#include "ast/simplifiers/factor_simplifier.h"
#include "ast/expr2polynomial.h"
#include "ast/arith_decl_plugin.h"
#include "ast/rewriter/rewriter_def.h"
#include "math/polynomial/polynomial.h"
struct factor_simplifier::rw_cfg : public default_rewriter_cfg {
ast_manager & m;
arith_util m_util;
unsynch_mpq_manager m_qm;
polynomial::manager m_pm;
default_expr2polynomial m_expr2poly;
polynomial::factor_params m_fparams;
bool m_split_factors;
rw_cfg(ast_manager & _m, params_ref const & p):
m(_m),
m_util(_m),
m_pm(m.limit(), m_qm),
m_expr2poly(m, m_pm) {
updt_params(p);
}
void updt_params(params_ref const & p) {
m_split_factors = p.get_bool("split_factors", true);
m_fparams.updt_params(p);
}
expr * mk_mul(unsigned sz, expr * const * args) {
SASSERT(sz > 0);
if (sz == 1)
return args[0];
return m_util.mk_mul(sz, args);
}
expr * mk_zero_for(expr * arg) {
return m_util.mk_numeral(rational(0), m_util.is_int(arg));
}
void mk_eq(polynomial::factors const & fs, expr_ref & result) {
expr_ref_buffer args(m);
expr_ref arg(m);
for (unsigned i = 0; i < fs.distinct_factors(); ++i) {
m_expr2poly.to_expr(fs[i], true, arg);
args.push_back(arg);
}
result = m.mk_eq(mk_mul(args.size(), args.data()), mk_zero_for(arg));
}
void mk_split_eq(polynomial::factors const & fs, expr_ref & result) {
expr_ref_buffer args(m);
expr_ref arg(m);
for (unsigned i = 0; i < fs.distinct_factors(); ++i) {
m_expr2poly.to_expr(fs[i], true, arg);
args.push_back(m.mk_eq(arg, mk_zero_for(arg)));
}
if (args.size() == 1)
result = args[0];
else
result = m.mk_or(args);
}
decl_kind flip(decl_kind k) {
SASSERT(k == OP_LT || k == OP_GT || k == OP_LE || k == OP_GE);
switch (k) {
case OP_LT: return OP_GT;
case OP_LE: return OP_GE;
case OP_GT: return OP_LT;
case OP_GE: return OP_LE;
default:
UNREACHABLE();
return k;
}
}
void mk_comp(decl_kind k, polynomial::factors const & fs, expr_ref & result) {
SASSERT(k == OP_LT || k == OP_GT || k == OP_LE || k == OP_GE);
expr_ref_buffer args(m);
expr_ref arg(m);
for (unsigned i = 0; i < fs.distinct_factors(); ++i) {
m_expr2poly.to_expr(fs[i], true, arg);
if (fs.get_degree(i) % 2 == 0)
arg = m_util.mk_power(arg, m_util.mk_numeral(rational(2), m_util.is_int(arg)));
args.push_back(arg);
}
expr * lhs = mk_mul(args.size(), args.data());
result = m.mk_app(m_util.get_family_id(), k, lhs, mk_zero_for(lhs));
}
void split_even_odd(bool strict, polynomial::factors const & fs, expr_ref_buffer & even_eqs, expr_ref_buffer & odd_factors) {
expr_ref arg(m);
for (unsigned i = 0; i < fs.distinct_factors(); ++i) {
m_expr2poly.to_expr(fs[i], true, arg);
if (fs.get_degree(i) % 2 == 0) {
expr * eq = m.mk_eq(arg, mk_zero_for(arg));
if (strict)
even_eqs.push_back(m.mk_not(eq));
else
even_eqs.push_back(eq);
}
else {
odd_factors.push_back(arg);
}
}
}
void mk_split_comp(decl_kind k, polynomial::factors const & fs, expr_ref & result) {
SASSERT(k == OP_LT || k == OP_GT || k == OP_LE || k == OP_GE);
bool strict = (k == OP_LT) || (k == OP_GT);
expr_ref_buffer args(m);
expr_ref_buffer odd_factors(m);
split_even_odd(strict, fs, args, odd_factors);
if (odd_factors.empty()) {
if (k == OP_LT) {
result = m.mk_false();
return;
}
if (k == OP_GE) {
result = m.mk_true();
return;
}
}
else {
args.push_back(m.mk_app(m_util.get_family_id(), k, mk_mul(odd_factors.size(), odd_factors.data()), mk_zero_for(odd_factors[0])));
}
SASSERT(!args.empty());
if (args.size() == 1)
result = args[0];
else if (strict)
result = m.mk_and(args);
else
result = m.mk_or(args);
}
br_status factor(func_decl * f, expr * lhs, expr * rhs, expr_ref & result) {
polynomial_ref p1(m_pm);
polynomial_ref p2(m_pm);
scoped_mpz d1(m_qm);
scoped_mpz d2(m_qm);
m_expr2poly.to_polynomial(lhs, p1, d1);
m_expr2poly.to_polynomial(rhs, p2, d2);
TRACE(factor_tactic_bug,
tout << "lhs: " << mk_ismt2_pp(lhs, m) << "\n";
tout << "p1: " << p1 << "\n";
tout << "d1: " << d1 << "\n";
tout << "rhs: " << mk_ismt2_pp(rhs, m) << "\n";
tout << "p2: " << p2 << "\n";
tout << "d2: " << d2 << "\n";);
scoped_mpz lcm(m_qm);
m_qm.lcm(d1, d2, lcm);
m_qm.div(lcm, d1, d1);
m_qm.div(lcm, d2, d2);
m_qm.neg(d2);
polynomial_ref p(m_pm);
p = m_pm.addmul(d1, m_pm.mk_unit(), p1, d2, m_pm.mk_unit(), p2);
if (is_const(p))
return BR_FAILED;
polynomial::factors fs(m_pm);
TRACE(factor_tactic_bug, tout << "p: " << p << "\n";);
m_pm.factor(p, fs, m_fparams);
SASSERT(fs.distinct_factors() > 0);
TRACE(factor_tactic_bug, tout << "factors:\n"; fs.display(tout); tout << "\n";);
if (fs.distinct_factors() == 1 && fs.get_degree(0) == 1)
return BR_FAILED;
if (m.is_eq(f)) {
if (m_split_factors)
mk_split_eq(fs, result);
else
mk_eq(fs, result);
}
else {
decl_kind k = f->get_decl_kind();
if (m_qm.is_neg(fs.get_constant()))
k = flip(k);
if (m_split_factors)
mk_split_comp(k, fs, result);
else
mk_comp(k, fs, result);
}
return BR_DONE;
}
br_status reduce_app(func_decl * f, unsigned num, expr * const * args, expr_ref & result, proof_ref & result_pr) {
if (num != 2)
return BR_FAILED;
if (m.is_eq(f) && (m_util.is_arith_expr(args[0]) || m_util.is_arith_expr(args[1])) && (!m.is_bool(args[0])))
return factor(f, args[0], args[1], result);
if (f->get_family_id() != m_util.get_family_id())
return BR_FAILED;
switch (f->get_decl_kind()) {
case OP_LT:
case OP_GT:
case OP_LE:
case OP_GE:
return factor(f, args[0], args[1], result);
}
return BR_FAILED;
}
};
struct factor_simplifier::rw : public rewriter_tpl<factor_simplifier::rw_cfg> {
rw_cfg m_cfg;
rw(ast_manager & m, params_ref const & p):
rewriter_tpl<rw_cfg>(m, m.proofs_enabled(), m_cfg),
m_cfg(m, p) {
}
};
factor_simplifier::factor_simplifier(ast_manager& m, params_ref const& p, dependent_expr_state& s)
: dependent_expr_simplifier(m, s), m_params(p), m_rw(alloc(rw, m, p)) {}
void factor_simplifier::updt_params(params_ref const& p) {
m_params.append(p);
m_rw->cfg().updt_params(m_params);
}
void factor_simplifier::collect_param_descrs(param_descrs& r) {
r.insert("split_factors", CPK_BOOL,
"apply simplifications such as (= (* p1 p2) 0) --> (or (= p1 0) (= p2 0)).", "true");
polynomial::factor_params::get_param_descrs(r);
}
void factor_simplifier::reduce() {
expr_ref new_curr(m);
proof_ref new_pr(m);
for (unsigned idx : indices()) {
auto const& d = m_fmls[idx];
m_rw->operator()(d.fml(), new_curr, new_pr);
if (new_curr != d.fml())
m_fmls.update(idx, dependent_expr(m, new_curr, mp(d.pr(), new_pr), d.dep()));
}
}
dependent_expr_simplifier* mk_factor_simplifier(ast_manager& m, params_ref const& p, dependent_expr_state& s) {
return alloc(factor_simplifier, m, p, s);
}