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quot_rem

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This commit is contained in:
Jakob Rath 2022-11-22 14:19:35 +01:00
parent 85a633a3e0
commit da762700d6
1 changed files with 29 additions and 6 deletions
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35
src/math/polysat/constraint_manager.cpp
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@ -276,10 +276,24 @@ namespace polysat {
std::pair<pdd, pdd> constraint_manager::quot_rem(pdd const& a, pdd const& b) {
auto& m = a.manager();
unsigned sz = m.power_of_2();
if (a.is_val() && b.is_val()) {
// TODO: just evaluate?
if (b.is_zero()) {
// By SMT-LIB specification, b = 0 ==> q = -1, r = a.
return {m.mk_val(m.max_value()), a};
}
if (a.is_val() && b.is_val()) {
rational const av = a.val();
rational const bv = b.val();
SASSERT(!bv.is_zero());
rational rv;
rational qv = machine_div_rem(av, bv, rv);
pdd q = m.mk_val(qv);
pdd r = m.mk_val(rv);
SASSERT_EQ(a, b * q + r);
SASSERT(b.val()*q.val() + r.val() <= m.max_value());
SASSERT(r.val() <= (b*q+r).val());
SASSERT(r.val() < b.val());
return {std::move(q), std::move(r)};
}
constraint_dedup::quot_rem_args args({a, b});
auto it = m_dedup.quot_rem_expr.find_iterator(args);
if (it != m_dedup.quot_rem_expr.end())
@ -292,18 +306,27 @@ namespace polysat {
// Axioms for quotient/remainder:
// a = b*q + r
// multiplication does not overflow in b*q
// addition does not overflow in (b*q) + r; for now expressed as: r <= bq+r (TODO: maybe the version with disjunction is easier for the solver; should compare later)
// addition does not overflow in (b*q) + r; for now expressed as: r <= bq+r
// b ≠ 0 ==> r < b
// b = 0 ==> q = -1
s.add_eq(a, b * q + r);
s.add_umul_noovfl(b, q);
s.add_ule(r, b*q+r);
// r <= b*q+r
// { apply equivalence: p <= q <=> q-p <= -p-1 }
// b*q <= -r-1
s.add_ule(b*q, -r-1);
#if 0
// b*q <= b*q+r
// { apply equivalence: p <= q <=> q-p <= -p-1 }
// r <= - b*q - 1
s.add_ule(r, -b*q-1); // redundant, but may help propagation
#endif
auto c_eq = eq(b);
s.add_clause(c_eq, ult(r, b), false);
s.add_clause(~c_eq, eq(q + 1), false);
return {q, r};
return {std::move(q), std::move(r)};
}
pdd constraint_manager::bnot(pdd const& p) {