mirror of
https://github.com/Z3Prover/z3
synced 2025-04-13 20:38:43 +00:00
rewrite horner scheme on top of nex_expr as a pointer
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson
parent
9fbd0da931
commit
a7449494a9
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@ -35,7 +35,7 @@ class cross_nested {
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};
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// fields
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nex_sum * m_e;
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nex * m_e;
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std::function<bool (const nex*)> m_call_on_result;
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std::function<bool (unsigned)> m_var_is_fixed;
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bool m_done;
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@ -43,6 +43,7 @@ class cross_nested {
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std::unordered_map<lpvar, unsigned> m_powers;
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vector<nex*> m_allocated;
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vector<nex*> m_b_vec;
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vector<nex*> m_b_split_vec;
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public:
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cross_nested(std::function<bool (const nex*)> call_on_result,
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std::function<bool (unsigned)> var_is_fixed):
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@ -51,16 +52,16 @@ public:
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m_done(false)
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{}
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void run(nex_sum *e) {
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void run(nex *e) {
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m_e = e;
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vector<nex_sum*> front;
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vector<nex**> front;
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explore_expr_on_front_elem(m_e, front);
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}
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static nex_sum* pop_back(vector<nex_sum*>& front) {
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nex_sum* c = front.back();
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TRACE("nla_cn", tout << *c << "\n";);
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static nex** pop_front(vector<nex**>& front) {
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nex** c = front.back();
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TRACE("nla_cn", tout << **c << "\n";);
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front.pop_back();
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return c;
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}
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@ -70,6 +71,14 @@ public:
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m_allocated.push_back(r);
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return r;
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}
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template <typename T>
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void add_children(T) { }
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template <typename T, typename K, typename ...Args>
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void add_children(T r, K e, Args ... es) {
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r->add_child(e);
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add_children(r, es ...);
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}
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nex_sum* mk_sum(const vector<nex*>& v) {
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auto r = new nex_sum();
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@ -78,40 +87,41 @@ public:
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return r;
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}
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nex_sum* mk_sum(nex *a, nex* b) {
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auto r = new nex_sum();
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nex_mul* mk_mul(const vector<nex*>& v) {
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auto r = new nex_mul();
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m_allocated.push_back(r);
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r->children().push_back(a);
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r->children().push_back(b);
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r->children() = v;
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return r;
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}
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template <typename K, typename...Args>
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nex_sum* mk_sum(K e, Args... es) {
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auto r = new nex_sum();
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m_allocated.push_back(r);
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r->add_child(e);
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add_children(r, es...);
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return r;
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}
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nex_var* mk_var(lpvar j) {
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auto r = new nex_var(j);
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m_allocated.push_back(r);
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return r;
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}
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nex_mul* mk_mul() {
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auto r = new nex_mul();
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m_allocated.push_back(r);
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return r;
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}
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nex_mul* mk_mul(nex * a, nex * b) {
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template <typename K, typename...Args>
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nex_mul* mk_mul(K e, Args... es) {
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auto r = new nex_mul();
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m_allocated.push_back(r);
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r->add_child(a); r->add_child(b);
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add_children(r, e, es...);
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return r;
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}
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nex_mul* mk_mul(nex * a, nex * b, nex *c) {
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auto r = new nex_mul();
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m_allocated.push_back(r);
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r->add_child(a); r->add_child(b); r->add_child(c);
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return r;
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}
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nex_scalar* mk_scalar(const rational& v) {
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auto r = new nex_scalar(v);
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m_allocated.push_back(r);
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@ -120,8 +130,32 @@ public:
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nex * mk_div(const nex* a, lpvar j) {
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SASSERT(false);
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return nullptr;
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TRACE("nla_cn_details", tout << "a=" << *a << ", v" << j << "\n";);
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SASSERT((a->is_mul() && a->contains(j)) || (a->is_var() && to_var(a)->var() == j));
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if (a->is_var())
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return mk_scalar(rational(1));
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m_b_vec.clear();
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bool seenj = false;
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for (nex* c : to_mul(a)->children()) {
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if (!seenj) {
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if (c->contains(j)) {
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if (!c->is_var())
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m_b_vec.push_back(mk_div(c, j));
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seenj = true;
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continue;
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}
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}
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m_b_vec.push_back(c);
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}
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if (m_b_vec.size() > 1) {
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return mk_mul(m_b_vec);
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}
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if (m_b_vec.size() == 1) {
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return m_b_vec[0];
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}
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SASSERT(m_b_vec.size() == 0);
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return mk_scalar(rational(1));
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}
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nex * mk_div(const nex* a, const nex* b) {
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@ -218,14 +252,14 @@ public:
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return false;
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}
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bool proceed_with_common_factor(nex*& c, vector<nex_sum*>& front, const vector<std::pair<lpvar, occ>> & occurences) {
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bool proceed_with_common_factor(nex*& c, vector<nex**>& front, const vector<std::pair<lpvar, occ>> & occurences) {
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TRACE("nla_cn", tout << "c=" << *c << "\n";);
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nex* f = extract_common_factor(c, occurences);
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if (f == nullptr)
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return false;
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nex_sum* c_over_f = to_sum(mk_div(c, f));
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c_over_f->simplify();
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nex* c_over_f = mk_div(c, f);
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to_sum(c_over_f)->simplify();
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c = mk_mul(f, c_over_f);
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TRACE("nla_cn", tout << "common factor=" << *f << ", c=" << *c << "\ne = " << *m_e << "\n";);
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@ -233,28 +267,28 @@ public:
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return true;
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}
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static void push(vector<nex_sum*>& front, nex_sum* e) {
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TRACE("nla_cn", tout << *e << "\n";);
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static void push(vector<nex**>& front, nex** e) {
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TRACE("nla_cn", tout << **e << "\n";);
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front.push_back(e);
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}
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static vector<nex_sum*> copy_front(const vector<nex_sum*>& front) {
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vector<nex_sum*> v;
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for (nex_sum* n: front)
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v.push_back(n);
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static vector<nex*> copy_front(const vector<nex**>& front) {
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vector<nex*> v;
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for (nex** n: front)
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v.push_back(*n);
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return v;
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}
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static void restore_front(const vector<nex_sum*> ©, vector<nex_sum*>& front) {
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static void restore_front(const vector<nex*> ©, vector<nex**>& front) {
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SASSERT(copy.size() == front.size());
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for (unsigned i = 0; i < front.size(); i++)
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front[i] = copy[i];
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*(front[i]) = copy[i];
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}
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void explore_expr_on_front_elem_occs(nex* c, vector<nex_sum*>& front, const vector<std::pair<lpvar, occ>> & occurences) {
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void explore_expr_on_front_elem_occs(nex* &c, vector<nex**>& front, const vector<std::pair<lpvar, occ>> & occurences) {
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if (proceed_with_common_factor(c, front, occurences))
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return;
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TRACE("nla_cn", tout << "save c=" << *c << "; front:"; print_vector_of_ptrs(front, tout) << "\n";);
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TRACE("nla_cn", tout << "save c=" << *c << "; front:"; print_front(front, tout) << "\n";);
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nex* copy_of_c = c;
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auto copy_of_front = copy_front(front);
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for(auto& p : occurences) {
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@ -269,11 +303,12 @@ public:
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explore_of_expr_on_sum_and_var(c, j, front);
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if (m_done)
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return;
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TRACE("nla_cn", tout << "before restore c=" << *c << ", m_e=" << *m_e << "\n";);
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c = copy_of_c;
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TRACE("nla_cn", tout << "restore c=" << *c << ", m_e=" << m_e << "\n";);
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TRACE("nla_cn", tout << "after restore c=" << *c << ", m_e=" << *m_e << "\n";);
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restore_front(copy_of_front, front);
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TRACE("nla_cn", tout << "restore c=" << *c << "\n";);
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TRACE("nla_cn", tout << "m_e=" << m_e << "\n";);
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TRACE("nla_cn", tout << "m_e=" << *m_e << "\n";);
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}
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}
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@ -288,18 +323,18 @@ public:
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return out;
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}
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void explore_expr_on_front_elem(nex_sum* c, vector<nex_sum*>& front) {
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auto occurences = get_mult_occurences(c);
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TRACE("nla_cn", tout << "m_e=" << m_e << "\nc=" << *c << ", c occurences=";
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dump_occurences(tout, occurences) << "; front:"; print_vector_of_ptrs(front, tout) << "\n";);
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void explore_expr_on_front_elem(nex*& c, vector<nex**>& front) {
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auto occurences = get_mult_occurences(to_sum(c));
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TRACE("nla_cn", tout << "m_e=" << *m_e << "\nc=" << *c << ", c occurences=";
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dump_occurences(tout, occurences) << "; front:"; print_front(front, tout) << "\n";);
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if (occurences.empty()) {
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if(front.empty()) {
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TRACE("nla_cn", tout << "got the cn form: =" << m_e << "\n";);
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TRACE("nla_cn", tout << "got the cn form: =" << *m_e << "\n";);
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m_done = m_call_on_result(m_e);
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} else {
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auto c = pop_back(front);
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explore_expr_on_front_elem(c, front);
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nex* f = *pop_front(front);
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explore_expr_on_front_elem(f, front);
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}
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} else {
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explore_expr_on_front_elem_occs(c, front, occurences);
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@ -311,15 +346,23 @@ public:
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return s.str();
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// return (char)('a'+j);
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}
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// e is the global expression, c is the sub expressiond which is going to changed from sum to the cross nested form
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void explore_of_expr_on_sum_and_var(nex* & c, lpvar j, vector<nex_sum*> front) {
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TRACE("nla_cn", tout << "m_e=" << m_e << "\nc=" << *c << "\nj = " << ch(j) << "\nfront="; print_vector_of_ptrs(front, tout) << "\n";);
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std::ostream& print_front(const vector<nex**>& front, std::ostream& out) const {
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for (auto e : front) {
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out << **e << "\n";
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}
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return out;
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}
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// c is the sub expressiond which is going to be changed from sum to the cross nested form
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// front will be explored more
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void explore_of_expr_on_sum_and_var(nex*& c, lpvar j, vector<nex**> front) {
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TRACE("nla_cn", tout << "m_e=" << *m_e << "\nc=" << *c << "\nj = " << ch(j) << "\nfront="; print_front(front, tout) << "\n";);
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if (!split_with_var(c, j, front))
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return;
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TRACE("nla_cn", tout << "after split c=" << *c << "\nfront="; print_vector_of_ptrs(front, tout) << "\n";);
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TRACE("nla_cn", tout << "after split c=" << *c << "\nfront="; print_front(front, tout) << "\n";);
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SASSERT(front.size());
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auto n = pop_back(front); TRACE("nla_cn", tout << "n=" << *n <<"\n";);
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explore_expr_on_front_elem(n, front);
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auto n = pop_front(front);
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explore_expr_on_front_elem(*n, front);
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}
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void add_var_occs(lpvar j) {
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@ -378,7 +421,7 @@ public:
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}
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}
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remove_singular_occurences();
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TRACE("nla_cn_details", tout << "e=" << e << "\noccs="; dump_occurences(tout, m_occurences_map) << "\n";);
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TRACE("nla_cn_details", tout << "e=" << *e << "\noccs="; dump_occurences(tout, m_occurences_map) << "\n";);
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vector<std::pair<lpvar, occ>> ret;
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for (auto & p : m_occurences_map)
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ret.push_back(p);
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@ -405,54 +448,57 @@ public:
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void pre_split(nex_sum * e, lpvar j, nex_sum* & a, nex* & b) {
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a = mk_sum();
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m_b_vec.clear();
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m_b_split_vec.clear();
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for (nex * ce: e->children()) {
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if (is_divisible_by_var(ce, j)) {
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a->add_child(mk_div(ce , j));
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} else {
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m_b_vec.push_back(ce);
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m_b_split_vec.push_back(ce);
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TRACE("nla_cn_details", tout << "ce = " << *ce << "\n";);
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}
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}
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TRACE("nla_cn_details", tout << "a = " << *a << "\n";);
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SASSERT(a->children().size() >= 2 && m_b_vec.size());
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SASSERT(a->children().size() >= 2 && m_b_split_vec.size());
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a->simplify();
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if (m_b_vec.size() == 1) {
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b = m_b_vec[0];
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if (m_b_split_vec.size() == 1) {
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b = m_b_split_vec[0];
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TRACE("nla_cn_details", tout << "b = " << *b << "\n";);
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} else {
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SASSERT(m_b_vec.size() > 1);
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b = mk_sum(m_b_vec);
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}
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SASSERT(m_b_split_vec.size() > 1);
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b = mk_sum(m_b_split_vec);
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TRACE("nla_cn_details", tout << "b = " << *b << "\n";);
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}
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}
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void update_front_with_split_with_non_empty_b(nex* &e, lpvar j, vector<nex_sum*> & front, nex_sum* a, nex* b) {
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void update_front_with_split_with_non_empty_b(nex* &e, lpvar j, vector<nex**> & front, nex* a, nex* b) {
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SASSERT(a->is_sum());
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TRACE("nla_cn_details", tout << "b = " << b << "\n";);
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TRACE("nla_cn_details", tout << "b = " << *b << "\n";);
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e = mk_sum(mk_mul(mk_var(j), a), b); // e = j*a + b
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push(front, a); // pushing 'a'
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TRACE("nla_cn", tout << "push to front " << *a << "\n";);
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nex **ptr_to_a = &(to_mul(to_sum(e)->children()[0]))->children()[1];
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push(front, ptr_to_a);
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if (b->is_sum()) {
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push(front, to_sum(b));
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TRACE("nla_cn", tout << "push to front " << *b << "\n";);
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nex **ptr_to_a = &(to_sum(e)->children()[1]);
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push(front, ptr_to_a);
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}
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}
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void update_front_with_split(nex* & e, lpvar j, vector<nex_sum*> & front, nex_sum* a, nex* b) {
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void update_front_with_split(nex* & e, lpvar j, vector<nex**> & front, nex* a, nex* b) {
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if (b == nullptr) {
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e = mk_mul(mk_var(j), a);
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push(front, a);
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TRACE("nla_cn_details", tout << "push to front " << *a << "\n";);
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push(front, &(to_mul(e)->children()[1]));
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} else {
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update_front_with_split_with_non_empty_b(e, j, front, a, b);
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}
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}
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// it returns true if the recursion brings a cross-nested form
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bool split_with_var(nex*& e, lpvar j, vector<nex_sum*> & front) {
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bool split_with_var(nex*& e, lpvar j, vector<nex**> & front) {
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SASSERT(e->is_sum());
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TRACE("nla_cn", tout << "e = " << e << ", j=" << ch(j) << "\n";);
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TRACE("nla_cn", tout << "e = " << *e << ", j=" << ch(j) << "\n";);
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nex_sum* a; nex * b;
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pre_split(to_sum(e), j, a, b);
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/*
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@ -70,6 +70,11 @@ public:
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virtual ~nex() {}
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virtual bool contains(lpvar j) const { return false; }
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virtual int get_degree() const = 0;
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virtual void simplify() {}
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virtual const vector<nex*> * children_ptr() const {
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UNREACHABLE();
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return nullptr;
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}
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};
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std::ostream& operator<<(std::ostream& out, const nex&);
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@ -107,6 +112,28 @@ public:
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};
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static void promote_children_by_type(vector<nex*> * children, expr_type t) {
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svector<nex*> to_promote;
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for(unsigned j = 0; j < children->size(); j++) {
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nex* e = (*children)[j];
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e->simplify();
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if (e->type() == t) {
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to_promote.push_back(e);
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} else {
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unsigned offset = to_promote.size();
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if (offset) {
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(*children)[j - offset] = e;
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}
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}
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for (nex *e : to_promote) {
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for (nex *ee : *(e->children_ptr())) {
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children->push_back(ee);
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}
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}
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}
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}
|
||||
|
||||
class nex_mul : public nex {
|
||||
vector<nex*> m_children;
|
||||
public:
|
||||
|
|
@ -115,6 +142,8 @@ public:
|
|||
expr_type type() const { return expr_type::MUL; }
|
||||
vector<nex*>& children() { return m_children;}
|
||||
const vector<nex*>& children() const { return m_children;}
|
||||
const vector<nex*>* children_ptr() const { return &m_children;}
|
||||
|
||||
std::ostream & print(std::ostream& out) const {
|
||||
bool first = true;
|
||||
for (const nex* v : m_children) {
|
||||
|
|
@ -180,9 +209,13 @@ public:
|
|||
return degree;
|
||||
}
|
||||
|
||||
void simplify() {
|
||||
promote_children_by_type(&m_children, expr_type::MUL);
|
||||
}
|
||||
|
||||
};
|
||||
|
||||
|
||||
class nex_sum : public nex {
|
||||
vector<nex*> m_children;
|
||||
public:
|
||||
|
|
@ -190,6 +223,7 @@ public:
|
|||
expr_type type() const { return expr_type::SUM; }
|
||||
vector<nex*>& children() { return m_children;}
|
||||
const vector<nex*>& children() const { return m_children;}
|
||||
const vector<nex*>* children_ptr() const { return &m_children;}
|
||||
unsigned size() const { return m_children.size(); }
|
||||
|
||||
// we need a linear combination of at least two variables
|
||||
|
|
@ -233,7 +267,7 @@ public:
|
|||
}
|
||||
|
||||
void simplify() {
|
||||
SASSERT(false);
|
||||
promote_children_by_type(&m_children, expr_type::SUM);
|
||||
}
|
||||
|
||||
int get_degree() const {
|
||||
|
|
|
|||
|
|
@ -86,7 +86,6 @@ void test_cn() {
|
|||
nex_var* c = cn.mk_var(2);
|
||||
nex_var* d = cn.mk_var(3);
|
||||
nex_var* e = cn.mk_var(4);
|
||||
nex_var* f = cn.mk_var(5);
|
||||
nex_var* g = cn.mk_var(6);
|
||||
nex* min_1 = cn.mk_scalar(rational(-1));
|
||||
// test_cn_on_expr(min_1*c*e + min_1*b*d + min_1*a*b + a*c);
|
||||
|
|
@ -94,8 +93,16 @@ void test_cn() {
|
|||
nex_mul* bcg = cn.mk_mul(b, c, g);
|
||||
bcg->add_child(min_1);
|
||||
nex_sum* t = cn.mk_sum(bcd, bcg);
|
||||
test_cn_on_expr(t, cn);
|
||||
// test_cn_on_expr(a*a*d + a*b*c*d + a*a*c*c*d + a*d*d + e*a*e + e*a*c + e*d);
|
||||
// test_cn_on_expr(t, cn);
|
||||
nex* aad = cn.mk_mul(a, a, d);
|
||||
nex* abcd = cn.mk_mul(a, b, c, d);
|
||||
nex* aaccd = cn.mk_mul(a, a, c, c, d);
|
||||
nex* add = cn.mk_mul(a, d, d);
|
||||
nex* eae = cn.mk_mul(e, a, e);
|
||||
nex* eac = cn.mk_mul(e, a, c);
|
||||
nex* ed = cn.mk_mul(e, d);
|
||||
|
||||
test_cn_on_expr(cn.mk_sum(aad, abcd, aaccd, add, eae, eac, ed), cn);
|
||||
// TRACE("nla_cn", tout << "done\n";);
|
||||
// test_cn_on_expr(a*b*d + a*b*c + c*b*d + a*c*d);
|
||||
// TRACE("nla_cn", tout << "done\n";);
|
||||
|
|
|
|||
Loading…
Reference in a new issue