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add support for non-unit coefficients

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2021-11-30 09:53:09 -08:00
parent 90bd5f186b
commit a81a00a93c
4 changed files with 210 additions and 90 deletions
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67
src/math/polysat/forbidden_intervals.cpp
View file

@ -29,9 +29,11 @@ namespace polysat {
* \returns True iff a forbidden interval exists and the output parameters were set.
*/
bool forbidden_intervals::get_interval(signed_constraint const& c, pvar v, eval_interval& out_interval, vector<signed_constraint>& out_side_cond) {
bool forbidden_intervals::get_interval(signed_constraint const& c, pvar v, rational & coeff, eval_interval& out_interval, vector<signed_constraint>& out_side_cond) {
if (!c->is_ule())
return false;
coeff = 1;
struct backtrack {
bool released = false;
@ -61,21 +63,26 @@ namespace polysat {
SASSERT(b1.is_val());
SASSERT(b2.is_val());
coeff = a1;
_backtrack.released = true;
// LOG("add " << c << " " << a1 << " " << b1 << " " << a2 << " " << b2);
if (match_linear1(c, a1, b1, e1, a2, b2, e2, out_interval, out_side_cond))
if (match_linear1(c, coeff, b1, e1, a2, b2, e2, out_interval, out_side_cond))
return true;
if (match_linear2(c, a1, b1, e1, a2, b2, e2, out_interval, out_side_cond))
if (match_linear2(c, coeff, b1, e1, a2, b2, e2, out_interval, out_side_cond))
return true;
if (match_linear3(c, a1, b1, e1, a2, b2, e2, out_interval, out_side_cond))
if (match_linear3(c, coeff, b1, e1, a2, b2, e2, out_interval, out_side_cond))
return true;
#if 0
if (match_linear4(c, a1, b1, e1, a2, b2, e2, out_interval, out_side_cond))
return true;
if (match_linear5(c, a1, b1, e1, a2, b2, e2, out_interval, out_side_cond))
return true;
#endif
_backtrack.released = false;
return false;
}
@ -114,7 +121,7 @@ namespace polysat {
};
eval_interval forbidden_intervals::to_interval(
signed_constraint const& c, bool is_trivial, rational const& coeff,
signed_constraint const& c, bool is_trivial, rational & coeff,
rational & lo_val, pdd & lo,
rational & hi_val, pdd & hi) {
@ -131,9 +138,12 @@ namespace polysat {
return eval_interval::full();
}
if (!coeff.is_one()) {
rational pow2 = m.max_value() + 1;
SASSERT(coeff == m.max_value());
rational pow2 = m.max_value() + 1;
if (coeff > pow2/2) {
coeff = pow2 - coeff;
SASSERT(coeff > 0);
// Transform according to: y \in [l;u[ <=> -y \in [1-u;1-l[
// -y \in [1-u;1-l[
// <=> -y - (1 - u) < (1 - l) - (1 - u) { by: y \in [l;u[ <=> y - l < u - l }
@ -156,14 +166,14 @@ namespace polysat {
}
/**
* Match e1 + t <= e2, with t = 2^j1*y
* Match e1 + t <= e2, with t = a1*y
* condition for empty/full: e2 == -1
*/
bool forbidden_intervals::match_linear1(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational const & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond) {
if (a2.is_zero() && coefficient_is_01(e1.manager(), a1)) {
if (a2.is_zero() && !a1.is_zero()) {
SASSERT(!a1.is_zero());
bool is_trivial = (b2 + 1).is_zero();
push_eq(is_trivial, e2 + 1, side_cond);
@ -178,36 +188,37 @@ namespace polysat {
}
/**
* e1 <= e2 + t, with t = 2^j2*y
* e1 <= e2 + t, with t = a2*y
* condition for empty/full: e1 == 0
*/
bool forbidden_intervals::match_linear2(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational const & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond) {
if (a1.is_zero() && coefficient_is_01(e1.manager(), a2)) {
if (a1.is_zero() && !a2.is_zero()) {
SASSERT(!a2.is_zero());
a1 = a2;
bool is_trivial = b1.is_zero();
push_eq(is_trivial, e1, side_cond);
auto lo = -e2;
rational lo_val = (-b2).val();
auto hi = e1 - e2;
rational hi_val = (b1 - b2).val();
interval = to_interval(c, is_trivial, a2, lo_val, lo, hi_val, hi);
interval = to_interval(c, is_trivial, a1, lo_val, lo, hi_val, hi);
return true;
}
return false;
}
/**
* e1 + t <= e2 + t, with t = 2^j1*y = 2^j2*y
* condition for empty/full: e1 == e2/
* e1 + t <= e2 + t, with t = a1*y = a2*y
* condition for empty/full: e1 == e2
*/
bool forbidden_intervals::match_linear3(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational const & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond) {
if (coefficient_is_01(e1.manager(), a1) && coefficient_is_01(e1.manager(), a2) && a1 == a2 && !a1.is_zero()) {
if (a1 == a2 && !a1.is_zero()) {
bool is_trivial = b1.val() == b2.val();
push_eq(is_trivial, e1 - e2, side_cond);
auto lo = -e2;
@ -220,12 +231,13 @@ namespace polysat {
return false;
}
#if 0
/**
* a1*y + e1 = 0, with a1 odd
*/
bool forbidden_intervals::match_linear4(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond) {
if (a1.is_odd() && a2.is_zero() && b2.val().is_zero()) {
push_eq(true, e2, side_cond);
@ -257,8 +269,8 @@ namespace polysat {
* - c < ax + b
*/
bool forbidden_intervals::match_linear5(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond) {
auto& m = e1.manager();
@ -323,4 +335,5 @@ namespace polysat {
}
return false;
}
#endif
}

28
src/math/polysat/forbidden_intervals.h
View file

@ -24,40 +24,42 @@ namespace polysat {
solver& s;
void push_eq(bool is_trivial, pdd const& p, vector<signed_constraint>& side_cond);
eval_interval to_interval(signed_constraint const& c, bool is_trivial, rational const& coeff,
eval_interval to_interval(signed_constraint const& c, bool is_trivial, rational& coeff,
rational & lo_val, pdd & lo, rational & hi_val, pdd & hi);
std::tuple<bool, rational, pdd, pdd> linear_decompose(pvar v, pdd const& p, vector<signed_constraint>& out_side_cond);
bool match_linear1(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational const & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond);
bool match_linear2(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational const & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond);
bool match_linear3(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational const & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond);
#if 0
bool match_linear4(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond);
bool match_linear5(signed_constraint const& c,
rational const& a1, pdd const& b1, pdd const& e1,
rational const& a2, pdd const& b2, pdd const& e2,
rational & a1, pdd const& b1, pdd const& e1,
rational & a2, pdd const& b2, pdd const& e2,
eval_interval& interval, vector<signed_constraint>& side_cond);
#endif
bool coefficient_is_01(dd::pdd_manager& m, rational const& r) { return r.is_zero() || r.is_one() || r == m.max_value(); };
// bool coefficient_is_01(dd::pdd_manager& m, rational const& r) { return r.is_zero() || r.is_one() || r == m.max_value(); };
public:
forbidden_intervals(solver& s) :s(s) {}
bool get_interval(signed_constraint const& c, pvar v, eval_interval& out_interval, vector<signed_constraint>& side_cond);
bool get_interval(signed_constraint const& c, pvar v, rational & coeff, eval_interval& out_interval, vector<signed_constraint>& side_cond);
};
}

184
src/math/polysat/viable.cpp
View file

@ -35,50 +35,66 @@ namespace polysat {
}
viable::entry* viable::alloc_entry() {
rational coeff(1);
if (m_alloc.empty())
return alloc(entry);
return alloc(entry, coeff);
auto* e = m_alloc.back();
e->side_cond.reset();
e->coeff = coeff;
m_alloc.pop_back();
return e;
}
void viable::pop_viable() {
auto& [v, e] = m_trail.back();
e->remove_from(m_viable[v], e);
auto& [v, is_unit, e] = m_trail.back();
auto& vec = is_unit ? m_units[v] : m_non_units[v];
e->remove_from(vec, e);
m_alloc.push_back(e);
m_trail.pop_back();
}
void viable::push_viable() {
auto& [v, e] = m_trail.back();
SASSERT(e->prev() != e || !m_viable[v]);
auto& [v, is_unit, e] = m_trail.back();
SASSERT(e->prev() != e || !m_units[v]);
SASSERT(e->prev() != e || e->next() == e);
SASSERT(is_unit);
(void)is_unit;
if (e->prev() != e) {
e->prev()->insert_after(e);
if (e->interval.lo_val() < e->next()->interval.lo_val())
m_viable[v] = e;
m_units[v] = e;
}
else
m_viable[v] = e;
m_units[v] = e;
m_trail.pop_back();
}
bool viable::intersect(pvar v, signed_constraint const& c) {
auto& fi = s.m_forbidden_intervals;
entry* ne = alloc_entry();
if (!fi.get_interval(c, v, ne->interval, ne->side_cond) || ne->interval.is_currently_empty()) {
if (!fi.get_interval(c, v, ne->coeff, ne->interval, ne->side_cond) || ne->interval.is_currently_empty()) {
m_alloc.push_back(ne);
return false;
}
else {
else if (ne->coeff == 1) {
ne->src = c;
return intersect(v, ne);
}
else {
ne->src = c;
m_trail.push_back({ v, false, ne });
s.m_trail.push_back(trail_instr_t::viable_add_i);
ne->init(ne);
if (!m_non_units[v])
m_non_units[v] = ne;
else
ne->insert_after(m_non_units[v]);
return true;
}
}
bool viable::intersect(pvar v, entry* ne) {
entry* e = m_viable[v];
entry* e = m_units[v];
if (e && e->interval.is_full()) {
m_alloc.push_back(ne);
return false;
@ -90,20 +106,20 @@ namespace polysat {
}
auto create_entry = [&]() {
m_trail.push_back({ v, ne });
m_trail.push_back({ v, true, ne });
s.m_trail.push_back(trail_instr_t::viable_add_i);
ne->init(ne);
return ne;
};
auto remove_entry = [&](entry* e) {
m_trail.push_back({ v, e });
m_trail.push_back({ v, true, e });
s.m_trail.push_back(trail_instr_t::viable_rem_i);
e->remove_from(m_viable[v], e);
e->remove_from(m_units[v], e);
};
if (!e)
m_viable[v] = create_entry();
m_units[v] = create_entry();
else {
entry* first = e;
do {
@ -114,8 +130,8 @@ namespace polysat {
while (ne->interval.contains(e->interval)) {
entry* n = e->next();
remove_entry(e);
if (!m_viable[v]) {
m_viable[v] = create_entry();
if (!m_units[v]) {
m_units[v] = create_entry();
return true;
}
if (e == first)
@ -130,8 +146,8 @@ namespace polysat {
}
e->insert_before(create_entry());
if (e == first)
m_viable[v] = e->prev();
SASSERT(well_formed(m_viable[v]));
m_units[v] = e->prev();
SASSERT(well_formed(m_units[v]));
return true;
}
e = e->next();
@ -140,32 +156,86 @@ namespace polysat {
// otherwise, append to end of list
first->insert_before(create_entry());
}
SASSERT(well_formed(m_viable[v]));
SASSERT(well_formed(m_units[v]));
return true;
}
bool viable::has_viable(pvar v) {
auto* e = m_viable[v];
/**
* Traverse all interval constraints with coefficients to check whether current value 'val' for
* 'v' is feasible. If not, extract a (maximal) interval to block 'v' from being assigned val.
*/
bool viable::refine_viable(pvar v, rational const& val) {
auto* e = m_non_units[v];
if (!e)
return true;
entry* first = e;
do {
rational coeff_val = mod(e->coeff * val, s.var2pdd(v).max_value() + 1);
if (e->interval.currently_contains(coeff_val)) {
rational delta_l = floor((coeff_val - e->interval.lo_val()) / e->coeff);
rational delta_u = floor((e->interval.hi_val() - coeff_val - 1) / e->coeff);
rational lo = val - delta_l;
rational hi = val + delta_u + 1;
if (e->interval.lo_val() < e->interval.hi_val()) {
// pass
}
else if (e->interval.lo_val() <= coeff_val) {
hi = val + 1;
if (hi > s.var2pdd(v).max_value())
hi = 0;
}
else {
SASSERT(coeff_val < e->interval.hi_val());
lo = val;
}
SASSERT(hi <= s.var2pdd(v).max_value());
LOG("forbidden interval [" << lo << ", " << hi << "[\n");
entry* ne = alloc_entry();
ne->src = e->src;
ne->side_cond = e->side_cond;
ne->coeff = 1;
pdd lop = s.var2pdd(v).mk_val(lo); // TODO?
pdd hip = s.var2pdd(v).mk_val(hi);
ne->interval = eval_interval::proper(lop, lo, hip, hi);
intersect(v, ne);
return false;
}
e = e->next();
}
while (e != first);
return true;
}
bool viable::has_viable(pvar v) {
refined:
auto* e = m_units[v];
#define CHECK_RETURN(val) { if (refine_viable(v, val)) return true; else goto refined; }
if (!e)
CHECK_RETURN(rational::zero());
entry* first = e;
entry* last = e->prev();
// quick check: last interval doesn't wrap around, so hi_val
// has not been covered
if (last->interval.lo_val() < last->interval.hi_val())
return true;
CHECK_RETURN(last->interval.hi_val());
do {
if (e->interval.is_full())
return false;
entry* n = e->next();
if (n == e)
return true;
CHECK_RETURN(e->interval.hi_val());
if (!n->interval.currently_contains(e->interval.hi_val()))
return true;
if (n == first)
return e->interval.lo_val() <= e->interval.hi_val();
CHECK_RETURN(e->interval.hi_val());
if (n == first) {
if (e->interval.lo_val() > e->interval.hi_val())
return false;
CHECK_RETURN(e->interval.hi_val());
}
e = n;
}
while (e != first);
@ -173,9 +243,9 @@ namespace polysat {
}
bool viable::is_viable(pvar v, rational const& val) {
auto* e = m_viable[v];
auto* e = m_units[v];
if (!e)
return true;
return refine_viable(v, val);
entry* first = e;
entry* last = first->prev();
if (last->interval.currently_contains(val))
@ -183,15 +253,18 @@ namespace polysat {
for (; e != last; e = e->next()) {
if (e->interval.currently_contains(val))
return false;
if (val < e->interval.lo_val())
return true;
if (val < e->interval.lo_val())
return refine_viable(v, val);
}
return true;
return refine_viable(v, val);
}
rational viable::min_viable(pvar v) {
refined:
rational lo(0);
auto* e = m_viable[v];
auto* e = m_units[v];
if (!e && !refine_viable(v, lo))
goto refined;
if (!e)
return lo;
entry* first = e;
@ -205,13 +278,18 @@ namespace polysat {
e = e->next();
}
while (e != first);
SASSERT(is_viable(v, lo));
if (!refine_viable(v, lo))
goto refined;
SASSERT(is_viable(v, lo));
return lo;
}
rational viable::max_viable(pvar v) {
refined:
rational hi = s.var2pdd(v).max_value();
auto* e = m_viable[v];
auto* e = m_units[v];
if (!e && !refine_viable(v, hi))
goto refined;
if (!e)
return hi;
entry* last = e->prev();
@ -223,13 +301,20 @@ namespace polysat {
e = e->prev();
}
while (e != last);
if (!refine_viable(v, hi))
goto refined;
SASSERT(is_viable(v, hi));
return hi;
}
dd::find_t viable::find_viable(pvar v, rational& lo) {
refined:
lo = 0;
auto* e = m_viable[v];
auto* e = m_units[v];
if (!e && !refine_viable(v, lo))
goto refined;
if (!e && !refine_viable(v, rational::one()))
goto refined;
if (!e)
return dd::find_t::multiple;
if (e->interval.is_full())
@ -244,6 +329,10 @@ namespace polysat {
if (last->interval.lo_val() < last->interval.hi_val() &&
last->interval.hi_val() < max_value) {
lo = last->interval.hi_val();
if (!refine_viable(v, lo))
goto refined;
if (!refine_viable(v, max_value))
goto refined;
return dd::find_t::multiple;
}
@ -271,6 +360,10 @@ namespace polysat {
e = e->prev();
}
while (e != last);
if (!refine_viable(v, lo))
goto refined;
if (!refine_viable(v, hi))
goto refined;
if (lo == hi)
return dd::find_t::singleton;
else
@ -280,7 +373,7 @@ namespace polysat {
bool viable::resolve(pvar v, conflict& core) {
if (has_viable(v))
return false;
auto* e = m_viable[v];
auto* e = m_units[v];
entry* first = e;
SASSERT(e);
core.reset();
@ -317,9 +410,9 @@ namespace polysat {
}
void viable::log(pvar v) {
if (!well_formed(m_viable[v]))
if (!well_formed(m_units[v]))
LOG("v" << v << " not well formed");
auto* e = m_viable[v];
auto* e = m_units[v];
if (!e)
return;
entry* first = e;
@ -331,16 +424,17 @@ namespace polysat {
}
void viable::log() {
for (pvar v = 0; v < std::min(10u, m_viable.size()); ++v)
for (pvar v = 0; v < std::min(10u, m_units.size()); ++v)
log(v);
}
std::ostream& viable::display(std::ostream& out, pvar v) const {
auto* e = m_viable[v];
std::ostream& viable::display(std::ostream& out, pvar v, entry* e) const {
if (!e)
return out;
entry* first = e;
do {
if (e->coeff != 1)
out << e->coeff << " * v" << v << " ";
out << e->interval << " " << e->side_cond << " " << e->src << " ";
e = e->next();
}
@ -348,8 +442,14 @@ namespace polysat {
return out;
}
std::ostream& viable::display(std::ostream& out, pvar v) const {
display(out, v, m_units[v]);
display(out, v, m_non_units[v]);
return out;
}
std::ostream& viable::display(std::ostream& out) const {
for (pvar v = 0; v < m_viable.size(); ++v)
for (pvar v = 0; v < m_units.size(); ++v)
display(out << "v" << v << ": ", v);
return out;
}

21
src/math/polysat/viable.h
View file

@ -32,13 +32,14 @@ namespace polysat {
solver& s;
struct entry : public dll_base<entry>, public fi_record {
public:
entry() : fi_record({ eval_interval::full(), {}, {} }) {}
rational coeff;
entry(rational const& m) : fi_record({ eval_interval::full(), {}, {} }), coeff(m) {}
};
ptr_vector<entry> m_alloc;
ptr_vector<entry> m_viable; // set of viable values.
svector<std::pair<pvar, entry*>> m_trail; // undo stack
ptr_vector<entry> m_units; // set of viable values based on unit multipliers
ptr_vector<entry> m_non_units; // entries that have non-unit multipliers
svector<std::tuple<pvar, bool, entry*>> m_trail; // undo stack
bool well_formed(entry* e);
@ -46,15 +47,19 @@ namespace polysat {
bool intersect(pvar v, entry* e);
bool refine_viable(pvar v, rational const& val);
std::ostream& display(std::ostream& out, pvar v, entry* e) const;
public:
viable(solver& s);
~viable();
// declare and remove var
void push(unsigned) { m_viable.push_back(nullptr); }
void push(unsigned) { m_units.push_back(nullptr); m_non_units.push_back(nullptr); }
void pop() { m_viable.pop_back(); }
void pop() { m_units.pop_back(); m_non_units.pop_back(); }
void pop_viable();
@ -135,8 +140,8 @@ namespace polysat {
pvar var;
public:
constraints(viable& v, pvar var) : v(v), var(var) {}
iterator begin() const { return iterator(v.m_viable[var], false); }
iterator end() const { return iterator(v.m_viable[var], true); }
iterator begin() const { return iterator(v.m_units[var], false); }
iterator end() const { return iterator(v.m_units[var], true); }
};
constraints get_constraints(pvar v) {