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Jakob Rath 2022-03-10 10:57:49 +01:00
parent 22411f8b43
commit 9b20f17f9c
2 changed files with 18 additions and 14 deletions
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src/math/polysat/smul_fl_constraint.cpp Normal file
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/*++
Copyright (c) 2021 Microsoft Corporation
Module Name:
polysat multiplication overflow constraint
Author:
Jakob Rath, Nikolaj Bjorner (nbjorner) 2021-12-09
--*/
#include "math/polysat/smul_fl_constraint.h"
#include "math/polysat/solver.h"
namespace polysat {
smul_fl_constraint::smul_fl_constraint(constraint_manager& m, pdd const& p, pdd const& q, bool is_overflow):
constraint(m, ckind_t::smul_fl_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())
if (!m_vars.contains(v))
m_vars.push_back(v);
}
void smul_fl_constraint::simplify() {
if (m_p.is_zero() || m_q.is_zero() ||
m_p.is_one() || m_q.is_one()) {
m_q = 0;
m_p = 0;
return;
}
if (m_p.index() > m_q.index())
std::swap(m_p, m_q);
}
std::ostream& smul_fl_constraint::display(std::ostream& out, lbool status) const {
switch (status) {
case l_true: return display(out);
case l_false: return display(out << "~");
case l_undef: return display(out << "?");
}
return out;
}
std::ostream& smul_fl_constraint::display(std::ostream& out) const {
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_fl_constraint::narrow(solver& s, bool is_positive, bool first) {
if (!first)
return;
signed_constraint sc(this, is_positive);
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 {
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);
}
}
}
unsigned smul_fl_constraint::hash() const {
return mk_mix(p().hash(), q().hash(), mk_mix(kind(), is_overflow(), 0));
}
bool smul_fl_constraint::operator==(constraint const& other) const {
return other.is_smul_fl()
&& is_overflow() == other.to_smul_fl().is_overflow()
&& p() == other.to_smul_fl().p()
&& q() == other.to_smul_fl().q();
}
}