup and more caching

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Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson 2025-12-19 08:42:34 -10:00
parent 2174cf5aaf
commit e1db01a5b2
2 changed files with 60 additions and 90 deletions
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146
src/nlsat/levelwise.cpp
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@ -29,8 +29,6 @@ namespace nlsat {
ord_inv, ord_inv,
sgn_inv, sgn_inv,
connected, connected,
an_sub,
sample_holds,
repr, repr,
_count _count
}; };
@ -187,8 +185,8 @@ namespace nlsat {
// helper overload so callers can pass either raw poly* or polynomial_ref // helper overload so callers can pass either raw poly* or polynomial_ref
unsigned max_var(poly* p) { return m_pm.max_var(p); } unsigned max_var(poly* p) const { return m_pm.max_var(p); }
unsigned max_var(polynomial_ref const & p) { return m_pm.max_var(p); } unsigned max_var(polynomial_ref const & p) const { return m_pm.max_var(p); }
// Wrapper to use cached PSC chain computation // Wrapper to use cached PSC chain computation
void psc_chain(polynomial_ref & p, polynomial_ref & q, unsigned x, polynomial_ref_vector & result) { void psc_chain(polynomial_ref & p, polynomial_ref & q, unsigned x, polynomial_ref_vector & result) {
@ -631,7 +629,6 @@ namespace nlsat {
void apply_pre_an_del(const property& p) { void apply_pre_an_del(const property& p) {
unsigned p_lvl = max_var(p.m_poly); unsigned p_lvl = max_var(p.m_poly);
if (p_lvl > 0) { if (p_lvl > 0) {
mk_prop(prop_enum::an_sub, level_t(p_lvl - 1));
mk_prop(prop_enum::connected, level_t(p_lvl - 1)); mk_prop(prop_enum::connected, level_t(p_lvl - 1));
} }
mk_prop(prop_enum::non_null, p.m_poly); mk_prop(prop_enum::non_null, p.m_poly);
@ -674,15 +671,28 @@ namespace nlsat {
} }
} }
// If a polynomial has a coefficient which is non-zero constant then non_null holds bool has_sgn_inv(const polynomial_ref& p, unsigned level) const {
bool has_const_coeff(const polynomial_ref& p) { SASSERT(level == max_var(p));
if (level >= m_Q.size())
return false;
unsigned const pid = m_pm.id(p.get());
for (auto const& pr : m_Q[level]) {
if (pr.m_prop_tag != prop_enum::sgn_inv)
continue;
poly* q = pr.m_poly.get();
if (q && m_pm.id(q) == pid)
return true;
}
return false;
}
// If a polynomial has a coefficient which is a non-zero constant or a non-vanishisg coefficient for which sgn_inv has been asserted already then non_null holds
bool has_non_null_coeff(const polynomial_ref& p) {
unsigned level = max_var(p); unsigned level = max_var(p);
unsigned deg = m_pm.degree(p, level); unsigned deg = m_pm.degree(p, level);
for (unsigned j = 0; j <= deg; ++j) { for (unsigned j = 0; j <= deg; ++j) {
polynomial_ref coeff(m_pm); polynomial_ref coeff(m_pm.coeff(p, level, j), m_pm);
coeff = m_pm.coeff(p, level, j);
TRACE(lws, tout << "coeff:" << coeff << "\n";); TRACE(lws, tout << "coeff:" << coeff << "\n";);
if(m_pm.nonzero_const_coeff(p, level, j)) if (is_const(coeff) || (sign(coeff, sample(), m_am) && has_sgn_inv(coeff, max_var(coeff))))
return true; return true;
} }
return false; return false;
@ -690,18 +700,45 @@ namespace nlsat {
void apply_pre_non_null(const property& p) { void apply_pre_non_null(const property& p) {
TRACE(lws, tout << "p:"; display(tout, p) << std::endl;); TRACE(lws, tout << "p:"; display(tout, p) << std::endl;);
if (has_const_coeff(p.m_poly)) if (has_non_null_coeff(p.m_poly))
return; return; // already satisfied
if (can_apply_pre_non_null_fallback(p)) polynomial_ref disc(m_pm);
apply_pre_non_null_fallback(p); disc = can_apply_pre_non_null_fallback(p);
if (disc)
for_each_distinct_factor(disc, [&](const polynomial::polynomial_ref & f) {
mk_prop(prop_enum::sgn_inv, f);
});
else else
try_non_null_via_coeffs(p); try_non_null_via_coeffs(p);
} }
bool can_apply_pre_non_null_fallback(const property & p) { // Rule 4.2, subrule 1:
// TODO: using apply_pre_non_null_fallback as a template, query with m_cache.contains_chain if the discriminant chain has been cached // sample(s)(R), degx_{i+1} (p) > 1, disc(x_{i+1} (p)(s)) ̸= 0, sgn_inv(disc(x_{i+1} (p))(R)
polynomial_ref can_apply_pre_non_null_fallback(const property & p) {
unsigned level = max_var(p.m_poly);
unsigned deg = m_pm.degree(p.m_poly, level);
if (deg <= 1)
return polynomial_ref(m_pm);
polynomial_ref d(m_pm);
d = derivative(p.m_poly, level);
if (!m_cache.contains_chain(p.m_poly.get(), d.get(), level))
return polynomial_ref(m_pm);
polynomial_ref_vector& chain = m_psc_tmp;
chain.reset();
m_cache.psc_chain(p.m_poly.get(), d.get(), level, chain);
polynomial_ref disc(m_pm);
for (unsigned i = 0; i < chain.size(); ++i) {
disc = polynomial_ref(chain.get(i), m_pm);
if (!is_const(disc))
break;
}
if (sign(disc, sample(), m_am))
return disc;
return polynomial_ref(m_pm); // nullptr
} }
// If some coefficient c_j of p is constant non-zero at the sample, or // If some coefficient c_j of p is constant non-zero at the sample, or
@ -709,7 +746,7 @@ namespace nlsat {
// then non_null(p) holds on the region represented by 'rs' (if provided). // then non_null(p) holds on the region represented by 'rs' (if provided).
// Returns true if non_null was established and the property p was removed. // Returns true if non_null was established and the property p was removed.
// TODO: use cached non-null properties // TODO: use cached non-null properties
bool try_non_null_via_coeffs(const property& p) { void try_non_null_via_coeffs(const property& p) {
unsigned level = max_var(p.m_poly); unsigned level = max_var(p.m_poly);
poly* pp = p.m_poly.get(); poly* pp = p.m_poly.get();
unsigned deg = m_pm.degree(pp, level); unsigned deg = m_pm.degree(pp, level);
@ -722,43 +759,11 @@ namespace nlsat {
for_each_distinct_factor(coeff, [&](const polynomial::polynomial_ref & f) { for_each_distinct_factor(coeff, [&](const polynomial::polynomial_ref & f) {
mk_prop(prop_enum::sgn_inv, f); mk_prop(prop_enum::sgn_inv, f);
}); });
return true;
}
TRACE(lws, tout << "false\n";);
return false;
}
// Helper for Rule 4.2, subrule 1: fallback when subrule 2 does not apply.
// sample(s)(R), degx_{i+1} (p) > 1, disc(x_{i+1} (p)(s)) ̸= 0, sgn_inv(disc(x_{i+1} (p))(R)
void apply_pre_non_null_fallback(const property& p) {
unsigned level = max_var(p.m_poly);
unsigned deg = m_pm.degree(p.m_poly, level);
// fallback applies only for degree > 1
if (deg <= 1) {
fail();
return; return;
} }
// compute discriminant w.r.t. the variable at p.level TRACE(lws, tout << "failing in try_non_null_via_coeffs\n";);
polynomial_ref disc(m_pm); // all coefficients are vanishing on the sample: we have a nullified polynomial
disc = psc_discriminant(p.m_poly, level); fail();
SASSERT (!is_zero(disc)); // p.m_poly is supposed to be square free
TRACE(lws, ::nlsat::display(tout << "discriminant: ", m_solver, disc) << "\n";);
for_each_distinct_factor(disc, [&](const polynomial::polynomial_ref & f) {
mk_prop(prop_enum::sgn_inv, f);
});
// non_null is established by the discriminant being non-zero at the sample
}
// an_sub(R) iff R is an analitical manifold
// Rule 4.7
void apply_pre_an_sub(const property& p) {
mk_prop(prop_enum::repr, level_t(m_level)) ;
if (m_level > 0)
mk_prop(prop_enum::an_sub, level_t(m_level -1));
// if level == 0 then an_sub holds - bcs an empty set is an analytical submanifold
} }
/* /*
@ -776,8 +781,6 @@ namespace nlsat {
void apply_pre_repr(const property& p) { void apply_pre_repr(const property& p) {
const auto& I = m_I[m_level]; const auto& I = m_I[m_level];
TRACE(lws, display(tout << "interval m_I[" << m_level << "]\n", I) << "\n";); TRACE(lws, display(tout << "interval m_I[" << m_level << "]\n", I) << "\n";);
if (m_level)
mk_prop(sample_holds, level_t(m_level - 1));
if (I.is_section()) { if (I.is_section()) {
/*sample(s)(R), holds(I)(R), I = (section, b), an_del(b.p)(R) */ /*sample(s)(R), holds(I)(R), I = (section, b), an_del(b.p)(R) */
mk_prop(an_del, I.l); mk_prop(an_del, I.l);
@ -792,13 +795,6 @@ namespace nlsat {
} }
} }
void apply_pre_sample(const property& p) {
if (m_level == 0)
return;
mk_prop(sample_holds, level_t(m_level - 1));
mk_prop(prop_enum::repr, level_t(m_level - 1));
}
void mk_prop(prop_enum pe, level_t level) { void mk_prop(prop_enum pe, level_t level) {
SASSERT(is_set(level.val)); SASSERT(is_set(level.val));
add_to_Q_if_new(property(pe, m_pm), level.val); add_to_Q_if_new(property(pe, m_pm), level.val);
@ -821,8 +817,6 @@ namespace nlsat {
if (roots.size() == 0) { if (roots.size() == 0) {
/* Rule 4.6. Let i ∈ N, R ⊆ Ri, s ∈ R_{i−1}, and realRoots(p(s, xi )) = ∅. /* Rule 4.6. Let i ∈ N, R ⊆ Ri, s ∈ R_{i−1}, and realRoots(p(s, xi )) = ∅.
sample(s)(R), an_del(p)(R) ⊢ sgn_inv(p)(R) */ sample(s)(R), an_del(p)(R) ⊢ sgn_inv(p)(R) */
if (m_level)
mk_prop(sample_holds, level_t(m_level - 1));
mk_prop(prop_enum::an_del, p.m_poly); mk_prop(prop_enum::an_del, p.m_poly);
return; return;
} }
@ -839,7 +833,6 @@ namespace nlsat {
Q, b.p ̸= p, ord_inv(resxi (b.p, p))(R) ⊢ sgn_inv(p)(R) Q, b.p ̸= p, ord_inv(resxi (b.p, p))(R) ⊢ sgn_inv(p)(R)
*/ */
if (m_level) { if (m_level) {
mk_prop(prop_enum::an_sub, level_t(m_level - 1));
mk_prop(prop_enum::connected, level_t(m_level - 1)); mk_prop(prop_enum::connected, level_t(m_level - 1));
mk_prop(prop_enum::repr, level_t(m_level - 1)); mk_prop(prop_enum::repr, level_t(m_level - 1));
} }
@ -863,7 +856,6 @@ namespace nlsat {
// todo - read the preconditions on p it needs to be diff // todo - read the preconditions on p it needs to be diff
SASSERT(precondition_on_sign_inv(p)); SASSERT(precondition_on_sign_inv(p));
if (m_level) { if (m_level) {
mk_prop(sample_holds, level_t(m_level - 1));
mk_prop(repr, level_t(m_level - 1)); mk_prop(repr, level_t(m_level - 1));
} }
mk_prop(ir_ord, level_t(m_level)); mk_prop(ir_ord, level_t(m_level));
@ -871,16 +863,7 @@ namespace nlsat {
} }
} }
/*
/*Assume that p is irreducible, irExpr(p, s) ̸= ∅, ξ.p is irreducible for all ξ ∈ dom(≼), ≼ matches s,
and for all ξ ∈ irExpr(p, s) it holds either ξ ≼t l or u ≼t ξ.*/
bool precondition_on_sign_inv(const property &p) {
SASSERT(is_square_free(p.m_poly));
SASSERT(max_var(p.m_poly) == m_level);
return true;
}
/*
Rule 4.5. Let i ∈ N>0 , R ⊆ Ri Rule 4.5. Let i ∈ N>0 , R ⊆ Ri
, s ∈ Ri , s ∈ Ri
, and p ∈ Q[x1, . . . , xi ], level(p) = i. Assume that p is irreducible. , and p ∈ Q[x1, . . . , xi ], level(p) = i. Assume that p is irreducible.
@ -891,12 +874,9 @@ namespace nlsat {
SASSERT(p.m_prop_tag == prop_enum::ord_inv && is_square_free(p.m_poly)); SASSERT(p.m_prop_tag == prop_enum::ord_inv && is_square_free(p.m_poly));
unsigned level = max_var(p.m_poly); unsigned level = max_var(p.m_poly);
auto sign_on_sample = sign(p.m_poly, sample(), m_am); auto sign_on_sample = sign(p.m_poly, sample(), m_am);
mk_prop(sample_holds, level_t(level));
if (sign_on_sample) { if (sign_on_sample) {
mk_prop(prop_enum::sgn_inv, p.m_poly); mk_prop(prop_enum::sgn_inv, p.m_poly);
} else { // sign is zero } else { // sign is zero
if (level)
mk_prop(prop_enum::an_sub, level_t(level - 1));
mk_prop(prop_enum::connected, level_t(level)); mk_prop(prop_enum::connected, level_t(level));
mk_prop(prop_enum::sgn_inv, p.m_poly); mk_prop(prop_enum::sgn_inv, p.m_poly);
mk_prop(prop_enum::an_del, p.m_poly); mk_prop(prop_enum::an_del, p.m_poly);
@ -916,15 +896,9 @@ namespace nlsat {
case prop_enum::non_null: case prop_enum::non_null:
apply_pre_non_null(p); apply_pre_non_null(p);
break; break;
case prop_enum::an_sub:
apply_pre_an_sub(p);
break;
case prop_enum::repr: case prop_enum::repr:
apply_pre_repr(p); apply_pre_repr(p);
break; break;
case sample_holds:
apply_pre_sample(p);
break;
case prop_enum::sgn_inv: case prop_enum::sgn_inv:
apply_pre_sgn_inv(p); apply_pre_sgn_inv(p);
break; break;
@ -954,8 +928,6 @@ namespace nlsat {
sample(s)(R), an_sub(i)(R), connected(i)(R), ∀ξ ∈ dom(≼). an_del(ξ.p)(R), ∀(ξ,ξ′) ∈≼. ord_inv(resx_{i+1} (ξ.p, ξ′.p))(R) ⊢ ir_ord(≼, s)(R) sample(s)(R), an_sub(i)(R), connected(i)(R), ∀ξ ∈ dom(≼). an_del(ξ.p)(R), ∀(ξ,ξ′) ∈≼. ord_inv(resx_{i+1} (ξ.p, ξ′.p))(R) ⊢ ir_ord(≼, s)(R)
*/ */
if (m_level > 0) { if (m_level > 0) {
mk_prop(sample_holds, level_t(m_level -1 ));
mk_prop(an_sub, level_t(m_level - 1));
mk_prop(connected, level_t(m_level - 1)); mk_prop(connected, level_t(m_level - 1));
} }
for (const auto & pair: m_rel.m_pairs) { for (const auto & pair: m_rel.m_pairs) {
@ -1026,8 +998,6 @@ namespace nlsat {
case prop_enum::ord_inv: return "ord_inv"; case prop_enum::ord_inv: return "ord_inv";
case prop_enum::sgn_inv: return "sgn_inv"; case prop_enum::sgn_inv: return "sgn_inv";
case prop_enum::connected: return "connected"; case prop_enum::connected: return "connected";
case prop_enum::an_sub: return "an_sub";
case sample_holds: return "sample";
case prop_enum::repr: return "repr"; case prop_enum::repr: return "repr";
case prop_enum::_count: return "_count"; case prop_enum::_count: return "_count";
} }

4
src/nlsat/nlsat_explain.cpp
View file

@ -1107,9 +1107,9 @@ namespace nlsat {
bool levelwise_single_cell(polynomial_ref_vector & ps, var max_x, polynomial::cache & cache) { bool levelwise_single_cell(polynomial_ref_vector & ps, var max_x, polynomial::cache & cache) {
levelwise lws(m_solver, ps, max_x, sample(), m_pm, m_am, cache); levelwise lws(m_solver, ps, max_x, sample(), m_pm, m_am, cache);
auto cell = lws.single_cell(); auto cell = lws.single_cell();
if (lws.failed()) { if (lws.failed())
return false; return false;
}
TRACE(lws, for (unsigned i = 0; i < cell.size(); i++) TRACE(lws, for (unsigned i = 0; i < cell.size(); i++)
display(tout << "I[" << i << "]:", m_solver, cell[i]) << "\n";); display(tout << "I[" << i << "]:", m_solver, cell[i]) << "\n";);
// Enumerate all intervals in the computed cell and add literals for each non-trivial interval. // Enumerate all intervals in the computed cell and add literals for each non-trivial interval.