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z3/src/sat/smt/polysat/viable.cpp
2024-03-20 12:11:14 +01:00

1265 lines
46 KiB
C++

/*++
Copyright (c) 2021 Microsoft Corporation
Module Name:
maintain viable domains
Author:
Nikolaj Bjorner (nbjorner) 2021-03-19
Jakob Rath 2021-04-06
Notes:
--*/
#include "util/debug.h"
#include "util/log.h"
#include "sat/smt/polysat/viable.h"
#include "sat/smt/polysat/core.h"
#include "sat/smt/polysat/number.h"
#include "sat/smt/polysat/refine.h"
#include "sat/smt/polysat/project_interval.h"
#include "sat/smt/polysat/ule_constraint.h"
namespace polysat {
using dd::val_pp;
viable::viable(core& c) : c(c), cs(c.cs()), m_forbidden_intervals(c), m_projection(c), m_fixed_bits(c) {}
viable::~viable() {
for (auto* e : m_alloc)
dealloc(e);
}
std::ostream& operator<<(std::ostream& out, find_t f) {
switch (f) {
case find_t::empty: return out << "empty";
case find_t::singleton: return out << "singleton";
case find_t::multiple: return out << "multiple";
case find_t::resource_out: return out << "resource-out";
default: return out << "<unknown>";
}
}
struct viable::pop_viable_trail : public trail {
viable& m_s;
entry* e;
entry_kind k;
public:
pop_viable_trail(viable& s, entry* e, entry_kind k)
: m_s(s), e(e), k(k) {}
void undo() override {
m_s.pop_viable(e, k);
}
};
struct viable::push_viable_trail : public trail {
viable& m_s;
entry* e;
public:
push_viable_trail(viable& s, entry* e)
: m_s(s), e(e) {}
void undo() override {
m_s.push_viable(e);
}
};
viable::entry* viable::alloc_entry(pvar var, constraint_id constraint_index) {
entry* e = nullptr;
if (m_alloc.empty())
e = alloc(entry);
else {
e = m_alloc.back();
m_alloc.pop_back();
}
e->reset();
e->var = var;
e->constraint_index = constraint_index;
return e;
}
bool viable::assign(pvar v, rational const& value, dependency dep) {
m_var = v;
m_explain_kind = explain_t::none;
m_num_bits = c.size(v);
m_fixed_bits.init(v);
m_explain.reset();
m_assign_dep = null_dependency;
init_overlaps(v);
bool first = true;
while (true) {
for (auto const& [w, offset] : m_overlaps) {
for (auto& layer : m_units[w].get_layers()) {
entry* e = find_overlap(w, layer, value);
if (!e)
continue;
m_explain.push_back({ e, value });
m_explain_kind = explain_t::assignment;
m_assign_dep = dep;
return false;
}
}
if (!first)
return true;
first = false;
if (!check_fixed_bits(v, value))
continue;
if (!check_disequal_lin(v, value))
continue;
if (!check_equal_lin(v, value))
continue;
break;
}
return true;
}
find_t viable::find_viable(pvar v, rational& lo) {
m_explain.reset();
m_var = v;
m_num_bits = c.size(v);
m_fixed_bits.init(v);
init_overlaps(v);
m_explain_kind = explain_t::none;
m_assign_dep = null_dependency;
for (unsigned rounds = 0; rounds < 10; ) {
entry* n = find_overlap(lo);
if (m_explain_kind == explain_t::conflict)
return find_t::empty;
if (n)
continue;
if (!check_fixed_bits(v, lo))
continue;
++rounds;
if (!check_disequal_lin(v, lo))
continue;
if (!check_equal_lin(v, lo))
continue;
if (is_propagation(lo)) {
m_explain_kind = explain_t::propagation;
return find_t::singleton;
}
return find_t::multiple;
}
TRACE("bv", display(tout << "resource-out v" << v << "\n"));
return find_t::resource_out;
}
void viable::init_overlaps(pvar v) {
m_overlaps.reset();
c.get_bitvector_suffixes(v, m_overlaps);
std::sort(m_overlaps.begin(), m_overlaps.end(), [&](auto const& x, auto const& y) { return c.size(x.child) < c.size(y.child); });
}
//
//
// from smallest size(w) overlap [w] to largest
// from smallest bit_width layer [bit_width, entries] to largest
// check if val is allowed by entries or advance val to next allowed value
//
viable::entry* viable::find_overlap(rational& val) {
entry* last = nullptr;
for (auto const& [w, offset] : m_overlaps) {
for (auto& layer : m_units[w].get_layers()) {
entry* e = find_overlap(w, layer, val);
if (!e)
continue;
last = e;
if (e->interval.is_proper())
update_value_to_high(val, e);
m_explain.push_back({ e, val });
if (is_conflict()) {
m_explain_kind = explain_t::conflict;
return nullptr;
}
}
}
return last;
}
viable::entry* viable::find_overlap(pvar w, layer& l, rational const& val) {
if (!l.entries)
return nullptr;
unsigned v_width = m_num_bits;
unsigned b_width = l.bit_width;
if (v_width == b_width)
return find_overlap(val, l.entries);
rational val1 = mod(val, rational::power_of_two(b_width));
return find_overlap(val1, l.entries);
}
void viable::update_value_to_high(rational& val, entry* e) {
unsigned v_width = m_num_bits;
unsigned b_width = e->bit_width;
SASSERT(b_width <= v_width);
auto const& hi = e->interval.hi_val();
auto const& lo = e->interval.lo_val();
if (b_width == v_width) {
val = hi;
SASSERT(0 <= val && val <= c.var2pdd(m_var).max_value());
return;
}
auto p2b = rational::power_of_two(b_width);
rational val2 = clear_lower_bits(val, b_width);
if (lo <= mod(val, p2b) && hi < lo) {
val2 += p2b;
if (val2 == rational::power_of_two(v_width))
val2 = 0;
}
val = val2 + hi;
SASSERT(0 <= hi && hi < p2b);
SASSERT(0 <= val && val <= c.var2pdd(m_var).max_value());
}
/*
* In either case we are checking a constraint $v[u-1:0]\not\in[lo, hi[$
* where $u := w'-k-1$ and using it to compute $\forward(v)$.
* Thus, suppose $v[u-1:0] \in [lo, hi[$.
* - $lo < hi$: $\forward(v) := \forward(2^u v[w-1:w-u] + hi)$.
* - $lo > hi$, $v[w-1:w-u]+1 = 2^{w-u}$: $\forward(v) := \bot$
* - $lo > hi$, $v[w-1:w-u]+1 < 2^{w-u}$: $\forward(v) := \forward(2^u (v[w-1:w-u]+1) + hi)$
*/
// Find interval that contains 'val', or, if no such interval exists, null.
viable::entry* viable::find_overlap(rational const& val, entry* entries) {
SASSERT(entries);
entry* const first = entries;
entry* e = entries;
do {
auto const& i = e->interval;
if (i.currently_contains(val))
return e;
entry* const n = e->next();
// there is only one interval, and it does not contain 'val'
if (e == n)
return nullptr;
// check whether 'val' is contained in the gap between e and n
bool const overlapping = e->interval.currently_contains(n->interval.lo_val());
if (!overlapping && r_interval::contains(e->interval.hi_val(), n->interval.lo_val(), val))
return nullptr;
e = n;
}
while (e != first);
UNREACHABLE();
return nullptr;
}
bool viable::check_equal_lin(pvar v, rational const& val) {
// LOG_H2("refine-equal-lin with v" << v << ", val = " << val);
entry const* e = m_equal_lin[v];
if (!e)
return true;
entry const* first = e;
auto& m = c.var2pdd(v);
unsigned const N = m.power_of_2();
rational const& max_value = m.max_value();
rational const& mod_value = m.two_to_N();
SASSERT(0 <= val && val <= max_value);
// Rotate the 'first' entry, to prevent getting stuck in a refinement loop
// with an early entry when a later entry could give a better interval.
m_equal_lin[v] = m_equal_lin[v]->next();
do {
rational coeff_val = mod(e->coeff * val, mod_value);
if (e->interval.currently_contains(coeff_val)) {
// IF_LOGGING(
// verbose_stream() << "refine-equal-lin for v" << v << " in src: ";
// for (const auto& src : e->src)
// verbose_stream() << lit_pp(s, src) << "\n";
// );
// LOG("forbidden interval v" << v << " " << num_pp(s, v, val) << " " << num_pp(s, v, e->coeff, true) << " * " << e->interval);
if (mod(e->interval.hi_val() + 1, mod_value) == e->interval.lo_val()) {
// We have an equation: a * v == b
rational const a = e->coeff;
rational const b = e->interval.hi_val();
LOG("refine-equal-lin: equation detected: " << dd::val_pp(m, a, true) << " * v" << v << " == " << dd::val_pp(m, b, false));
unsigned const parity_a = get_parity(a, N);
unsigned const parity_b = get_parity(b, N);
if (parity_a > parity_b) {
// No solution
LOG("refined: no solution due to parity");
entry* ne = alloc_entry(v, e->constraint_index);
ne->refined = true;
ne->src = e->src;
ne->side_cond = e->side_cond;
ne->coeff = 1;
ne->bit_width = e->bit_width;
ne->interval = eval_interval::full();
intersect(v, ne);
return false;
}
if (parity_a == 0) {
// "fast path" for odd a
rational a_inv;
VERIFY(a.mult_inverse(N, a_inv));
rational const hi = mod(a_inv * b, mod_value);
rational const lo = mod(hi + 1, mod_value);
// LOG("refined to [" << num_pp(c, v, lo) << ", " << num_pp(c, v, hi) << "[");
SASSERT_EQ(mod(a * hi, mod_value), b); // hi is the solution
entry* ne = alloc_entry(v, e->constraint_index);
ne->refined = true;
ne->src = e->src;
ne->side_cond = e->side_cond;
ne->coeff = 1;
ne->bit_width = e->bit_width;
ne->interval = eval_interval::proper(m.mk_val(lo), lo, m.mk_val(hi), hi);
SASSERT(ne->interval.currently_contains(val));
intersect(v, ne);
return false;
}
// 2^k * v == a_inv * b
// 2^k solutions because only the lower N-k bits of v are fixed.
//
// Smallest solution is v0 == a_inv * (b >> k)
// Solutions are of the form v_i = v0 + 2^(N-k) * i for i in { 0, 1, ..., 2^k - 1 }.
// Forbidden intervals: [v_i + 1; v_{i+1}[ == [ v_i + 1; v_i + 2^(N-k) [
// We need the interval that covers val:
// v_i + 1 <= val < v_i + 2^(N-k)
//
// TODO: create one interval for v[N-k:] instead of 2^k intervals for v.
unsigned const k = parity_a;
rational const a_inv = a.pseudo_inverse(N);
unsigned const N_minus_k = N - k;
rational const two_to_N_minus_k = rational::power_of_two(N_minus_k);
rational const v0 = mod(a_inv * machine_div2k(b, k), two_to_N_minus_k);
SASSERT(mod(val, two_to_N_minus_k) != v0); // val is not a solution
rational const vi = v0 + clear_lower_bits(mod(val - v0, mod_value), N_minus_k);
rational const lo = mod(vi + 1, mod_value);
rational const hi = mod(vi + two_to_N_minus_k, mod_value);
// LOG("refined to [" << num_pp(c, v, lo) << ", " << num_pp(c, v, hi) << "[");
SASSERT_EQ(mod(a * (lo - 1), mod_value), b); // lo-1 is a solution
SASSERT_EQ(mod(a * hi, mod_value), b); // hi is a solution
entry* ne = alloc_entry(v, e->constraint_index);
ne->refined = true;
ne->src = e->src;
ne->side_cond = e->side_cond;
ne->coeff = 1;
ne->bit_width = e->bit_width;
ne->interval = eval_interval::proper(m.mk_val(lo), lo, m.mk_val(hi), hi);
SASSERT(ne->interval.currently_contains(val));
intersect(v, ne);
return false;
}
// TODO: special handling for the even factors of e->coeff = 2^k * a', a' odd
// (create one interval for v[N-k:] instead of 2^k intervals for v)
// TODO: often, the intervals alternate between short forbidden and short allowed intervals.
// we should be able to handle this similarly to compute_y_bounds,
// and be able to represent such periodic intervals (inside safe bounds).
//
// compute_y_bounds calculates with inclusive upper bound, so we need to adjust argument and result accordingly.
rational const hi_val_incl = e->interval.hi_val().is_zero() ? max_value : (e->interval.hi_val() - 1);
auto [lo, hi] = refine_equal::compute_y_bounds(val, e->coeff, e->interval.lo_val(), hi_val_incl, mod_value);
hi += 1;
//LOG("refined to [" << num_pp(c, v, lo) << ", " << num_pp(c, v, hi) << "[");
// verbose_stream() << "lo=" << lo << " val=" << val << " hi=" << hi << "\n";
if (lo <= hi) {
SASSERT(0 <= lo && lo <= val && val < hi && hi <= mod_value);
}
else {
SASSERT(0 < hi && hi < lo && lo < mod_value && (val < hi || lo <= val));
}
bool full = (lo == 0 && hi == mod_value);
if (hi == mod_value)
hi = 0;
entry* ne = alloc_entry(v, e->constraint_index);
ne->refined = true;
ne->src = e->src;
ne->side_cond = e->side_cond;
ne->coeff = 1;
ne->bit_width = e->bit_width;
if (full)
ne->interval = eval_interval::full();
else
ne->interval = eval_interval::proper(m.mk_val(lo), lo, m.mk_val(hi), hi);
SASSERT(ne->interval.currently_contains(val));
intersect(v, ne);
return false;
}
e = e->next();
} while (e != first);
return true;
}
bool viable::check_fixed_bits(pvar v, rational const& val) {
auto e = alloc_entry(v, constraint_id::null());
if (m_fixed_bits.check(val, *e)) {
m_alloc.push_back(e);
return true;
}
else {
TRACE("bv", tout << "fixed " << val << " " << *e << "\n");
if (!intersect(v, e)) {
display(verbose_stream());
display_explain(verbose_stream() << "explain\n");
UNREACHABLE();
SASSERT(false);
}
return false;
}
}
bool viable::check_disequal_lin(pvar v, rational const& val) {
// LOG_H2("refine-disequal-lin with v" << v << ", val = " << val);
entry const* e = m_diseq_lin[v];
if (!e)
return true;
entry const* first = e;
auto& m = c.var2pdd(v);
rational const& max_value = m.max_value();
rational const& mod_value = m.two_to_N();
SASSERT(0 <= val && val <= max_value);
// Rotate the 'first' entry, to prevent getting stuck in a refinement loop
// with an early entry when a later entry could give a better interval.
m_diseq_lin[v] = m_diseq_lin[v]->next();
do {
// We compute an interval if the concrete value 'val' violates the constraint:
// p*val + q > r*val + s if e->src.is_positive()
// p*val + q >= r*val + s if e->src.is_negative()
// Note that e->interval is meaningless in this case,
// we just use it to transport the values p,q,r,s
rational const& p = e->interval.lo_val();
rational const& q_ = e->interval.lo().val();
rational const& r = e->interval.hi_val();
rational const& s_ = e->interval.hi().val();
SASSERT(p != r && p != 0 && r != 0);
SASSERT(e->src.size() == 1);
rational const a = mod(p * val + q_, mod_value);
rational const b = mod(r * val + s_, mod_value);
rational const np = mod_value - p;
rational const nr = mod_value - r;
int const corr = e->src[0].is_negative() ? 1 : 0;
auto delta_l = [&](rational const& val) {
rational num = a - b + corr;
rational l1 = floor(b / r);
rational l2 = val;
if (p > r)
l2 = ceil(num / (p - r)) - 1;
rational l3 = ceil(num / (p + nr)) - 1;
rational l4 = ceil((mod_value - a) / np) - 1;
rational d1 = l3;
rational d2 = std::min(l1, l2);
rational d3 = std::min(l1, l4);
rational d4 = std::min(l2, l4);
rational dmax = std::max(std::max(d1, d2), std::max(d3, d4));
return std::min(val, dmax);
};
auto delta_u = [&](rational const& val) {
rational num = a - b + corr;
rational h1 = floor(b / nr);
rational h2 = max_value - val;
if (r > p)
h2 = ceil(num / (r - p)) - 1;
rational h3 = ceil(num / (np + r)) - 1;
rational h4 = ceil((mod_value - a) / p) - 1;
rational d1 = h3;
rational d2 = std::min(h1, h2);
rational d3 = std::min(h1, h4);
rational d4 = std::min(h2, h4);
rational dmax = std::max(std::max(d1, d2), std::max(d3, d4));
return std::min(max_value - val, dmax);
};
if (a > b || (e->src[0].is_negative() && a == b)) {
rational lo = val - delta_l(val);
rational hi = val + delta_u(val) + 1;
LOG("refine-disequal-lin: " << " [" << lo << ", " << hi << "[");
SASSERT(0 <= lo && lo <= val);
SASSERT(val <= hi && hi <= mod_value);
if (hi == mod_value) hi = 0;
pdd lop = c.var2pdd(v).mk_val(lo);
pdd hip = c.var2pdd(v).mk_val(hi);
entry* ne = alloc_entry(v, e->constraint_index);
ne->refined = true;
ne->src = e->src;
ne->side_cond = e->side_cond;
ne->coeff = 1;
ne->bit_width = e->bit_width;
ne->interval = eval_interval::proper(lop, lo, hip, hi);
intersect(v, ne);
return false;
}
e = e->next();
} while (e != first);
return true;
}
/*
* The current explanation trail is a conflict if the top-most entry
* is repeated below and there is no entry with higher bit-width between.
*/
bool viable::is_conflict() {
auto last = m_explain.back();
unsigned bw = last.e->bit_width;
if (last.e->interval.is_full()) {
m_explain.reset();
m_explain.push_back(last);
return true;
}
for (unsigned i = m_explain.size() - 1; i-- > 0; ) {
auto e = m_explain[i];
if (bw < e.e->bit_width)
return false;
if (last.e == e.e)
return true;
}
return false;
}
bool viable::is_propagation(rational const& val) {
// disable for now
return false;
if (m_explain.empty())
return false;
auto last = m_explain.back();
auto first = m_explain[0];
if (first.e->interval.lo_val() == val + 1 &&
last.e->interval.hi_val() == val &&
first.e->bit_width == last.e->bit_width &&
first.e->bit_width == c.size(m_var)) {
return true;
}
return false;
}
std::ostream& operator<<(std::ostream& out, viable::explain_t e) {
switch(e) {
case viable::explain_t::conflict: return out << "conflict";
case viable::explain_t::propagation: return out << "propagation";
case viable::explain_t::assignment: return out << "assignment";
case viable::explain_t::none: return out << "none";
default: UNREACHABLE();
}
return out;
}
/*
* Explain why the current variable is not viable or
* or why it can only have a single value.
*/
dependency_vector viable::explain() {
dependency_vector result;
auto last = m_explain.back();
auto after = last;
verbose_stream() << "viable::explain: " << m_explain_kind << " v" << m_var << "\n";
if (c.inconsistent())
verbose_stream() << "inconsistent explain\n";
TRACE("bv", display_explain(tout));
auto unmark = [&]() {
for (auto e : m_explain)
e.e->marked = false;
};
auto explain_entry = [&](entry* e) {
auto index = e->constraint_index;
if (c.inconsistent())
return;
if (e->marked)
return;
e->marked = true;
if (m_var != e->var)
result.push_back(offset_claim(m_var, { e->var, 0 }));
for (auto const& sc : e->side_cond) {
auto d = c.propagate(sc, c.explain_weak_eval(sc), "entry weak eval");
if (c.inconsistent()) {
verbose_stream() << "inconsistent " << d << " " << sc << "\n";
}
result.push_back(d);
}
result.append(e->deps);
if (!index.is_null()) {
VERIFY_EQ(e->src.size(), 1);
VERIFY_EQ(c.get_constraint(index), e->src[0]);
result.push_back(c.get_dependency(index));
}
};
if (last.e->interval.is_full()) {
SASSERT(m_explain_kind == explain_t::none);
explain_entry(last.e);
SASSERT(m_explain.size() == 1);
unmark();
return result;
}
SASSERT(m_explain_kind != explain_t::none);
for (unsigned i = m_explain.size() - 1; i-- > 0; ) {
auto e = m_explain[i];
explain_overlap(e, after, result);
after = e;
explain_entry(e.e);
if (e.e == last.e)
break;
}
if (m_explain_kind == explain_t::propagation) {
// assume first and last have same bit-width
auto first = m_explain[0];
SASSERT(first.e->bit_width == last.e->bit_width);
explain_entry(first.e);
// add constraint that there is only a single viable value.
auto sc = cs.eq(last.e->interval.hi() + 1, first.e->interval.lo());
auto exp = c.propagate(sc, c.explain_weak_eval(sc));
if (c.inconsistent()) {
verbose_stream() << "inconsistent " << sc << " " << exp << "\n";
}
result.push_back(exp);
}
if (m_explain_kind == explain_t::assignment) {
// there is just one entry
SASSERT(m_explain.size() == 1);
SASSERT(!m_assign_dep.is_null());
entry* e = last.e;
explain_entry(e);
// assignment conflict and propagation from containing slice depends on concrete values,
// so we also need the evaluations of linear terms
SASSERT(!c.is_assigned(m_var)); // assignment of m_var is justified by m_assign_dep
auto index = last.e->constraint_index;
if (!index.is_null())
result.append(c.explain_weak_eval(c.get_constraint(index)));
// 'result' so far contains explanation for e and its weak evaluation
m_projection.init(e->var, e->interval, e->bit_width, result);
switch (m_projection()) {
case l_true:
// propagated interval onto subslice
m_projection.explain(result);
break;
case l_false:
// conflict (projected interval is full)
m_projection.explain(result);
break;
case l_undef:
// unable to propagate interval to containing slice
// fallback explanation uses assignment of m_var
result.push_back(m_assign_dep);
break;
};
}
unmark();
if (c.inconsistent())
verbose_stream() << "inconsistent after explain\n";
return result;
}
/*
* For two consecutive intervals
*
* - 2^kx \not\in [lo, hi[,
* - 2^k'y \not\in [lo', hi'[
* - a value v such that
* - 2^kv \not\in [lo, hi[
* - 2^k'v \in [lo', hi'[
* - hi \in ] (v - 1) * 2^{bw - ebw} ; v * 2^{bw - ebw} ]
*
* Where:
* - bw is the width of x, aw the width of y
* - ebw is the bit-width of x, abw the bit-width of y
* - k = bw - ebw, k' = aw - abw
*
* We want to encode the constraint that (2^k' hi)[w'] in [lo', hi'[
*
* Note that x in [lo, hi[ <=> x - lo < hi - lo
* If bw = aw, ebw = abw there is nothing else to do.
* - hi \in [lo', hi'[
*
* If bw != aw or aw < bw:
* - hi \in ] (v - 1) * 2^{bw - ebw} ; v * 2^{bw - ebw} ]
* - hi := v mod aw
*
* - 2^k'hi \in [lo', hi'[
*
*/
void viable::explain_overlap(explanation const& e, explanation const& after, dependency_vector& deps) {
auto bw = c.size(e.e->var);
auto ebw = e.e->bit_width;
auto aw = c.size(after.e->var);
auto abw = after.e->bit_width;
auto t = e.e->interval.hi();
auto lo = after.e->interval.lo();
auto hi = after.e->interval.hi();
SASSERT(abw <= aw);
SASSERT(ebw <= bw);
if (ebw < bw || aw != bw) {
auto const& p2b = rational::power_of_two(bw);
auto const& p2eb = rational::power_of_two(bw - ebw);
// let coeff = 2^{bw - ebw}
// let assume coeff * x \not\in [lo, t[
// Then value is chosen, min x . coeff * x >= t.
// In other words:
//
// x >= t div coeff
// => t <= coeff * x
// (x - 1) * coeff < t <= x * coeff
// a < x <= b <=>
// a + 1 <= x < b + 1
// x - a - 1 < b - a
auto vlo = c.value(mod((e.value - 1) * p2eb + 1, p2b), bw);
auto vhi = c.value(mod(e.value * p2eb + 1, p2b), bw);
#if 0
verbose_stream() << "value " << e.value << "\n";
verbose_stream() << "t " << t << "\n";
verbose_stream() << "[" << vlo << " " << vhi << "[\n";
verbose_stream() << "before bw " << ebw << " " << bw << " " << *e.e << "\nafter bw " << abw << " " << aw << " " << *after.e << "\n";
if (!t.is_val())
IF_VERBOSE(0, verbose_stream() << "symbolic t : " << t << "\n");
verbose_stream() << t - vlo << " " << vhi - vlo << "\n";
#endif
auto sc = cs.ult(t - vlo, vhi - vlo);
CTRACE("bv", sc.is_always_false(), c.display(tout));
VERIFY(!sc.is_always_false());
if (!sc.is_always_true())
deps.push_back(c.propagate(sc, c.explain_weak_eval(sc)));
t.reset(lo.manager());
t = c.value(mod(e.value, rational::power_of_two(aw)), aw);
// verbose_stream() << "after " << t << "\n";
if (c.inconsistent())
verbose_stream() << "inconsistent overlap " << sc << " " << "\n";
}
if (abw < aw)
t *= rational::power_of_two(aw - abw);
auto sc = cs.ult(t - lo, hi - lo);
SASSERT(!sc.is_always_false());
if (!sc.is_always_true())
deps.push_back(c.propagate(sc, c.explain_weak_eval(sc)));
if (c.inconsistent()) {
verbose_stream() << "inconsistent ult " << sc << " " << "\n";
verbose_stream() << "before bw " << ebw << " " << bw << " " << *e.e << "\nafter bw " << abw << " " << aw << " " << *after.e << "\n";
display(verbose_stream());
// UNREACHABLE();
}
}
/*
* Register constraint at index 'idx' as unitary in v.
* Returns 'multiple' when either intervals are unchanged or there really are multiple values left.
*/
find_t viable::add_unitary(pvar v, constraint_id idx, rational& var_value) {
if (c.is_assigned(v))
return find_t::multiple;
auto [sc, d, truth_value] = c.m_constraint_index[idx.id];
SASSERT(truth_value != l_undef);
if (truth_value == l_false)
sc = ~sc;
if (!sc.is_linear())
return find_t::multiple;
entry* ne = alloc_entry(v, idx);
if (!m_forbidden_intervals.get_interval(sc, v, *ne)) {
m_alloc.push_back(ne);
return find_t::multiple;
}
// verbose_stream() << "v" << v << " " << sc << " " << ne->interval << "\n";
TRACE("bv", tout << "v" << v << " " << sc << " " << ne->interval << "\n"; display_one(tout, ne) << "\n");
if (ne->interval.is_currently_empty()) {
m_alloc.push_back(ne);
return find_t::multiple;
}
if (ne->coeff == 1)
intersect(v, ne);
else if (ne->coeff == -1)
insert(ne, v, m_diseq_lin, entry_kind::diseq_e);
else if (!ne->coeff.is_power_of_two())
insert(ne, v, m_equal_lin, entry_kind::equal_e);
else if (ne->interval.is_full())
insert(ne, v, m_equal_lin, entry_kind::equal_e);
else {
unsigned const w = c.size(v);
unsigned const k = ne->coeff.parity(w);
SASSERT(k > 0);
IF_VERBOSE(3, display_one(verbose_stream() << "try to reduce entry: ", ne) << "\n");
// reduction of coeff gives us a unit entry
//
// 2^k x \not\in [ lo ; hi [
//
// new_lo = lo[w-1:k] if lo[k-1:0] = 0
// lo[w-1:k] + 1 otherwise
//
// new_hi = hi[w-1:k] if hi[k-1:0] = 0
// hi[w-1:k] + 1 otherwise
//
// Reference: Fig. 1 (dtrim) in BitvectorsMCSAT
TRACE("bv", display_one(tout << "try to reduce entry: ", ne) << "\n");
pdd const& pdd_lo = ne->interval.lo();
pdd const& pdd_hi = ne->interval.hi();
rational const& lo = ne->interval.lo_val();
rational const& hi = ne->interval.hi_val();
rational twoK = rational::power_of_two(k);
rational new_lo = machine_div2k(mod2k(lo + twoK - 1, w), k);
pdd lo_eq = pdd_lo * rational::power_of_two(w - k);
if (mod2k(lo, k).is_zero()) {
if (!lo_eq.is_zero())
ne->side_cond.push_back(cs.eq(lo_eq));
}
else {
SASSERT(!lo_eq.is_val() || !lo_eq.is_zero());
if (!lo_eq.is_val())
ne->side_cond.push_back(~cs.eq(lo_eq));
}
rational new_hi = machine_div2k(mod2k(hi + twoK - 1, w), k);
pdd hi_eq = pdd_hi * rational::power_of_two(w - k);
if (mod2k(hi, k).is_zero()) {
if (!hi_eq.is_zero())
ne->side_cond.push_back(cs.eq(hi_eq));
}
else {
SASSERT(!hi_eq.is_val() || !hi_eq.is_zero());
if (!hi_eq.is_val())
ne->side_cond.push_back(~cs.eq(hi_eq));
}
//
// If new_lo = new_hi it means that
// mod(ceil(lo / 2^k), 2^(w-k)) = mod(ceil(hi / 2^k), 2^(w-k))
// or
// div(mod(lo + 2^k - 1, 2^w), 2^k) = div(mod(hi + 2^k - 1, 2^w), 2^k)
// but we also have lo != hi.
//
// Cases:
// 0 < lo < hi: empty (2^k does not divide any of [lo, hi[)
// 0 == lo < hi: full
// 0 < hi < lo: full
// 0 == hi < lo: empty
//
if (new_lo == new_hi) {
bool is_empty_ivl;
if (lo < hi) {
ne->side_cond.push_back(cs.ult(pdd_lo, pdd_hi));
if (lo == 0) {
ne->side_cond.push_back(cs.eq(pdd_lo));
is_empty_ivl = false;
}
else {
ne->side_cond.push_back(~cs.eq(pdd_lo));
is_empty_ivl = true;
}
}
else {
SASSERT(hi < lo);
ne->side_cond.push_back(cs.ult(pdd_hi, pdd_lo));
if (hi == 0) {
ne->side_cond.push_back(cs.eq(pdd_hi));
is_empty_ivl = true;
}
else {
ne->side_cond.push_back(~cs.eq(pdd_hi));
is_empty_ivl = false;
}
}
if (is_empty_ivl) {
m_alloc.push_back(ne);
return find_t::multiple;
}
else {
ne->interval = eval_interval::full();
ne->coeff = 1;
m_explain.reset();
m_explain.push_back({ ne, rational::zero() });
m_fixed_bits.reset();
m_var = v;
return find_t::empty;
}
}
ne->coeff = 1;
ne->interval = eval_interval::proper(pdd_lo, new_lo, pdd_hi, new_hi);
ne->bit_width -= k;
TRACE("bv", display_one(tout << "reduced: ", ne) << "\n");
intersect(v, ne);
}
if (ne->interval.is_full()) {
m_explain.reset();
m_explain.push_back({ ne, rational::zero() });
m_fixed_bits.reset();
m_var = v;
return find_t::empty;
}
return find_viable(v, var_value);
}
void viable::ensure_var(pvar v) {
while (v >= m_units.size()) {
m_units.push_back(layers());
m_equal_lin.push_back(nullptr);
m_diseq_lin.push_back(nullptr);
}
}
bool viable::intersect(pvar v, entry* ne) {
SASSERT(!c.is_assigned(v));
entry*& entries = m_units[v].ensure_layer(ne->bit_width).entries;
entry* e = entries;
if (e && e->interval.is_full()) {
m_alloc.push_back(ne);
return false;
}
if (ne->interval.is_currently_empty()) {
m_alloc.push_back(ne);
return false;
}
auto create_entry = [&]() {
c.trail().push(pop_viable_trail(*this, ne, entry_kind::unit_e));
ne->init(ne);
return ne;
};
auto remove_entry = [&](entry* e) {
c.trail().push(push_viable_trail(*this, e));
e->remove_from(entries, e);
e->active = false;
};
if (ne->interval.is_full()) {
while (entries)
remove_entry(entries);
entries = create_entry();
return true;
}
if (!e)
entries = create_entry();
else {
entry* first = e;
do {
if (e->interval.currently_contains(ne->interval)) {
m_alloc.push_back(ne);
return false;
}
while (ne->interval.currently_contains(e->interval)) {
entry* n = e->next();
remove_entry(e);
if (!entries) {
entries = create_entry();
return true;
}
if (e == first)
first = n;
e = n;
}
SASSERT(e->interval.lo_val() != ne->interval.lo_val());
if (e->interval.lo_val() > ne->interval.lo_val()) {
if (first->prev()->interval.currently_contains(ne->interval)) {
m_alloc.push_back(ne);
return false;
}
e->insert_before(create_entry());
if (e == first)
entries = e->prev();
SASSERT(well_formed(m_units[v]));
return true;
}
e = e->next();
}
while (e != first);
// otherwise, append to end of list
first->insert_before(create_entry());
}
SASSERT(well_formed(m_units[v]));
return true;
}
viable::layer& viable::layers::ensure_layer(unsigned bit_width) {
for (unsigned i = 0; i < m_layers.size(); ++i) {
layer& l = m_layers[i];
if (l.bit_width == bit_width)
return l;
else if (l.bit_width > bit_width) {
m_layers.push_back(layer(0));
for (unsigned j = m_layers.size(); --j > i; )
m_layers[j] = m_layers[j - 1];
m_layers[i] = layer(bit_width);
return m_layers[i];
}
}
m_layers.push_back(layer(bit_width));
return m_layers.back();
}
viable::layer* viable::layers::get_layer(unsigned bit_width) {
return const_cast<layer*>(std::as_const(*this).get_layer(bit_width));
}
viable::layer const* viable::layers::get_layer(unsigned bit_width) const {
for (layer const& l : m_layers)
if (l.bit_width == bit_width)
return &l;
return nullptr;
}
void viable::pop_viable(entry* e, entry_kind k) {
unsigned v = e->var;
SASSERT(well_formed(m_units[v]));
SASSERT(e->active);
e->active = false;
switch (k) {
case entry_kind::unit_e:
entry::remove_from(m_units[v].get_layer(e)->entries, e);
break;
case entry_kind::equal_e:
entry::remove_from(m_equal_lin[v], e);
break;
case entry_kind::diseq_e:
entry::remove_from(m_diseq_lin[v], e);
break;
default:
UNREACHABLE();
break;
}
SASSERT(well_formed(m_units[v]));
m_alloc.push_back(e);
}
void viable::push_viable(entry* e) {
// display_one(verbose_stream() << "Push entry: ", e) << "\n";
auto v = e->var;
entry*& entries = m_units[v].get_layer(e)->entries;
SASSERT(e->prev() != e || !entries);
SASSERT(e->prev() != e || e->next() == e);
SASSERT(!e->active);
e->active = true;
SASSERT(well_formed(m_units[v]));
if (e->prev() != e) {
entry* pos = e->prev();
e->init(e);
pos->insert_after(e);
if (!entries || e->interval.lo_val() < entries->interval.lo_val())
entries = e;
}
else
entries = e;
SASSERT(well_formed(m_units[v]));
}
void viable::insert(entry* e, pvar v, ptr_vector<entry>& entries, entry_kind k) {
SASSERT(well_formed(m_units[v]));
c.trail().push(pop_viable_trail(*this, e, k));
e->init(e);
if (!entries[v])
entries[v] = e;
else
e->insert_after(entries[v]);
SASSERT(entries[v]->invariant());
SASSERT(well_formed(m_units[v]));
}
std::ostream& viable::display_one(std::ostream& out, entry const* e) const {
auto& m = c.var2pdd(e->var);
if (e->coeff == -1) {
// p*val + q > r*val + s if e->src.is_positive()
// p*val + q >= r*val + s if e->src.is_negative()
// Note that e->interval is meaningless in this case,
// we just use it to transport the values p,q,r,s
rational const& p = e->interval.lo_val();
rational const& q_ = e->interval.lo().val();
rational const& r = e->interval.hi_val();
rational const& s_ = e->interval.hi().val();
out << "[ ";
out << val_pp(m, p, true) << "*v" << e->var << " + " << val_pp(m, q_);
out << (e->src[0].is_positive() ? " > " : " >= ");
out << val_pp(m, r, true) << "*v" << e->var << " + " << val_pp(m, s_);
out << " ] ";
}
else {
if (e->coeff != 1)
out << e->coeff << " * ";
out << "v" << e->var;
if (e->bit_width != c.size(e->var))
out << "[" << e->bit_width << "]";
out << " " << e->interval << " ";
}
if (!e->deps.empty())
out << " deps " << e->deps;
if (e->side_cond.empty())
;
else if (e->side_cond.size() <= 5)
out << " side-conds " << e->side_cond;
else
out << " side-conds " << e->side_cond.size() << " side-conditions";
out << " src ";
unsigned count = 0;
for (const auto& src : e->src) {
++count;
out << src << "; ";
if (count > 10) {
out << " ...";
break;
}
}
return out;
}
std::ostream& viable::display_all(std::ostream& out, entry const* e, char const* delimiter) const {
if (!e)
return out;
entry const* first = e;
unsigned count = 0;
do {
display_one(out, e) << delimiter;
e = e->next();
++count;
if (count > 10) {
out << " ... (total: " << count << " entries)";
break;
}
}
while (e != first);
return out;
}
std::ostream& viable::display(std::ostream& out) const {
for (unsigned v = 0; v < m_units.size(); ++v) {
for (auto const& layer : m_units[v].get_layers()) {
if (!layer.entries)
continue;
out << "v" << v << "[" << layer.bit_width << "]: ";
display_all(out, layer.entries, " ");
out << "\n";
}
}
return out;
}
std::ostream& viable::display_state(std::ostream& out) const {
out << "v" << m_var << ":";
for (auto const& slice : m_overlaps) {
out << " v" << slice.child << ":" << c.size(slice.child) << "@" << slice.offset;
if (c.is_assigned(slice.child))
out << " value=" << c.get_assignment().value(slice.child);
}
out << "\n";
return out;
}
std::ostream& viable::display_explain(std::ostream& out) const {
out << "explain_kind " << m_explain_kind << "\n";
display_state(out);
for (auto const& e : m_explain)
display_one(out << "v" << m_var << "[" << e.e->bit_width << "] := " << e.value << " ", e.e) << "\n";
return out;
}
/*
* Lower bounds are strictly ascending.
* Intervals don't contain each-other (since lower bounds are ascending, it suffices to check containment in one direction).
*/
bool viable::well_formed(entry* e) {
if (!e)
return true;
entry* first = e;
while (true) {
CTRACE("bv", !e->active, tout << "inactive entry v" << e->var << " " << e->interval << "\n"; display(tout));
if (!e->active)
return false;
if (e->interval.is_full())
return e->next() == e;
if (e->interval.is_currently_empty())
return false;
auto* n = e->next();
if (n != e && e->interval.currently_contains(n->interval)) {
TRACE("bv", tout << "currently contains\n");
return false;
}
if (n == first)
break;
if (e->interval.lo_val() >= n->interval.lo_val()) {
TRACE("bv", tout << "lo-val >= n->lo_val\n");
return false;
}
e = n;
}
return true;
}
/*
* Layers are ordered in strictly ascending bit-width.
* Entries in each layer are well-formed.
*/
bool viable::well_formed(layers const& ls) {
bool first = true;
unsigned prev_width = 0;
for (layer const& l : ls.get_layers()) {
if (!well_formed(l.entries)) {
TRACE("bv", tout << "entries are not well-formed\n");
return false;
}
if (!all_of(dll_elements(l.entries), [&l](entry const& e) { return e.bit_width == l.bit_width; })) {
TRACE("bv", tout << "elements don't have same bit-width\n");
return false;
}
if (!first && prev_width >= l.bit_width) {
TRACE("bv", tout << "previous width is " << prev_width << " vs " << l.bit_width << "\n");
return false;
}
first = false;
prev_width = l.bit_width;
}
return true;
}
}