mirrors/z3
3
0
Fork 0
mirror of https://github.com/Z3Prover/z3 synced 2025-06-29 01:18:45 +00:00
Code Activity

cheap_eqs - work on fixed_phase

Browse source 
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson 2020-07-01 19:02:30 -07:00
parent cb3ebac3dd
commit 29b3f438bc
1 changed files with 161 additions and 118 deletions
Download patch file Download diff file Expand all files Collapse all files

265
src/math/lp/lp_bound_propagator.h
View file

@ -25,24 +25,19 @@ class lp_bound_propagator {
vertex* m_parent; vertex* m_parent;
unsigned m_level; // the distance in hops to the root; unsigned m_level; // the distance in hops to the root;
// it is handy to find the common ancestor // it is handy to find the common ancestor
bool m_neg; // false if grows with the root, true if grows with -root
public: public:
vertex() {} vertex() {}
vertex(unsigned row, vertex(unsigned row,
unsigned column, unsigned column) :
bool neg) :
m_row(row), m_row(row),
m_column(column), m_column(column),
m_parent(nullptr), m_parent(nullptr),
m_level(0), m_level(0)
m_neg(neg)
{} {}
unsigned column() const { return m_column; } unsigned column() const { return m_column; }
unsigned row() const { return m_row; } unsigned row() const { return m_row; }
vertex* parent() const { return m_parent; } vertex* parent() const { return m_parent; }
unsigned level() const { return m_level; } unsigned level() const { return m_level; }
bool neg() const { return m_neg; }
bool& neg() { return m_neg; }
void add_child(vertex* child) { void add_child(vertex* child) {
SASSERT(!(*this == *child)); SASSERT(!(*this == *child));
child->m_parent = this; child->m_parent = this;
@ -50,17 +45,24 @@ class lp_bound_propagator {
child->m_level = m_level + 1; child->m_level = m_level + 1;
} }
const ptr_vector<vertex> & children() const { return m_children; } const ptr_vector<vertex> & children() const { return m_children; }
std::ostream& print(std::ostream & out) const {
out << "r = " << m_row << ", c = " << m_column << ", P = {";
if (m_parent) { out << "(" << m_parent->row() << ", " << m_parent->column() << ")";}
else { out << "null"; }
out << "} , lvl = " << m_level << (neg()? " -":" +");
return out;
}
bool operator==(const vertex& o) const { bool operator==(const vertex& o) const {
return m_row == o.m_row && m_column == o.m_column; return m_row == o.m_row && m_column == o.m_column;
} }
}; };
std::ostream& print(std::ostream & out, const vertex* v) const {
out << "r = " << v->row() << ", c = " << v->column() << ", P = {";
if (v->parent()) { out << "(" << v->parent()->row() << ", " << v->parent()->column() << ")";}
else { out << "null"; }
out << "} , lvl = " << v->level();
if (m_pol.contains(v->column())) {
tout << (pol(v) == -1? " -":" +");
} else {
tout << " not in m_pol";
}
return out;
}
hashtable<unsigned, u_hash, u_eq> m_visited_rows; hashtable<unsigned, u_hash, u_eq> m_visited_rows;
hashtable<unsigned, u_hash, u_eq> m_visited_columns; hashtable<unsigned, u_hash, u_eq> m_visited_columns;
vertex* m_root; vertex* m_root;
@ -69,26 +71,20 @@ class lp_bound_propagator {
// by adjusting the vertices offsets, so they become absolute. // by adjusting the vertices offsets, so they become absolute.
// If the tree is fixed then in addition to checking with the m_vals_to_verts // If the tree is fixed then in addition to checking with the m_vals_to_verts
// we are going to check with the m_fixed_var_tables. // we are going to check with the m_fixed_var_tables.
vertex* m_fixed_vertex; const vertex* m_fixed_vertex;
explanation m_fixed_vertex_explanation;
// a pair (o, j) belongs to m_vals_to_verts iff x[j] = x[m_root->column()] + o // a pair (o, j) belongs to m_vals_to_verts iff x[j] = x[m_root->column()] + o
map<mpq, vertex*, obj_hash<mpq>, default_eq<mpq>> m_vals_to_verts; map<mpq, vertex*, obj_hash<mpq>, default_eq<mpq>> m_vals_to_verts;
// a pair (o, j) belongs to m_vals_to_verts_neg iff -x[j] = x[m_root->column()] + o // a pair (o, j) belongs to m_vals_to_verts_neg iff -x[j] = x[m_root->column()] + o
map<mpq, vertex*, obj_hash<mpq>, default_eq<mpq>> m_vals_to_verts_neg; map<mpq, vertex*, obj_hash<mpq>, default_eq<mpq>> m_vals_to_verts_neg;
// x[m_root->column()] - m_pol[j]*x[j] == const;
u_map<int> m_pol;
// if m_pos.contains(j) then x[j] = x[m_root->column()] + o
uint_set m_pos;
// these maps map a column index to the corresponding index in ibounds // these maps map a column index to the corresponding index in ibounds
std::unordered_map<unsigned, unsigned> m_improved_lower_bounds; std::unordered_map<unsigned, unsigned> m_improved_lower_bounds;
std::unordered_map<unsigned, unsigned> m_improved_upper_bounds; std::unordered_map<unsigned, unsigned> m_improved_upper_bounds;
class signed_column {
bool m_sign;
unsigned m_column;
public:
signed_column() : m_column(UINT_MAX) {}
bool not_set() const { return m_column == UINT_MAX; }
bool is_set() const { return m_column != UINT_MAX; }
bool sign() const { return m_sign; }
bool& sign() { return m_sign; }
unsigned column() const { return m_column; }
unsigned& column() { return m_column; }
};
T& m_imp; T& m_imp;
vector<implied_bound> m_ibounds; vector<implied_bound> m_ibounds;
@ -172,19 +168,6 @@ public:
m_imp.consume(a, ci); m_imp.consume(a, ci);
} }
bool set_sign_and_column(signed_column& i, const row_cell<mpq> & c) const {
if (c.coeff().is_one()) {
i.sign() = false;
i.column() = c.var();
return true;
}
else if (c.coeff().is_minus_one()){
i.sign() = true;
i.column() = c.var();
return true;
}
return false;
}
const mpq& val(unsigned j) const { const mpq& val(unsigned j) const {
return lp().get_column_value(j).x; return lp().get_column_value(j).x;
} }
@ -200,11 +183,11 @@ public:
if (!lp().find_in_fixed_tables(val(v_j), is_int(v_j), j)) if (!lp().find_in_fixed_tables(val(v_j), is_int(v_j), j))
return; return;
TRACE("cheap_eq", tout << "found j=" << j << " for v="; TRACE("cheap_eq", tout << "found j=" << j << " for v=";
v->print(tout) << "\n in lp.fixed tables\n";); print(tout, v) << "\n in lp.fixed tables\n";);
ptr_vector<vertex> path; ptr_vector<const vertex> path;
find_path_on_tree(path, v, m_fixed_vertex); find_path_on_tree(path, v, m_fixed_vertex);
explanation ex = get_explanation_from_path(path); explanation ex = get_explanation_from_path(path);
explain_fixed_column(ex, j); ex.add_expl(m_fixed_vertex_explanation);
add_eq_on_columns(ex, j, v->column()); add_eq_on_columns(ex, j, v->column());
} }
@ -218,34 +201,81 @@ public:
return false; return false;
} }
// pol for polarity
int pol(const vertex* v) const { return pol(v->column()); }
int pol(unsigned j) const { return m_pol[j]; }
void set_polarity(unsigned j, int p) {
SASSERT(p == 1 || p == -1);
SASSERT(!m_pol.contains(j));
m_pol.insert(j, p);
}
void check_polarity(vertex* v, int polarity) {
int prev_pol;
if (!m_pol.find(v->column(), prev_pol)) {
m_pol.insert(v->column(), polarity);
return;
}
if (prev_pol == polarity)
return;
TRACE("cheap_eq", tout << "polarity switch:"; print(tout , v) << "\n";);
const vertex *u = find_other_vertex_with_same_column(v);
ptr_vector<const vertex> path;
find_path_on_tree(path, u, v);
m_fixed_vertex_explanation = get_explanation_from_path(path);
set_fixed_vertex(v);
}
const vertex* find_other_vertex_with_same_column(const vertex* t) const {
return find_other_vertex_with_same_column_under(m_root, t);
}
const vertex * find_other_vertex_with_same_column_under(const vertex* v, const vertex* t) const {
if (v != t && v->column() == t->column())
return v;
for (const vertex* c : v->children()) {
auto u = find_other_vertex_with_same_column_under(c, t);
if (u)
return u;
}
UNREACHABLE();
return nullptr;
}
bool tree_contains(vertex *v) const { bool tree_contains(vertex *v) const {
if (!m_root) if (!m_root)
return false; return false;
return tree_contains_r(m_root, v); return tree_contains_r(m_root, v);
} }
vertex * alloc_v(unsigned row_index, unsigned column, bool neg) { vertex * alloc_v(unsigned row_index, unsigned column) {
vertex * v = alloc(vertex, row_index, column, neg); vertex * v = alloc(vertex, row_index, column);
SASSERT(!tree_contains(v)); SASSERT(!tree_contains(v));
return v; return v;
} }
static bool not_set(unsigned j) { return j == UINT_MAX; }
static bool is_set(unsigned j) { return j != UINT_MAX; }
void create_root(unsigned row_index) { void create_root(unsigned row_index) {
SASSERT(!m_root && !m_fixed_vertex); SASSERT(!m_root && !m_fixed_vertex);
signed_column x, y; unsigned x, y;
int polarity;
TRACE("cheap_eq", print_row(tout, row_index);); TRACE("cheap_eq", print_row(tout, row_index););
if (!is_tree_offset_row(row_index, x, y)) { if (!is_tree_offset_row(row_index, x, y, polarity)) {
TRACE("cheap_eq", tout << "not an offset row\n";); TRACE("cheap_eq", tout << "not an offset row\n";);
return; return;
} }
const mpq& r = val(x.column()); const mpq& r = val(x);
m_root = alloc_v(row_index, x.column(), false); m_root = alloc_v(row_index, x);
if (y.not_set()) { set_polarity(x, 1);
if (not_set(y)) {
set_fixed_vertex(m_root); set_fixed_vertex(m_root);
explain_fixed_in_row(row_index, m_fixed_vertex_explanation);
} else { } else {
bool neg = x.sign() == y.sign(); vertex *v = alloc_v(row_index, y);
vertex *v = alloc_v(row_index, y.column(), neg);
m_root->add_child(v); m_root->add_child(v);
set_polarity(y, polarity);
} }
// keep root in the positive table // keep root in the positive table
m_vals_to_verts.insert(r, m_root); m_vals_to_verts.insert(r, m_root);
@ -261,29 +291,33 @@ public:
// It is assumed that parent->column() is present in the row // It is assumed that parent->column() is present in the row
vertex* add_child_from_row(unsigned row_index, vertex* parent) { vertex* add_child_from_row(unsigned row_index, vertex* parent) {
TRACE("cheap_eq", print_row(tout, row_index);); TRACE("cheap_eq", print_row(tout, row_index););
signed_column x, y; unsigned x, y; int polarity;
if (!is_tree_offset_row(row_index, x, y)) { if (!is_tree_offset_row(row_index, x, y, polarity)) {
TRACE("cheap_eq", tout << "not an offset row\n"; ); TRACE("cheap_eq", tout << "not an offset row\n"; );
return nullptr; return nullptr;
} }
if (y.not_set()) { if (not_set(y)) {
SASSERT(parent->column() == x.column()); SASSERT(parent->column() == x);
vertex *v = alloc_v( row_index, x.column(), parent->neg()); vertex *v = alloc_v(row_index, x);
parent->add_child(v); parent->add_child(v);
if (!fixed_phase()) {
set_fixed_vertex(v); set_fixed_vertex(v);
explain_fixed_in_row(row_index, m_fixed_vertex_explanation);
}
return v; return v;
} }
SASSERT(x.is_set() && y.is_set()); SASSERT(is_set(x) && is_set(y));
// v is exactly like parent, but the row is different // v has the column of the parent, but the row is different
vertex *v = alloc_v(row_index, parent->column(), parent->neg()); vertex *v = alloc_v(row_index, parent->column());
parent->add_child(v); parent->add_child(v);
SASSERT(x.column() == v->column() || y.column() == v->column()); SASSERT(x == v->column() || y == v->column());
unsigned col = v->column() == y.column()? x.column(): y.column(); unsigned col = v->column() == y? x : y;
bool neg = x.sign() == y.sign() ? !v->neg(): v->neg(); vertex *vy = alloc_v(v->row(), col);
vertex *vy = alloc_v(v->row(), col, neg);
v->add_child(vy); v->add_child(vy);
if (!fixed_phase())
check_polarity(vy, polarity * pol(v));
return v; return v;
} }
@ -292,26 +326,32 @@ public:
} }
void check_for_eq_and_add_to_val_table(vertex* v, map<mpq, vertex*, obj_hash<mpq>, default_eq<mpq>>& table) { void check_for_eq_and_add_to_val_table(vertex* v, map<mpq, vertex*, obj_hash<mpq>, default_eq<mpq>>& table) {
TRACE("cheap_eq", tout << "v="; print(tout, v) << "\n";);
vertex *k; // the other vertex vertex *k; // the other vertex
if (table.find(val(v), k)) { if (table.find(val(v), k)) {
TRACE("cheap_eq", tout << "found k " ; k->print(tout) << "\n";); TRACE("cheap_eq", tout << "found k " ; print(tout, k) << "\n";);
if (k->column() != v->column() && if (k->column() != v->column() &&
is_int(k->column()) == is_int(v->column()) && is_int(k->column()) == is_int(v->column()) &&
!is_equal(k->column(), v->column())) !is_equal(k->column(), v->column())) {
report_eq(k, v); report_eq(k, v);
} else { } else {
TRACE("cheap_eq", tout << "registered: " << val(v) << " -> { "; v->print(tout) << "} \n";); TRACE("cheap_eq", tout << "no report\n";);
}
} else {
TRACE("cheap_eq", tout << "registered: " << val(v) << " -> { "; print(tout, v) << "} \n";);
table.insert(val(v), v); table.insert(val(v), v);
} }
} }
void check_for_eq_and_add_to_val_tables(vertex* v) { void check_for_eq_and_add_to_val_tables(vertex* v) {
TRACE("cheap_eq_det", v->print(tout) << "\n";); TRACE("cheap_eq_det", print(tout, v) << "\n";);
if (v->neg()) if (!fixed_phase()) {
if (pol(v->column()) == -1)
check_for_eq_and_add_to_val_table(v, m_vals_to_verts_neg); check_for_eq_and_add_to_val_table(v, m_vals_to_verts_neg);
else else
check_for_eq_and_add_to_val_table(v, m_vals_to_verts); check_for_eq_and_add_to_val_table(v, m_vals_to_verts);
} }
}
void clear_for_eq() { void clear_for_eq() {
m_visited_rows.reset(); m_visited_rows.reset();
@ -319,11 +359,11 @@ public:
m_root = nullptr; m_root = nullptr;
} }
std::ostream& print_path(const ptr_vector<vertex>& path, std::ostream& out) const { std::ostream& print_path(const ptr_vector<const vertex>& path, std::ostream& out) const {
unsigned pr = UINT_MAX; unsigned pr = UINT_MAX;
out << "path = \n"; out << "path = \n";
for (vertex* k : path) { for (const vertex* k : path) {
k->print(out) << "\n"; print(out, k) << "\n";
if (k->row() != pr) { if (k->row() != pr) {
print_row(out, pr = k->row()); print_row(out, pr = k->row());
} }
@ -336,13 +376,13 @@ public:
SASSERT(v_i != v_j); SASSERT(v_i != v_j);
SASSERT(lp().get_column_value(v_i->column()) == lp().get_column_value(v_j->column())); SASSERT(lp().get_column_value(v_i->column()) == lp().get_column_value(v_j->column()));
TRACE("cheap_eq", tout << v_i->column() << " = " << v_j->column() << "\nu = "; TRACE("cheap_eq", tout << v_i->column() << " = " << v_j->column() << "\nu = ";
v_i->print(tout) << "\nv = "; v_j->print(tout) <<"\n"; print(tout, v_i) << "\nv = "; print(tout, v_j) <<"\n";
display_row_of_vertex(v_i, tout); display_row_of_vertex(v_i, tout);
if (v_j->row() != v_i->row()) if (v_j->row() != v_i->row())
display_row_of_vertex(v_j, tout); display_row_of_vertex(v_j, tout);
); );
ptr_vector<vertex> path; ptr_vector<const vertex> path;
find_path_on_tree(path, v_i, v_j); find_path_on_tree(path, v_i, v_j);
lp::explanation exp = get_explanation_from_path(path); lp::explanation exp = get_explanation_from_path(path);
add_eq_on_columns(exp, v_i->column(), v_j->column()); add_eq_on_columns(exp, v_i->column(), v_j->column());
@ -364,19 +404,6 @@ public:
lp().settings().stats().m_cheap_eqs++; lp().settings().stats().m_cheap_eqs++;
} }
/**
The table functionality:
Cheap propagation of equalities x_i = x_j, when
x_i = y + k
x_j = y + k
This equalities are detected by maintaining a map:
(y, k) -> row_id when a row is of the form x = y + k
If x = k, then y is null_lpvar
This methods checks whether the given row is an offset row (is_offset_row())
and uses the map to find new equalities if that is the case.
Some equalities, those spreading more than two rows, can be missed
*/
// column to theory_var // column to theory_var
unsigned col_to_imp(unsigned j) const { unsigned col_to_imp(unsigned j) const {
return lp().local_to_external(lp().column_to_reported_index(j)); return lp().local_to_external(lp().column_to_reported_index(j));
@ -391,10 +418,10 @@ public:
return lp().column_is_int(j); return lp().column_is_int(j);
} }
explanation get_explanation_from_path(const ptr_vector<vertex>& path) const { explanation get_explanation_from_path(const ptr_vector<const vertex>& path) const {
explanation ex; explanation ex;
unsigned prev_row = UINT_MAX; unsigned prev_row = UINT_MAX;
for (vertex* k : path) { for (const vertex* k : path) {
unsigned row = k->row(); unsigned row = k->row();
if (row == prev_row) if (row == prev_row)
continue; continue;
@ -423,11 +450,11 @@ public:
return print_row(out, k->row()); return print_row(out, k->row());
} }
void find_path_on_tree(ptr_vector<vertex> & path, vertex* u, vertex* v) const { void find_path_on_tree(ptr_vector<const vertex> & path, const vertex* u, const vertex* v) const {
TRACE("cheap_eq_details", tout << "u = " ;u->print(tout); tout << "\nv = ";v->print(tout) << "\n";); TRACE("cheap_eq_details", tout << "u = " ; print(tout, u); tout << "\nv = ";print(tout, v) << "\n";);
vertex* up; // u parent vertex* up; // u parent
vertex* vp; // v parent vertex* vp; // v parent
ptr_vector<vertex> v_branch; vector<const vertex*> v_branch;
path.push_back(u); path.push_back(u);
v_branch.push_back(v); v_branch.push_back(v);
// equalize the levels // equalize the levels
@ -445,7 +472,7 @@ public:
v = vp; v = vp;
} }
SASSERT(u->level() == v->level()); SASSERT(u->level() == v->level());
TRACE("cheap_eq_details", tout << "u = " ;u->print(tout); tout << "\nv = ";v->print(tout) << "\n";); TRACE("cheap_eq_details", tout << "u = " ; print(tout, u); tout << "\nv = "; print(tout, v) << "\n";);
while (u != v) { while (u != v) {
up = u->parent(); up = u->parent();
vp = v->parent(); vp = v->parent();
@ -457,7 +484,7 @@ public:
} }
for (unsigned i = v_branch.size(); i--; ) { for (unsigned i = v_branch.size(); i--; ) {
vertex * bv = v_branch[i]; const vertex * bv = v_branch[i];
if (path.back() != bv) if (path.back() != bv)
path.push_back(bv); path.push_back(bv);
} }
@ -477,8 +504,8 @@ public:
return false; return false;
} }
bool tree_is_correct(vertex* v, ptr_vector<vertex>& vs) const { bool tree_is_correct(vertex* v, ptr_vector<vertex>& vs) const {
if (fixed_phase() && v->neg()) if (fixed_phase())
return false; return true;
for (vertex * u : v->children()) { for (vertex * u : v->children()) {
if (contains_vertex(u, vs)) if (contains_vertex(u, vs))
return false; return false;
@ -495,7 +522,7 @@ public:
return true; return true;
} }
std::ostream& print_tree(std::ostream & out, vertex* v) const { std::ostream& print_tree(std::ostream & out, vertex* v) const {
v->print(out); print(out, v);
out << "\nchildren :\n"; out << "\nchildren :\n";
for (auto * c : v->children()) { for (auto * c : v->children()) {
print_tree(out, c); print_tree(out, c);
@ -514,16 +541,15 @@ public:
TRACE("cheap_eq", tout << "tree = "; print_tree(tout, m_root) << "\n";); TRACE("cheap_eq", tout << "tree = "; print_tree(tout, m_root) << "\n";);
SASSERT(tree_is_correct()); SASSERT(tree_is_correct());
explore_under(m_root); explore_under(m_root);
if (fixed_phase()) {
create_fixed_eqs(m_root);
}
TRACE("cheap_eq", tout << "done for row_index " << row_index << "\n";); TRACE("cheap_eq", tout << "done for row_index " << row_index << "\n";);
TRACE("cheap_eq", tout << "tree size = " << verts_size();); TRACE("cheap_eq", tout << "tree size = " << verts_size(););
delete_tree(m_root); delete_tree(m_root);
m_root = nullptr; m_root = nullptr;
set_fixed_vertex(nullptr); set_fixed_vertex(nullptr);
m_fixed_vertex_explanation.clear();
m_vals_to_verts.reset(); m_vals_to_verts.reset();
m_vals_to_verts_neg.reset(); m_vals_to_verts_neg.reset();
m_pol.reset();
} }
void create_fixed_eqs(vertex* v) { void create_fixed_eqs(vertex* v) {
@ -533,8 +559,8 @@ public:
} }
std::ostream& print_row(std::ostream & out, unsigned row_index) const { std::ostream& print_row(std::ostream & out, unsigned row_index) const {
signed_column x, y; unsigned x, y; int polarity;
if (true || !is_tree_offset_row(row_index, x, y)) if (true || !is_tree_offset_row(row_index, x, y, polarity))
return lp().get_int_solver()->display_row_info(out, row_index); return lp().get_int_solver()->display_row_info(out, row_index);
bool first = true; bool first = true;
@ -554,11 +580,12 @@ public:
return out; return out;
} }
void set_fixed_vertex(vertex *v) { void set_fixed_vertex(vertex *v) {
TRACE("cheap_eq", if (v) v->print(tout); else tout << "set m_fixed_vertex to nullptr"; tout << "\n";); TRACE("cheap_eq", if (v) print(tout, v); else tout << "set m_fixed_vertex to nullptr"; tout << "\n";);
SASSERT(!m_fixed_vertex || v == nullptr);
m_fixed_vertex = v; m_fixed_vertex = v;
} }
unsigned verts_size() const { unsigned verts_size() const {
return subtree_size(m_root); return subtree_size(m_root);
} }
@ -612,23 +639,39 @@ public:
// In case of only one non fixed column, and the function returns true, // In case of only one non fixed column, and the function returns true,
// this column would be represened by x. // this column would be represened by x.
bool is_tree_offset_row( unsigned row_index, bool is_tree_offset_row( unsigned row_index,
signed_column & x, unsigned & x, unsigned & y, int & polarity ) const {
signed_column & y) const { x = y = UINT_MAX;
const row_cell<mpq>* x_cell = nullptr;
const row_cell<mpq>* y_cell = nullptr;
const auto & row = lp().get_row(row_index); const auto & row = lp().get_row(row_index);
for (unsigned k = 0; k < row.size(); k++) { for (unsigned k = 0; k < row.size(); k++) {
const auto& c = row[k]; const auto& c = row[k];
if (column_is_fixed(c.var())) if (column_is_fixed(c.var()))
continue; continue;
if (x.not_set()) { if (not_set(x)) {
if (!set_sign_and_column(x, c)) if (c.coeff().is_one() || c.coeff().is_minus_one()) {
x = c.var();
x_cell = & c;
} else {
return false; return false;
} else if (y.not_set()) { }
if (!set_sign_and_column(y, c)) } else if (not_set(y)) {
if (c.coeff().is_one() || c.coeff().is_minus_one()) {
y = c.var();
y_cell = & c;
} else
return false; return false;
} else } else
return false; return false;
} }
return x.is_set() || y.is_set(); if (is_set(x)) {
if (is_set(y))
polarity = x_cell->coeff().is_pos() == y_cell->coeff().is_pos()? -1 : 1;
else
polarity = 1;
return true;
}
return false;
} }
}; };
} }