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more saturation for overflow

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2024-01-31 20:12:01 -08:00
parent 7dc61ca646
commit e6f7ba90f1
5 changed files with 116 additions and 8 deletions
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113
src/sat/smt/polysat/saturation.cpp
View file

@ -175,12 +175,12 @@ namespace polysat {
}
// Ovfl(x, y) & ~Ovfl(y, z) ==> x > z
void saturation::try_umul_ovfl(pvar v, umul_ovfl const& sc) {
void saturation::try_umul_monotonicity(umul_ovfl const& sc) {
auto p = sc.p(), q = sc.q();
auto match_mul_arg = [&](auto const& sc2) {
auto p2 = sc2.to_umul_ovfl().p(), q2 = sc2.to_umul_ovfl().q();
auto match_mul_arg = [&](auto const& sc2) {
auto p2 = sc2.to_umul_ovfl().p(), q2 = sc2.to_umul_ovfl().q();
return p == p2 || p == q2 || q == p2 || q == q2;
};
};
auto extract_mul_args = [&](auto const& sc2) -> std::pair<pdd, pdd> {
auto p2 = sc2.to_umul_ovfl().p(), q2 = sc2.to_umul_ovfl().q();
if (p == p2)
@ -193,7 +193,7 @@ namespace polysat {
SASSERT(q == q2);
return { p, p2 };
}
};
};
for (auto id : constraint_iterator(c, [&](auto const& sc2) { return sc2.is_umul_ovfl() && sc.sign() != sc2.sign() && match_mul_arg(sc2); })) {
auto sc2 = c.get_constraint(id);
auto d1 = c.get_dependency(sc.id());
@ -201,9 +201,106 @@ namespace polysat {
auto [q1, q2] = extract_mul_args(sc2);
if (sc.sign())
add_clause("[y] ~ovfl(p, q1) & ovfl(p, q2) ==> q1 < q2", { d1, d2, C.ult(q1, q2) }, true);
else
add_clause("[y] ovfl(p, q1) & ~ovfl(p, q2) ==> q1 > q2", { d1, d2, C.ult(q2, q1)}, true);
}
else
add_clause("[y] ovfl(p, q1) & ~ovfl(p, q2) ==> q1 > q2", { d1, d2, C.ult(q2, q1) }, true);
}
}
/**
* Expand the following axioms:
* Ovfl(x, y) & msb(x) <= k => msb(y) >= N - k - 1
* Ovfl(x, y) & msb(x) <= k & msb(y) <= N - k - 1 => 0x * 0y >= 2^{N-1}
*
* ~Ovfl(x,y) & msb(x) >= k => msb(y) <= N - k - 1
* ~Ovfl(x,y) & msb(x) >= k & msb(y) >= N - k - 1 => 0x * 0y < 2^{N-1}
*/
void saturation::try_umul_blast(umul_ovfl const& sc) {
auto x = sc.p();
auto y = sc.q();
if (!x.is_val())
return;
if (!y.is_val())
return;
auto N = x.manager().power_of_2();
auto d = c.get_dependency(sc.id());
auto vx = x.val();
auto vy = y.val();
auto bx = vx.get_num_bits();
auto by = vy.get_num_bits();
if (bx > by) {
std::swap(bx, by);
std::swap(x, y);
}
// Keep in mind that
// num-bits(0) = 1
// num-bits(1) = 1
// num-bits(2) = 2
// num-bits(4) = 3
// msb(0) = 0
// msb(1) = 0
// msb(2) = 1
// msb(3) = 1
// msb(2^N - 1) = N-1
// msb(x) >= k <=> x >= 2^k, for k > 0
// msb(x) <= k <=> x < 2^{k+1}, for k + 1 < N
auto msb_ge = [&](pdd const& x, unsigned k) {
SASSERT(k > 0);
return C.uge(x, rational::power_of_two(k));
};
auto msb_le = [&](pdd const& x, unsigned k) {
SASSERT(k + 1 < N);
return C.ult(x, rational::power_of_two(k + 1));
};
if (sc.sign()) {
// Case ~Ovfl(x,y) is asserted by current assignment x * y is overflow
SASSERT(bx > 1 && by > 1);
SASSERT(bx + by >= N + 1);
auto k = bx - 1;
if (bx + by > N + 1)
add_clause("~Ovfl(x, y) & msb(x) >= k => msb(y) <= N - k - 1",
{d, ~msb_ge(x, k), msb_le(y, N - k - 1)},
true);
else {
auto x1 = c.mk_zero_extend(1, x);
auto y1 = c.mk_zero_extend(1, y);
add_clause("~Ovfl(x, y) & msb(x) >= k & msb(y) >= N - k - 1 => 0x * 0y < 2^{N-1}",
{ d, ~msb_ge(x, k),
~msb_ge(y, N - k - 1),
C.ult(x1 * y1, rational::power_of_two(N - 1))
}, true);
}
}
else {
// Case Ovfl(x,y)
if (bx == 0) {
add_clause("Ovfl(x, y) => x > 1", { d, C.ugt(x, 1) }, true);
}
else if (bx + by < N + 1) {
SASSERT(bx <= by);
auto k = bx - 1;
add_clause("Ovfl(x, y) & msb(x) <= k => msb(y) >= N - k - 1",
{ d, ~msb_le(x, k), msb_ge(y, N - k - 1) }, true);
}
else {
auto k = bx - 1;
auto x1 = c.mk_zero_extend(1, x);
auto y1 = c.mk_zero_extend(1, y);
add_clause("Ovfl(x, y) & msb(x) <= k & msb(y) <= N - k - 1 = > 0x * 0y >= 2 ^ {N - 1}",
{ d, ~msb_le(x, k), ~msb_le(y, N - k - 1), C.uge(x1 * y1, rational::power_of_two(N - 1)) },
true);
}
}
}
void saturation::try_umul_ovfl(pvar v, umul_ovfl const& sc) {
try_umul_monotonicity(sc);
try_umul_blast(sc);
}
void saturation::try_eq_resolve(pvar v, inequality const& i) {

2
src/sat/smt/polysat/saturation.h
View file

@ -65,6 +65,8 @@ namespace polysat {
void try_ugt_y(pvar v, inequality const& i);
void try_ugt_z(pvar z, inequality const& i);
void try_umul_ovfl(pvar v, umul_ovfl const& sc);
void try_umul_monotonicity(umul_ovfl const& sc);
void try_umul_blast(umul_ovfl const& sc);
void try_op(pvar v, signed_constraint& sc, dependency const& d);
signed_constraint ineq(bool is_strict, pdd const& x, pdd const& y);

1
src/sat/smt/polysat/types.h
View file

@ -149,6 +149,7 @@ namespace polysat {
virtual void get_bitvector_super_slices(pvar v, offset_slices& out) = 0;
virtual void get_fixed_bits(pvar v, fixed_bits_vector& fixed_slice) = 0;
virtual pdd mk_ite(signed_constraint const& sc, pdd const& p, pdd const& q) = 0;
virtual pdd mk_zero_extend(unsigned sz, pdd const& p) = 0;
virtual unsigned level(dependency const& d) = 0;
};

7
src/sat/smt/polysat_internalize.cpp
View file

@ -858,6 +858,13 @@ namespace polysat {
return expr2pdd(ite);
}
pdd solver::mk_zero_extend(unsigned n, pdd const& p) {
expr_ref pe = pdd2expr(p);
auto ze = bv.mk_zero_extend(n, pe);
ctx.internalize(ze);
return expr2pdd(ze);
}
dd::pdd solver::expr2pdd(expr* e) {
return var2pdd(get_th_var(e));
}

1
src/sat/smt/polysat_solver.h
View file

@ -225,6 +225,7 @@ namespace polysat {
void get_bitvector_suffixes(pvar v, offset_slices& out) override;
void get_fixed_bits(pvar v, fixed_bits_vector& fixed_bits) override;
pdd mk_ite(signed_constraint const& sc, pdd const& p, pdd const& q) override;
pdd mk_zero_extend(unsigned sz, pdd const& p) override;
unsigned level(dependency const& d) override;
dependency explain_slice(pvar v, pvar w, unsigned offset);