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add smul over and underflow predicate

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2022-02-20 11:39:45 +02:00
parent dc3b921712
commit 1faccffd0d
8 changed files with 88 additions and 50 deletions
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69
src/math/polysat/smul_ovfl_constraint.cpp
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@ -15,8 +15,8 @@ Author:
namespace polysat {
smul_ovfl_constraint::smul_ovfl_constraint(constraint_manager& m, pdd const& p, pdd const& q):
constraint(m, ckind_t::smul_ovfl_t), m_p(p), m_q(q) {
smul_ovfl_constraint::smul_ovfl_constraint(constraint_manager& m, pdd const& p, pdd const& q, bool is_overflow):
constraint(m, ckind_t::smul_ovfl_t), m_is_overflow(is_overflow), m_p(p), m_q(q) {
simplify();
m_vars.append(m_p.free_vars());
for (auto v : m_q.free_vars())
@ -45,27 +45,66 @@ namespace polysat {
}
std::ostream& smul_ovfl_constraint::display(std::ostream& out) const {
return out << "sovfl*(" << m_p << ", " << m_q << ")";
if (m_is_overflow)
return out << "sovfl*(" << m_p << ", " << m_q << ")";
else
return out << "sudfl*(" << m_p << ", " << m_q << ")";
}
/**
* TODO - verify the rules for small bit-widths.
*
* sovfl(p,q) => p >= 2, q >= 2
* sovfl(p,q) => p >s 0 <=> q >s 0
* sovfl(p,q) & p >s 0 => p*q < 0 or ovfl(p,q)
* sovfl(p,q) & p <s 0 => p*q < 0 or ovfl(-p,-q)
* ~sovfl(p,q) & p >s 0 = q >s 0 => q > 0 => ~ovfl(p,q) & p*q >=s 0
* smul_noovfl(p,q) => sign(p) != sign(q) or p'*q' < 2^{K-1}
* sudfl(p, q) => p >= 2, q >= 2
* sudfl(p, q) => p >s 0 xor q >s 0
* sudfl(p, q) & p >s 0 => p*q > 0 or ovfl(p, -q)
* sudfl(p, q) & q >s 0 => p*q > 0 or ovfl(-p, q)
*
* ~sudfl(p, q) & p >s 0 & q <s 0 => ~ovfl(p, -q) & p*q <s 0
* ~sudfl(p, q) & p <s 0 & q >s 0 => ~ovfl(-p, q) & p*q <s 0
*/
void smul_ovfl_constraint::narrow(solver& s, bool is_positive, bool first) {
if (!first)
return;
signed_constraint sc(this, is_positive);
if (is_positive) {
s.add_clause(~sc, s.ule(2, p()), false);
s.add_clause(~sc, s.ule(2, q()), false);
s.add_clause(~sc, ~s.sgt(p(), 0), s.sgt(q(), 0), false);
s.add_clause(~sc, ~s.sgt(q(), 0), s.sgt(p(), 0), false);
s.add_clause(~sc, ~s.sgt(p(), 0), s.slt(p()*q(), 0), s.mul_ovfl(p(), q()), false);
s.add_clause(~sc, s.sgt(p(), 0), s.slt(p()*q(), 0), s.mul_ovfl(-p(), -q()), false);
if (m_is_overflow) {
if (is_positive) {
s.add_clause(~sc, s.ule(2, p()), false);
s.add_clause(~sc, s.ule(2, q()), false);
s.add_clause(~sc, ~s.sgt(p(), 0), s.sgt(q(), 0), false);
s.add_clause(~sc, ~s.sgt(q(), 0), s.sgt(p(), 0), false);
s.add_clause(~sc, ~s.sgt(p(), 0), s.slt(p()*q(), 0), s.mul_ovfl(p(), q()), false);
s.add_clause(~sc, s.sgt(p(), 0), s.slt(p()*q(), 0), s.mul_ovfl(-p(), -q()), false);
}
else {
s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), ~s.mul_ovfl(p(), q()), false);
s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), ~s.slt(p()*q(), 0), false);
s.add_clause(~sc, ~s.slt(p(), 0), ~s.slt(q(), 0), ~s.mul_ovfl(-p(), -q()), false);
s.add_clause(~sc, ~s.slt(p(), 0), ~s.slt(q(), 0), ~s.slt((-p())*(-q()), 0), false);
}
}
else {
// smul_noovfl(p,q) => sign(p) != sign(q) or p'*q' < 2^{K-1}
s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), ~s.mul_ovfl(p(), q()), false);
s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), ~s.slt(p()*q(), 0), false);
s.add_clause(~sc, ~s.slt(p(), 0), ~s.slt(q(), 0), ~s.mul_ovfl(-p(), -q()), false);
s.add_clause(~sc, ~s.slt(p(), 0), ~s.slt(q(), 0), ~s.slt((-p())*(-q()), 0), false);
if (is_positive) {
s.add_clause(~sc, s.ule(2, p()), false);
s.add_clause(~sc, s.ule(2, q()), false);
s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), false);
s.add_clause(~sc, s.sgt(q(), 0), s.sgt(p(), 0), false);
s.add_clause(~sc, ~s.sgt(p(), 0), s.sgt(p()*q(), 0), s.mul_ovfl(p(), -q()), false);
s.add_clause(~sc, ~s.sgt(q(), 0), s.sgt(p()*q(), 0), s.mul_ovfl(-p(), q()), false);
}
else {
s.add_clause(sc, ~s.sgt(p(), 0), ~s.slt(q(), 0), s.mul_ovfl(p(), -q()), false);
s.add_clause(sc, ~s.sgt(p(), 0), ~s.slt(q(), 0), s.slt(p()*q(), 0), false);
s.add_clause(sc, ~s.slt(p(), 0), ~s.sgt(q(), 0), s.mul_ovfl(-p(), q()), false);
s.add_clause(sc, ~s.slt(p(), 0), ~s.sgt(q(), 0), s.slt(p()*q(), 0), false);
}
}
}