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arithmetic

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2024-01-13 10:29:50 -08:00
parent 33c43a474d
commit 93be3d2b2c
4 changed files with 53 additions and 22 deletions
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3
src/sat/smt/polysat/forbidden_intervals.cpp
View file

@ -22,7 +22,8 @@ Author:
namespace polysat {
std::ostream& operator<<(std::ostream& out, fi_record const& fi) {
out << "fi_record(bw = " << fi.bit_width << ", coeff = " << fi.coeff << ", " << fi.interval << ", " << fi.src << fi.side_cond << fi.deps << ")";
out << "fi_record(bw = " << fi.bit_width << ", coeff = " << fi.coeff << ", " << fi.interval << ", "
<< fi.src << (fi.src.empty()?"": " ") << fi.side_cond << (fi.side_cond.empty()?"":" ") << fi.deps << ")";
return out;
}

13
src/sat/smt/polysat/viable.cpp
View file

@ -643,9 +643,15 @@ namespace polysat {
// Then value is chosen, min x . coeff * x >= t.
// In other words:
//
// coeff * (value - 1) <= t < coeff*value + 1
//
auto vlo = c.value(mod((e.value - 1) * p2eb, p2b), bw);
// x >= t div coeff
// => t <= coeff * x
// (x - 1) * coeff < t <= x * coeff
// a < x <= b <=>
// a + 1 <= x < b + 1
auto vlo = c.value(mod((e.value - 1) * p2eb + 1, p2b), bw);
auto vhi = c.value(mod(e.value * p2eb + 1, p2b), bw);
#if 0
@ -655,6 +661,7 @@ namespace polysat {
verbose_stream() << "before bw " << ebw << " " << bw << " " << *e.e << "\nafter bw " << abw << " " << aw << " " << *after.e << "\n";
if (!t.is_val())
IF_VERBOSE(0, verbose_stream() << "symbolic t : " << t << "\n");
#endif
auto sc = cs.ult(t - vlo, vhi - vlo);
CTRACE("bv", sc.is_always_false(), c.display(tout));

13
src/sat/smt/polysat_internalize.cpp
View file

@ -531,12 +531,12 @@ namespace polysat {
// Axioms for quotient/remainder
//
// a = b*q + r
// x = y*q + r
// multiplication does not overflow in b*q
// addition does not overflow in (b*q) + r; for now expressed as: r <= bq+r
// b ≠ 0 ==> r < b
// b = 0 ==> q = -1
// TODO: when a,b become evaluable, can we actually propagate q,r? doesn't seem like it.
// addition does not overflow in (y*q) + r; for now expressed as: r <= yq+r
// y ≠ 0 ==> r < y
// y = 0 ==> q = -1
// TODO: when x,y become evaluable, can we actually propagate q,r? doesn't seem like it.
// Maybe we need something like an op_constraint for better propagation.
add_axiom("quot-rem", { eq_internalize(bv.mk_bv_add(bv.mk_bv_mul(y, quot), rem), x)}, false);
@ -545,12 +545,11 @@ namespace polysat {
// { apply equivalence: p <= q <=> q-p <= -p-1 }
// b*q <= -r-1
auto minus_one = bv.mk_numeral(rational::power_of_two(sz) - 1, sz);
auto one = bv.mk_numeral(1, sz);
auto zero = bv.mk_numeral(0, sz);
add_axiom("quot-rem", { mk_literal(bv.mk_ule(bv.mk_bv_mul(y, quot), bv.mk_bv_sub(minus_one, rem))) }, false);
auto c_eq = eq_internalize(y, zero);
add_axiom("quot-rem", { c_eq, ~mk_literal(bv.mk_ule(y, rem)) }, false);
add_axiom("quot-rem", { ~c_eq, eq_internalize(bv.mk_bv_add(quot, one), zero) }, false);
add_axiom("quot-rem", { ~c_eq, eq_internalize(quot, minus_one) }, false);
}
void solver::internalize_sign_extend(app* e) {

46
src/sat/smt/polysat_solver.cpp
View file

@ -459,18 +459,42 @@ namespace polysat {
}
expr_ref solver::pdd2expr(pdd const& p) {
if (p.is_val()) {
expr* n = bv.mk_numeral(p.val(), p.power_of_2());
return expr_ref(n, m);
}
auto v = var2enode(m_pddvar2var[p.var()]);
auto mk_num = [&](rational const& c) {
return bv.mk_numeral(c, p.power_of_2());
};
auto mk_var = [&](pvar v) {
return var2expr(m_pddvar2var[v]);
};
if (p.is_val())
return expr_ref(mk_num(p.val()), m);
expr_ref_vector args(m);
for (auto const& mon : p) {
auto c = mon.coeff;
if (mon.vars.empty())
args.push_back(mk_num(c));
else if (mon.coeff == 1 && mon.vars.size() == 1)
args.push_back(mk_var(mon.vars[0]));
else if (mon.vars.size() == 1)
args.push_back(bv.mk_bv_mul(mk_num(c), mk_var(mon.vars[0])));
else {
expr_ref_vector args2(m);
for (auto v : mon.vars)
args2.push_back(mk_var(v));
if (c == 1)
args.push_back(bv.mk_bv_mul(args2));
else
args.push_back(bv.mk_bv_mul(mk_num(c), bv.mk_bv_mul(args2)));
}
}
expr_ref r(m);
r = v->get_expr();
if (!p.hi().is_one())
r = bv.mk_bv_mul(r, pdd2expr(p.hi()));
if (!p.lo().is_zero())
r = bv.mk_bv_add(r, pdd2expr(p.lo()));
ctx.get_rewriter()(r);
if (args.size() == 1)
r = args.get(0);
else
r = bv.mk_bv_add(args);
return r;
}