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 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;
}