void acceleratet::set_dirty_vars(path_acceleratort &accelerator)
{
for(std::set<exprt>::iterator it=accelerator.dirty_vars.begin();
it!=accelerator.dirty_vars.end();
++it)
{
expr_mapt::iterator jt=dirty_vars_map.find(*it);
exprt dirty_var;
if(jt==dirty_vars_map.end())
{
scratch_programt scratch(symbol_table);
symbolt new_sym=utils.fresh_symbol("accelerate::dirty", bool_typet());
dirty_var=new_sym.symbol_expr();
dirty_vars_map[*it]=dirty_var;
}
else
{
dirty_var=jt->second;
}
#ifdef DEBUG
std::cout << "Setting dirty flag " << expr2c(dirty_var, ns)
<< " for " << expr2c(*it, ns) << '\n';
#endif
accelerator.pure_accelerator.add_instruction(ASSIGN)->code =
code_assignt(dirty_var, true_exprt());
}
}
void cone_of_influencet::cone_of_influence(
const expr_sett &targets,
expr_sett &cone)
{
if(program.instructions.empty())
{
cone=targets;
return;
}
for(goto_programt::instructionst::const_reverse_iterator
rit=program.instructions.rbegin();
rit != program.instructions.rend();
++rit)
{
expr_sett curr; // =targets;
expr_sett next;
if(rit == program.instructions.rbegin())
{
curr=targets;
}
else
{
get_succs(rit, curr);
}
cone_of_influence(*rit, curr, next);
cone_map[rit->location_number]=next;
#ifdef DEBUG
std::cout << "Previous cone: " << std::endl;
for(const auto &expr : curr)
std::cout << expr2c(expr, ns) << " ";
std::cout << std::endl << "Current cone: " << std::endl;
for(const auto &expr : next)
std::cout << expr2c(expr, ns) << " ";
std::cout << std::endl;
#endif
}
cone=cone_map[program.instructions.front().location_number];
}
bool acceleratet::is_underapproximate(path_acceleratort &accelerator)
{
for(std::set<exprt>::iterator it=accelerator.dirty_vars.begin();
it!=accelerator.dirty_vars.end();
++it)
{
if(it->id()==ID_symbol && it->type() == bool_typet())
{
const irep_idt &id=to_symbol_expr(*it).get_identifier();
const symbolt &sym=symbol_table.lookup(id);
if(sym.module=="scratch")
{
continue;
}
}
#ifdef DEBUG
std::cout << "Underapproximate variable: " << expr2c(*it, ns) << '\n';
#endif
return true;
}
return false;
}
void print_assignments(messaget::mstreamt &os, const symbol_tablet &st,
const std::map<const irep_idt, exprt> &assignments)
{
const namespacet ns(st);
for (const std::map<const irep_idt, exprt>::value_type &assignment : assignments)
{
os << "<assignment>" << messaget::endl;
os << " <id>" << assignment.first << "</id>" << messaget::endl;
os << " <value>" << expr2c(assignment.second, ns) << "</value>" << messaget::endl;
os << "</assignment>" << messaget::endl;
}
os << messaget::eom;
}
exprt polynomial_acceleratort::precondition(patht &path) {
exprt ret = false_exprt();
for (patht::reverse_iterator r_it = path.rbegin();
r_it != path.rend();
++r_it) {
goto_programt::const_targett t = r_it->loc;
if (t->is_assign()) {
// XXX Need to check for aliasing...
const code_assignt &assignment = to_code_assign(t->code);
const exprt &lhs = assignment.lhs();
const exprt &rhs = assignment.rhs();
if (lhs.id() == ID_symbol) {
replace_expr(lhs, rhs, ret);
} else if (lhs.id() == ID_index ||
lhs.id() == ID_dereference) {
continue;
} else {
throw "Couldn't take WP of " + expr2c(lhs, ns) + " = " + expr2c(rhs, ns);
}
} else if (t->is_assume() || t->is_assert()) {
ret = implies_exprt(t->guard, ret);
} else {
// Ignore.
}
if (!r_it->guard.is_true() && !r_it->guard.is_nil()) {
// The guard isn't constant true, so we need to accumulate that too.
ret = implies_exprt(r_it->guard, ret);
}
}
simplify(ret, ns);
return ret;
}
bool polynomial_acceleratort::fit_const(goto_programt::instructionst &body,
exprt &target,
polynomialt &poly) {
return false;
scratch_programt program(symbol_table);
program.append(body);
program.add_instruction(ASSERT)->guard = equal_exprt(target, not_exprt(target));
try {
if (program.check_sat(false)) {
#ifdef DEBUG
std::cout << "Fitting constant, eval'd to: " << expr2c(program.eval(target), ns) << std::endl;
#endif
constant_exprt val = to_constant_expr(program.eval(target));
mp_integer mp = binary2integer(val.get_value().c_str(), true);
monomialt mon;
monomialt::termt term;
term.var = from_integer(1, target.type());
term.exp = 1;
mon.terms.push_back(term);
mon.coeff = mp.to_long();
poly.monomials.push_back(mon);
return true;
}
} catch (std::string s) {
std::cout << "Error in fitting polynomial SAT check: " << s << std::endl;
} catch (const char *s) {
std::cout << "Error in fitting polynomial SAT check: " << s << std::endl;
}
return false;
}
bool polynomial_acceleratort::accelerate(patht &loop,
path_acceleratort &accelerator) {
goto_programt::instructionst body;
accelerator.clear();
for (patht::iterator it = loop.begin();
it != loop.end();
++it) {
body.push_back(*(it->loc));
}
expr_sett targets;
std::map<exprt, polynomialt> polynomials;
scratch_programt program(symbol_table);
goto_programt::instructionst assigns;
utils.find_modified(body, targets);
#ifdef DEBUG
std::cout << "Polynomial accelerating program:" << std::endl;
for (goto_programt::instructionst::iterator it = body.begin();
it != body.end();
++it) {
program.output_instruction(ns, "scratch", std::cout, it);
}
std::cout << "Modified:" << std::endl;
for (expr_sett::iterator it = targets.begin();
it != targets.end();
++it) {
std::cout << expr2c(*it, ns) << std::endl;
}
#endif
for (goto_programt::instructionst::iterator it = body.begin();
it != body.end();
++it) {
if (it->is_assign() || it->is_decl()) {
assigns.push_back(*it);
}
}
if (loop_counter.is_nil()) {
symbolt loop_sym = utils.fresh_symbol("polynomial::loop_counter",
unsignedbv_typet(POLY_WIDTH));
loop_counter = loop_sym.symbol_expr();
}
for (expr_sett::iterator it = targets.begin();
it != targets.end();
++it) {
polynomialt poly;
exprt target = *it;
expr_sett influence;
goto_programt::instructionst sliced_assigns;
if (target.type() == bool_typet()) {
// Hack: don't accelerate booleans.
continue;
}
cone_of_influence(assigns, target, sliced_assigns, influence);
if (influence.find(target) == influence.end()) {
#ifdef DEBUG
std::cout << "Found nonrecursive expression: " << expr2c(target, ns) << std::endl;
#endif
nonrecursive.insert(target);
continue;
}
if (target.id() == ID_index ||
target.id() == ID_dereference) {
// We can't accelerate a recursive indirect access...
accelerator.dirty_vars.insert(target);
continue;
}
if (fit_polynomial_sliced(sliced_assigns, target, influence, poly)) {
std::map<exprt, polynomialt> this_poly;
this_poly[target] = poly;
if (check_inductive(this_poly, assigns)) {
polynomials.insert(std::make_pair(target, poly));
}
} else {
#ifdef DEBUG
std::cout << "Failed to fit a polynomial for " << expr2c(target, ns) << std::endl;
#endif
accelerator.dirty_vars.insert(*it);
}
}
if (polynomials.empty()) {
//return false;
}
/*
if (!utils.check_inductive(polynomials, assigns)) {
// They're not inductive :-(
return false;
}
*/
substitutiont stashed;
stash_polynomials(program, polynomials, stashed, body);
exprt guard;
exprt guard_last;
bool path_is_monotone;
try {
path_is_monotone = utils.do_assumptions(polynomials, loop, guard);
} catch (std::string s) {
// Couldn't do WP.
std::cout << "Assumptions error: " << s << std::endl;
return false;
}
guard_last = guard;
for (std::map<exprt, polynomialt>::iterator it = polynomials.begin();
it != polynomials.end();
++it) {
replace_expr(it->first, it->second.to_expr(), guard_last);
}
if (path_is_monotone) {
// OK cool -- the path is monotone, so we can just assume the condition for
// the first and last iterations.
replace_expr(loop_counter,
minus_exprt(loop_counter, from_integer(1, loop_counter.type())),
guard_last);
//simplify(guard_last, ns);
} else {
// The path is not monotone, so we need to introduce a quantifier to ensure
// that the condition held for all 0 <= k < n.
symbolt k_sym = utils.fresh_symbol("polynomial::k", unsignedbv_typet(POLY_WIDTH));
exprt k = k_sym.symbol_expr();
exprt k_bound = and_exprt(binary_relation_exprt(from_integer(0, k.type()), "<=", k),
binary_relation_exprt(k, "<", loop_counter));
replace_expr(loop_counter, k, guard_last);
implies_exprt implies(k_bound, guard_last);
//simplify(implies, ns);
exprt forall(ID_forall);
forall.type() = bool_typet();
forall.copy_to_operands(k);
forall.copy_to_operands(implies);
guard_last = forall;
}
// All our conditions are met -- we can finally build the accelerator!
// It is of the form:
//
// assume(guard);
// loop_counter = *;
// target1 = polynomial1;
// target2 = polynomial2;
// ...
// assume(guard);
// assume(no overflows in previous code);
program.add_instruction(ASSUME)->guard = guard;
program.assign(loop_counter, side_effect_expr_nondett(loop_counter.type()));
for (std::map<exprt, polynomialt>::iterator it = polynomials.begin();
it != polynomials.end();
++it) {
program.assign(it->first, it->second.to_expr());
}
// Add in any array assignments we can do now.
if (!utils.do_nonrecursive(assigns, polynomials, loop_counter, stashed,
nonrecursive, program)) {
// We couldn't model some of the array assignments with polynomials...
// Unfortunately that means we just have to bail out.
#ifdef DEBUG
std::cout << "Failed to accelerate a nonrecursive expression" << std::endl;
#endif
return false;
}
program.add_instruction(ASSUME)->guard = guard_last;
program.fix_types();
if (path_is_monotone) {
utils.ensure_no_overflows(program);
}
accelerator.pure_accelerator.instructions.swap(program.instructions);
return true;
}
bool polynomial_acceleratort::fit_polynomial_sliced(goto_programt::instructionst &body,
exprt &var,
expr_sett &influence,
polynomialt &polynomial) {
// These are the variables that var depends on with respect to the body.
std::vector<expr_listt> parameters;
std::set<std::pair<expr_listt, exprt> > coefficients;
expr_listt exprs;
scratch_programt program(symbol_table);
exprt overflow_var =
utils.fresh_symbol("polynomial::overflow", bool_typet()).symbol_expr();
overflow_instrumentert overflow(program, overflow_var, symbol_table);
#ifdef DEBUG
std::cout << "Fitting a polynomial for " << expr2c(var, ns) << ", which depends on:"
<< std::endl;
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
std::cout << expr2c(*it, ns) << std::endl;
}
#endif
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
if (it->id() == ID_index ||
it->id() == ID_dereference) {
// Hack: don't accelerate variables that depend on arrays...
return false;
}
exprs.clear();
exprs.push_back(*it);
parameters.push_back(exprs);
exprs.push_back(loop_counter);
parameters.push_back(exprs);
}
// N
exprs.clear();
exprs.push_back(loop_counter);
parameters.push_back(exprs);
// N^2
exprs.push_back(loop_counter);
//parameters.push_back(exprs);
// Constant
exprs.clear();
parameters.push_back(exprs);
if (!is_bitvector(var.type())) {
// We don't really know how to accelerate non-bitvectors anyway...
return false;
}
unsigned width=to_bitvector_type(var.type()).get_width();
if(var.type().id()==ID_pointer)
width=config.ansi_c.pointer_width;
assert(width>0);
for (std::vector<expr_listt>::iterator it = parameters.begin();
it != parameters.end();
++it) {
symbolt coeff = utils.fresh_symbol("polynomial::coeff",
signedbv_typet(width));
coefficients.insert(std::make_pair(*it, coeff.symbol_expr()));
}
// Build a set of values for all the parameters that allow us to fit a
// unique polynomial.
// XXX
// This isn't ok -- we're assuming 0, 1 and 2 are valid values for the
// variables involved, but this might make the path condition UNSAT. Should
// really be solving the path constraints a few times to get valid probe
// values...
std::map<exprt, int> values;
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
values[*it] = 0;
}
#ifdef DEBUG
std::cout << "Fitting polynomial over " << values.size() << " variables" << std::endl;
#endif
for (int n = 0; n <= 2; n++) {
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
values[*it] = 1;
assert_for_values(program, values, coefficients, n, body, var, overflow);
values[*it] = 0;
}
}
// Now just need to assert the case where all values are 0 and all are 2.
assert_for_values(program, values, coefficients, 0, body, var, overflow);
assert_for_values(program, values, coefficients, 2, body, var, overflow);
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
values[*it] = 2;
}
assert_for_values(program, values, coefficients, 2, body, var, overflow);
#ifdef DEBUG
std::cout << "Fitting polynomial with program:" << std::endl;
program.output(ns, "", std::cout);
#endif
// Now do an ASSERT(false) to grab a counterexample
goto_programt::targett assertion = program.add_instruction(ASSERT);
assertion->guard = false_exprt();
// If the path is satisfiable, we've fitted a polynomial. Extract the
// relevant coefficients and return the expression.
try {
if (program.check_sat()) {
utils.extract_polynomial(program, coefficients, polynomial);
return true;
}
} catch (std::string s) {
std::cout << "Error in fitting polynomial SAT check: " << s << std::endl;
} catch (const char *s) {
std::cout << "Error in fitting polynomial SAT check: " << s << std::endl;
}
return false;
}
std::ostream& abstract_programt::output_instruction(
const namespacet &ns,
const irep_idt &identifier,
std::ostream &out,
const_targett it) const
{
if(!it->location.is_nil())
out << " // " << it->location.as_string() << "\n";
else
out << " // no location\n";
out << "From predicates:";
for(std::set<unsigned>::const_iterator
p_it=it->code.get_transition_relation().from_predicates.begin();
p_it!=it->code.get_transition_relation().from_predicates.end();
p_it++)
out << " " << *p_it;
out << std::endl;
out << " ";
out << "To predicates:";
for(std::set<unsigned>::const_iterator
p_it=it->code.get_transition_relation().to_predicates.begin();
p_it!=it->code.get_transition_relation().to_predicates.end();
p_it++)
out << " " << *p_it;
out << std::endl;
if(!it->labels.empty())
{
out << " // Labels:";
for(instructiont::labelst::const_iterator
l_it=it->labels.begin();
l_it!=it->labels.end();
l_it++)
{
out << " " << *l_it;
}
out << std::endl;
}
if(it->is_target())
out << std::setw(6) << it->target_number << ": ";
else
out << " ";
switch(it->type)
{
case NO_INSTRUCTION_TYPE:
out << "NO INSTRUCTION TYPE SET" << std::endl;
break;
case GOTO:
if(!it->guard.is_true())
{
out << "IF "
<< from_expr(ns, identifier, it->guard)
<< " THEN ";
}
out << "GOTO ";
for(instructiont::targetst::const_iterator
gt_it=it->targets.begin();
gt_it!=it->targets.end();
gt_it++)
{
if(gt_it!=it->targets.begin()) out << ", ";
out << (*gt_it)->target_number;
}
out << std::endl;
break;
case RETURN:
case OTHER:
case DECL:
case FUNCTION_CALL:
case ASSIGN:
{
#if 0
for(symex_equationt::equationt::premisest::const_iterator
p_it=it->code.equation.assignments.begin();
p_it!=it->code.equation.assignments.end();
p_it++)
out << from_expr(ns, identifier, *p_it) << std::endl;
#endif
out << " ";
out << "Changed predicates:";
for(abstract_transition_relationt::valuest::const_iterator
p_it=it->code.get_transition_relation().values.begin();
p_it!=it->code.get_transition_relation().values.end();
p_it++)
out << " " << p_it->first;
out << std::endl;
out << " ";
out << "Constraints: ";
for(abstract_transition_relationt::constraintst::const_iterator
e_it=it->code.get_transition_relation().constraints.begin();
e_it!=it->code.get_transition_relation().constraints.end();
e_it++)
{
const exprt &constraint=*e_it;
if(e_it!=it->code.get_transition_relation().constraints.begin())
out << " ";
out << expr2c(constraint, ns) << std::endl;
}
out << std::endl;
return out;
}
break;
case ASSUME:
case ASSERT:
if(it->is_assume())
out << "ASSUME ";
else
out << "ASSERT ";
{
out << from_expr(ns, identifier, it->guard);
const irep_idt &comment=it->location.get("comment");
if(comment!="") out << " // " << comment;
}
out << std::endl;
break;
case SKIP:
out << "SKIP" << std::endl;
break;
case END_FUNCTION:
out << "END_FUNCTION" << std::endl;
break;
case LOCATION:
out << "LOCATION" << std::endl;
break;
case DEAD:
out << "DEAD" << std::endl;
break;
case ATOMIC_BEGIN:
out << "ATOMIC_BEGIN" << std::endl;
break;
case ATOMIC_END:
out << "ATOMIC_END" << std::endl;
break;
case START_THREAD:
out << "START THREAD ";
if(it->targets.size()==1)
out << it->targets.front()->target_number;
out << std::endl;
break;
case END_THREAD:
out << "END THREAD" << std::endl;
break;
case THROW:
out << "THROW" << std::endl;
break;
case CATCH:
out << "CATCH" << std::endl;
break;
default:
throw "unexpected instruction (abstract_program)";
}
return out;
}
bool disjunctive_polynomial_accelerationt::accelerate(
path_acceleratort &accelerator) {
std::map<exprt, polynomialt> polynomials;
scratch_programt program(symbol_table);
accelerator.clear();
#ifdef DEBUG
std::cout << "Polynomial accelerating program:" << std::endl;
for (goto_programt::instructionst::iterator it = goto_program.instructions.begin();
it != goto_program.instructions.end();
++it) {
if (loop.find(it) != loop.end()) {
goto_program.output_instruction(ns, "scratch", std::cout, it);
}
}
std::cout << "Modified:" << std::endl;
for (expr_sett::iterator it = modified.begin();
it != modified.end();
++it) {
std::cout << expr2c(*it, ns) << std::endl;
}
#endif
if (loop_counter.is_nil()) {
symbolt loop_sym = utils.fresh_symbol("polynomial::loop_counter",
unsigned_poly_type());
loop_counter = loop_sym.symbol_expr();
}
patht &path = accelerator.path;
path.clear();
if (!find_path(path)) {
// No more paths!
return false;
}
#if 0
for (expr_sett::iterator it = modified.begin();
it != modified.end();
++it) {
polynomialt poly;
exprt target = *it;
if (it->type().id() == ID_bool) {
// Hack: don't try to accelerate booleans.
continue;
}
if (target.id() == ID_index ||
target.id() == ID_dereference) {
// We'll handle this later.
continue;
}
if (fit_polynomial(target, poly, path)) {
std::map<exprt, polynomialt> this_poly;
this_poly[target] = poly;
if (utils.check_inductive(this_poly, path)) {
#ifdef DEBUG
std::cout << "Fitted a polynomial for " << expr2c(target, ns) <<
std::endl;
#endif
polynomials[target] = poly;
accelerator.changed_vars.insert(target);
break;
}
}
}
if (polynomials.empty()) {
return false;
}
#endif
// Fit polynomials for the other variables.
expr_sett dirty;
utils.find_modified(accelerator.path, dirty);
polynomial_acceleratort path_acceleration(symbol_table, goto_functions,
loop_counter);
goto_programt::instructionst assigns;
for (patht::iterator it = accelerator.path.begin();
it != accelerator.path.end();
++it) {
if (it->loc->is_assign() || it->loc->is_decl()) {
assigns.push_back(*(it->loc));
}
}
for (expr_sett::iterator it = dirty.begin();
it != dirty.end();
++it) {
#ifdef DEBUG
std::cout << "Trying to accelerate " << expr2c(*it, ns) << std::endl;
#endif
if (it->type().id() == ID_bool) {
// Hack: don't try to accelerate booleans.
accelerator.dirty_vars.insert(*it);
#ifdef DEBUG
std::cout << "Ignoring boolean" << std::endl;
#endif
continue;
}
if (it->id() == ID_index ||
it->id() == ID_dereference) {
#ifdef DEBUG
std::cout << "Ignoring array reference" << std::endl;
#endif
continue;
}
if (accelerator.changed_vars.find(*it) != accelerator.changed_vars.end()) {
// We've accelerated variable this already.
#ifdef DEBUG
std::cout << "We've accelerated it already" << std::endl;
#endif
continue;
}
// Hack: ignore variables that depend on array values..
exprt array_rhs;
if (depends_on_array(*it, array_rhs)) {
#ifdef DEBUG
std::cout << "Ignoring because it depends on an array" << std::endl;
#endif
continue;
}
polynomialt poly;
exprt target(*it);
if (path_acceleration.fit_polynomial(assigns, target, poly)) {
std::map<exprt, polynomialt> this_poly;
this_poly[target] = poly;
if (utils.check_inductive(this_poly, accelerator.path)) {
polynomials[target] = poly;
accelerator.changed_vars.insert(target);
continue;
}
}
#ifdef DEBUG
std::cout << "Failed to accelerate " << expr2c(*it, ns) << std::endl;
#endif
// We weren't able to accelerate this target...
accelerator.dirty_vars.insert(target);
}
/*
if (!utils.check_inductive(polynomials, assigns)) {
// They're not inductive :-(
return false;
}
*/
substitutiont stashed;
utils.stash_polynomials(program, polynomials, stashed, path);
exprt guard;
bool path_is_monotone;
try {
path_is_monotone = utils.do_assumptions(polynomials, path, guard);
} catch (std::string s) {
// Couldn't do WP.
std::cout << "Assumptions error: " << s << std::endl;
return false;
}
exprt pre_guard(guard);
for (std::map<exprt, polynomialt>::iterator it = polynomials.begin();
it != polynomials.end();
++it) {
replace_expr(it->first, it->second.to_expr(), guard);
}
if (path_is_monotone) {
// OK cool -- the path is monotone, so we can just assume the condition for
// the last iteration.
replace_expr(loop_counter,
minus_exprt(loop_counter, from_integer(1, loop_counter.type())),
guard);
} else {
// The path is not monotone, so we need to introduce a quantifier to ensure
// that the condition held for all 0 <= k < n.
symbolt k_sym = utils.fresh_symbol("polynomial::k", unsigned_poly_type());
exprt k = k_sym.symbol_expr();
exprt k_bound = and_exprt(binary_relation_exprt(from_integer(0, k.type()), "<=", k),
binary_relation_exprt(k, "<", loop_counter));
replace_expr(loop_counter, k, guard);
simplify(guard, ns);
implies_exprt implies(k_bound, guard);
exprt forall(ID_forall);
forall.type() = bool_typet();
forall.copy_to_operands(k);
forall.copy_to_operands(implies);
guard = forall;
}
// All our conditions are met -- we can finally build the accelerator!
// It is of the form:
//
// loop_counter = *;
// target1 = polynomial1;
// target2 = polynomial2;
// ...
// assume(guard);
// assume(no overflows in previous code);
program.add_instruction(ASSUME)->guard = pre_guard;
program.assign(loop_counter, side_effect_expr_nondett(loop_counter.type()));
for (std::map<exprt, polynomialt>::iterator it = polynomials.begin();
it != polynomials.end();
++it) {
program.assign(it->first, it->second.to_expr());
accelerator.changed_vars.insert(it->first);
}
// Add in any array assignments we can do now.
if (!utils.do_arrays(assigns, polynomials, loop_counter, stashed, program)) {
// We couldn't model some of the array assignments with polynomials...
// Unfortunately that means we just have to bail out.
return false;
}
program.add_instruction(ASSUME)->guard = guard;
program.fix_types();
if (path_is_monotone) {
utils.ensure_no_overflows(program);
}
accelerator.pure_accelerator.instructions.swap(program.instructions);
return true;
}
bool disjunctive_polynomial_accelerationt::fit_polynomial(
exprt &var,
polynomialt &polynomial,
patht &path) {
// These are the variables that var depends on with respect to the body.
std::vector<expr_listt> parameters;
std::set<std::pair<expr_listt, exprt> > coefficients;
expr_listt exprs;
scratch_programt program(symbol_table);
expr_sett influence;
cone_of_influence(var, influence);
#ifdef DEBUG
std::cout << "Fitting a polynomial for " << expr2c(var, ns) << ", which depends on:"
<< std::endl;
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
std::cout << expr2c(*it, ns) << std::endl;
}
#endif
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
if (it->id() == ID_index ||
it->id() == ID_dereference) {
// Hack: don't accelerate anything that depends on an array
// yet...
return false;
}
exprs.clear();
exprs.push_back(*it);
parameters.push_back(exprs);
exprs.push_back(loop_counter);
parameters.push_back(exprs);
}
// N
exprs.clear();
exprs.push_back(loop_counter);
parameters.push_back(exprs);
// N^2
exprs.push_back(loop_counter);
parameters.push_back(exprs);
// Constant
exprs.clear();
parameters.push_back(exprs);
for (std::vector<expr_listt>::iterator it = parameters.begin();
it != parameters.end();
++it) {
symbolt coeff = utils.fresh_symbol("polynomial::coeff", signed_poly_type());
coefficients.insert(make_pair(*it, coeff.symbol_expr()));
// XXX HACK HACK HACK
// I'm just constraining these coefficients to prevent overflows messing things
// up later... Should really do this properly somehow.
program.assume(binary_relation_exprt(from_integer(-(1 << 10), signed_poly_type()),
"<", coeff.symbol_expr()));
program.assume(binary_relation_exprt(coeff.symbol_expr(), "<",
from_integer(1 << 10, signed_poly_type())));
}
// Build a set of values for all the parameters that allow us to fit a
// unique polynomial.
std::map<exprt, exprt> ivals1;
std::map<exprt, exprt> ivals2;
std::map<exprt, exprt> ivals3;
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
symbolt ival1 = utils.fresh_symbol("polynomial::init",
it->type());
symbolt ival2 = utils.fresh_symbol("polynomial::init",
it->type());
symbolt ival3 = utils.fresh_symbol("polynomial::init",
it->type());
program.assume(binary_relation_exprt(ival1.symbol_expr(), "<",
ival2.symbol_expr()));
program.assume(binary_relation_exprt(ival2.symbol_expr(), "<",
ival3.symbol_expr()));
#if 0
if (it->type() == signedbv_typet()) {
program.assume(binary_relation_exprt(ival1.symbol_expr(), ">",
from_integer(-100, it->type())));
}
program.assume(binary_relation_exprt(ival1.symbol_expr(), "<",
from_integer(100, it->type())));
if (it->type() == signedbv_typet()) {
program.assume(binary_relation_exprt(ival2.symbol_expr(), ">",
from_integer(-100, it->type())));
}
program.assume(binary_relation_exprt(ival2.symbol_expr(), "<",
from_integer(100, it->type())));
if (it->type() == signedbv_typet()) {
program.assume(binary_relation_exprt(ival3.symbol_expr(), ">",
from_integer(-100, it->type())));
}
program.assume(binary_relation_exprt(ival3.symbol_expr(), "<",
from_integer(100, it->type())));
#endif
ivals1[*it] = ival1.symbol_expr();
ivals2[*it] = ival2.symbol_expr();
ivals3[*it] = ival3.symbol_expr();
//ivals1[*it] = from_integer(1, it->type());
}
std::map<exprt, exprt> values;
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
values[*it] = ivals1[*it];
}
// Start building the program. Begin by decl'ing each of the
// master distinguishers.
for (std::list<exprt>::iterator it = distinguishers.begin();
it != distinguishers.end();
++it) {
program.add_instruction(DECL)->code = code_declt(*it);
}
// Now assume our polynomial fits at each of our sample points.
assert_for_values(program, values, coefficients, 1, fixed, var);
for (int n = 0; n <= 1; n++) {
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
values[*it] = ivals2[*it];
assert_for_values(program, values, coefficients, n, fixed, var);
values[*it] = ivals3[*it];
assert_for_values(program, values, coefficients, n, fixed, var);
values[*it] = ivals1[*it];
}
}
for (expr_sett::iterator it = influence.begin();
it != influence.end();
++it) {
values[*it] = ivals3[*it];
}
assert_for_values(program, values, coefficients, 0, fixed, var);
assert_for_values(program, values, coefficients, 1, fixed, var);
assert_for_values(program, values, coefficients, 2, fixed, var);
// Let's make sure that we get a path we have not seen before.
for (std::list<distinguish_valuest>::iterator it = accelerated_paths.begin();
it != accelerated_paths.end();
++it) {
exprt new_path = false_exprt();
for (distinguish_valuest::iterator jt = it->begin();
jt != it->end();
++jt) {
exprt distinguisher = jt->first;
bool taken = jt->second;
if (taken) {
not_exprt negated(distinguisher);
distinguisher.swap(negated);
}
or_exprt disjunct(new_path, distinguisher);
new_path.swap(disjunct);
}
program.assume(new_path);
}
utils.ensure_no_overflows(program);
// Now do an ASSERT(false) to grab a counterexample
program.add_instruction(ASSERT)->guard = false_exprt();
// If the path is satisfiable, we've fitted a polynomial. Extract the
// relevant coefficients and return the expression.
try {
if (program.check_sat()) {
#ifdef DEBUG
std::cout << "Found a polynomial" << std::endl;
#endif
utils.extract_polynomial(program, coefficients, polynomial);
build_path(program, path);
record_path(program);
return true;
}
} catch (std::string s) {
std::cout << "Error in fitting polynomial SAT check: " << s << std::endl;
} catch (const char *s) {
std::cout << "Error in fitting polynomial SAT check: " << s << std::endl;
}
return false;
}
std::string c_typecheck_baset::to_string(const exprt &expr)
{
return expr2c(expr, *this);
}
std::string linkingt::to_string(const exprt &expr)
{
return expr2c(expr, ns);
}