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support checking pseudo-inverses

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This commit is contained in:
Jakob Rath 2023-03-12 18:31:57 +01:00
parent 07d1f86575
commit 233baf170c
2 changed files with 70 additions and 2 deletions
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64
src/math/polysat/polysat_ast.cpp
View file

@ -44,7 +44,7 @@ namespace polysat {
ast* store(ast* a) { storage.push_back(ast_ref{a, m}); return a; }
expr* store(expr* e) { storage.push_back(ast_ref{e, m}); return e; }
app* store(app* a) { storage.push_back(ast_ref{a, m}); return a; }
};
polysat_ast::polysat_ast(solver& s)
@ -57,6 +57,12 @@ namespace polysat {
ast_manager& polysat_ast::m() const { return d->m; }
bv_util& polysat_ast::bv() const { return *d->bv; }
expr* polysat_ast::mk_fresh_bool_const(char const* prefix) {
app* b = d->store(m().mk_fresh_const(prefix, m().mk_bool_sort()));
d->decls.push_back(b->get_decl());
return b;
}
expr* polysat_ast::mk_val(rational const& val, unsigned bit_width) {
return d->store(bv().mk_numeral(val, bit_width));
}
@ -67,7 +73,7 @@ namespace polysat {
unsigned bit_width = s.size(x);
std::string name = "v";
name += std::to_string(x);
auto decl = m().mk_const_decl(name, bv().mk_sort(bit_width));
func_decl* decl = m().mk_const_decl(name, bv().mk_sort(bit_width));
d->decls.push_back(decl);
node = d->store(m().mk_const(decl));
d->var_expr.insert(x, node);
@ -108,6 +114,51 @@ namespace polysat {
return d->store(bv().mk_bv_add(args));
}
expr* polysat_ast::mk_parity(pdd const& p) {
unsigned const N = p.power_of_2();
if (p.is_val())
return mk_val(rational(p.val().parity(N)), N);
app* parity = d->store(m().mk_fresh_const("parity", bv().mk_sort(N)));
d->decls.push_back(parity->get_decl());
expr* parity_1 = d->store(bv().mk_bv_add(parity, mk_val(rational(1), N)));
expr* v = mk_poly(p);
// if v = 0
// then parity = N
// else v = (v >> parity) << parity
// && v != (v >> parity+1) << parity+1
// TODO: what about: v[k:] = 0 && v[k+1:] != 0 ==> parity = k for each k?
// TODO: add helper axiom like parity <= N ?
expr* definition =
m().mk_ite(
m().mk_eq(v, mk_val(rational(0), N)),
m().mk_eq(parity, mk_val(rational(N), N)),
m().mk_and(
m().mk_eq(v, bv().mk_bv_shl(bv().mk_bv_lshr(v, parity), parity)),
m().mk_not(m().mk_eq(v, bv().mk_bv_shl(bv().mk_bv_lshr(v, parity_1), parity_1)))
));
add(definition);
return parity;
}
expr* polysat_ast::mk_inv(pdd const& p, pdd const& p_inv) {
unsigned const N = p.power_of_2();
// p_inv == smallest_pseudo_inverse(p)
expr* v = mk_poly(p);
expr* v_inv = mk_poly(p_inv);
expr* parity = mk_parity(p);
expr* one = mk_val(rational(1), N);
// 2^parity = v * v_inv
expr* definition1 = m().mk_eq(bv().mk_bv_shl(one, parity), bv().mk_bv_mul(v, v_inv));
// v_inv <= 2^(N - parity) - 1
expr* v_inv_max = bv().mk_bv_sub(bv().mk_bv_shl(one, bv().mk_bv_sub(mk_val(rational(N), N), parity)), one);
expr* definition2 = bv().mk_ule(v_inv, v_inv_max);
// conditional on b
expr* b = mk_fresh_bool_const("parity_enable");
add(m().mk_iff(b, definition1));
add(m().mk_iff(b, definition2));
return b;
}
expr* polysat_ast::mk_not(expr* e) {
return d->store(m().mk_not(e));
}
@ -142,6 +193,15 @@ namespace polysat {
return mk_ule(c->to_ule().lhs(), c->to_ule().rhs(), c.sign());
if (c->is_umul_ovfl())
return mk_umul_ovfl(c->to_umul_ovfl().p(), c->to_umul_ovfl().q(), c.sign());
if (c->is_op()) {
op_constraint& op = c->to_op();
switch (op.get_op()) {
case op_constraint::code::inv_op:
return mk_inv(op.p(), op.r());
default:
break;
}
}
verbose_stream() << "polysat_ast not yet supported: " << c << "\n";
m_ok = false;
// NOT_IMPLEMENTED_YET();

8
src/math/polysat/polysat_ast.h
View file

@ -33,6 +33,11 @@ namespace polysat {
ast_manager& m() const;
bv_util& bv() const;
expr* mk_fresh_bool_const(char const* prefix);
// expression for "parity of p"
expr* mk_parity(pdd const& p);
public:
polysat_ast(solver&);
~polysat_ast();
@ -59,6 +64,9 @@ namespace polysat {
// ovfl*(p, q)
expr* mk_umul_ovfl(pdd const& p, pdd const& q, bool sign);
// p_inv = pseudo-inverse(p)
expr* mk_inv(pdd const& p, pdd const& p_inv);
expr* mk_not(expr* e);
expr* mk_lit(sat::literal lit);