mirror of
https://github.com/Z3Prover/z3
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1265 lines
46 KiB
C++
1265 lines
46 KiB
C++
/*++
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Copyright (c) 2021 Microsoft Corporation
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Module Name:
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maintain viable domains
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Author:
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Nikolaj Bjorner (nbjorner) 2021-03-19
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Jakob Rath 2021-04-06
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Notes:
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--*/
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#include "util/debug.h"
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#include "util/log.h"
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#include "sat/smt/polysat/viable.h"
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#include "sat/smt/polysat/core.h"
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#include "sat/smt/polysat/number.h"
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#include "sat/smt/polysat/refine.h"
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#include "sat/smt/polysat/project_interval.h"
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#include "sat/smt/polysat/ule_constraint.h"
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namespace polysat {
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using dd::val_pp;
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viable::viable(core& c) : c(c), cs(c.cs()), m_forbidden_intervals(c), m_projection(c), m_fixed_bits(c) {}
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viable::~viable() {
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for (auto* e : m_alloc)
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dealloc(e);
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}
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std::ostream& operator<<(std::ostream& out, find_t f) {
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switch (f) {
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case find_t::empty: return out << "empty";
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case find_t::singleton: return out << "singleton";
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case find_t::multiple: return out << "multiple";
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case find_t::resource_out: return out << "resource-out";
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default: return out << "<unknown>";
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}
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}
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struct viable::pop_viable_trail : public trail {
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viable& m_s;
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entry* e;
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entry_kind k;
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public:
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pop_viable_trail(viable& s, entry* e, entry_kind k)
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: m_s(s), e(e), k(k) {}
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void undo() override {
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m_s.pop_viable(e, k);
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}
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};
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struct viable::push_viable_trail : public trail {
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viable& m_s;
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entry* e;
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public:
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push_viable_trail(viable& s, entry* e)
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: m_s(s), e(e) {}
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void undo() override {
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m_s.push_viable(e);
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}
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};
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viable::entry* viable::alloc_entry(pvar var, constraint_id constraint_index) {
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entry* e = nullptr;
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if (m_alloc.empty())
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e = alloc(entry);
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else {
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e = m_alloc.back();
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m_alloc.pop_back();
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}
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e->reset();
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e->var = var;
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e->constraint_index = constraint_index;
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return e;
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}
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bool viable::assign(pvar v, rational const& value, dependency dep) {
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m_var = v;
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m_explain_kind = explain_t::none;
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m_num_bits = c.size(v);
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m_fixed_bits.init(v);
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m_explain.reset();
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m_assign_dep = null_dependency;
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init_overlaps(v);
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bool first = true;
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while (true) {
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for (auto const& [w, offset] : m_overlaps) {
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for (auto& layer : m_units[w].get_layers()) {
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entry* e = find_overlap(w, layer, value);
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if (!e)
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continue;
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m_explain.push_back({ e, value });
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m_explain_kind = explain_t::assignment;
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m_assign_dep = dep;
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return false;
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}
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}
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if (!first)
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return true;
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first = false;
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if (!check_fixed_bits(v, value))
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continue;
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if (!check_disequal_lin(v, value))
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continue;
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if (!check_equal_lin(v, value))
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continue;
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break;
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}
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return true;
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}
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find_t viable::find_viable(pvar v, rational& lo) {
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m_explain.reset();
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m_var = v;
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m_num_bits = c.size(v);
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m_fixed_bits.init(v);
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init_overlaps(v);
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m_explain_kind = explain_t::none;
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m_assign_dep = null_dependency;
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for (unsigned rounds = 0; rounds < 10; ) {
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entry* n = find_overlap(lo);
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if (m_explain_kind == explain_t::conflict)
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return find_t::empty;
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if (n)
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continue;
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if (!check_fixed_bits(v, lo))
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continue;
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++rounds;
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if (!check_disequal_lin(v, lo))
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continue;
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if (!check_equal_lin(v, lo))
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continue;
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if (is_propagation(lo)) {
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m_explain_kind = explain_t::propagation;
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return find_t::singleton;
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}
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return find_t::multiple;
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}
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TRACE("bv", display(tout << "resource-out v" << v << "\n"));
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return find_t::resource_out;
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}
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void viable::init_overlaps(pvar v) {
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m_overlaps.reset();
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c.get_bitvector_suffixes(v, m_overlaps);
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std::sort(m_overlaps.begin(), m_overlaps.end(), [&](auto const& x, auto const& y) { return c.size(x.child) < c.size(y.child); });
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}
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//
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//
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// from smallest size(w) overlap [w] to largest
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// from smallest bit_width layer [bit_width, entries] to largest
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// check if val is allowed by entries or advance val to next allowed value
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//
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viable::entry* viable::find_overlap(rational& val) {
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entry* last = nullptr;
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for (auto const& [w, offset] : m_overlaps) {
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for (auto& layer : m_units[w].get_layers()) {
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entry* e = find_overlap(w, layer, val);
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if (!e)
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continue;
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last = e;
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if (e->interval.is_proper())
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update_value_to_high(val, e);
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m_explain.push_back({ e, val });
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if (is_conflict()) {
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m_explain_kind = explain_t::conflict;
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return nullptr;
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}
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}
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}
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return last;
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}
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viable::entry* viable::find_overlap(pvar w, layer& l, rational const& val) {
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if (!l.entries)
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return nullptr;
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unsigned v_width = m_num_bits;
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unsigned b_width = l.bit_width;
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if (v_width == b_width)
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return find_overlap(val, l.entries);
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rational val1 = mod(val, rational::power_of_two(b_width));
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return find_overlap(val1, l.entries);
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}
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void viable::update_value_to_high(rational& val, entry* e) {
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unsigned v_width = m_num_bits;
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unsigned b_width = e->bit_width;
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SASSERT(b_width <= v_width);
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auto const& hi = e->interval.hi_val();
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auto const& lo = e->interval.lo_val();
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if (b_width == v_width) {
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val = hi;
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SASSERT(0 <= val && val <= c.var2pdd(m_var).max_value());
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return;
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}
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auto p2b = rational::power_of_two(b_width);
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rational val2 = clear_lower_bits(val, b_width);
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if (lo <= mod(val, p2b) && hi < lo) {
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val2 += p2b;
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if (val2 == rational::power_of_two(v_width))
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val2 = 0;
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}
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val = val2 + hi;
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SASSERT(0 <= hi && hi < p2b);
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SASSERT(0 <= val && val <= c.var2pdd(m_var).max_value());
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}
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/*
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* In either case we are checking a constraint $v[u-1:0]\not\in[lo, hi[$
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* where $u := w'-k-1$ and using it to compute $\forward(v)$.
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* Thus, suppose $v[u-1:0] \in [lo, hi[$.
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* - $lo < hi$: $\forward(v) := \forward(2^u v[w-1:w-u] + hi)$.
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* - $lo > hi$, $v[w-1:w-u]+1 = 2^{w-u}$: $\forward(v) := \bot$
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* - $lo > hi$, $v[w-1:w-u]+1 < 2^{w-u}$: $\forward(v) := \forward(2^u (v[w-1:w-u]+1) + hi)$
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*/
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// Find interval that contains 'val', or, if no such interval exists, null.
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viable::entry* viable::find_overlap(rational const& val, entry* entries) {
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SASSERT(entries);
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entry* const first = entries;
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entry* e = entries;
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do {
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auto const& i = e->interval;
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if (i.currently_contains(val))
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return e;
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entry* const n = e->next();
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// there is only one interval, and it does not contain 'val'
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if (e == n)
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return nullptr;
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// check whether 'val' is contained in the gap between e and n
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bool const overlapping = e->interval.currently_contains(n->interval.lo_val());
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if (!overlapping && r_interval::contains(e->interval.hi_val(), n->interval.lo_val(), val))
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return nullptr;
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e = n;
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}
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while (e != first);
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UNREACHABLE();
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return nullptr;
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}
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bool viable::check_equal_lin(pvar v, rational const& val) {
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// LOG_H2("refine-equal-lin with v" << v << ", val = " << val);
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entry const* e = m_equal_lin[v];
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if (!e)
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return true;
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entry const* first = e;
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auto& m = c.var2pdd(v);
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unsigned const N = m.power_of_2();
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rational const& max_value = m.max_value();
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rational const& mod_value = m.two_to_N();
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SASSERT(0 <= val && val <= max_value);
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// Rotate the 'first' entry, to prevent getting stuck in a refinement loop
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// with an early entry when a later entry could give a better interval.
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m_equal_lin[v] = m_equal_lin[v]->next();
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do {
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rational coeff_val = mod(e->coeff * val, mod_value);
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if (e->interval.currently_contains(coeff_val)) {
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// IF_LOGGING(
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// verbose_stream() << "refine-equal-lin for v" << v << " in src: ";
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// for (const auto& src : e->src)
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// verbose_stream() << lit_pp(s, src) << "\n";
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// );
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// LOG("forbidden interval v" << v << " " << num_pp(s, v, val) << " " << num_pp(s, v, e->coeff, true) << " * " << e->interval);
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if (mod(e->interval.hi_val() + 1, mod_value) == e->interval.lo_val()) {
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// We have an equation: a * v == b
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rational const a = e->coeff;
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rational const b = e->interval.hi_val();
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LOG("refine-equal-lin: equation detected: " << dd::val_pp(m, a, true) << " * v" << v << " == " << dd::val_pp(m, b, false));
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unsigned const parity_a = get_parity(a, N);
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unsigned const parity_b = get_parity(b, N);
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if (parity_a > parity_b) {
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// No solution
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LOG("refined: no solution due to parity");
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entry* ne = alloc_entry(v, e->constraint_index);
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ne->refined = true;
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ne->src = e->src;
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ne->side_cond = e->side_cond;
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ne->coeff = 1;
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ne->bit_width = e->bit_width;
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ne->interval = eval_interval::full();
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intersect(v, ne);
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return false;
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}
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if (parity_a == 0) {
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// "fast path" for odd a
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rational a_inv;
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VERIFY(a.mult_inverse(N, a_inv));
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rational const hi = mod(a_inv * b, mod_value);
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rational const lo = mod(hi + 1, mod_value);
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// LOG("refined to [" << num_pp(c, v, lo) << ", " << num_pp(c, v, hi) << "[");
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SASSERT_EQ(mod(a * hi, mod_value), b); // hi is the solution
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entry* ne = alloc_entry(v, e->constraint_index);
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ne->refined = true;
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ne->src = e->src;
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ne->side_cond = e->side_cond;
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ne->coeff = 1;
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ne->bit_width = e->bit_width;
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ne->interval = eval_interval::proper(m.mk_val(lo), lo, m.mk_val(hi), hi);
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SASSERT(ne->interval.currently_contains(val));
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intersect(v, ne);
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return false;
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}
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// 2^k * v == a_inv * b
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// 2^k solutions because only the lower N-k bits of v are fixed.
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//
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// Smallest solution is v0 == a_inv * (b >> k)
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// Solutions are of the form v_i = v0 + 2^(N-k) * i for i in { 0, 1, ..., 2^k - 1 }.
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// Forbidden intervals: [v_i + 1; v_{i+1}[ == [ v_i + 1; v_i + 2^(N-k) [
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// We need the interval that covers val:
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// v_i + 1 <= val < v_i + 2^(N-k)
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//
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// TODO: create one interval for v[N-k:] instead of 2^k intervals for v.
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unsigned const k = parity_a;
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rational const a_inv = a.pseudo_inverse(N);
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unsigned const N_minus_k = N - k;
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rational const two_to_N_minus_k = rational::power_of_two(N_minus_k);
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rational const v0 = mod(a_inv * machine_div2k(b, k), two_to_N_minus_k);
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SASSERT(mod(val, two_to_N_minus_k) != v0); // val is not a solution
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rational const vi = v0 + clear_lower_bits(mod(val - v0, mod_value), N_minus_k);
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rational const lo = mod(vi + 1, mod_value);
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rational const hi = mod(vi + two_to_N_minus_k, mod_value);
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// LOG("refined to [" << num_pp(c, v, lo) << ", " << num_pp(c, v, hi) << "[");
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SASSERT_EQ(mod(a * (lo - 1), mod_value), b); // lo-1 is a solution
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SASSERT_EQ(mod(a * hi, mod_value), b); // hi is a solution
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entry* ne = alloc_entry(v, e->constraint_index);
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ne->refined = true;
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ne->src = e->src;
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ne->side_cond = e->side_cond;
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ne->coeff = 1;
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ne->bit_width = e->bit_width;
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ne->interval = eval_interval::proper(m.mk_val(lo), lo, m.mk_val(hi), hi);
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SASSERT(ne->interval.currently_contains(val));
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intersect(v, ne);
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return false;
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}
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// TODO: special handling for the even factors of e->coeff = 2^k * a', a' odd
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// (create one interval for v[N-k:] instead of 2^k intervals for v)
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// TODO: often, the intervals alternate between short forbidden and short allowed intervals.
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// we should be able to handle this similarly to compute_y_bounds,
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// and be able to represent such periodic intervals (inside safe bounds).
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//
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// compute_y_bounds calculates with inclusive upper bound, so we need to adjust argument and result accordingly.
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rational const hi_val_incl = e->interval.hi_val().is_zero() ? max_value : (e->interval.hi_val() - 1);
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auto [lo, hi] = refine_equal::compute_y_bounds(val, e->coeff, e->interval.lo_val(), hi_val_incl, mod_value);
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hi += 1;
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//LOG("refined to [" << num_pp(c, v, lo) << ", " << num_pp(c, v, hi) << "[");
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// verbose_stream() << "lo=" << lo << " val=" << val << " hi=" << hi << "\n";
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if (lo <= hi) {
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SASSERT(0 <= lo && lo <= val && val < hi && hi <= mod_value);
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}
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else {
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SASSERT(0 < hi && hi < lo && lo < mod_value && (val < hi || lo <= val));
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}
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bool full = (lo == 0 && hi == mod_value);
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if (hi == mod_value)
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hi = 0;
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entry* ne = alloc_entry(v, e->constraint_index);
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ne->refined = true;
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ne->src = e->src;
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ne->side_cond = e->side_cond;
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ne->coeff = 1;
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ne->bit_width = e->bit_width;
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if (full)
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ne->interval = eval_interval::full();
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else
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ne->interval = eval_interval::proper(m.mk_val(lo), lo, m.mk_val(hi), hi);
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SASSERT(ne->interval.currently_contains(val));
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intersect(v, ne);
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return false;
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}
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e = e->next();
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} while (e != first);
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return true;
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}
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bool viable::check_fixed_bits(pvar v, rational const& val) {
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auto e = alloc_entry(v, constraint_id::null());
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if (m_fixed_bits.check(val, *e)) {
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m_alloc.push_back(e);
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return true;
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}
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else {
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TRACE("bv", tout << "fixed " << val << " " << *e << "\n");
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if (!intersect(v, e)) {
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display(verbose_stream());
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display_explain(verbose_stream() << "explain\n");
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UNREACHABLE();
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SASSERT(false);
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}
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return false;
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}
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}
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bool viable::check_disequal_lin(pvar v, rational const& val) {
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// LOG_H2("refine-disequal-lin with v" << v << ", val = " << val);
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entry const* e = m_diseq_lin[v];
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if (!e)
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return true;
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entry const* first = e;
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auto& m = c.var2pdd(v);
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rational const& max_value = m.max_value();
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rational const& mod_value = m.two_to_N();
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SASSERT(0 <= val && val <= max_value);
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// Rotate the 'first' entry, to prevent getting stuck in a refinement loop
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// with an early entry when a later entry could give a better interval.
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m_diseq_lin[v] = m_diseq_lin[v]->next();
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do {
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// We compute an interval if the concrete value 'val' violates the constraint:
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// p*val + q > r*val + s if e->src.is_positive()
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// p*val + q >= r*val + s if e->src.is_negative()
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// Note that e->interval is meaningless in this case,
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// we just use it to transport the values p,q,r,s
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rational const& p = e->interval.lo_val();
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rational const& q_ = e->interval.lo().val();
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rational const& r = e->interval.hi_val();
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rational const& s_ = e->interval.hi().val();
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SASSERT(p != r && p != 0 && r != 0);
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SASSERT(e->src.size() == 1);
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rational const a = mod(p * val + q_, mod_value);
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rational const b = mod(r * val + s_, mod_value);
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rational const np = mod_value - p;
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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;
|
|
}
|
|
}
|