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/*++
Copyright (c) 2006 Microsoft Corporation
Module Name:
theory_arith_eq.h
Abstract:
Author:
Leonardo de Moura (leonardo) 2008-06-22.
Revision History:
--*/
#pragma once
// #define PROFILE_OFFSET_ROW
#ifdef PROFILE_OFFSET_ROW
#include "util/stopwatch.h"
#undef max
#undef min
#endif
namespace smt {
/**
\brief This method is invoked when a variable was non fixed and become fixed.
*/
template
void theory_arith::fixed_var_eh(theory_var v) {
if (!propagate_eqs())
return;
SASSERT(is_fixed(v));
// WARNING: it is not safe to use get_value(v) here, since
// get_value(v) may not satisfy v bounds at this point.
if (!lower_bound(v).is_rational())
return;
numeral const & val = lower_bound(v).get_rational();
value_sort_pair key(val, is_int_src(v));
theory_var v2;
if (m_fixed_var_table.find(key, v2)) {
if (v2 < static_cast(get_num_vars()) && is_fixed(v2) && lower_bound(v2).get_rational() == val) {
// It only makes sense to propagate equality to the core when v and v2 have the same sort.
// The table m_fixed_var_table is not restored during backtrack. So, it may
// contain invalid (key -> value) pairs. So, we must check whether v2 is really equal to val (previous test) AND it has
// the same sort of v. The following test was missing in a previous version of Z3.
if (!is_equal(v, v2) && is_int_src(v) == is_int_src(v2)) {
antecedents ante(*this);
//
// v <= k <= v2 => v <= v2
// v >= k >= v2 => v >= v2
//
lower(v)->push_justification(ante, numeral::zero(), proofs_enabled());
upper(v2)->push_justification(ante, numeral::zero(), proofs_enabled());
lower(v2)->push_justification(ante, numeral::zero(), proofs_enabled());
upper(v)->push_justification(ante, numeral::zero(), proofs_enabled());
TRACE("arith_eq", tout << "propagate eq: v" << v << " = v" << v2 << "\n";
display_var(tout, v);
display_var(tout, v2););
m_stats.m_fixed_eqs++;
propagate_eq_to_core(v, v2, ante);
}
}
else {
// the original fixed variable v2 was deleted or its bounds were removed
// during backtracking.
m_fixed_var_table.erase(key);
m_fixed_var_table.insert(key, v);
}
}
else {
m_fixed_var_table.insert(key, v);
}
}
/**
\brief Returns true if r is a offset row.
A offset row is a row that can be written as:
x = y + M
where x and y are non fixed variables, and
M is linear polynomials where all variables are fixed,
and M evaluates to k.
When true is returned, x, y and k are stored in the given arguments.
\remark The following rule is used to select x and y.
- if the base variable is not fixed, then x is the base var.
- otherwise x is the smallest var.
*/
template
bool theory_arith::is_offset_row(row const & r, theory_var & x, theory_var & y, numeral & k) const {
#ifdef PROFILE_OFFSET_ROW
static stopwatch timer;
static unsigned total = 0;
static unsigned ok = 0;
timer.start();
total ++;
#endif
// Quick check without using big numbers...
// Check if there are more than 2 unbounded vars.
unsigned bad = 0;
typename vector::const_iterator it = r.begin_entries();
typename vector::const_iterator end = r.end_entries();
for (; it != end; ++it) {
if (!it->is_dead()) {
theory_var v = it->m_var;
if (lower(v) != nullptr && upper(v) != nullptr)
continue;
bad++;
if (bad > 2) {
#ifdef PROFILE_OFFSET_ROW
timer.stop();
#endif
return false;
}
}
}
// Full check using == for big numbers...
x = null_theory_var;
y = null_theory_var;
it = r.begin_entries();
for (; it != end; ++it) {
if (!it->is_dead()) {
theory_var v = it->m_var;
if (is_fixed(v))
continue;
if (it->m_coeff.is_one() && x == null_theory_var) {
x = v;
continue;
}
if (it->m_coeff.is_minus_one() && y == null_theory_var) {
y = v;
continue;
}
#ifdef PROFILE_OFFSET_ROW
timer.stop();
#endif
return false;
}
}
if (x == null_theory_var && y == null_theory_var) {
#ifdef PROFILE_OFFSET_ROW
timer.stop();
#endif
return false;
}
k.reset();
it = r.begin_entries();
for (; it != end; ++it) {
if (!it->is_dead()) {
theory_var v = it->m_var;
if (v == x || v == y)
continue;
SASSERT(is_fixed(v));
k -= it->m_coeff * lower_bound(v).get_rational();
}
}
#ifdef PROFILE_OFFSET_ROW
timer.stop();
ok++;
if (ok % 100000 == 0) {
TRACE("arith_eq",
tout << total << " " << ok << " "
<< static_cast(ok)/static_cast(total)
<< " " << timer.get_seconds() << "\n";
tout.flush(););
}
#endif
if (y == null_theory_var)
return true;
if (x == null_theory_var) {
std::swap(x, y);
k.neg();
SASSERT(x != null_theory_var);
return true;
}
if (r.get_base_var() != x && x > y) {
std::swap(x, y);
k.neg();
}
return true;
}
/**
\brief 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
This methods checks whether the given row is an offset row (See is_offset_row),
and uses the map to find new equalities if that is the case.
*/
template
void theory_arith::propagate_cheap_eq(unsigned rid) {
if (!propagate_eqs())
return;
TRACE("arith_eq_verbose", tout << "checking if row " << rid << " can propagate equality.\n";
display_row_info(tout, rid););
row const & r = m_rows[rid];
theory_var x;
theory_var y;
numeral k;
if (is_offset_row(r, x, y, k)) {
if (y == null_theory_var) {
// x is an implied fixed var at k.
value_sort_pair key(k, is_int_src(x));
theory_var x2;
if (m_fixed_var_table.find(key, x2) &&
x2 < static_cast(get_num_vars()) &&
is_fixed(x2) &&
lower_bound(x2).get_rational() == k &&
// We must check whether x2 is an integer.
// The table m_fixed_var_table is not restored during backtrack. So, it may
// contain invalid (key -> value) pairs.
// So, we must check whether x2 is really equal to k (previous test)
// AND has the same sort of x.
// The following test was missing in a previous version of Z3.
is_int_src(x) == is_int_src(x2) &&
!is_equal(x, x2)) {
antecedents ante(*this);
collect_fixed_var_justifications(r, ante);
//
// x1 <= k1 x1 >= k1, x2 <= x1 + k2 x2 >= x1 + k2
//
TRACE("arith_eq", tout << "fixed\n";);
lower(x2)->push_justification(ante, numeral::zero(), proofs_enabled());
upper(x2)->push_justification(ante, numeral::zero(), proofs_enabled());
m_stats.m_fixed_eqs++;
propagate_eq_to_core(x, x2, ante);
}
//return;
}
if (k.is_zero() && y != null_theory_var && !is_equal(x, y) && is_int_src(x) == is_int_src(y)) {
// found equality x = y
antecedents ante(*this);
collect_fixed_var_justifications(r, ante);
TRACE("arith_eq", tout << "propagate eq using x-y=0 row:\n"; display_row_info(tout, r););
m_stats.m_offset_eqs++;
propagate_eq_to_core(x, y, ante);
}
int row_id;
var_offset key(y, k);
if (m_var_offset2row_id.find(key, row_id)) {
row & r2 = m_rows[row_id];
if (r.get_base_var() == r2.get_base_var()) {
// it is the same row.
return;
}
theory_var x2;
theory_var y2;
numeral k2;
if (r2.get_base_var() != null_theory_var && is_offset_row(r2, x2, y2, k2)) {
bool new_eq = false;
if (y == y2 && k == k2) {
new_eq = true;
}
else if (y2 != null_theory_var) {
std::swap(x2, y2);
k2.neg();
if (y == y2 && k == k2) {
new_eq = true;
}
}
if (new_eq) {
if (!is_equal(x, x2) && is_int_src(x) == is_int_src(x2)) {
SASSERT(y == y2 && k == k2);
antecedents ante(*this);
collect_fixed_var_justifications(r, ante);
collect_fixed_var_justifications(r2, ante);
TRACE("arith_eq", tout << "propagate eq two rows:\n";
tout << "x : v" << x << "\n";
tout << "x2 : v" << x2 << "\n";
display_row_info(tout, r);
display_row_info(tout, r2););
m_stats.m_offset_eqs++;
propagate_eq_to_core(x, x2, ante);
}
return;
}
}
// the original row was delete or it is not offset row anymore ===> remove it from table
}
// add new entry
m_var_offset2row_id.insert(key, rid);
}
}
template
void theory_arith::propagate_eq_to_core(theory_var x, theory_var y, antecedents& antecedents) {
// Ignore equality if variables are already known to be equal.
if (is_equal(x, y))
return;
enode * _x = get_enode(x);
enode * _y = get_enode(y);
// I doesn't make sense to propagate an equality (to the core) of variables of different sort.
CTRACE("arith", _x->get_sort() != _y->get_sort(), tout << enode_pp(_x, ctx) << " = " << enode_pp(_y, ctx) << "\n");
if (_x->get_sort() != _y->get_sort())
return;
eq_vector const& eqs = antecedents.eqs();
literal_vector const& lits = antecedents.lits();
justification * js =
ctx.mk_justification(
ext_theory_eq_propagation_justification(
get_id(), ctx,
lits.size(), lits.data(),
eqs.size(), eqs.data(),
_x, _y,
antecedents.num_params(), antecedents.params("eq-propagate")));
TRACE("arith_eq", tout << "detected equality: #" << _x->get_owner_id() << " = #" << _y->get_owner_id() << "\n";
display_var(tout, x);
display_var(tout, y);
for (literal lit : lits)
ctx.display_detailed_literal(tout, lit) << "\n";
for (auto const& p : eqs)
tout << enode_pp(p.first, ctx) << " = " << enode_pp(p.second, ctx) << "\n";
tout << " ==> ";
tout << enode_pp(_x, ctx) << " = " << enode_pp(_y, ctx) << "\n";);
ctx.assign_eq(_x, _y, eq_justification(js));
}
};
