mirror of
https://github.com/Z3Prover/z3
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t
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
b443d4590b
commit
dc2a7dc170
3 changed files with 45 additions and 232 deletions
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@ -1475,16 +1475,50 @@ namespace nlsat {
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if (max_var(new_lit) < max) {
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if (max_var(new_lit) < max) {
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if (m_solver.value(new_lit) == l_true) {
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if (m_solver.value(new_lit) == l_true) {
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new_lit = l;
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TRACE(nlsat_simplify_bug,
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tout << "literal normalized away because it is already true after rewriting:\n";
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display(tout << " original: ", l) << "\n";
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display(tout << " rewritten: ", new_lit) << "\n";
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if (info.m_eq) {
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polynomial_ref eq_ref(const_cast<poly*>(info.m_eq), m_pm);
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m_pm.display(tout << " equation used: ", eq_ref, m_solver.display_proc());
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tout << " = 0\n";
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});
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new_lit = l; // SIMP_BUG
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}
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}
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else {
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else {
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add_literal(new_lit);
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literal assumption = new_lit;
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new_lit = true_literal;
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TRACE(nlsat_simplify_bug,
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tout << "literal replaced by lower-stage assumption due to rewriting:\n";
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display(tout << " original: ", l) << "\n";
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display(tout << " assumption: ", assumption) << "\n";
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if (info.m_eq) {
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polynomial_ref eq_ref(const_cast<poly*>(info.m_eq), m_pm);
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m_pm.display(tout << " equation used: ", eq_ref, m_solver.display_proc());
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tout << " = 0\n";
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});
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add_literal(assumption);
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new_lit = true_literal; // SIMP_BUG
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}
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}
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}
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}
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else {
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else {
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literal before = new_lit;
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(void)before;
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new_lit = normalize(new_lit, max);
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new_lit = normalize(new_lit, max);
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TRACE(nlsat_simplify_core, tout << "simplified literal after normalization:\n"; display(tout, new_lit); tout << " " << m_solver.value(new_lit) << "\n";);
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TRACE(nlsat_simplify_core, tout << "simplified literal after normalization:\n"; display(tout, new_lit); tout << " " << m_solver.value(new_lit) << "\n";);
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if (new_lit == true_literal || new_lit == false_literal) {
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TRACE(nlsat_simplify_bug,
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tout << "normalize() turned rewritten literal into constant value:\n";
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display(tout << " original: ", l) << "\n";
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display(tout << " rewritten: ", before) << "\n";
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tout << " result: " << (new_lit == true_literal ? "true" : "false") << "\n";
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if (info.m_eq) {
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polynomial_ref eq_ref(const_cast<poly*>(info.m_eq), m_pm);
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m_pm.display(tout << " equation used: ", eq_ref, m_solver.display_proc());
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tout << " = 0\n";
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});
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// SIMP_BUG
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}
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}
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}
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}
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}
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else {
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else {
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@ -1814,12 +1848,7 @@ namespace nlsat {
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m_solver.display(tout););
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m_solver.display(tout););
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}
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}
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elim_vanishing(m_ps);
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elim_vanishing(m_ps);
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if (m_signed_project) {
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project(m_ps, mx_var);
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signed_project(m_ps, mx_var);
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}
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else {
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project(m_ps, mx_var);
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}
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reset_already_added();
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reset_already_added();
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m_result = nullptr;
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m_result = nullptr;
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if (x != mx_var) {
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if (x != mx_var) {
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@ -1855,183 +1884,8 @@ namespace nlsat {
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}
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}
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}
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}
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}
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}
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/**
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Signed projection.
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Assumptions:
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- any variable in ps is at most x.
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- root expressions are satisfied (positive literals)
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Effect:
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- if x not in p, then
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- if sign(p) < 0: p < 0
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- if sign(p) = 0: p = 0
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- if sign(p) > 0: p > 0
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else:
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- let roots_j be the roots of p_j or roots_j[i]
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- let L = { roots_j[i] | M(roots_j[i]) < M(x) }
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- let U = { roots_j[i] | M(roots_j[i]) > M(x) }
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- let E = { roots_j[i] | M(roots_j[i]) = M(x) }
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- let glb in L, s.t. forall l in L . M(glb) >= M(l)
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- let lub in U, s.t. forall u in U . M(lub) <= M(u)
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- if root in E, then
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- add E x . x = root & x > lb for lb in L
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- add E x . x = root & x < ub for ub in U
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- add E x . x = root & x = root2 for root2 in E \ { root }
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- else
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- assume |L| <= |U| (other case is symmetric)
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- add E x . lb <= x & x <= glb for lb in L
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- add E x . x = glb & x < ub for ub in U
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*/
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void signed_project(polynomial_ref_vector& ps, var x) {
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TRACE(nlsat_explain, tout << "Signed projection\n";);
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polynomial_ref p(m_pm);
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unsigned eq_index = 0;
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bool eq_valid = false;
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unsigned eq_degree = 0;
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for (unsigned i = 0; i < ps.size(); ++i) {
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p = ps.get(i);
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int s = sign(p);
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if (max_var(p) != x) {
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atom::kind k = (s == 0)?(atom::EQ):((s < 0)?(atom::LT):(atom::GT));
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add_simple_assumption(k, p, false);
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ps[i] = ps.back();
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ps.pop_back();
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--i;
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}
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else if (s == 0) {
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if (!eq_valid || degree(p, x) < eq_degree) {
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eq_index = i;
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eq_valid = true;
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eq_degree = degree(p, x);
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}
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}
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}
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if (ps.empty()) {
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return;
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}
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if (ps.size() == 1) {
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project_single(x, ps.get(0));
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return;
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}
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// ax + b = 0, p(x) > 0 ->
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if (eq_valid) {
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p = ps.get(eq_index);
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if (degree(p, x) == 1) {
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// ax + b = 0
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// let d be maximal degree of x in p.
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// p(x) -> a^d*p(-b/a), a
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// perform virtual substitution with equality.
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solve_eq(x, eq_index, ps);
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}
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else {
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add_zero_assumption(p);
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for (unsigned j = 0; j < ps.size(); ++j) {
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if (j == eq_index)
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continue;
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p = ps.get(j);
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int s = sign(p);
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atom::kind k = (s == 0)?(atom::EQ):((s < 0)?(atom::LT):(atom::GT));
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add_simple_assumption(k, p, false);
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}
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}
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return;
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}
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unsigned num_lub = 0, num_glb = 0;
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unsigned glb_index = 0, lub_index = 0;
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scoped_anum lub(m_am), glb(m_am), x_val(m_am);
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x_val = m_assignment.value(x);
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bool glb_valid = false, lub_valid = false;
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for (unsigned i = 0; i < ps.size(); ++i) {
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p = ps.get(i);
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scoped_anum_vector & roots = m_roots_tmp;
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roots.reset();
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m_am.isolate_roots(p, undef_var_assignment(m_assignment, x), roots);
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for (auto const& r : roots) {
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int s = m_am.compare(x_val, r);
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SASSERT(s != 0);
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if (s < 0 && (!lub_valid || m_am.lt(r, lub))) {
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lub_index = i;
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m_am.set(lub, r);
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lub_valid = true;
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}
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if (s > 0 && (!glb_valid || m_am.lt(glb, r))) {
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glb_index = i;
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m_am.set(glb, r);
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glb_valid = true;
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}
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if (s < 0) ++num_lub;
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if (s > 0) ++num_glb;
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}
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}
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TRACE(nlsat_explain, tout << "glb: " << num_glb << " lub: " << num_lub << "\n" << lub_index << "\n" << glb_index << "\n" << ps << "\n";);
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if (num_lub == 0) {
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project_plus_infinity(x, ps);
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return;
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}
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if (num_glb == 0) {
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project_minus_infinity(x, ps);
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return;
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}
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if (num_lub <= num_glb) {
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glb_index = lub_index;
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}
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project_pairs(x, glb_index, ps);
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}
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void project_plus_infinity(var x, polynomial_ref_vector const& ps) {
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polynomial_ref p(m_pm), lc(m_pm);
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for (unsigned i = 0; i < ps.size(); ++i) {
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p = ps.get(i);
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unsigned d = degree(p, x);
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lc = m_pm.coeff(p, x, d);
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if (!is_const(lc)) {
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int s = sign(p);
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SASSERT(s != 0);
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atom::kind k = (s > 0)?(atom::GT):(atom::LT);
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add_simple_assumption(k, lc);
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}
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}
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}
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void project_minus_infinity(var x, polynomial_ref_vector const& ps) {
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polynomial_ref p(m_pm), lc(m_pm);
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for (unsigned i = 0; i < ps.size(); ++i) {
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p = ps.get(i);
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unsigned d = degree(p, x);
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lc = m_pm.coeff(p, x, d);
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if (!is_const(lc)) {
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int s = sign(p);
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TRACE(nlsat_explain, tout << "degree: " << d << " " << lc << " sign: " << s << "\n";);
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SASSERT(s != 0);
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atom::kind k;
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if (s > 0) {
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k = (d % 2 == 0)?(atom::GT):(atom::LT);
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}
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else {
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k = (d % 2 == 0)?(atom::LT):(atom::GT);
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}
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add_simple_assumption(k, lc);
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}
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}
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}
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void project_pairs(var x, unsigned idx, polynomial_ref_vector const& ps) {
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void project_pairs(var x, unsigned idx, polynomial_ref_vector const& ps) {
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TRACE(nlsat_explain, tout << "project pairs\n";);
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TRACE(nlsat_explain, tout << "project pairs\n";);
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polynomial_ref p(m_pm);
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polynomial_ref p(m_pm);
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@ -2056,49 +1910,7 @@ namespace nlsat {
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project(m_ps2, x);
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project(m_ps2, x);
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}
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}
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void solve_eq(var x, unsigned idx, polynomial_ref_vector const& ps) {
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polynomial_ref p(m_pm), A(m_pm), B(m_pm), C(m_pm), D(m_pm), E(m_pm), q(m_pm), r(m_pm);
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polynomial_ref_vector As(m_pm), Bs(m_pm);
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p = ps.get(idx);
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SASSERT(degree(p, x) == 1);
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A = m_pm.coeff(p, x, 1);
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B = m_pm.coeff(p, x, 0);
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As.push_back(m_pm.mk_const(rational(1)));
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Bs.push_back(m_pm.mk_const(rational(1)));
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B = neg(B);
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TRACE(nlsat_explain, tout << "p: " << p << " A: " << A << " B: " << B << "\n";);
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// x = B/A
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for (unsigned i = 0; i < ps.size(); ++i) {
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if (i != idx) {
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q = ps.get(i);
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unsigned d = degree(q, x);
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D = m_pm.mk_const(rational(1));
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E = D;
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r = m_pm.mk_zero();
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for (unsigned j = As.size(); j <= d; ++j) {
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D = As.back(); As.push_back(A * D);
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D = Bs.back(); Bs.push_back(B * D);
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}
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for (unsigned j = 0; j <= d; ++j) {
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// A^d*p0 + A^{d-1}*B*p1 + ... + B^j*A^{d-j}*pj + ... + B^d*p_d
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C = m_pm.coeff(q, x, j);
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TRACE(nlsat_explain, tout << "coeff: q" << j << ": " << C << "\n";);
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if (!is_zero(C)) {
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D = As.get(d - j);
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E = Bs.get(j);
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r = r + D*E*C;
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}
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}
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TRACE(nlsat_explain, tout << "p: " << p << " q: " << q << " r: " << r << "\n";);
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ensure_sign(r);
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}
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else {
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ensure_sign(A);
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}
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}
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}
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void maximize(var x, unsigned num, literal const * ls, scoped_anum& val, bool& unbounded) {
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void maximize(var x, unsigned num, literal const * ls, scoped_anum& val, bool& unbounded) {
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svector<literal> lits;
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svector<literal> lits;
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polynomial_ref p(m_pm);
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polynomial_ref p(m_pm);
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@ -1138,7 +1138,7 @@ namespace nlsat {
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for (var v : vars)
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for (var v : vars)
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used_vars[v] = true;
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used_vars[v] = true;
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}
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}
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display(out << "(echo \"#" << m_lemma_count++ << ":" << annotation << "\n", n, cls) << "\")\n";
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display(out << "(echo \"#" << m_lemma_count++ << ":" << annotation << ":", n, cls) << "\")\n";
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out << "(set-logic ALL)\n";
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out << "(set-logic ALL)\n";
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out << "(set-option :rlimit " << m_lemma_rlimit << ")\n";
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out << "(set-option :rlimit " << m_lemma_rlimit << ")\n";
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if (is_valid) {
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if (is_valid) {
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@ -3640,8 +3640,8 @@ namespace nlsat {
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template<typename Printer>
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template<typename Printer>
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std::ostream& display_root_quantified(std::ostream& out, root_atom const& a, display_var_proc const& proc, Printer const& printer) const {
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std::ostream& display_root_quantified(std::ostream& out, root_atom const& a, display_var_proc const& proc, Printer const& printer) const {
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if (a.i() == 1 && m_pm.degree(a.p(), a.x()) == 1)
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// if (a.i() == 1 && m_pm.degree(a.p(), a.x()) == 1)
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return display_linear_root_smt2(out, a, proc);
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// return display_linear_root_smt2(out, a, proc);
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auto mk_y_name = [](unsigned j) {
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auto mk_y_name = [](unsigned j) {
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return std::string("y") + std::to_string(j);
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return std::string("y") + std::to_string(j);
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@ -708,6 +708,7 @@ X(Global, nlsat_resolve_done, "nlsat resolve done")
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X(Global, nlsat_root, "nlsat root")
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X(Global, nlsat_root, "nlsat root")
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X(Global, nlsat_simpilfy_core, "nlsat simpilfy core")
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X(Global, nlsat_simpilfy_core, "nlsat simpilfy core")
|
||||||
X(Global, nlsat_simplify_core, "nlsat simplify core")
|
X(Global, nlsat_simplify_core, "nlsat simplify core")
|
||||||
|
X(Global, nlsat_simplify_bug, "nlsat simplify bug")
|
||||||
X(Global, nlsat_smt2, "nlsat smt2")
|
X(Global, nlsat_smt2, "nlsat smt2")
|
||||||
X(Global, nlsat_solver, "nlsat solver")
|
X(Global, nlsat_solver, "nlsat solver")
|
||||||
X(Global, nlsat_sort, "nlsat sort")
|
X(Global, nlsat_sort, "nlsat sort")
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue