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z3/src/math/lp/int_solver.cpp
Lev Nachmanson 52653e6e43 a version with less pointers: got a conflict 
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
2025-02-11 12:23:00 -10:00

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/*
Copyright (c) 2017 Microsoft Corporation
Author: Lev Nachmanson
*/
#include "math/lp/int_solver.h"
#include "math/lp/lar_solver.h"
#include "math/lp/lp_utils.h"
#include "math/lp/monic.h"
#include "math/lp/gomory.h"
#include "math/lp/int_branch.h"
#include "math/lp/int_cube.h"
#include "math/lp/dioph_eq.h"
namespace lp {
bool get_patching_deltas(const rational& x, const rational& alpha,
rational& delta_plus, rational& delta_minus);
// this will allow to enable and disable tracking of the pivot rows
struct check_return_helper {
lar_solver& lra;
bool m_track_touched_rows;
check_return_helper(lar_solver& ls) :
lra(ls),
m_track_touched_rows(lra.touched_rows_are_tracked()) {
lra.track_touched_rows(false);
}
~check_return_helper() {
lra.track_touched_rows(m_track_touched_rows);
}
};
class int_solver::imp {
public:
int_solver& lia;
lar_solver& lra;
lar_core_solver& lrac;
unsigned m_number_of_calls = 0;
lar_term m_t; // the term to return in the cut
bool m_upper; // cut is an upper bound
explanation *m_ex; // the conflict explanation
mpq m_k; // the right side of the cut
hnf_cutter m_hnf_cutter;
unsigned m_hnf_cut_period;
int_gcd_test m_gcd;
bool column_is_int_inf(unsigned j) const {
return lra.column_is_int(j) && (!lia.value_is_int(j));
}
imp(int_solver& lia): lia(lia), lra(lia.lra), lrac(lia.lrac), m_hnf_cutter(lia), m_gcd(lia) {}
bool has_lower(unsigned j) const {
switch (lrac.m_column_types()[j]) {
case column_type::fixed:
case column_type::boxed:
case column_type::lower_bound:
return true;
default:
return false;
}
}
bool has_upper(unsigned j) const {
switch (lrac.m_column_types()[j]) {
case column_type::fixed:
case column_type::boxed:
case column_type::upper_bound:
return true;
default:
return false;
}
}
const impq& upper_bound(unsigned j) const {
return lra.column_upper_bound(j);
}
const impq& lower_bound(unsigned j) const {
return lra.column_lower_bound(j);
}
void patch_basic_column(unsigned v) {
SASSERT(!lia.is_fixed(v));
for (auto const& c : lra.basic2row(v))
if (patch_basic_column_on_row_cell(v, c))
return;
}
bool try_patch_column(unsigned v, unsigned j, mpq const& delta) {
const auto & A = lra.A_r();
if (delta < 0) {
if (has_lower(j) && lia.get_value(j) + impq(delta) < lra.get_lower_bound(j))
return false;
}
else {
if (lia.has_upper(j) && lia.get_value(j) + impq(delta) > lra.get_upper_bound(j))
return false;
}
for (auto const& c : A.column(j)) {
unsigned row_index = c.var();
unsigned bj = lrac.m_r_basis[row_index];
auto old_val = lia.get_value(bj);
auto new_val = old_val - impq(c.coeff()*delta);
if (has_lower(bj) && new_val < lra.get_lower_bound(bj))
return false;
if (has_upper(bj) && new_val > lra.get_upper_bound(bj))
return false;
if (old_val.is_int() && !new_val.is_int()){
return false; // do not waste resources on this case
}
// if bj == v, then, because we are patching the lra.get_value(v),
// we just need to assert that the lra.get_value(v) would be integral.
lp_assert(bj != v || lra.from_model_in_impq_to_mpq(new_val).is_int());
}
lra.set_value_for_nbasic_column(j, lia.get_value(j) + impq(delta));
return true;
}
unsigned random() {
return settings().random_next();
}
bool all_columns_are_integral() const {
for (lpvar j = 0; j < lra.number_of_vars(); j++)
if (!lra.column_is_int(j))
return false;
return true;
}
bool patch_basic_column_on_row_cell(unsigned v, row_cell<mpq> const& c) {
if (v == c.var())
return false;
if (!lra.column_is_int(c.var())) // could use real to patch integer
return false;
if (c.coeff().is_int())
return false;
mpq a = fractional_part(c.coeff());
mpq r = fractional_part(lra.get_value(v));
lp_assert(0 < r && r < 1);
lp_assert(0 < a && a < 1);
mpq delta_plus, delta_minus;
if (!get_patching_deltas(r, a, delta_plus, delta_minus))
return false;
if (random() % 2)
return try_patch_column(v, c.var(), delta_plus) ||
try_patch_column(v, c.var(), delta_minus);
else
return try_patch_column(v, c.var(), delta_minus) ||
try_patch_column(v, c.var(), delta_plus);
}
lia_move patch_basic_columns() {
lia.settings().stats().m_patches++;
lra.remove_fixed_vars_from_base();
lp_assert(lia.is_feasible());
for (unsigned j : lra.r_basis())
if (!lra.get_value(j).is_int() && lra.column_is_int(j) && !lia.is_fixed(j))
patch_basic_column(j);
if (!lra.has_inf_int()) {
lia.settings().stats().m_patches_success++;
return lia_move::sat;
}
return lia_move::undef;
}
lia_move solve_dioph_eq() {
dioph_eq de(lia);
lia_move r = de.check();
if (r == lia_move::unsat) {
de.explain(*this->m_ex);
} else if (r == lia_move::sat) {
NOT_IMPLEMENTED_YET();
}
return lia_move::undef;
}
lp_settings& settings() { return lra.settings(); }
bool should_find_cube() {
return m_number_of_calls % settings().m_int_find_cube_period == 0;
}
bool should_gomory_cut() {
return m_number_of_calls % settings().m_int_gomory_cut_period == 0;
}
bool should_solve_dioph_eq() {
return lia.settings().dioph_eq() && m_number_of_calls % settings().m_dioph_eq_period == 0;
}
bool should_hnf_cut() {
return settings().enable_hnf() && m_number_of_calls % settings().hnf_cut_period() == 0;
}
lia_move hnf_cut() {
lia_move r = m_hnf_cutter.make_hnf_cut();
if (r == lia_move::undef)
m_hnf_cut_period *= 2;
else
m_hnf_cut_period = settings().hnf_cut_period();
return r;
}
lia_move check(lp::explanation * e) {
SASSERT(lra.ax_is_correct());
if (!lra.has_inf_int())
return lia_move::sat;
m_t.clear();
m_k.reset();
m_ex = e;
m_ex->clear();
m_upper = false;
lia_move r = lia_move::undef;
if (m_gcd.should_apply())
r = m_gcd();
check_return_helper pc(lra);
if (settings().get_cancel_flag())
return lia_move::undef;
++m_number_of_calls;
if (r == lia_move::undef) r = patch_basic_columns();
if (r == lia_move::undef && should_find_cube()) r = int_cube(lia)();
if (r == lia_move::undef && should_solve_dioph_eq()) r = solve_dioph_eq();
if (r == lia_move::undef) lra.move_non_basic_columns_to_bounds();
if (r == lia_move::undef && should_hnf_cut()) r = hnf_cut();
if (r == lia_move::undef && should_gomory_cut()) r = gomory(lia).get_gomory_cuts(2);
if (r == lia_move::undef) r = int_branch(lia)();
if (settings().get_cancel_flag()) r = lia_move::undef;
return r;
}
bool cut_indices_are_columns() const {
for (lar_term::ival p : m_t) {
if (p.j() >= lra.A_r().column_count())
return false;
}
return true;
}
bool current_solution_is_inf_on_cut() const {
SASSERT(cut_indices_are_columns());
const auto & x = lrac.m_r_x;
impq v = m_t.apply(x);
mpq sign = m_upper ? one_of_type<mpq>() : -one_of_type<mpq>();
CTRACE("current_solution_is_inf_on_cut", v * sign <= impq(m_k) * sign,
tout << "m_upper = " << m_upper << std::endl;
tout << "v = " << v << ", k = " << m_k << std::endl;
tout << "term:";lra.print_term(m_t, tout) << "\n";
);
return v * sign > impq(m_k) * sign;
}
int select_int_infeasible_var() {
int r_small_box = -1;
int r_small_value = -1;
int r_any_value = -1;
unsigned n_small_box = 1;
unsigned n_small_value = 1;
unsigned n_any_value = 1;
mpq range;
mpq new_range;
mpq small_value(1024);
unsigned prev_usage = 0;
auto add_column = [&](bool improved, int& result, unsigned& n, unsigned j) {
if (result == -1)
result = j;
else if (improved && ((random() % (++n)) == 0))
result = j;
};
for (unsigned j : lra.r_basis()) {
if (!column_is_int_inf(j))
continue;
SASSERT(!lia.is_fixed(j));
unsigned usage = lra.usage_in_terms(j);
if (lia.is_boxed(j) && (new_range = lra.bound_span_x(j) - rational(2*usage)) <= small_value) {
bool improved = new_range <= range || r_small_box == -1;
if (improved)
range = new_range;
add_column(improved, r_small_box, n_small_box, j);
continue;
}
impq const& value = lia.get_value(j);
if (abs(value.x) < small_value ||
(lra.column_has_upper_bound(j) && small_value > upper_bound(j).x - value.x) ||
(has_lower(j) && small_value > value.x - lower_bound(j).x)) {
TRACE("int_solver", tout << "small j" << j << "\n");
add_column(true, r_small_value, n_small_value, j);
continue;
}
TRACE("int_solver", tout << "any j" << j << "\n");
add_column(usage >= prev_usage, r_any_value, n_any_value, j);
if (usage > prev_usage)
prev_usage = usage;
}
if (r_small_box != -1 && (random() % 3 != 0))
return r_small_box;
if (r_small_value != -1 && (random() % 3) != 0)
return r_small_value;
if (r_any_value != -1)
return r_any_value;
if (r_small_box != -1)
return r_small_box;
return r_small_value;
}
std::ostream & display_row(std::ostream & out, lp::row_strip<rational> const & row) const {
bool first = true;
auto & rslv = lrac.m_r_solver;
for (const auto &c : row) {
if (lia.is_fixed(c.var())) {
if (!lia.get_value(c.var()).is_zero()) {
impq val = lia.get_value(c.var()) * c.coeff();
if (!first && val.is_pos())
out << "+";
if (val.y.is_zero())
out << val.x << " ";
else
out << val << " ";
}
first = false;
continue;
}
if (c.coeff().is_one()) {
if (!first)
out << "+";
}
else if (c.coeff().is_minus_one())
out << "-";
else {
if (c.coeff().is_pos() && !first)
out << "+";
if (c.coeff().is_big())
out << " b*";
else
out << c.coeff();
}
out << rslv.column_name(c.var()) << " ";
first = false;
}
out << "\n";
for (const auto &c : row) {
if (lia.is_fixed(c.var()))
continue;
rslv.print_column_info(c.var(), out);
if (lia.is_base(c.var()))
out << "j" << c.var() << " base\n";
}
return out;
}
};
// clang-format on
/**
* \brief find integral and minimal, in the absolute values, deltas such that x - alpha*delta is integral too.
*/
bool get_patching_deltas(const rational& x, const rational& alpha,
rational& delta_plus, rational& delta_minus) {
auto a1 = numerator(alpha);
auto a2 = denominator(alpha);
auto x1 = numerator(x);
auto x2 = denominator(x);
if (!divides(x2, a2))
return false;
// delta has to be integral.
// We need to find delta such that x1/x2 + (a1/a2)*delta is integral (we are going to flip the delta sign later).
// Then a2*x1/x2 + a1*delta is integral, but x2 and x1 are coprime:
// that means that t = a2/x2 is
// integral. We established that a2 = x2*t Then x1 + a1*delta*(x2/a2) = x1
// + a1*(delta/t) is integral. Taking into account that t and a1 are
// coprime we have delta = t*k, where k is an integer.
rational t = a2 / x2;
// Now we have x1/x2 + (a1/x2)*k is integral, or (x1 + a1*k)/x2 is integral.
// It is equivalent to x1 + a1*k = x2*m, where m is an integer
// We know that a2 and a1 are coprime, and x2 divides a2, so x2 and a1 are
// coprime. We can find u and v such that u*a1 + v*x2 = 1.
rational u, v;
gcd(a1, x2, u, v);
lp_assert(gcd(a1, x2, u, v).is_one());
lp_assert((x + (a1 / a2) * (-u * t) * x1).is_int());
// 1 = (u- l*x2 ) * a1 + (v + l*a1)*x2, for every integer l.
rational d = u * t * x1;
// We can prove that x+alpha*d is integral,
// and any other delta, satisfying x+alpha*delta, is equal to d modulo a2.
delta_plus = mod(d, a2);
lp_assert(delta_plus > 0);
delta_minus = delta_plus - a2;
lp_assert(delta_minus < 0);
return true;
}
int_solver::int_solver(lar_solver& lar_slv) :
lra(lar_slv),
lrac(lra.m_mpq_lar_core_solver) {
m_imp = alloc(imp, *this);
lra.set_int_solver(this);
}
int_solver::~int_solver() {
dealloc(m_imp);
}
lia_move int_solver::check(lp::explanation * e) {
return m_imp->check(e);
}
std::ostream& int_solver::display_inf_rows(std::ostream& out) const {
unsigned num = lra.A_r().column_count();
for (unsigned v = 0; v < num; v++) {
if (column_is_int(v) && !get_value(v).is_int()) {
display_column(out, v);
}
}
num = 0;
for (unsigned i = 0; i < lra.A_r().row_count(); i++) {
unsigned j = lrac.m_r_basis[i];
if (column_is_int_inf(j)) {
num++;
lra.print_row(lra.A_r().m_rows[i], out);
out << "\n";
}
}
out << "num of int infeasible: " << num << "\n";
return out;
}
u_dependency* int_solver::column_upper_bound_constraint(unsigned j) const {
return lra.get_column_upper_bound_witness(j);
}
u_dependency* int_solver::column_lower_bound_constraint(unsigned j) const {
return lra.get_column_lower_bound_witness(j);
}
unsigned int_solver::row_of_basic_column(unsigned j) const {
return lra.row_of_basic_column(j);
}
lp_settings& int_solver::settings() {
return lra.settings();
}
const lp_settings& int_solver::settings() const {
return lra.settings();
}
bool int_solver::column_is_int(lpvar j) const {
return lra.column_is_int(j);
}
bool int_solver::is_real(unsigned j) const {
return !column_is_int(j);
}
bool int_solver::value_is_int(unsigned j) const {
return lra.column_value_is_int(j);
}
bool int_solver::is_term(unsigned j) const {
return lra.column_has_term(j);
}
unsigned int_solver::column_count() const {
return lra.column_count();
}
static void set_lower(impq & l, bool & inf_l, impq const & v ) {
if (inf_l || v > l) {
l = v;
inf_l = false;
}
}
static void set_upper(impq & u, bool & inf_u, impq const & v) {
if (inf_u || v < u) {
u = v;
inf_u = false;
}
}
// this function assumes that all basic columns dependend on j are feasible
bool int_solver::get_freedom_interval_for_column(unsigned j, bool & inf_l, impq & l, bool & inf_u, impq & u, mpq & m) {
if (lrac.m_r_heading[j] >= 0 || is_fixed(j)) // basic or fixed var
return false;
TRACE("random_update", display_column(tout, j) << ", is_int = " << column_is_int(j) << "\n";);
impq const & xj = get_value(j);
inf_l = true;
inf_u = true;
l = u = zero_of_type<impq>();
m = mpq(1);
if (has_lower(j))
set_lower(l, inf_l, lower_bound(j) - xj);
if (has_upper(j))
set_upper(u, inf_u, upper_bound(j) - xj);
const auto & A = lra.A_r();
TRACE("random_update", tout << "m = " << m << "\n";);
auto delta = [](mpq const& x, impq const& y, impq const& z) {
if (x.is_one())
return y - z;
if (x.is_minus_one())
return z - y;
return (y - z) / x;
};
for (auto c : A.column(j)) {
unsigned row_index = c.var();
const mpq & a = c.coeff();
unsigned i = lrac.m_r_basis[row_index];
impq const & xi = get_value(i);
lp_assert(lrac.m_r_solver.column_is_feasible(i));
if (column_is_int(i) && !a.is_int() && xi.is_int())
m = lcm(m, denominator(a));
if (!inf_l && !inf_u && l == u)
continue;
if (a.is_neg()) {
if (has_lower(i))
set_lower(l, inf_l, delta(a, xi, lra.get_lower_bound(i)));
if (has_upper(i))
set_upper(u, inf_u, delta(a, xi, lra.get_upper_bound(i)));
}
else {
if (has_upper(i))
set_lower(l, inf_l, delta(a, xi, lra.get_upper_bound(i)));
if (has_lower(i))
set_upper(u, inf_u, delta(a, xi, lra.get_lower_bound(i)));
}
}
l += xj;
u += xj;
TRACE("freedom_interval",
tout << "freedom variable for:\n";
tout << lra.get_variable_name(j);
tout << "[";
if (inf_l) tout << "-oo"; else tout << l;
tout << "; ";
if (inf_u) tout << "oo"; else tout << u;
tout << "]\n";
tout << "val = " << get_value(j) << "\n";
tout << "return " << (inf_l || inf_u || l <= u);
);
return (inf_l || inf_u || l <= u);
}
bool int_solver::is_feasible() const {
lp_assert(
lrac.m_r_solver.calc_current_x_is_feasible_include_non_basis() ==
lrac.m_r_solver.current_x_is_feasible());
return lrac.m_r_solver.current_x_is_feasible();
}
const impq & int_solver::get_value(unsigned j) const {
return lrac.m_r_x[j];
}
std::ostream& int_solver::display_column(std::ostream & out, unsigned j) const {
return lrac.m_r_solver.print_column_info(j, out);
}
bool int_solver::is_base(unsigned j) const {
return lrac.m_r_heading[j] >= 0;
}
bool int_solver::is_boxed(unsigned j) const {
return lrac.m_column_types[j] == column_type::boxed;
}
bool int_solver::is_fixed(unsigned j) const {
return lrac.m_column_types[j] == column_type::fixed;
}
bool int_solver::is_free(unsigned j) const {
return lrac.m_column_types[j] == column_type::free_column;
}
bool int_solver::at_bound(unsigned j) const {
auto & mpq_solver = lrac.m_r_solver;
switch (mpq_solver.m_column_types[j] ) {
case column_type::fixed:
case column_type::boxed:
return
mpq_solver.m_lower_bounds[j] == get_value(j) ||
mpq_solver.m_upper_bounds[j] == get_value(j);
case column_type::lower_bound:
return mpq_solver.m_lower_bounds[j] == get_value(j);
case column_type::upper_bound:
return mpq_solver.m_upper_bounds[j] == get_value(j);
default:
return false;
}
}
bool int_solver::at_lower(unsigned j) const {
auto & mpq_solver = lrac.m_r_solver;
switch (mpq_solver.m_column_types[j] ) {
case column_type::fixed:
case column_type::boxed:
case column_type::lower_bound:
return mpq_solver.m_lower_bounds[j] == get_value(j);
default:
return false;
}
}
bool int_solver::at_upper(unsigned j) const {
auto & mpq_solver = lrac.m_r_solver;
switch (mpq_solver.m_column_types[j] ) {
case column_type::fixed:
case column_type::boxed:
case column_type::upper_bound:
return mpq_solver.m_upper_bounds[j] == get_value(j);
default:
return false;
}
}
std::ostream& int_solver::display_row_info(std::ostream & out, unsigned row_index) const {
auto & rslv = lrac.m_r_solver;
auto const& row = rslv.m_A.m_rows[row_index];
return display_row(out, row);
}
std::ostream & int_solver::display_row(std::ostream & out, vector<row_cell<rational>> const & row) const {
return m_imp->display_row(out, row);
}
bool int_solver::shift_var(unsigned j, unsigned range) {
if (is_fixed(j) || is_base(j))
return false;
if (settings().get_cancel_flag())
return false;
bool inf_l = false, inf_u = false;
impq l, u;
mpq m;
if (!get_freedom_interval_for_column(j, inf_l, l, inf_u, u, m))
return false;
if (settings().get_cancel_flag())
return false;
const impq & x = get_value(j);
// x, the value of j column, might be shifted on a multiple of m
if (inf_l && inf_u) {
impq new_val = m * impq(lra.settings().random_next() % (range + 1)) + x;
lra.set_value_for_nbasic_column(j, new_val);
return true;
}
if (column_is_int(j)) {
if (!inf_l)
l = impq(ceil(l));
if (!inf_u)
u = impq(floor(u));
}
if (!inf_l && !inf_u && l >= u)
return false;
if (inf_u) {
SASSERT(!inf_l);
impq new_val = x + m * impq(lra.settings().random_next() % (range + 1));
lra.set_value_for_nbasic_column(j, new_val);
return true;
}
if (inf_l) {
SASSERT(!inf_u);
impq new_val = x - m * impq(lra.settings().random_next() % (range + 1));
lra.set_value_for_nbasic_column(j, new_val);
return true;
}
SASSERT(!inf_l && !inf_u);
// The shift has to be a multiple of m: let us look for s, such that the shift is m*s.
// We have new_val = x+m*s <= u, so m*s <= u-x and, finally, s <= floor((u- x)/m) = a
// The symmetric reasoning gives us s >= ceil((l-x)/m) = b
// We randomly pick s in the segment [b, a]
mpq a = floor((u - x) / m);
mpq b = ceil((l - x) / m);
mpq r = a - b;
if (!r.is_pos())
return false;
TRACE("int_solver", tout << "a = " << a << ", b = " << b << ", r = " << r<< ", m = " << m << "\n";);
if (r < mpq(range))
range = static_cast<unsigned>(r.get_uint64());
mpq s = b + mpq(lra.settings().random_next() % (range + 1));
impq new_val = x + m * impq(s);
TRACE("int_solver", tout << "new_val = " << new_val << "\n";);
SASSERT(l <= new_val && new_val <= u);
lra.set_value_for_nbasic_column(j, new_val);
return true;
}
void int_solver::simplify(std::function<bool(unsigned)>& is_root) {
return;
#if 0
// in-processing simplification can go here, such as bounds improvements.
if (!lra.is_feasible()) {
lra.find_feasible_solution();
if (!lra.is_feasible())
return;
}
lp::explanation exp;
m_ex = &exp;
m_t.clear();
m_k.reset();
if (has_inf_int())
local_gomory(5);
stopwatch sw;
explanation exp1, exp2;
//
// identify equalities
//
m_equalities.reset();
map<rational, unsigned_vector, rational::hash_proc, rational::eq_proc> value2roots;
vector<std::pair<lp::mpq, unsigned>> coeffs;
coeffs.push_back({-rational::one(), 0});
coeffs.push_back({rational::one(), 0});
num_checks = 0;
// make sure values are sampled with respect to the same state of the Simplex.
vector<rational> values;
for (lpvar j = 0; j < lra.column_count(); ++j)
values.push_back(get_value(j).x);
sw.reset();
sw.start();
start = random();
for (lpvar j0 = 0; j0 < lra.column_count(); ++j0) {
lpvar j = (j0 + start) % lra.column_count();
if (is_fixed(j))
continue;
if (!lra.column_is_int(j))
continue;
if (!is_root(j))
continue;
rational value = values[j];
if (!value2roots.contains(value)) {
unsigned_vector vec;
vec.push_back(j);
value2roots.insert(value, vec);
continue;
}
auto& roots = value2roots.find(value);
bool has_eq = false;
//
// Super inefficient check. There are better ways.
// 1. call into equality finder:
// the cheap equality finder can also be used.
// 2. value sweeping:
// update partitions of values based on feasible tableaus
// instead of having just the values vector use the values
// collected when the find_feasible_solution succeeds with
// a new assignment.
// 3. a more expensive equality finder:
// use the tableau to extract equalities from tight rows.
// If x = y is implied, there is a set of rows that link x and y
// and such that the variables are at their bounds.
// 4. retain information between calls:
// If simplification is invoked at the same backtracking level (or above)
// form the previous call and it is established that x <= y (but not x == y), then no need to
// recheck the inequality x <= y.
for (auto k : roots) {
bool le = false, ge = false;
u_dependency* dep = nullptr;
lra.push();
coeffs[0].second = j;
coeffs[1].second = k;
lp::lpvar term_index = lra.add_term(coeffs, UINT_MAX);
term_index = lra.map_term_index_to_column_index(term_index);
lra.push();
lra.update_column_type_and_bound(term_index, lp::lconstraint_kind::GE, mpq(1), nullptr);
lra.find_feasible_solution();
if (!lra.is_feasible()) {
lra.get_infeasibility_explanation(exp1);
le = true;
}
lra.pop(1);
++num_checks;
if (le) {
lra.push();
lra.update_column_type_and_bound(term_index, lp::lconstraint_kind::LE, mpq(-1), nullptr);
lra.find_feasible_solution();
if (!lra.is_feasible()) {
lra.get_infeasibility_explanation(exp2);
exp1.add_expl(exp2);
ge = true;
}
lra.pop(1);
++num_checks;
}
lra.pop(1);
if (le && ge) {
has_eq = true;
m_equalities.push_back({j, k, exp1});
break;
}
// artificial throttle.
if (num_checks > 10000)
break;
}
if (!has_eq)
roots.push_back(j);
// artificial throttle.
if (num_checks > 10000)
break;
}
sw.stop();
std::cout << "equalities " << m_equalities.size() << " num checks " << num_checks << " time: " << sw.get_seconds() << "\n";
std::cout.flush();
//
// Cuts? Eg. for 0-1 variables or bounded integers?
//
#endif
}
lar_term const& int_solver::get_term() const { return m_imp->m_t; }
lar_term & int_solver::get_term() { return m_imp->m_t; }
mpq const& int_solver::offset() const { return m_imp->m_k; }
mpq & int_solver::offset() { return m_imp->m_k; }
bool int_solver::is_upper() const { return m_imp->m_upper; }
bool& int_solver::is_upper() { return m_imp->m_upper; }
explanation* int_solver::expl() { return m_imp->m_ex; }
bool int_solver::column_is_int_inf(unsigned j) const {
return m_imp->column_is_int_inf(j);
}
bool int_solver::has_lower(unsigned j) const {
return m_imp->has_lower(j);
}
bool int_solver::has_upper(unsigned j) const {
return m_imp->has_upper(j);
}
int int_solver::select_int_infeasible_var() { return m_imp->select_int_infeasible_var(); }
bool int_solver::current_solution_is_inf_on_cut() const { return m_imp->current_solution_is_inf_on_cut(); }
const impq & int_solver::lower_bound(unsigned j) const { return m_imp->lower_bound(j);}
const impq & int_solver::upper_bound(unsigned j) const { return m_imp->upper_bound(j);}
}
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