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https://github.com/Z3Prover/z3
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move interval functionality from horner to intervals
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
b84ac3f27e
commit
9b3ebfdd2a
4 changed files with 477 additions and 473 deletions
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@ -32,6 +32,459 @@ void intervals::set_var_interval_with_deps(lpvar v, interval& b) const {
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}
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}
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void intervals::set_interval_for_scalar(interv& a, const rational& v) {
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set_lower(a, v);
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set_upper(a, v);
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set_lower_is_open(a, false);
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set_lower_is_inf(a, false);
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set_upper_is_open(a, false);
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set_upper_is_inf(a, false);
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}
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intervals::interv intervals::power_with_deps(const interv& a, unsigned n) {
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interv b;
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interval_deps_combine_rule combine_rule;
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power(a, n, b, combine_rule);
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combine_deps(a, combine_rule, b);
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TRACE("nla_horner_details", tout << "power of "; display(tout, a) << " = ";
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display(tout, b) << "\n"; );
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return b;
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}
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intervals::interv intervals::interval_of_expr_with_deps(const nex* e, unsigned power) {
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interv a;
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switch (e->type()) {
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case expr_type::SCALAR:
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set_interval_for_scalar(a, to_scalar(e)->value());
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if (power != 1) {
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return power_with_deps(a, power);
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}
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return a;
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case expr_type::SUM:
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{
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interv b = interval_of_sum_with_deps(to_sum(e));
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if (power != 1)
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return power_with_deps(b, power);
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return b;
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}
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case expr_type::MUL:
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{
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interv b = interval_of_mul_with_deps(to_mul(e));
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if (power != 1)
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return power_with_deps(b, power);;
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return b;
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}
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case expr_type::VAR:
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set_var_interval_with_deps(to_var(e)->var(), a);
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if (power != 1)
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return power_with_deps(a, power);;
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return a;
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default:
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TRACE("nla_intervals_details", tout << e->type() << "\n";);
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SASSERT(false);
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return interv();
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}
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}
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intervals::interv intervals::interval_of_expr(const nex* e, unsigned power) {
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TRACE("nla_intervals_details", tout << "e = " << *e << "\n";);
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interv a;
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switch (e->type()) {
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case expr_type::SCALAR:
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set_interval_for_scalar(a, to_scalar(e)->value());
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break;
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case expr_type::SUM:
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{
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interv b = interval_of_sum(to_sum(e));
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if (power != 1) {
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return power_with_deps(b, power);;
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}
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return b;
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}
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case expr_type::MUL:
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{
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interv b = interval_of_mul(to_mul(e));
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if (power != 1) {
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return power_with_deps(b, power);;
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}
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return b;
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}
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case expr_type::VAR:
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set_var_interval(to_var(e)->var(), a);
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break;
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default:
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TRACE("nla_intervals_details", tout << e->type() << "\n";);
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SASSERT(false);
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return interv();
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}
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if (power != 1) {
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return power_with_deps(a, power);;
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}
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return a;
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}
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const nex* intervals::get_inf_interval_child(const nex_sum* e) const {
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for (auto * c : e->children()) {
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if (has_inf_interval(c))
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return c;
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}
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return nullptr;
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}
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bool intervals::mul_has_inf_interval(const nex_mul* e) const {
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bool has_inf = false;
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for (const auto & p : e->children()) {
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const nex *c = p.e();
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if (!c->is_elementary())
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return false;
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if (has_zero_interval(c))
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return false;
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has_inf |= has_inf_interval(c);
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}
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return has_inf;
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}
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bool intervals::has_inf_interval(const nex* e) const {
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if (e->is_var())
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return m_core->no_bounds(to_var(e)->var());
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if (e->is_mul()) {
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return mul_has_inf_interval(to_mul(e));
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}
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if (e->is_scalar())
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return false;
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for (auto * c : to_sum(e)->children()) {
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if (has_inf_interval(c))
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return true;
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}
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return false;
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}
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bool intervals::has_zero_interval(const nex* e) const {
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SASSERT(!e->is_scalar() || !to_scalar(e)->value().is_zero());
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if (! e->is_var())
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return false;
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return m_core->var_is_fixed_to_zero(to_var(e)->var());
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}
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const nex* intervals::get_zero_interval_child(const nex_mul* e) const {
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for (const auto & p : e->children()) {
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const nex * c = p.e();
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if (has_zero_interval(c))
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return c;
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}
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return nullptr;
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}
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intervals::interv intervals::interval_of_mul_with_deps(const nex_mul* e) {
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const nex * zero_interval_child = get_zero_interval_child(e);
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if (zero_interval_child) {
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interv a = interval_of_expr_with_deps(zero_interval_child, 1);
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set_zero_interval_deps_for_mult(a);
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TRACE("nla_intervals_details", tout << "zero_interval_child = "<< *zero_interval_child << std::endl << "a = "; display(tout, a); );
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return a;
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}
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SASSERT(e->is_mul());
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interv a;
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set_interval_for_scalar(a, e->coeff());
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TRACE("nla_intervals_details", tout << "a = "; display(tout, a); );
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for (const auto & ep : *e) {
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interv b = interval_of_expr_with_deps(ep.e(), ep.pow());
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TRACE("nla_intervals_details", tout << "ep = " << ep << ", "; display(tout, b); );
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interv c;
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interval_deps_combine_rule comb_rule;
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mul_two_intervals(a, b, c, comb_rule);
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TRACE("nla_intervals_details", tout << "c before combine_deps() "; display(tout, c););
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combine_deps(a, b, comb_rule, c);
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TRACE("nla_intervals_details", tout << "a "; display(tout, a););
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TRACE("nla_intervals_details", tout << "c "; display(tout, c););
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set_with_deps(a, c);
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TRACE("nla_intervals_details", tout << "part mult "; display(tout, a););
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}
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TRACE("nla_intervals_details", tout << "e=" << *e << "\n";
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tout << " return "; display(tout, a););
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return a;
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}
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intervals::interv intervals::interval_of_mul(const nex_mul* e) {
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TRACE("nla_intervals_details", tout << "e = " << *e << "\n";);
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const nex * zero_interval_child = get_zero_interval_child(e);
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if (zero_interval_child) {
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interv a = interval_of_expr(zero_interval_child, 1);
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set_zero_interval_deps_for_mult(a);
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TRACE("nla_intervals_details", tout << "zero_interval_child = "<< *zero_interval_child << std::endl << "a = "; display(tout, a); );
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return a;
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}
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interv a;
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set_interval_for_scalar(a, e->coeff());
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TRACE("nla_intervals_details", tout << "a = "; display(tout, a); );
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for (const auto & ep : *e) {
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interv b = interval_of_expr(ep.e(), ep.pow() );
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TRACE("nla_intervals_details", tout << "ep = " << ep << ", "; display(tout, b); );
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interv c;
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interval_deps_combine_rule comb_rule;
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mul_two_intervals(a, b, c, comb_rule);
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TRACE("nla_intervals_details", tout << "c before combine_deps() "; display(tout, c););
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combine_deps(a, b, comb_rule, c);
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TRACE("nla_intervals_details", tout << "a "; display(tout, a););
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TRACE("nla_intervals_details", tout << "c "; display(tout, c););
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set(a, c, 33);
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TRACE("nla_intervals_details", tout << "part mult "; display(tout, a););
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}
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TRACE("nla_intervals_details", tout << "e=" << *e << "\n";
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tout << " return "; display(tout, a););
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return a;
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}
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bool intervals::check_cross_nested_expr(const nex* n, ci_dependency* initial_deps) {
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TRACE("nla_intervals", tout << "cross-nested n = " << *n << ", n->type() == " << n->type() << "\n";);
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m_core->lp_settings().stats().m_cross_nested_forms++;
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auto i = interval_of_expr(n, 1);
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TRACE("nla_intervals", tout << "callback n = " << *n << "\ni="; display(tout, i) << "\n";);
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if (!separated_from_zero(i)) {
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reset();
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return false;
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}
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auto interv_wd = interval_of_expr_with_deps(n, 1);
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TRACE("nla_intervals", tout << "conflict: interv_wd = "; display(tout, interv_wd ) << *n << "\n";);
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check_interval_for_conflict_on_zero(interv_wd, initial_deps);
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reset(); // clean the memory allocated by the interval bound dependencies
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return true;
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}
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intervals::interv intervals::interval_of_sum_no_term_with_deps(const nex_sum* e) {
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const nex* inf_e = get_inf_interval_child(e);
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if (inf_e) {
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return interv();
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}
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auto & es = e->children();
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interv a = interval_of_expr_with_deps(es[0], 1);
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for (unsigned k = 1; k < es.size(); k++) {
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TRACE("nla_intervals_details_sum", tout << "es[" << k << "]= " << *es[k] << "\n";);
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interv b = interval_of_expr_with_deps(es[k], 1);
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interv c;
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interval_deps_combine_rule combine_rule;
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TRACE("nla_intervals_details_sum", tout << "a = "; display(tout, a) << "\nb = "; display(tout, b) << "\n";);
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add(a, b, c, combine_rule);
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combine_deps(a, b, combine_rule, c);
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set_with_deps(a, c);
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TRACE("nla_intervals_details_sum", tout << *es[k] << ", ";
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display(tout, a); tout << "\n";);
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}
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TRACE("nla_intervals_details", tout << "e=" << *e << "\n";
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tout << " interv = "; display(tout, a););
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return a;
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}
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intervals::interv intervals::interval_of_sum_no_term(const nex_sum* e) {
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const nex* inf_e = get_inf_interval_child(e);
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if (inf_e) {
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return interv();
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}
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auto & es = e->children();
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interv a = interval_of_expr(es[0], 1);
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for (unsigned k = 1; k < es.size(); k++) {
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TRACE("nla_intervals_details_sum", tout << "es[" << k << "]= " << *es[k] << "\n";);
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interv b = interval_of_expr(es[k], 1);
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interv c;
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interval_deps_combine_rule combine_rule;
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TRACE("nla_intervals_details_sum", tout << "a = "; display(tout, a) << "\nb = "; display(tout, b) << "\n";);
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add(a, b, c, combine_rule);
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combine_deps(a, b, combine_rule, c);
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set(a, c, 22);
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TRACE("nla_intervals_details_sum", tout << *es[k] << ", ";
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display(tout, a); tout << "\n";);
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}
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TRACE("nla_intervals_details", tout << "e=" << *e << "\n";
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tout << " interv = "; display(tout, a););
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return a;
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}
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void intervals::add_mul_of_degree_one_to_vector(const nex_mul* e, vector<std::pair<rational, lpvar>> &v) {
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TRACE("nla_horner_details", tout << *e << "\n";);
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SASSERT(e->size() == 1);
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SASSERT((*e)[0].pow() == 1);
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const nex *ev = (*e)[0].e();
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lpvar j = to_var(ev)->var();
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v.push_back(std::make_pair(e->coeff(), j));
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}
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void intervals::add_linear_to_vector(const nex* e, vector<std::pair<rational, lpvar>> &v) {
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TRACE("nla_horner_details", tout << *e << "\n";);
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switch (e->type()) {
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case expr_type::MUL:
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add_mul_of_degree_one_to_vector(to_mul(e), v);
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break;
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case expr_type::VAR:
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v.push_back(std::make_pair(rational(1), to_var(e)->var()));
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break;
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default:
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SASSERT(!e->is_sum());
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// noop
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}
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}
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// e = a * can_t + b
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lp::lar_term intervals::expression_to_normalized_term(const nex_sum* e, rational& a, rational& b) {
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TRACE("nla_horner_details", tout << *e << "\n";);
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lpvar smallest_j;
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vector<std::pair<rational, lpvar>> v;
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b = rational(0);
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unsigned a_index;
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for (const nex* c : e->children()) {
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if (c->is_scalar()) {
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b += to_scalar(c)->value();
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} else {
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add_linear_to_vector(c, v);
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if (v.empty())
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continue;
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if (v.size() == 1 || smallest_j > v.back().second) {
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smallest_j = v.back().second;
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a_index = v.size() - 1;
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}
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}
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}
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TRACE("nla_horner_details", tout << "a_index = " << a_index << ", v="; print_vector(v, tout) << "\n";);
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a = v[a_index].first;
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lp::lar_term t;
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if (a.is_one()) {
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for (unsigned k = 0; k < v.size(); k++) {
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auto& p = v[k];
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t.add_coeff_var(p.first, p.second);
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}
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} else {
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for (unsigned k = 0; k < v.size(); k++) {
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auto& p = v[k];
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if (k != a_index)
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t.add_coeff_var(p.first/a, p.second);
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else
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t.add_var(p.second);
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}
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}
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TRACE("nla_horner_details", tout << a << "* (";
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lp::lar_solver::print_term_as_indices(t, tout) << ") + " << b << std::endl;);
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SASSERT(t.is_normalized());
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return t;
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}
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// we should have in the case of found a * m_terms[k] + b = e,
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// where m_terms[k] corresponds to the returned lpvar
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lpvar intervals::find_term_column(const lp::lar_term & norm_t, rational& a) const {
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std::pair<rational, lpvar> a_j;
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if (m_core->m_lar_solver.fetch_normalized_term_column(norm_t, a_j)) {
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a /= a_j.first;
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return a_j.second;
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}
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return -1;
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}
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bool intervals::interval_from_term_with_deps(const nex* e, interv & i) const {
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rational a, b;
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lp::lar_term norm_t = expression_to_normalized_term(to_sum(e), a, b);
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lp::explanation exp;
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if (m_core->explain_by_equiv(norm_t, exp)) {
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set_zero_interval_with_explanation(i, exp);
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TRACE("nla_intervals", tout << "explain_by_equiv\n";);
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return true;
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}
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lpvar j = find_term_column(norm_t, a);
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if (j + 1 == 0)
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return false;
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set_var_interval_with_deps(j, i);
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interv bi;
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mul_with_deps(a, i, bi);
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add(b, bi);
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set_with_deps(i, bi);
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TRACE("nla_intervals",
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m_core->m_lar_solver.print_column_info(j, tout) << "\n";
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tout << "a=" << a << ", b=" << b << "\n";
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tout << *e << ", interval = "; display(tout, i););
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return true;
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}
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bool intervals::interval_from_term(const nex* e, interv & i) const {
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rational a, b;
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lp::lar_term norm_t = expression_to_normalized_term(to_sum(e), a, b);
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lp::explanation exp;
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if (m_core->explain_by_equiv(norm_t, exp)) {
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set_zero_interval(i);
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TRACE("nla_intervals", tout << "explain_by_equiv\n";);
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return true;
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}
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lpvar j = find_term_column(norm_t, a);
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if (j + 1 == 0)
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return false;
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set_var_interval(j, i);
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interv bi;
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mul_no_deps(a, i, bi);
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add(b, bi);
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set(i, bi, 44);
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TRACE("nla_intervals",
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m_core->m_lar_solver.print_column_info(j, tout) << "\n";
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tout << "a=" << a << ", b=" << b << "\n";
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tout << *e << ", interval = "; display(tout, i););
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return true;
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}
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intervals::interv intervals::interval_of_sum_with_deps(const nex_sum* e) {
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TRACE("nla_intervals_details", tout << "e=" << *e << "\n";);
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interv i_e = interval_of_sum_no_term_with_deps(e);
|
||||
if (e->is_a_linear_term()) {
|
||||
SASSERT(e->is_sum() && e->size() > 1);
|
||||
interv i_from_term ;
|
||||
if (interval_from_term_with_deps(e, i_from_term)) {
|
||||
interv r = intersect_with_deps(i_e, i_from_term);
|
||||
TRACE("nla_intervals_details", tout << "intersection="; display(tout, r) << "\n";);
|
||||
if (is_empty(r)) {
|
||||
SASSERT(false); // not implemented
|
||||
}
|
||||
return r;
|
||||
|
||||
}
|
||||
}
|
||||
return i_e;
|
||||
}
|
||||
|
||||
intervals::interv intervals::interval_of_sum(const nex_sum* e) {
|
||||
interv i_e = interval_of_sum_no_term(e);
|
||||
TRACE("nla_intervals_details", tout << "e=" << *e << "\ni_e="; display(tout, i_e) << "\n";);
|
||||
if (e->is_a_linear_term()) {
|
||||
SASSERT(e->is_sum() && e->size() > 1);
|
||||
interv i_from_term ;
|
||||
if (interval_from_term(e, i_from_term)) {
|
||||
TRACE("nla_intervals_details", tout << "i_from_term="; display(tout, i_from_term) << "\n";);
|
||||
interv r = intersect(i_e, i_from_term, 44);
|
||||
TRACE("nla_intervals_details", tout << "intersection="; display(tout, r) << "\n";);
|
||||
if (is_empty(r)) {
|
||||
SASSERT(false); // not implemented
|
||||
}
|
||||
return r;
|
||||
|
||||
}
|
||||
}
|
||||
return i_e;
|
||||
}
|
||||
|
||||
|
||||
void intervals::set_var_interval(lpvar v, interval& b) const {
|
||||
lp::constraint_index ci;
|
||||
rational val;
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue