From a7449494a9be1cc8cfcaa296c3aa853138d00ff1 Mon Sep 17 00:00:00 2001
From: Lev Nachmanson <levnach@hotmail.com>
Date: Fri, 16 Aug 2019 18:10:12 -0700
Subject: [PATCH] rewrite horner scheme on top of nex_expr as a pointer
Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
---
src/math/lp/cross_nested.h | 188 +++++++++++++++++++++++--------------
src/math/lp/nla_expr.h | 36 ++++++-
src/test/lp/lp.cpp | 13 ++-
3 files changed, 162 insertions(+), 75 deletions(-)
diff --git a/src/math/lp/cross_nested.h b/src/math/lp/cross_nested.h
index cda1c98cb..50f70b6f4 100644
--- a/src/math/lp/cross_nested.h
+++ b/src/math/lp/cross_nested.h
@@ -35,7 +35,7 @@ class cross_nested {
};
// fields
- nex_sum * m_e;
+ nex * m_e;
std::function<bool (const nex*)> m_call_on_result;
std::function<bool (unsigned)> m_var_is_fixed;
bool m_done;
@@ -43,6 +43,7 @@ class cross_nested {
std::unordered_map<lpvar, unsigned> m_powers;
vector<nex*> m_allocated;
vector<nex*> m_b_vec;
+ vector<nex*> m_b_split_vec;
public:
cross_nested(std::function<bool (const nex*)> call_on_result,
std::function<bool (unsigned)> var_is_fixed):
@@ -51,16 +52,16 @@ public:
m_done(false)
{}
- void run(nex_sum *e) {
+ void run(nex *e) {
m_e = e;
- vector<nex_sum*> front;
+ vector<nex**> front;
explore_expr_on_front_elem(m_e, front);
}
- static nex_sum* pop_back(vector<nex_sum*>& front) {
- nex_sum* c = front.back();
- TRACE("nla_cn", tout << *c << "\n";);
+ static nex** pop_front(vector<nex**>& front) {
+ nex** c = front.back();
+ TRACE("nla_cn", tout << **c << "\n";);
front.pop_back();
return c;
}
@@ -70,6 +71,14 @@ public:
m_allocated.push_back(r);
return r;
}
+ template <typename T>
+ void add_children(T) { }
+
+ template <typename T, typename K, typename ...Args>
+ void add_children(T r, K e, Args ... es) {
+ r->add_child(e);
+ add_children(r, es ...);
+ }
nex_sum* mk_sum(const vector<nex*>& v) {
auto r = new nex_sum();
@@ -78,40 +87,41 @@ public:
return r;
}
- nex_sum* mk_sum(nex *a, nex* b) {
- auto r = new nex_sum();
+ nex_mul* mk_mul(const vector<nex*>& v) {
+ auto r = new nex_mul();
m_allocated.push_back(r);
- r->children().push_back(a);
- r->children().push_back(b);
+ r->children() = v;
return r;
}
+ template <typename K, typename...Args>
+ nex_sum* mk_sum(K e, Args... es) {
+ auto r = new nex_sum();
+ m_allocated.push_back(r);
+ r->add_child(e);
+ add_children(r, es...);
+ return r;
+ }
nex_var* mk_var(lpvar j) {
auto r = new nex_var(j);
m_allocated.push_back(r);
return r;
}
-
+
nex_mul* mk_mul() {
auto r = new nex_mul();
m_allocated.push_back(r);
return r;
}
- nex_mul* mk_mul(nex * a, nex * b) {
+ template <typename K, typename...Args>
+ nex_mul* mk_mul(K e, Args... es) {
auto r = new nex_mul();
m_allocated.push_back(r);
- r->add_child(a); r->add_child(b);
+ add_children(r, e, es...);
return r;
}
-
- nex_mul* mk_mul(nex * a, nex * b, nex *c) {
- auto r = new nex_mul();
- m_allocated.push_back(r);
- r->add_child(a); r->add_child(b); r->add_child(c);
- return r;
- }
-
+
nex_scalar* mk_scalar(const rational& v) {
auto r = new nex_scalar(v);
m_allocated.push_back(r);
@@ -120,8 +130,32 @@ public:
nex * mk_div(const nex* a, lpvar j) {
- SASSERT(false);
- return nullptr;
+ TRACE("nla_cn_details", tout << "a=" << *a << ", v" << j << "\n";);
+ SASSERT((a->is_mul() && a->contains(j)) || (a->is_var() && to_var(a)->var() == j));
+ if (a->is_var())
+ return mk_scalar(rational(1));
+ m_b_vec.clear();
+ bool seenj = false;
+ for (nex* c : to_mul(a)->children()) {
+ if (!seenj) {
+ if (c->contains(j)) {
+ if (!c->is_var())
+ m_b_vec.push_back(mk_div(c, j));
+ seenj = true;
+ continue;
+ }
+ }
+ m_b_vec.push_back(c);
+ }
+ if (m_b_vec.size() > 1) {
+ return mk_mul(m_b_vec);
+ }
+ if (m_b_vec.size() == 1) {
+ return m_b_vec[0];
+ }
+
+ SASSERT(m_b_vec.size() == 0);
+ return mk_scalar(rational(1));
}
nex * mk_div(const nex* a, const nex* b) {
@@ -218,14 +252,14 @@ public:
return false;
}
- bool proceed_with_common_factor(nex*& c, vector<nex_sum*>& front, const vector<std::pair<lpvar, occ>> & occurences) {
+ bool proceed_with_common_factor(nex*& c, vector<nex**>& front, const vector<std::pair<lpvar, occ>> & occurences) {
TRACE("nla_cn", tout << "c=" << *c << "\n";);
nex* f = extract_common_factor(c, occurences);
if (f == nullptr)
return false;
- nex_sum* c_over_f = to_sum(mk_div(c, f));
- c_over_f->simplify();
+ nex* c_over_f = mk_div(c, f);
+ to_sum(c_over_f)->simplify();
c = mk_mul(f, c_over_f);
TRACE("nla_cn", tout << "common factor=" << *f << ", c=" << *c << "\ne = " << *m_e << "\n";);
@@ -233,28 +267,28 @@ public:
return true;
}
- static void push(vector<nex_sum*>& front, nex_sum* e) {
- TRACE("nla_cn", tout << *e << "\n";);
+ static void push(vector<nex**>& front, nex** e) {
+ TRACE("nla_cn", tout << **e << "\n";);
front.push_back(e);
}
- static vector<nex_sum*> copy_front(const vector<nex_sum*>& front) {
- vector<nex_sum*> v;
- for (nex_sum* n: front)
- v.push_back(n);
+ static vector<nex*> copy_front(const vector<nex**>& front) {
+ vector<nex*> v;
+ for (nex** n: front)
+ v.push_back(*n);
return v;
}
- static void restore_front(const vector<nex_sum*> ©, vector<nex_sum*>& front) {
+ static void restore_front(const vector<nex*> ©, vector<nex**>& front) {
SASSERT(copy.size() == front.size());
for (unsigned i = 0; i < front.size(); i++)
- front[i] = copy[i];
+ *(front[i]) = copy[i];
}
- void explore_expr_on_front_elem_occs(nex* c, vector<nex_sum*>& front, const vector<std::pair<lpvar, occ>> & occurences) {
+ void explore_expr_on_front_elem_occs(nex* &c, vector<nex**>& front, const vector<std::pair<lpvar, occ>> & occurences) {
if (proceed_with_common_factor(c, front, occurences))
return;
- TRACE("nla_cn", tout << "save c=" << *c << "; front:"; print_vector_of_ptrs(front, tout) << "\n";);
+ TRACE("nla_cn", tout << "save c=" << *c << "; front:"; print_front(front, tout) << "\n";);
nex* copy_of_c = c;
auto copy_of_front = copy_front(front);
for(auto& p : occurences) {
@@ -269,11 +303,12 @@ public:
explore_of_expr_on_sum_and_var(c, j, front);
if (m_done)
return;
+ TRACE("nla_cn", tout << "before restore c=" << *c << ", m_e=" << *m_e << "\n";);
c = copy_of_c;
- TRACE("nla_cn", tout << "restore c=" << *c << ", m_e=" << m_e << "\n";);
+ TRACE("nla_cn", tout << "after restore c=" << *c << ", m_e=" << *m_e << "\n";);
restore_front(copy_of_front, front);
TRACE("nla_cn", tout << "restore c=" << *c << "\n";);
- TRACE("nla_cn", tout << "m_e=" << m_e << "\n";);
+ TRACE("nla_cn", tout << "m_e=" << *m_e << "\n";);
}
}
@@ -288,18 +323,18 @@ public:
return out;
}
- void explore_expr_on_front_elem(nex_sum* c, vector<nex_sum*>& front) {
- auto occurences = get_mult_occurences(c);
- TRACE("nla_cn", tout << "m_e=" << m_e << "\nc=" << *c << ", c occurences=";
- dump_occurences(tout, occurences) << "; front:"; print_vector_of_ptrs(front, tout) << "\n";);
+ void explore_expr_on_front_elem(nex*& c, vector<nex**>& front) {
+ auto occurences = get_mult_occurences(to_sum(c));
+ TRACE("nla_cn", tout << "m_e=" << *m_e << "\nc=" << *c << ", c occurences=";
+ dump_occurences(tout, occurences) << "; front:"; print_front(front, tout) << "\n";);
if (occurences.empty()) {
if(front.empty()) {
- TRACE("nla_cn", tout << "got the cn form: =" << m_e << "\n";);
+ TRACE("nla_cn", tout << "got the cn form: =" << *m_e << "\n";);
m_done = m_call_on_result(m_e);
} else {
- auto c = pop_back(front);
- explore_expr_on_front_elem(c, front);
+ nex* f = *pop_front(front);
+ explore_expr_on_front_elem(f, front);
}
} else {
explore_expr_on_front_elem_occs(c, front, occurences);
@@ -311,15 +346,23 @@ public:
return s.str();
// return (char)('a'+j);
}
- // e is the global expression, c is the sub expressiond which is going to changed from sum to the cross nested form
- void explore_of_expr_on_sum_and_var(nex* & c, lpvar j, vector<nex_sum*> front) {
- TRACE("nla_cn", tout << "m_e=" << m_e << "\nc=" << *c << "\nj = " << ch(j) << "\nfront="; print_vector_of_ptrs(front, tout) << "\n";);
+
+ std::ostream& print_front(const vector<nex**>& front, std::ostream& out) const {
+ for (auto e : front) {
+ out << **e << "\n";
+ }
+ return out;
+ }
+ // c is the sub expressiond which is going to be changed from sum to the cross nested form
+ // front will be explored more
+ void explore_of_expr_on_sum_and_var(nex*& c, lpvar j, vector<nex**> front) {
+ TRACE("nla_cn", tout << "m_e=" << *m_e << "\nc=" << *c << "\nj = " << ch(j) << "\nfront="; print_front(front, tout) << "\n";);
if (!split_with_var(c, j, front))
return;
- TRACE("nla_cn", tout << "after split c=" << *c << "\nfront="; print_vector_of_ptrs(front, tout) << "\n";);
+ TRACE("nla_cn", tout << "after split c=" << *c << "\nfront="; print_front(front, tout) << "\n";);
SASSERT(front.size());
- auto n = pop_back(front); TRACE("nla_cn", tout << "n=" << *n <<"\n";);
- explore_expr_on_front_elem(n, front);
+ auto n = pop_front(front);
+ explore_expr_on_front_elem(*n, front);
}
void add_var_occs(lpvar j) {
@@ -378,7 +421,7 @@ public:
}
}
remove_singular_occurences();
- TRACE("nla_cn_details", tout << "e=" << e << "\noccs="; dump_occurences(tout, m_occurences_map) << "\n";);
+ TRACE("nla_cn_details", tout << "e=" << *e << "\noccs="; dump_occurences(tout, m_occurences_map) << "\n";);
vector<std::pair<lpvar, occ>> ret;
for (auto & p : m_occurences_map)
ret.push_back(p);
@@ -405,54 +448,57 @@ public:
void pre_split(nex_sum * e, lpvar j, nex_sum* & a, nex* & b) {
a = mk_sum();
- m_b_vec.clear();
+ m_b_split_vec.clear();
for (nex * ce: e->children()) {
if (is_divisible_by_var(ce, j)) {
a->add_child(mk_div(ce , j));
} else {
- m_b_vec.push_back(ce);
+ m_b_split_vec.push_back(ce);
+ TRACE("nla_cn_details", tout << "ce = " << *ce << "\n";);
+
}
}
TRACE("nla_cn_details", tout << "a = " << *a << "\n";);
- SASSERT(a->children().size() >= 2 && m_b_vec.size());
+ SASSERT(a->children().size() >= 2 && m_b_split_vec.size());
a->simplify();
- if (m_b_vec.size() == 1) {
- b = m_b_vec[0];
+ if (m_b_split_vec.size() == 1) {
+ b = m_b_split_vec[0];
+ TRACE("nla_cn_details", tout << "b = " << *b << "\n";);
} else {
- SASSERT(m_b_vec.size() > 1);
- b = mk_sum(m_b_vec);
- }
+ SASSERT(m_b_split_vec.size() > 1);
+ b = mk_sum(m_b_split_vec);
+ TRACE("nla_cn_details", tout << "b = " << *b << "\n";);
+ }
}
- void update_front_with_split_with_non_empty_b(nex* &e, lpvar j, vector<nex_sum*> & front, nex_sum* a, nex* b) {
+ void update_front_with_split_with_non_empty_b(nex* &e, lpvar j, vector<nex**> & front, nex* a, nex* b) {
SASSERT(a->is_sum());
- TRACE("nla_cn_details", tout << "b = " << b << "\n";);
+ TRACE("nla_cn_details", tout << "b = " << *b << "\n";);
e = mk_sum(mk_mul(mk_var(j), a), b); // e = j*a + b
- push(front, a); // pushing 'a'
- TRACE("nla_cn", tout << "push to front " << *a << "\n";);
+ nex **ptr_to_a = &(to_mul(to_sum(e)->children()[0]))->children()[1];
+ push(front, ptr_to_a);
if (b->is_sum()) {
- push(front, to_sum(b));
- TRACE("nla_cn", tout << "push to front " << *b << "\n";);
+ nex **ptr_to_a = &(to_sum(e)->children()[1]);
+ push(front, ptr_to_a);
}
}
- void update_front_with_split(nex* & e, lpvar j, vector<nex_sum*> & front, nex_sum* a, nex* b) {
+ void update_front_with_split(nex* & e, lpvar j, vector<nex**> & front, nex* a, nex* b) {
if (b == nullptr) {
e = mk_mul(mk_var(j), a);
- push(front, a);
- TRACE("nla_cn_details", tout << "push to front " << *a << "\n";);
+ push(front, &(to_mul(e)->children()[1]));
} else {
update_front_with_split_with_non_empty_b(e, j, front, a, b);
}
}
// it returns true if the recursion brings a cross-nested form
- bool split_with_var(nex*& e, lpvar j, vector<nex_sum*> & front) {
+ bool split_with_var(nex*& e, lpvar j, vector<nex**> & front) {
SASSERT(e->is_sum());
- TRACE("nla_cn", tout << "e = " << e << ", j=" << ch(j) << "\n";);
+ TRACE("nla_cn", tout << "e = " << *e << ", j=" << ch(j) << "\n";);
nex_sum* a; nex * b;
pre_split(to_sum(e), j, a, b);
/*
diff --git a/src/math/lp/nla_expr.h b/src/math/lp/nla_expr.h
index f35a4fc9a..0d6319eff 100644
--- a/src/math/lp/nla_expr.h
+++ b/src/math/lp/nla_expr.h
@@ -70,6 +70,11 @@ public:
virtual ~nex() {}
virtual bool contains(lpvar j) const { return false; }
virtual int get_degree() const = 0;
+ virtual void simplify() {}
+ virtual const vector<nex*> * children_ptr() const {
+ UNREACHABLE();
+ return nullptr;
+ }
};
std::ostream& operator<<(std::ostream& out, const nex&);
@@ -107,6 +112,28 @@ public:
};
+static void promote_children_by_type(vector<nex*> * children, expr_type t) {
+ svector<nex*> to_promote;
+ for(unsigned j = 0; j < children->size(); j++) {
+ nex* e = (*children)[j];
+ e->simplify();
+ if (e->type() == t) {
+ to_promote.push_back(e);
+ } else {
+ unsigned offset = to_promote.size();
+ if (offset) {
+ (*children)[j - offset] = e;
+ }
+ }
+ for (nex *e : to_promote) {
+ for (nex *ee : *(e->children_ptr())) {
+ children->push_back(ee);
+ }
+ }
+ }
+
+}
+
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 {
diff --git a/src/test/lp/lp.cpp b/src/test/lp/lp.cpp
index a0ff48209..e72f4f9a7 100644
--- a/src/test/lp/lp.cpp
+++ b/src/test/lp/lp.cpp
@@ -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";);