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;
}
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;
}
