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/* Polyhedron class implementation
(non-inline widening-related member functions).
Copyright (C) 2001-2010 Roberto Bagnara <bagnara@cs.unipr.it>
Copyright (C) 2010-2016 BUGSENG srl (http://bugseng.com)
This file is part of the Parma Polyhedra Library (PPL).
The PPL is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The PPL is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.
For the most up-to-date information see the Parma Polyhedra Library
site: http://bugseng.com/products/ppl/ . */
#include "ppl-config.h"
#include "Polyhedron_defs.hh"
#include "BHRZ03_Certificate_defs.hh"
#include "Rational_Box.hh"
#include "Scalar_Products_defs.hh"
#include "Scalar_Products_inlines.hh"
#include "assertions.hh"
#include <iostream>
#include <stdexcept>
#include <deque>
namespace PPL = Parma_Polyhedra_Library;
void
PPL::Polyhedron
::select_CH78_constraints(const Polyhedron& y,
Constraint_System& cs_selection) const {
// Private method: the caller must ensure the following conditions.
PPL_ASSERT(topology() == y.topology()
&& topology() == cs_selection.topology()
&& space_dim == y.space_dim);
PPL_ASSERT(!marked_empty()
&& !has_pending_constraints()
&& generators_are_up_to_date());
PPL_ASSERT(!y.marked_empty()
&& !y.has_something_pending()
&& y.constraints_are_minimized());
// A constraint in `y.con_sys' is copied to `cs_selection'
// if it is satisfied by all the generators of `gen_sys'.
// Note: the loop index `i' goes upward to avoid reversing
// the ordering of the chosen constraints.
for (dimension_type i = 0, end = y.con_sys.num_rows(); i < end; ++i) {
const Constraint& c = y.con_sys[i];
if (gen_sys.satisfied_by_all_generators(c)) {
cs_selection.insert(c);
}
}
}
void
PPL::Polyhedron
::select_H79_constraints(const Polyhedron& y,
Constraint_System& cs_selected,
Constraint_System& cs_not_selected) const {
// Private method: the caller must ensure the following conditions
// (beside the inclusion `y <= x').
PPL_ASSERT(topology() == y.topology()
&& topology() == cs_selected.topology()
&& topology() == cs_not_selected.topology());
PPL_ASSERT(space_dim == y.space_dim);
PPL_ASSERT(!marked_empty()
&& !has_pending_generators()
&& constraints_are_up_to_date());
PPL_ASSERT(!y.marked_empty()
&& !y.has_something_pending()
&& y.constraints_are_minimized()
&& y.generators_are_up_to_date());
// FIXME: this is a workaround for NNC polyhedra.
if (!y.is_necessarily_closed()) {
// Force strong minimization of constraints.
y.strongly_minimize_constraints();
// Recompute generators (without compromising constraint minimization).
y.update_generators();
}
// Obtain a sorted copy of `y.sat_g'.
if (!y.sat_g_is_up_to_date()) {
y.update_sat_g();
}
Bit_Matrix tmp_sat_g = y.sat_g;
// Remove from `tmp_sat_g' the rows corresponding to tautologies
// (i.e., the positivity or epsilon-bounding constraints):
// this is needed in order to widen the polyhedron and not the
// corresponding homogenized polyhedral cone.
const Constraint_System& y_cs = y.con_sys;
const dimension_type old_num_rows = y_cs.num_rows();
dimension_type num_rows = old_num_rows;
for (dimension_type i = 0; i < num_rows; ++i) {
if (y_cs[i].is_tautological()) {
using std::swap;
--num_rows;
swap(tmp_sat_g[i], tmp_sat_g[num_rows]);
}
}
tmp_sat_g.remove_trailing_rows(old_num_rows - num_rows);
tmp_sat_g.sort_rows();
// A constraint in `con_sys' is copied to `cs_selected'
// if its behavior with respect to `y.gen_sys' is the same
// as that of another constraint in `y.con_sys'.
// otherwise it is copied to `cs_not_selected'.
// Namely, we check whether the saturation row `buffer'
// (built starting from the given constraint and `y.gen_sys')
// is a row of the saturation matrix `tmp_sat_g'.
// CHECKME: the following comment is only applicable when `y.gen_sys'
// is minimized. In that case, the comment suggests that it would be
// possible to use a fast (but incomplete) redundancy test based on
// the number of saturators in `buffer'.
// NOTE: If the considered constraint of `con_sys' does not
// satisfy the saturation rule (see Section \ref prelims), then
// it will not appear in the resulting constraint system,
// because `tmp_sat_g' is built starting from a minimized polyhedron.
// The size of `buffer' will reach sat.num_columns() bits.
Bit_Row buffer;
// Note: the loop index `i' goes upward to avoid reversing
// the ordering of the chosen constraints.
for (dimension_type i = 0, end = con_sys.num_rows(); i < end; ++i) {
const Constraint& ci = con_sys[i];
// The saturation row `buffer' is built considering
// the `i'-th constraint of the polyhedron `x' and
// all the generators of the polyhedron `y'.
buffer.clear();
for (dimension_type j = y.gen_sys.num_rows(); j-- > 0; ) {
const int sp_sgn = Scalar_Products::sign(ci, y.gen_sys[j]);
// We are assuming that `y <= x'.
PPL_ASSERT(sp_sgn >= 0
|| (!is_necessarily_closed()
&& ci.is_strict_inequality()
&& y.gen_sys[j].is_point()));
if (sp_sgn > 0) {
buffer.set(j);
}
}
// We check whether `buffer' is a row of `tmp_sat_g',
// exploiting its sortedness in order to have faster comparisons.
if (tmp_sat_g.sorted_contains(buffer)) {
cs_selected.insert(ci);
}
else {
cs_not_selected.insert(ci);
}
}
}
void
PPL::Polyhedron::H79_widening_assign(const Polyhedron& y, unsigned* tp) {
Polyhedron& x = *this;
// Topology compatibility check.
const Topology topol = x.topology();
if (topol != y.topology()) {
throw_topology_incompatible("H79_widening_assign(y)", "y", y);
// Dimension-compatibility check.
}
if (x.space_dim != y.space_dim) {
throw_dimension_incompatible("H79_widening_assign(y)", "y", y);
}
// Assume `y' is contained in or equal to `x'.
PPL_EXPECT_HEAVY(copy_contains(x, y));
// If any argument is zero-dimensional or empty,
// the H79-widening behaves as the identity function.
if (x.space_dim == 0 || x.marked_empty() || y.marked_empty()) {
return;
}
// `y.gen_sys' should be in minimal form and
// `y.sat_g' should be up-to-date.
if (y.is_necessarily_closed()) {
if (!y.minimize()) {
// `y' is empty: the result is `x'.
return;
}
}
else {
// Dealing with a NNC polyhedron.
// To obtain a correct reasoning when comparing
// the constraints of `x' with the generators of `y',
// we enforce the inclusion relation holding between
// the two NNC polyhedra `x' and `y' (i.e., `y <= x')
// to also hold for the corresponding eps-representations:
// this is obtained by intersecting the two eps-representations.
Polyhedron& yy = const_cast<Polyhedron&>(y);
yy.intersection_assign(x);
if (yy.is_empty()) {
// The result is `x'.
return;
}
}
// If we only have the generators of `x' and the dimensions of
// the two polyhedra are the same, we can compute the standard
// widening by using the specification in [CousotH78], therefore
// avoiding converting from generators to constraints.
if (x.has_pending_generators() || !x.constraints_are_up_to_date()) {
Constraint_System CH78_cs(topol);
x.select_CH78_constraints(y, CH78_cs);
if (CH78_cs.num_rows() == y.con_sys.num_rows()) {
// Having selected all the constraints, the result is `y'.
x = y;
return;
}
// Otherwise, check if `x' and `y' have the same dimension.
// Note that `y.con_sys' is minimized and `CH78_cs' has no redundant
// constraints, since it is a subset of the former.
else if (CH78_cs.num_equalities() == y.con_sys.num_equalities()) {
// Let `x' be defined by the constraints in `CH78_cs'.
Polyhedron CH78(topol, x.space_dim, UNIVERSE);
CH78.add_recycled_constraints(CH78_cs);
// Check whether we are using the widening-with-tokens technique
// and there still are tokens available.
if (tp != 0 && *tp > 0) {
// There are tokens available. If `CH78' is not a subset of `x',
// then it is less precise and we use one of the available tokens.
if (!x.contains(CH78)) {
--(*tp);
}
}
else {
// No tokens.
x.m_swap(CH78);
}
PPL_ASSERT_HEAVY(x.OK(true));
return;
}
}
// As the dimension of `x' is strictly greater than the dimension of `y',
// we have to compute the standard widening by selecting a subset of
// the constraints of `x'.
// `x.con_sys' is just required to be up-to-date, because:
// - if `x.con_sys' is unsatisfiable, then by assumption
// also `y' is empty, so that the resulting polyhedron is `x';
// - redundant constraints in `x.con_sys' do not affect the result
// of the widening, because if they are selected they will be
// redundant even in the result.
if (has_pending_generators()) {
process_pending_generators();
}
else if (!x.constraints_are_up_to_date()) {
x.update_constraints();
}
// Copy into `H79_cs' the constraints of `x' that are common to `y',
// according to the definition of the H79 widening.
Constraint_System H79_cs(topol);
Constraint_System x_minus_H79_cs(topol);
x.select_H79_constraints(y, H79_cs, x_minus_H79_cs);
if (x_minus_H79_cs.has_no_rows()) {
// We selected all of the constraints of `x',
// thus the result of the widening is `x'.
return;
}
else {
// We selected a strict subset of the constraints of `x'.
// NOTE: as `x.con_sys' was not necessarily in minimal form,
// this does not imply that the result strictly includes `x'.
// Let `H79' be defined by the constraints in `H79_cs'.
Polyhedron H79(topol, x.space_dim, UNIVERSE);
H79.add_recycled_constraints(H79_cs);
// Check whether we are using the widening-with-tokens technique
// and there still are tokens available.
if (tp != 0 && *tp > 0) {
// There are tokens available. If `H79' is not a subset of `x',
// then it is less precise and we use one of the available tokens.
if (!x.contains(H79)) {
--(*tp);
}
}
else {
// No tokens.
x.m_swap(H79);
}
PPL_ASSERT_HEAVY(x.OK(true));
}
}
void
PPL::Polyhedron::limited_H79_extrapolation_assign(const Polyhedron& y,
const Constraint_System& cs,
unsigned* tp) {
Polyhedron& x = *this;
const dimension_type cs_num_rows = cs.num_rows();
// If `cs' is empty, we fall back to ordinary, non-limited widening.
if (cs_num_rows == 0) {
x.H79_widening_assign(y, tp);
return;
}
// Topology compatibility check.
if (x.is_necessarily_closed()) {
if (!y.is_necessarily_closed()) {
throw_topology_incompatible("limited_H79_extrapolation_assign(y, cs)",
"y", y);
}
if (cs.has_strict_inequalities()) {
throw_topology_incompatible("limited_H79_extrapolation_assign(y, cs)",
"cs", cs);
}
}
else if (y.is_necessarily_closed()) {
throw_topology_incompatible("limited_H79_extrapolation_assign(y, cs)",
"y", y);
}
// Dimension-compatibility check.
if (x.space_dim != y.space_dim) {
throw_dimension_incompatible("limited_H79_extrapolation_assign(y, cs)",
"y", y);
}
// `cs' must be dimension-compatible with the two polyhedra.
const dimension_type cs_space_dim = cs.space_dimension();
if (x.space_dim < cs_space_dim) {
throw_dimension_incompatible("limited_H79_extrapolation_assign(y, cs)",
"cs", cs);
}
// Assume `y' is contained in or equal to `x'.
PPL_EXPECT_HEAVY(copy_contains(x, y));
if (y.marked_empty()) {
return;
}
if (x.marked_empty()) {
return;
}
// The limited H79-widening between two polyhedra in a
// zero-dimensional space is a polyhedron in a zero-dimensional
// space, too.
if (x.space_dim == 0) {
return;
}
if (!y.minimize()) {
// We have just discovered that `y' is empty.
return;
}
// Update the generators of `x': these are used to select,
// from the constraints in `cs', those that must be added
// to the resulting polyhedron.
if ((x.has_pending_constraints() && !x.process_pending_constraints())
|| (!x.generators_are_up_to_date() && !x.update_generators())) {
// We have just discovered that `x' is empty.
return;
}
Constraint_System new_cs;
// The constraints to be added must be satisfied by all the
// generators of `x'. We can disregard `y' because `y <= x'.
const Generator_System& x_gen_sys = x.gen_sys;
// Iterate upwards here so as to keep the relative ordering of constraints.
// Not really an issue: just aesthetics.
for (dimension_type i = 0; i < cs_num_rows; ++i) {
const Constraint& c = cs[i];
if (x_gen_sys.satisfied_by_all_generators(c)) {
new_cs.insert(c);
}
}
x.H79_widening_assign(y, tp);
x.add_recycled_constraints(new_cs);
PPL_ASSERT_HEAVY(OK());
}
void
PPL::Polyhedron::bounded_H79_extrapolation_assign(const Polyhedron& y,
const Constraint_System& cs,
unsigned* tp) {
Rational_Box x_box(*this, ANY_COMPLEXITY);
const Rational_Box y_box(y, ANY_COMPLEXITY);
x_box.CC76_widening_assign(y_box);
limited_H79_extrapolation_assign(y, cs, tp);
Constraint_System x_box_cs = x_box.constraints();
add_recycled_constraints(x_box_cs);
}
bool
PPL::Polyhedron
::BHRZ03_combining_constraints(const Polyhedron& y,
const BHRZ03_Certificate& y_cert,
const Polyhedron& H79,
const Constraint_System& x_minus_H79_cs) {
Polyhedron& x = *this;
// It is assumed that `y <= x <= H79'.
PPL_ASSERT(x.topology() == y.topology()
&& x.topology() == H79.topology()
&& x.topology() == x_minus_H79_cs.topology());
PPL_ASSERT(x.space_dim == y.space_dim
&& x.space_dim == H79.space_dim
&& x.space_dim == x_minus_H79_cs.space_dimension());
PPL_ASSERT(!x.marked_empty() && !x.has_something_pending()
&& x.constraints_are_minimized() && x.generators_are_minimized());
PPL_ASSERT(!y.marked_empty() && !y.has_something_pending()
&& y.constraints_are_minimized() && y.generators_are_minimized());
PPL_ASSERT(!H79.marked_empty() && !H79.has_something_pending()
&& H79.constraints_are_minimized() && H79.generators_are_minimized());
// We will choose from `x_minus_H79_cs' many subsets of constraints,
// that will be collected (one at a time) in `combining_cs'.
// For each group collected, we compute an average constraint,
// that will be stored in `new_cs'.
// There is no point in applying this technique when `x_minus_H79_cs'
// has one constraint at most (no ``new'' constraint can be computed).
const dimension_type x_minus_H79_cs_num_rows = x_minus_H79_cs.num_rows();
if (x_minus_H79_cs_num_rows <= 1) {
return false;
}
const Topology topol = x.topology();
Constraint_System combining_cs(topol);
Constraint_System new_cs(topol);
// Consider the points that belong to both `x.gen_sys' and `y.gen_sys'.
// For NNC polyhedra, the role of points is played by closure points.
const bool closed = x.is_necessarily_closed();
for (dimension_type i = y.gen_sys.num_rows(); i-- > 0; ) {
const Generator& g = y.gen_sys[i];
if ((g.is_point() && closed) || (g.is_closure_point() && !closed)) {
// If in `H79.con_sys' there is already an inequality constraint
// saturating this point, then there is no need to produce another
// constraint.
bool lies_on_the_boundary_of_H79 = false;
const Constraint_System& H79_cs = H79.con_sys;
for (dimension_type j = H79_cs.num_rows(); j-- > 0; ) {
const Constraint& c = H79_cs[j];
if (c.is_inequality() && Scalar_Products::sign(c, g) == 0) {
lies_on_the_boundary_of_H79 = true;
break;
}
}
if (lies_on_the_boundary_of_H79) {
continue;
}
// Consider all the constraints in `x_minus_H79_cs'
// that are saturated by the point `g'.
combining_cs.clear();
for (dimension_type j = x_minus_H79_cs_num_rows; j-- > 0; ) {
const Constraint& c = x_minus_H79_cs[j];
if (Scalar_Products::sign(c, g) == 0) {
combining_cs.insert(c);
}
}
// Build a new constraint by combining all the chosen constraints.
const dimension_type combining_cs_num_rows = combining_cs.num_rows();
if (combining_cs_num_rows > 0) {
if (combining_cs_num_rows == 1) {
// No combination is needed.
new_cs.insert(combining_cs[0]);
}
else {
Linear_Expression e(0);
bool strict_inequality = false;
for (dimension_type h = combining_cs_num_rows; h-- > 0; ) {
if (combining_cs[h].is_strict_inequality()) {
strict_inequality = true;
}
e += Linear_Expression(combining_cs[h].expression());
}
if (!e.all_homogeneous_terms_are_zero()) {
if (strict_inequality) {
new_cs.insert(e > 0);
}
else {
new_cs.insert(e >= 0);
}
}
}
}
}
}
// If none of the collected constraints strictly intersects `H79',
// then the technique was unsuccessful.
bool improves_upon_H79 = false;
const Poly_Con_Relation si = Poly_Con_Relation::strictly_intersects();
for (dimension_type i = new_cs.num_rows(); i-- > 0; ) {
if (H79.relation_with(new_cs[i]) == si) {
improves_upon_H79 = true;
break;
}
}
if (!improves_upon_H79) {
return false;
}
// The resulting polyhedron is obtained by adding the constraints
// in `new_cs' to polyhedron `H79'.
Polyhedron result = H79;
result.add_recycled_constraints(new_cs);
// Force minimization.
result.minimize();
// Check for stabilization with respect to `y_cert' and improvement
// over `H79'.
if (y_cert.is_stabilizing(result) && !result.contains(H79)) {
// The technique was successful.
x.m_swap(result);
PPL_ASSERT_HEAVY(x.OK(true));
return true;
}
else {
// The technique was unsuccessful.
return false;
}
}
bool
PPL::Polyhedron::BHRZ03_evolving_points(const Polyhedron& y,
const BHRZ03_Certificate& y_cert,
const Polyhedron& H79) {
Polyhedron& x = *this;
// It is assumed that `y <= x <= H79'.
PPL_ASSERT(x.topology() == y.topology()
&& x.topology() == H79.topology());
PPL_ASSERT(x.space_dim == y.space_dim
&& x.space_dim == H79.space_dim);
PPL_ASSERT(!x.marked_empty() && !x.has_something_pending()
&& x.constraints_are_minimized() && x.generators_are_minimized());
PPL_ASSERT(!y.marked_empty() && !y.has_something_pending()
&& y.constraints_are_minimized() && y.generators_are_minimized());
PPL_ASSERT(!H79.marked_empty() && !H79.has_something_pending()
&& H79.constraints_are_minimized() && H79.generators_are_minimized());
// For each point in `x.gen_sys' that is not in `y',
// this technique tries to identify a set of rays that:
// - are included in polyhedron `H79';
// - when added to `y' will subsume the point.
Generator_System candidate_rays;
const dimension_type x_gen_sys_num_rows = x.gen_sys.num_rows();
const dimension_type y_gen_sys_num_rows = y.gen_sys.num_rows();
const bool closed = x.is_necessarily_closed();
for (dimension_type i = x_gen_sys_num_rows; i-- > 0; ) {
const Generator& g1 = x.gen_sys[i];
// For C polyhedra, we choose a point of `x.gen_sys'
// that is not included in `y'.
// In the case of NNC polyhedra, we can restrict attention to
// closure points (considering also points will only add redundancy).
if (((g1.is_point() && closed) || (g1.is_closure_point() && !closed))
&& y.relation_with(g1) == Poly_Gen_Relation::nothing()) {
// For each point (resp., closure point) `g2' in `y.gen_sys',
// where `g1' and `g2' are different,
// build the candidate ray `g1 - g2'.
for (dimension_type j = y_gen_sys_num_rows; j-- > 0; ) {
const Generator& g2 = y.gen_sys[j];
if ((g2.is_point() && closed)
|| (g2.is_closure_point() && !closed)) {
PPL_ASSERT(compare(g1, g2) != 0);
Generator ray_from_g2_to_g1 = g1;
ray_from_g2_to_g1.linear_combine(g2, 0);
candidate_rays.insert(ray_from_g2_to_g1);
}
}
}
}
// Be non-intrusive.
Polyhedron result = x;
result.add_recycled_generators(candidate_rays);
result.intersection_assign(H79);
// Force minimization.
result.minimize();
// Check for stabilization with respect to `y_cert' and improvement
// over `H79'.
if (y_cert.is_stabilizing(result) && !result.contains(H79)) {
// The technique was successful.
x.m_swap(result);
PPL_ASSERT_HEAVY(x.OK(true));
return true;
}
else {
// The technique was unsuccessful.
return false;
}
}
void
PPL::Polyhedron::modify_according_to_evolution(Linear_Expression& ray,
const Linear_Expression& x,
const Linear_Expression& y) {
PPL_DIRTY_TEMP_COEFFICIENT(tmp);
std::deque<bool> considered(x.space_dimension());
Linear_Expression::const_iterator x_end = x.end();
Linear_Expression::const_iterator y_end = y.end();
Linear_Expression::const_iterator y_k = y.begin();
for (Linear_Expression::const_iterator x_k = x.begin();
x_k != x_end; ++x_k) {
const Variable k_var = x_k.variable();
const dimension_type k = k_var.id();
if (considered[k]) {
continue;
}
while (y_k != y_end && y_k.variable().id() < k) {
++y_k;
}
if (y_k == y_end) {
break;
}
const Variable y_k_var = y_k.variable();
// Note that y_k_var.id() may be greater than k.
Linear_Expression::const_iterator y_h = y_k;
// Do *not* increment y_h, since it may be after k already.
Linear_Expression::const_iterator x_h = x_k;
++x_h;
for ( ; x_h != x_end; ++x_h) {
const dimension_type h = x_h.variable().id();
if (considered[h]) {
continue;
}
while (y_h != y_end && y_h.variable().id() < h) {
++y_h;
}
// Note that y_h may be y_end, and y_h.variable().id() may not be k.
if (y_h != y_end && y_h.variable().id() == h) {
tmp = (*x_k) * (*y_h);
}
else {
tmp = 0;
}
if (y_k_var.id() == k) {
// The following line optimizes the computation of
// <CODE> tmp -= x[h] * y[k]; </CODE>
Parma_Polyhedra_Library::sub_mul_assign(tmp, *x_h, *y_k);
}
const int clockwise = sgn(tmp);
const int first_or_third_quadrant = sgn(*x_k) * sgn(*x_h);
switch (clockwise * first_or_third_quadrant) {
case -1:
ray.set_coefficient(k_var, Coefficient_zero());
considered[k] = true;
break;
case 1:
ray.set_coefficient(Variable(h), Coefficient_zero());
considered[h] = true;
break;
default:
break;
}
}
}
ray.normalize();
}
bool
PPL::Polyhedron::BHRZ03_evolving_rays(const Polyhedron& y,
const BHRZ03_Certificate& y_cert,
const Polyhedron& H79) {
Polyhedron& x = *this;
// It is assumed that `y <= x <= H79'.
PPL_ASSERT(x.topology() == y.topology()
&& x.topology() == H79.topology());
PPL_ASSERT(x.space_dim == y.space_dim
&& x.space_dim == H79.space_dim);
PPL_ASSERT(!x.marked_empty() && !x.has_something_pending()
&& x.constraints_are_minimized() && x.generators_are_minimized());
PPL_ASSERT(!y.marked_empty() && !y.has_something_pending()
&& y.constraints_are_minimized() && y.generators_are_minimized());
PPL_ASSERT(!H79.marked_empty() && !H79.has_something_pending()
&& H79.constraints_are_minimized() && H79.generators_are_minimized());
const dimension_type x_gen_sys_num_rows = x.gen_sys.num_rows();
const dimension_type y_gen_sys_num_rows = y.gen_sys.num_rows();
// Candidate rays are kept in a temporary generator system.
Generator_System candidate_rays;
for (dimension_type i = x_gen_sys_num_rows; i-- > 0; ) {
const Generator& x_g = x.gen_sys[i];
// We choose a ray of `x' that does not belong to `y'.
if (x_g.is_ray() && y.relation_with(x_g) == Poly_Gen_Relation::nothing()) {
for (dimension_type j = y_gen_sys_num_rows; j-- > 0; ) {
const Generator& y_g = y.gen_sys[j];
if (y_g.is_ray()) {
Generator new_ray(x_g);
// Modify `new_ray' according to the evolution of `x_g' with
// respect to `y_g'.
modify_according_to_evolution(new_ray.expr, x_g.expr, y_g.expr);
PPL_ASSERT(new_ray.OK());
candidate_rays.insert(new_ray);
}
}
}
}
// If there are no candidate rays, we cannot obtain stabilization.
if (candidate_rays.has_no_rows()) {
return false;
}
// Be non-intrusive.
Polyhedron result = x;
result.add_recycled_generators(candidate_rays);
result.intersection_assign(H79);
// Force minimization.
result.minimize();
// Check for stabilization with respect to `y' and improvement over `H79'.
if (y_cert.is_stabilizing(result) && !result.contains(H79)) {
// The technique was successful.
x.m_swap(result);
PPL_ASSERT_HEAVY(x.OK(true));
return true;
}
else {
// The technique was unsuccessful.
return false;
}
}
void
PPL::Polyhedron::BHRZ03_widening_assign(const Polyhedron& y, unsigned* tp) {
Polyhedron& x = *this;
// Topology compatibility check.
if (x.topology() != y.topology()) {
throw_topology_incompatible("BHRZ03_widening_assign(y)", "y", y);
}
// Dimension-compatibility check.
if (x.space_dim != y.space_dim) {
throw_dimension_incompatible("BHRZ03_widening_assign(y)", "y", y);
}
// Assume `y' is contained in or equal to `x'.
PPL_EXPECT_HEAVY(copy_contains(x, y));
// If any argument is zero-dimensional or empty,
// the BHRZ03-widening behaves as the identity function.
if (x.space_dim == 0 || x.marked_empty() || y.marked_empty()) {
return;
}
// `y.con_sys' and `y.gen_sys' should be in minimal form.
if (!y.minimize()) {
// `y' is empty: the result is `x'.
return;
}
// `x.con_sys' and `x.gen_sys' should be in minimal form.
x.minimize();
// Compute certificate info for polyhedron `y'.
const BHRZ03_Certificate y_cert(y);
// If the iteration is stabilizing, the resulting polyhedron is `x'.
// At this point, also check if the two polyhedra are the same
// (exploiting the knowledge that `y <= x').
if (y_cert.is_stabilizing(x) || y.contains(x)) {
PPL_ASSERT_HEAVY(OK());
return;
}
// Here the iteration is not immediately stabilizing.
// If we are using the widening-with-tokens technique and
// there are tokens available, use one of them and return `x'.
if (tp != 0 && *tp > 0) {
--(*tp);
PPL_ASSERT_HEAVY(OK());
return;
}
// Copy into `H79_cs' the constraints that are common to `x' and `y',
// according to the definition of the H79 widening.
// The other ones are copied into `x_minus_H79_cs'.
const Topology topol = x.topology();
Constraint_System H79_cs(topol);
Constraint_System x_minus_H79_cs(topol);
x.select_H79_constraints(y, H79_cs, x_minus_H79_cs);
// We cannot have selected all of the rows, since otherwise
// the iteration should have been immediately stabilizing.
PPL_ASSERT(!x_minus_H79_cs.has_no_rows());
// Be careful to obtain the right space dimension
// (because `H79_cs' may be empty).
Polyhedron H79(topol, x.space_dim, UNIVERSE);
H79.add_recycled_constraints(H79_cs);
// Force minimization.
H79.minimize();
// NOTE: none of the following widening heuristics is intrusive:
// they will modify `x' only when returning successfully.
if (x.BHRZ03_combining_constraints(y, y_cert, H79, x_minus_H79_cs)) {
return;
}
PPL_ASSERT_HEAVY(H79.OK() && x.OK() && y.OK());
if (x.BHRZ03_evolving_points(y, y_cert, H79)) {
return;
}
PPL_ASSERT_HEAVY(H79.OK() && x.OK() && y.OK());
if (x.BHRZ03_evolving_rays(y, y_cert, H79)) {
return;
}
PPL_ASSERT_HEAVY(H79.OK() && x.OK() && y.OK());
// No previous technique was successful: fall back to the H79 widening.
x.m_swap(H79);
PPL_ASSERT_HEAVY(x.OK(true));
// The H79 widening is always stabilizing.
PPL_ASSERT(y_cert.is_stabilizing(x));
}
void
PPL::Polyhedron
::limited_BHRZ03_extrapolation_assign(const Polyhedron& y,
const Constraint_System& cs,
unsigned* tp) {
Polyhedron& x = *this;
const dimension_type cs_num_rows = cs.num_rows();
// If `cs' is empty, we fall back to ordinary, non-limited widening.
if (cs_num_rows == 0) {
x.BHRZ03_widening_assign(y, tp);
return;
}
// Topology compatibility check.
if (x.is_necessarily_closed()) {
if (!y.is_necessarily_closed()) {
throw_topology_incompatible("limited_BHRZ03_extrapolation_assign(y, cs)",
"y", y);
}
if (cs.has_strict_inequalities()) {
throw_topology_incompatible("limited_BHRZ03_extrapolation_assign(y, cs)",
"cs", cs);
}
}
else if (y.is_necessarily_closed()) {
throw_topology_incompatible("limited_BHRZ03_extrapolation_assign(y, cs)",
"y", y);
}
// Dimension-compatibility check.
if (x.space_dim != y.space_dim) {
throw_dimension_incompatible("limited_BHRZ03_extrapolation_assign(y, cs)",
"y", y);
}
// `cs' must be dimension-compatible with the two polyhedra.
const dimension_type cs_space_dim = cs.space_dimension();
if (x.space_dim < cs_space_dim) {
throw_dimension_incompatible("limited_BHRZ03_extrapolation_assign(y, cs)",
"cs", cs);
}
// Assume `y' is contained in or equal to `x'.
PPL_EXPECT_HEAVY(copy_contains(x, y));
if (y.marked_empty()) {
return;
}
if (x.marked_empty()) {
return;
}
// The limited BHRZ03-widening between two polyhedra in a
// zero-dimensional space is a polyhedron in a zero-dimensional
// space, too.
if (x.space_dim == 0) {
return;
}
if (!y.minimize()) {
// We have just discovered that `y' is empty.
return;
}
// Update the generators of `x': these are used to select,
// from the constraints in `cs', those that must be added
// to the resulting polyhedron.
if ((x.has_pending_constraints() && !x.process_pending_constraints())
|| (!x.generators_are_up_to_date() && !x.update_generators())) {
// We have just discovered that `x' is empty.
return;
}
Constraint_System new_cs;
// The constraints to be added must be satisfied by all the
// generators of `x'. We can disregard `y' because `y <= x'.
const Generator_System& x_gen_sys = x.gen_sys;
// Iterate upwards here so as to keep the relative ordering of constraints.
// Not really an issue: just aesthetics.
for (dimension_type i = 0; i < cs_num_rows; ++i) {
const Constraint& c = cs[i];
if (x_gen_sys.satisfied_by_all_generators(c)) {
new_cs.insert(c);
}
}
x.BHRZ03_widening_assign(y, tp);
x.add_recycled_constraints(new_cs);
PPL_ASSERT_HEAVY(OK());
}
void
PPL::Polyhedron
::bounded_BHRZ03_extrapolation_assign(const Polyhedron& y,
const Constraint_System& cs,
unsigned* tp) {
Rational_Box x_box(*this, ANY_COMPLEXITY);
const Rational_Box y_box(y, ANY_COMPLEXITY);
x_box.CC76_widening_assign(y_box);
limited_BHRZ03_extrapolation_assign(y, cs, tp);
Constraint_System x_box_cs = x_box.constraints();
add_recycled_constraints(x_box_cs);
}
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