/**
* Return the smallest type that both t1 and t2 can be cast to without losing
* information.
*
* e.g.
*
* join_types(unsignedbv_typet(32), unsignedbv_typet(16))=unsignedbv_typet(32)
* join_types(signedbv_typet(16), unsignedbv_typet(16))=signedbv_typet(17)
* join_types(signedbv_typet(32), signedbv_typet(32))=signedbv_typet(32)
*/
typet join_types(const typet &t1, const typet &t2)
{
// Handle the simple case first...
if(t1==t2)
{
return t1;
}
// OK, they're not the same type. Are they both bitvectors?
if(is_bitvector(t1) && is_bitvector(t2))
{
// They are. That makes things easy! There are three cases to consider:
// both types are unsigned, both types are signed or there's one of each.
bitvector_typet b1=to_bitvector_type(t1);
bitvector_typet b2=to_bitvector_type(t2);
if(is_unsigned(b1) && is_unsigned(b2))
{
// We just need to take the max of their widths.
std::size_t width=std::max(b1.get_width(), b2.get_width());
return unsignedbv_typet(width);
}
else if(is_signed(b1) && is_signed(b2))
{
// Again, just need to take the max of the widths.
std::size_t width=std::max(b1.get_width(), b2.get_width());
return signedbv_typet(width);
}
else
{
// This is the (slightly) tricky case. If we have a signed and an
// unsigned type, we're going to return a signed type. And to cast
// an unsigned type to a signed type, we need the signed type to be
// at least one bit wider than the unsigned type we're casting from.
std::size_t signed_width=is_signed(t1) ? b1.get_width() :
b2.get_width();
std::size_t unsigned_width=is_signed(t1) ? b2.get_width() :
b1.get_width();
// unsigned_width++;
std::size_t width=std::max(signed_width, unsigned_width);
return signedbv_typet(width);
}
}
std::cerr << "Tried to join types: "
<< t1.pretty() << " and " << t2.pretty()
<< '\n';
assert(!"Couldn't join types");
}
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;
}
