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Fix redundant lemma in umul_ovfl::narrow_bound

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This commit is contained in:
Jakob Rath 2023-03-06 12:59:35 +01:00
parent ac5682409e
commit ac66622b05
1 changed files with 50 additions and 23 deletions
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73
src/math/polysat/umul_ovfl_constraint.cpp
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@ -31,7 +31,7 @@ namespace polysat {
return; return;
} }
if (m_p.index() > m_q.index()) if (m_p.index() > m_q.index())
std::swap(m_p, m_q); swap(m_p, m_q);
} }
std::ostream& umul_ovfl_constraint::display(std::ostream& out, lbool status) const { std::ostream& umul_ovfl_constraint::display(std::ostream& out, lbool status) const {
@ -112,38 +112,65 @@ namespace polysat {
if (!p.is_val()) if (!p.is_val())
return false; return false;
VERIFY(!p.is_zero() && !p.is_one()); // evaluation should catch this case
SASSERT(!p.is_zero() && !p.is_one()); rational const& M = p.manager().two_to_N();
auto const& max = p.manager().max_value();
// p * q >= max + 1 <=> q >= (max + 1)/p <=> q >= ceil((max+1)/p)
auto bound = ceil((max + 1) / p.val());
SASSERT(bound.is_pos());
SASSERT(bound * p.val() > max);
SASSERT((bound - 1) * p.val() <= max);
rational relaxed_p = p.val(); // Lowest value such that bound is correct // q_bound
relaxed_p = ceil((max + 1) / bound); // = min q . Ovfl(p_val, q)
SASSERT(relaxed_p <= p.val()); // = min q . p_val * q >= M
// // = min q . q >= M / p_val
// the clause that explains bound <= q or bound > q // = ceil(M / p_val)
// rational const q_bound = ceil(M / p.val());
// Ovfl(p, q) & p <= p.val() => q >= bound SASSERT(2 <= q_bound && q_bound <= M/2);
// ~Ovfl(p, q) & p >= p.val() => q < bound SASSERT(p.val() * q_bound >= M);
// SASSERT(p.val() * (q_bound - 1) < M);
// LOG("q_bound: " << q.manager().mk_val(q_bound));
// We need the following properties for the bounds:
//
// p_bound * (q_bound - 1) < M
// p_bound * q_bound >= M
//
// With these properties we get:
//
// p <= p_bound & q < q_bound ==> ~Ovfl(p, q)
// p >= p_bound & q >= q_bound ==> Ovfl(p, q)
//
// Written as lemmas:
//
// Ovfl(p, q) & p <= p_bound ==> q >= q_bound
// ~Ovfl(p, q) & p >= p_bound ==> q < q_bound
//
signed_constraint sc(this, is_positive); signed_constraint sc(this, is_positive);
if (is_positive) { if (is_positive) {
clause_builder lemma(s, "Ovfl(p, q) & p <= relaxed(p.val()) ==> q >= bound"); // Find largest bound for p such that q_bound is still correct.
// p_bound = max p . (q_bound - 1)*p < M
// = max p . p < M / (q_bound - 1)
// = ceil(M / (q_bound - 1)) - 1
rational const p_bound = ceil(M / (q_bound - 1)) - 1;
SASSERT(p.val() <= p_bound);
SASSERT(p_bound * q_bound >= M);
SASSERT(p_bound * (q_bound - 1) < M);
// LOG("p_bound: " << p.manager().mk_val(p_bound));
clause_builder lemma(s, "Ovfl(p, q) & p <= p_bound ==> q >= q_bound");
lemma.insert_eval(~sc); lemma.insert_eval(~sc);
lemma.insert_eval(~s.ule(p0, relaxed_p)); lemma.insert_eval(~s.ule(p0, p_bound));
lemma.insert(s.ule(bound, q0)); lemma.insert(s.ule(q_bound, q0));
s.add_clause(lemma.build()); s.add_clause(lemma.build());
} }
else { else {
clause_builder lemma(s, "~Ovfl(p, q) & p >= relaxed(p.val()) ==> q < bound"); // Find lowest bound for p such that q_bound is still correct.
// p_bound = min p . Ovfl(p, q_bound) = ceil(M / q_bound)
rational const p_bound = ceil(M / q_bound);
SASSERT(p_bound <= p.val());
SASSERT(p_bound * q_bound >= M);
SASSERT(p_bound * (q_bound - 1) < M);
// LOG("p_bound: " << p.manager().mk_val(p_bound));
clause_builder lemma(s, "~Ovfl(p, q) & p >= p_bound ==> q < q_bound");
lemma.insert_eval(~sc); lemma.insert_eval(~sc);
lemma.insert_eval(~s.ule(relaxed_p, p0)); lemma.insert_eval(~s.ule(p_bound, p0));
lemma.insert(s.ult(q0, bound)); lemma.insert(s.ult(q0, q_bound));
s.add_clause(lemma.build()); s.add_clause(lemma.build());
} }
return true; return true;