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z3-z3-4.13.0.src.math.lp.nex_creator.cpp Maven / Gradle / Ivy
/*++
Copyright (c) 2017 Microsoft Corporation
Author:
Lev Nachmanson (levnach)
--*/
#include "util/lbool.h"
#include "math/lp/nex_creator.h"
#include
using namespace nla;
// divides by variable j. A precondition is that a is a multiple of j.
nex * nex_creator::mk_div(const nex& a, lpvar j) {
SASSERT(is_simplified(a));
SASSERT(a.contains(j));
SASSERT(a.is_mul() || (a.is_var() && a.to_var().var() == j));
if (a.is_var())
return mk_scalar(rational(1));
mul_factory mf(*this);
bool seenj = false;
auto ma = a.to_mul();
for (auto& p : ma) {
const nex * c = p.e();
int pow = p.pow();
if (!seenj && c->contains(j)) {
SASSERT(!c->is_var() || c->to_var().var() == j);
if (!c->is_var()) {
mf *= nex_pow(mk_div(*c, j), 1);
}
if (pow != 1) {
mf *= nex_pow(clone(c), pow - 1);
}
seenj = true;
} else {
mf *= nex_pow(clone(c), pow);
}
}
mf *= ma.coeff();
return mf.mk_reduced();
}
// return true if p is a constant, update r with value of p raised to pow.
bool nex_creator::eat_scalar_pow(rational& r, const nex_pow& p, unsigned pow) {
if (p.e()->is_mul() && p.e()->to_mul().size() == 0) {
auto const& m = p.e()->to_mul();
if (!m.coeff().is_one()) {
r *= m.coeff().expt(p.pow() * pow);
}
return true;
}
if (!p.e()->is_scalar())
return false;
const nex_scalar &pe = p.e()->to_scalar();
if (!pe.value().is_one()) {
r *= pe.value().expt(p.pow() * pow);
}
return true;
}
void nex_creator::simplify_children_of_mul(vector & children, rational& coeff) {
TRACE("grobner_d", print_vector(children, tout << "children_of_mul: "); tout << "\n";);
vector to_promote;
unsigned j = 0;
for (nex_pow& p : children) {
if (eat_scalar_pow(coeff, p, 1)) {
continue;
}
p.e() = simplify(p.e());
if (p.e()->is_mul()) {
to_promote.push_back(p);
} else {
children[j++] = p;
}
}
children.shrink(j);
for (nex_pow & p : to_promote) {
TRACE("grobner_d", tout << p << "\n";);
nex_mul &pm = p.e()->to_mul();
for (nex_pow& pp : pm) {
TRACE("grobner_d", tout << pp << "\n";);
if (!eat_scalar_pow(coeff, pp, p.pow()))
children.push_back(nex_pow(pp.e(), pp.pow() * p.pow()));
}
coeff *= pm.coeff().expt(p.pow());
}
mul_to_powers(children);
TRACE("grobner_d", print_vector(children, tout););
}
template
bool nex_creator::gt_on_powers_mul_same_degree(const T& a, const nex_mul& b) const {
bool ret = false;
unsigned a_pow = a.begin()->pow();
unsigned b_pow = b.begin()->pow();
auto it_a = a.begin();
auto it_b = b.begin();
for (; it_a != a.end() && it_b != b.end(); ) {
if (gt(it_a->e(), it_b->e())){
ret = true;
break;
}
if (gt(it_b->e(), it_a->e())){
ret = false;
break;
}
if (a_pow > b_pow) {
ret = true;
break;
}
if (a_pow < b_pow) {
ret = false;
break;
}
++it_a;
++it_b;
if (it_a != a.end()) a_pow = it_a->pow();
if (it_b != b.end()) b_pow = it_b->pow();
}
TRACE("nex_gt", tout << "a = "; print_vector(a, tout) << (ret?" > ":" <= ") << b << "\n";);
return ret;
}
bool nex_creator::gt_on_mul_mul(const nex_mul& a, const nex_mul& b) const {
TRACE("grobner_d", tout << "a = " << a << " , b = " << b << "\n";);
SASSERT(is_simplified(a) && is_simplified(b));
unsigned a_deg = a.get_degree();
unsigned b_deg = b.get_degree();
return a_deg == b_deg ? gt_on_powers_mul_same_degree(a, b) : a_deg > b_deg;
}
bool nex_creator::gt_on_var_nex(const nex_var& a, const nex& b) const {
switch (b.type()) {
case expr_type::SCALAR:
return true;
case expr_type::VAR:
return gt(a.var(), b.to_var().var());
case expr_type::MUL:
return b.get_degree() <= 1 && gt_on_var_nex(a, *b.to_mul()[0].e());
case expr_type::SUM:
SASSERT(b.size() > 1);
if(gt(&a, b.to_sum()[0]))
return true;
if (gt(b.to_sum()[0], &a ))
return false;
return true;
default:
UNREACHABLE();
return false;
}
}
bool nex_creator::gt_on_mul_nex(nex_mul const& m, nex const& b) const {
switch (b.type()) {
case expr_type::SCALAR:
return false;
case expr_type::VAR:
if (m.get_degree() > 1)
return true;
SASSERT(m[0].pow() == 1);
SASSERT(!m[0].e()->is_scalar());
return gt(m[0].e(), &b);
case expr_type::MUL:
return gt_on_mul_mul(m, b.to_mul());
case expr_type::SUM:
return gt_on_mul_nex(m, *b.to_sum()[0]);
default:
UNREACHABLE();
return false;
}
}
bool nex_creator::gt_on_sum_sum(const nex_sum& a, const nex_sum& b) const {
unsigned size = std::min(a.size(), b.size());
for (unsigned j = 0; j < size; j++) {
if (gt(a[j], b[j]))
return true;
if (gt(b[j], a[j]))
return false;
}
return a.size() > size;
}
// the only difference with gt() that it disregards the coefficient in nex_mul
bool nex_creator::gt_for_sort_join_sum(const nex* a, const nex* b) const {
TRACE("grobner_d_", tout << *a << " ? " << *b << "\n";);
if (a == b)
return false;
bool ret;
switch (a->type()) {
case expr_type::VAR:
ret = gt_on_var_nex(a->to_var(), *b);
break;
case expr_type::SCALAR:
if (b->is_scalar())
ret = a->to_scalar().value() > b->to_scalar().value();
else
ret = false; // the scalars are the largest
break;
case expr_type::MUL:
ret = gt_on_mul_nex(a->to_mul(), *b);
break;
case expr_type::SUM:
if (b->is_sum())
return gt_on_sum_sum(a->to_sum(), b->to_sum());
return gt(a->to_sum()[0], b);
default:
UNREACHABLE();
return false;
}
TRACE("grobner_d_", tout << *a << (ret?" < ":" >= ") << *b << "\n";);
return ret;
}
bool nex_creator::gt(const nex& a, const nex& b) const {
TRACE("grobner_d_", tout << a << " ? " << b << "\n";);
if (&a == &b)
return false;
bool ret;
switch (a.type()) {
case expr_type::VAR:
ret = gt_on_var_nex(a.to_var(), b);
break;
case expr_type::SCALAR:
ret = b.is_scalar() && a.to_scalar().value() > b.to_scalar().value();
// the scalars are the largest
break;
case expr_type::MUL:
ret = gt_on_mul_nex(a.to_mul(), b);
break;
case expr_type::SUM:
if (b.is_sum())
return gt_on_sum_sum(a.to_sum(), b.to_sum());
return gt(*a.to_sum()[0], b);
default:
UNREACHABLE();
return false;
}
TRACE("grobner_d_", tout << a << (ret?" < ":" >= ") << b << "\n";);
return ret;
}
bool nex_creator::is_sorted(const nex_mul& e) const {
for (unsigned j = 0; j < e.size() - 1; j++) {
if (!(gt_on_nex_pow(e[j], e[j+1]))) {
TRACE("grobner_d", tout << "not sorted e " << e << "\norder is incorrect " <<
e[j] << " >= " << e[j + 1]<< "\n";);
return false;
}
}
return true;
}
bool nex_creator::mul_is_simplified(const nex_mul& e) const {
TRACE("nla_cn_", tout << "e = " << e << "\n";);
if (e.size() == 0) {
TRACE("nla_cn", );
return false; // it has to be a scalar
}
if (e.size() == 1 && e.begin()->pow() == 1 && e.coeff().is_one()) {
TRACE("nla_cn", );
return false;
}
std::set s([this](const nex* a, const nex* b) {return gt(a, b); });
for (const auto &p : e) {
const nex* ee = p.e();
if (p.pow() == 0) {
TRACE("nla_cn", tout << "not simplified " << *ee << "\n";);
return false;
}
if (ee->is_mul()) {
TRACE("nla_cn", tout << "not simplified " << *ee << "\n";);
return false;
}
if (ee->is_scalar() && to_scalar(ee)->value().is_one()) {
TRACE("nla_cn", tout << "not simplified " << *ee << "\n";);
return false;
}
auto it = s.find(ee);
if (it == s.end()) {
s.insert(ee);
} else {
TRACE("nla_cn", tout << "not simplified " << *ee << "\n";);
return false;
}
}
return is_sorted(e);
}
nex * nex_creator::simplify_mul(nex_mul *e) {
TRACE("grobner_d", tout << *e << "\n";);
rational& coeff = e->m_coeff;
simplify_children_of_mul(e->m_children, coeff);
if (e->size() == 1 && (*e)[0].pow() == 1 && coeff.is_one())
return (*e)[0].e();
if (e->size() == 0 || e->coeff().is_zero())
return mk_scalar(e->coeff());
TRACE("grobner_d", tout << *e << "\n";);
SASSERT(is_simplified(*e));
return e;
}
nex* nex_creator::simplify_sum(nex_sum *e) {
TRACE("grobner_d", tout << "was e = " << *e << "\n";);
simplify_children_of_sum(*e);
nex *r;
if (e->size() == 1) {
r = const_cast((*e)[0]);
} else if (e->size() == 0) {
r = mk_scalar(rational(0));
} else {
r = const_cast(e);
}
TRACE("grobner_d", tout << "became r = " << *r << "\n";);
return r;
}
bool nex_creator::sum_is_simplified(const nex_sum& e) const {
if (e.size() < 2) return false;
bool scalar = false;
for (nex const* ee : e) {
TRACE("nla_cn_details", tout << "ee = " << *ee << "\n";);
if (ee->is_sum()) {
TRACE("nla_cn", tout << "not simplified e = " << e << "\n"
<< " has a child which is a sum " << *ee << "\n";);
return false;
}
if (ee->is_scalar()) {
if (scalar) {
TRACE("nla_cn", tout << "not simplified e = " << e << "\n"
<< " have more than one scalar " << *ee << "\n";);
return false;
}
if (to_scalar(ee)->value().is_zero()) {
if (scalar) {
TRACE("nla_cn", tout << "have a zero scalar " << *ee << "\n";);
return false;
}
scalar = true;
}
}
if (!is_simplified(*ee))
return false;
}
return true;
}
void nex_creator::mul_to_powers(vector& children) {
std::map m([this](const nex* a, const nex* b) { return gt(a, b); });
for (auto & p : children) {
auto it = m.find(p.e());
if (it == m.end()) {
m[p.e()] = p.pow();
} else {
it->second += p.pow();
}
}
children.clear();
for (auto & p : m) {
children.push_back(nex_pow(p.first, p.second));
}
std::sort(children.begin(), children.end(), [this](const nex_pow& a, const nex_pow& b) {
return gt_on_nex_pow(a, b);
});
}
// returns true if the key exists already
bool nex_creator::register_in_join_map(std::map& map, nex const* e, const rational& r) const{
TRACE("grobner_d", tout << *e << ", r = " << r << std::endl;);
auto map_it = map.find(e);
if (map_it == map.end()) {
map[e] = r;
TRACE("grobner_d", tout << "inserting " << std::endl;);
return false;
} else {
map_it->second += r;
TRACE("grobner_d", tout << "adding " << r << " , got " << map_it->second << std::endl;);
return true;
}
}
bool nex_creator::fill_join_map_for_sum(
nex_sum & sum,
std::map& map,
std::unordered_set& existing_nex,
rational& common_scalar) {
bool simplified = false;
for (auto e : sum) {
if (e->is_scalar()) {
simplified = true;
common_scalar += e->to_scalar().value();
continue;
}
existing_nex.insert(e);
if (e->is_mul()) {
nex_mul const * m = to_mul(e);
simplified |= register_in_join_map(map, m, m->coeff());
} else {
SASSERT(e->is_var());
simplified |= register_in_join_map(map, e, rational(1));
}
}
return simplified;
}
// a + 3bc + 2bc => a + 5bc
void nex_creator::sort_join_sum(nex_sum& sum) {
TRACE("grobner_d", tout << sum << "\n";);
std::map map([this](const nex *a , const nex *b)
{ return gt_for_sort_join_sum(a, b); });
std::unordered_set allocated_nexs; // handling (nex*) as numbers
rational common_scalar(0);
fill_join_map_for_sum(sum, map, allocated_nexs, common_scalar);
TRACE("grobner_d", for (auto & p : map ) { tout << "(" << *p.first << ", " << p.second << ") ";});
sum.m_children.reset();
for (auto& p : map) {
process_map_pair(const_cast(p.first), p.second, sum, allocated_nexs);
}
if (!common_scalar.is_zero()) {
sum.m_children.push_back(mk_scalar(common_scalar));
}
TRACE("grobner_d",
tout << "map=";
for (auto & p : map ) tout << "(" << *p.first << ", " << p.second << ") ";
tout << "\nchildren=" << sum << "\n";);
}
void nex_creator::simplify_children_of_sum(nex_sum& s) {
ptr_vector to_promote;
unsigned k = 0;
for (unsigned j = 0; j < s.size(); j++) {
nex* e = s[j] = simplify(s[j]);
if (e->is_sum()) {
to_promote.push_back(e);
} else if (is_zero_scalar(e)) {
continue;
} else if (e->is_mul() && to_mul(e)->coeff().is_zero() ) {
continue;
} else {
s.m_children[k++] = e;
}
}
s.m_children.shrink(k);
for (nex *e : to_promote) {
for (nex const*ee : e->to_sum()) {
if (!is_zero_scalar(ee))
s.m_children.push_back(const_cast(ee));
}
}
sort_join_sum(s);
}
bool nex_mul::all_factors_are_elementary() const {
for (auto & p : *this)
if (!p.e()->is_elementary())
return false;
return true;
}
nex * nex_creator::mk_div_sum_by_mul(const nex_sum& m, const nex_mul& b) {
sum_factory sf(*this);
for (auto e : m) {
sf += mk_div_by_mul(*e, b);
}
nex* r = sf.mk();
TRACE("grobner_d", tout << *r << "\n";);
return r;
}
nex * nex_creator::mk_div_mul_by_mul(const nex_mul& a, const nex_mul& b) {
SASSERT(a.all_factors_are_elementary() && b.all_factors_are_elementary());
b.get_powers_from_mul(m_powers);
m_mk_mul.reset();
for (auto& p_from_a : a) {
TRACE("grobner_d", tout << "p_from_a = " << p_from_a << "\n";);
const nex* e = p_from_a.e();
if (e->is_scalar()) {
m_mk_mul *= nex_pow(clone(e), p_from_a.pow());
TRACE("grobner_d", tout << "processed scalar\n";);
continue;
}
SASSERT(e->is_var());
lpvar j = to_var(e)->var();
auto it = m_powers.find(j);
if (it == m_powers.end()) {
m_mk_mul *= nex_pow(clone(e), p_from_a.pow());
} else {
unsigned pa = p_from_a.pow();
unsigned& pb = it->second;
SASSERT(pa);
if (pa > pb) {
m_mk_mul *= nex_pow(mk_var(j), pa - pb);
m_powers.erase(it);
} else if (pa == pb) {
m_powers.erase(it);
} else {
SASSERT(pa < pb);
// not adding the factor here, it was eaten by b,
// but the key j in m_powers remains
pb -= pa;
}
}
}
SASSERT(m_powers.size() == 0);
m_mk_mul *= (a.coeff() / b.coeff());
nex* ret = m_mk_mul.mk_reduced();
TRACE("grobner_d", tout << *ret << "\n";);
return ret;
}
nex * nex_creator::mk_div_by_mul(const nex& a, const nex_mul& b) {
SASSERT(!a.is_var() || (b.get_degree() == 1 && get_vars_of_expr(&a) == get_vars_of_expr(&b) && b.coeff().is_one()));
if (a.is_sum()) {
return mk_div_sum_by_mul(a.to_sum(), b);
}
if (a.is_var()) {
return mk_scalar(rational(1));
}
return mk_div_mul_by_mul(a.to_mul(), b);
}
nex * nex_creator::mk_div(const nex& a, const nex& b) {
TRACE("grobner_d", tout << a <<" / " << b << "\n";);
if (b.is_var()) {
return mk_div(a, b.to_var().var());
}
return mk_div_by_mul(a, b.to_mul());
}
nex* nex_creator::simplify(nex* e) {
nex* es;
TRACE("grobner_d", tout << *e << std::endl;);
if (e->is_mul())
es = simplify_mul(to_mul(e));
else if (e->is_sum())
es = simplify_sum(to_sum(e));
else
es = e;
TRACE("grobner_d", tout << "simplified = " << *es << std::endl;);
SASSERT(is_simplified(*es));
return es;
}
// adds to children the corrected expression and also adds to allocated the new expressions
void nex_creator::process_map_pair(nex*e, const rational& coeff, nex_sum & sum, std::unordered_set& allocated_nexs) {
TRACE("grobner_d", tout << "e=" << *e << " , coeff= " << coeff << "\n";);
if (coeff.is_zero()) {
TRACE("grobner_d", tout << "did nothing\n";);
return;
}
bool e_is_old = allocated_nexs.find(e) != allocated_nexs.end();
if (!e_is_old) {
add_to_allocated(e);
}
if (e->is_mul()) {
e->to_mul().m_coeff = coeff;
sum.m_children.push_back(simplify(e));
} else {
SASSERT(e->is_var());
if (coeff.is_one()) {
sum.m_children.push_back(e);
} else {
mul_factory mf(*this);
mf *= coeff;
mf *= e;
sum.m_children.push_back(mf.mk());
}
}
}
bool nex_creator::is_simplified(const nex& e) const {
TRACE("nla_cn_details", tout << "e = " << e << "\n";);
if (e.is_mul())
return mul_is_simplified(e.to_mul());
if (e.is_sum())
return sum_is_simplified(e.to_sum());
return true;
}
unsigned nex_creator::find_sum_in_mul(const nex_mul* a) const {
for (unsigned j = 0; j < a->size(); j++)
if ((*a)[j].e()->is_sum())
return j;
return -1;
}
nex* nex_creator::canonize_mul(nex_mul *a) {
TRACE("grobner_d", tout << "a = " << *a << "\n";);
unsigned j = find_sum_in_mul(a);
if (j + 1 == 0)
return a;
nex_pow& np = (*a)[j];
SASSERT(np.pow());
unsigned power = np.pow();
nex_sum const& s = np.e()->to_sum(); // s is going to explode
sum_factory sf(*this);
nex *sclone = power > 1 ? clone(&s) : nullptr;
for (nex const*e : s) {
mul_factory mf(*this);
if (power > 1)
mf *= nex_pow(sclone, power - 1);
mf *= nex_pow(e, 1);
for (unsigned k = 0; k < a->size(); k++) {
if (k == j)
continue;
mf *= nex_pow(clone((*a)[k].e()), (*a)[k].pow());
}
sf += mf.mk();
}
nex* r = sf.mk();
TRACE("grobner_d", tout << "canonized a = " << *r << "\n";);
return canonize(r);
}
nex* nex_creator::canonize(const nex *a) {
if (a->is_elementary())
return clone(a);
nex *t = simplify(clone(a));
if (t->is_sum()) {
nex_sum & s = t->to_sum();
for (unsigned j = 0; j < s.size(); j++) {
s[j] = canonize(s[j]);
}
t = simplify(&s);
TRACE("grobner_d", tout << *t << "\n";);
return t;
}
return canonize_mul(to_mul(t));
}
bool nex_creator::equal(const nex* a, const nex* b) {
TRACE("grobner_d", tout << *a << " against " << *b << "\n";);
nex_creator cn;
unsigned n = 0;
for (lpvar j : get_vars_of_expr(a)) {
n = std::max(j + 1, n);
}
for (lpvar j : get_vars_of_expr(b)) {
n = std::max(j + 1, n);
}
cn.set_number_of_vars(n);
for (lpvar j = 0; j < n; j++) {
cn.set_var_weight(j, j);
}
nex * ca = cn.canonize(a);
nex * cb = cn.canonize(b);
TRACE("grobner_d", tout << "a = " << *a << ", canonized a = " << *ca << "\n";);
TRACE("grobner_d", tout << "b = " << *b << ", canonized b = " << *cb << "\n";);
return !(cn.gt(ca, cb) || cn.gt(cb, ca));
}
