redo fixed bits, add simplifications to intblast solver

src/sat/smt/intblast_solver.cpp

@@ -471,18 +471,25 @@ namespace intblast {
         });
     }
 
+    bool solver::is_non_negative(expr* bv_expr, expr* e) {
+        auto N = rational::power_of_two(bv.get_bv_size(bv_expr));
+        rational r;
+        if (a.is_numeral(e, r))
+            return r >= 0;
+        if (is_bounded(e, N))
+            return true;
+        expr* x, * y;
+        if (a.is_mul(e, x, y)) 
+            return is_non_negative(bv_expr, x) && is_non_negative(bv_expr, y);
+        if (a.is_add(e, x, y))
+            return is_non_negative(bv_expr, x) && is_non_negative(bv_expr, y);
+        return false;
+    }
+
     expr* solver::umod(expr* bv_expr, unsigned i) {
         expr* x = arg(i);
-        rational r;
         rational N = bv_size(bv_expr);
-        if (a.is_numeral(x, r)) {
+        return amod(bv_expr, x, N);
-            if (0 <= r && r < N)
-                return x;
-            return a.mk_int(mod(r, N));
-        }
-        if (is_bounded(x, N))
-            return x;
-        return a.mk_mod(x, a.mk_int(N));
     }
 
     expr* solver::smod(expr* bv_expr, unsigned i) {
@@ -492,7 +499,7 @@ namespace intblast {
         rational r;
         if (a.is_numeral(x, r))
             return a.mk_int(mod(r + shift, N));
-        return a.mk_mod(add(x, a.mk_int(shift)), a.mk_int(N));
+        return amod(bv_expr, add(x, a.mk_int(shift)), N);
     }
 
     expr_ref solver::mul(expr* x, expr* y) {
@@ -505,6 +512,9 @@ namespace intblast {
             return _y;
         if (a.is_one(y))
             return _x;
+        rational v1, v2;
+        if (a.is_numeral(x, v1) && a.is_numeral(y, v2))
+            return expr_ref(a.mk_int(v1 * v2), m);
         _x = a.mk_mul(x, y);
         return _x;
     }
@@ -515,10 +525,37 @@ namespace intblast {
             return _y;
         if (a.is_zero(y))
             return _x;
+        rational v1, v2;
+        if (a.is_numeral(x, v1) && a.is_numeral(y, v2))
+            return expr_ref(a.mk_int(v1 + v2), m);
         _x = a.mk_add(x, y);
         return _x;
     }
 
+    /*
+    * Perform simplifications that are claimed sound when the bit-vector interpretations of
+    * mod/div always guard the mod and dividend to be non-zero.
+    * Potentially shady area is for arithmetic expressions created by int2bv. 
+    * They will be guarded by a modulus which dose not disappear.
+    */
+    expr* solver::amod(expr* bv_expr, expr* x, rational const& N) {
+        rational v;
+        expr* r, *c, * t, * e;
+        if (m.is_ite(x, c, t, e))
+            r = m.mk_ite(c, amod(bv_expr, t, N), amod(bv_expr, e, N));
+        else if (a.is_idiv(x, t, e) && a.is_numeral(t, v) && 0 <= v && v < N && is_non_negative(bv_expr, e))
+            r = x;
+        else if (a.is_mod(x, t, e) && a.is_numeral(t, v) && 0 <= v && v < N)
+            r = x;
+        else if (a.is_numeral(x, v))
+            r = a.mk_int(mod(v, N));
+        else if (is_bounded(x, N))
+            r = x;
+        else 
+            r = a.mk_mod(x, a.mk_int(N));
+        return r;
+    }
+
     rational solver::bv_size(expr* bv_expr) {
         return rational::power_of_two(bv.get_bv_size(bv_expr->get_sort()));
     }
@@ -649,7 +686,7 @@ namespace intblast {
                 auto A = rational::power_of_two(sz - n);
                 auto B = rational::power_of_two(n);
                 auto hi = mul(r, a.mk_int(A));
-                auto lo = a.mk_mod(a.mk_idiv(umod(e, 0), a.mk_int(B)), a.mk_int(A));
+                auto lo = amod(e, a.mk_idiv(umod(e, 0), a.mk_int(B)), A);
                 r = add(hi, lo);
             }
             return r;

src/sat/smt/intblast_solver.h

@@ -74,8 +74,10 @@ namespace intblast {
         expr* umod(expr* bv_expr, unsigned i);
         expr* smod(expr* bv_expr, unsigned i);
         bool is_bounded(expr* v, rational const& N);
+        bool is_non_negative(expr* bv_expr, expr* e);
         expr_ref mul(expr* x, expr* y);
         expr_ref add(expr* x, expr* y);
+        expr* amod(expr* bv_expr, expr* x, rational const& N);
         rational bv_size(expr* bv_expr);
 
         void translate_expr(expr* e);

src/sat/smt/polysat/fixed_bits.cpp

@@ -20,96 +20,41 @@ namespace polysat {
     void fixed_bits::reset() {
         m_fixed_slices.reset();
         m_var = null_var;
-        m_fixed.reset();
-        m_bits.reset();
     }
 
     // reset with fixed bits information for variable v
-    void fixed_bits::reset(pvar v) {
+    void fixed_bits::init(pvar v) {
         m_fixed_slices.reset();
         m_var = v;
-        m_fixed.reset();
+        c.get_fixed_bits(v, m_fixed_slices);
-        m_fixed.resize(c.size(v), l_undef);
-        m_bits.reserve(c.size(v));
-        fixed_bits_vector fbs;
-        c.get_fixed_bits(v, fbs);
-        for (auto const& fb : fbs) 
-            for (unsigned i = fb.lo; i <= fb.hi; ++i) 
-                m_fixed[i] = to_lbool(fb.value.get_bit(i - fb.lo));
     }
 
-    // find then next value >= val that agrees with fixed bits, or false if none exists within the maximal value for val.
+    // if x[hi:lo] = value, then 
-    // examples
+    // 2^(w-hi+1)* x >= 
-    //  fixed bits:  1?0 (least significant bit is last)
+    bool fixed_bits::check(rational const& val, fi_record& fi) {
-    //  val:         101
+        for (auto const& s : m_fixed_slices) {
-    //  next:        110
+            rational bw = rational::power_of_two(s.hi - s.lo + 1);
-
+            if (s.value != mod(machine_div2k(val, s.lo + 1), bw)) {
-    // fixed bits   ?1?0
+                rational hi_val = s.value;
-    // val          1011
+                rational lo_val = mod(s.value + 1, bw);
-    // next         1100
+                unsigned sz = c.size(m_var);
-
+                pdd lo = c.value(rational::power_of_two(sz - s.hi - 1) * lo_val, c.size(m_var));
-    // algorithm: Let i be the most significant index where fixed bits disagree with val.
+                pdd hi = c.value(rational::power_of_two(sz - s.hi - 1) * hi_val, c.size(m_var));
-    // Set non-fixed values below i to 0.
+                fi.reset();
-    // If m_fixed[i] == l_true; then updating val to mask by fixed bits sufficies.
+                fi.interval = eval_interval::proper(lo, lo_val, hi, hi_val);
-    // Otherwise, the range above the disagreement has to be incremented.
+                fi.deps.push_back(dependency({ m_var, s }));
-    // Increment the non-fixed bits by 1
+                fi.bit_width = s.hi - s.lo + 1;
-    // The first non-fixed 0 position is set to 1, non-fixed positions below are set to 0.
+                fi.coeff = 1;
-    // If there are none, then the value is maximal and we return false.
-
-    bool fixed_bits::next(rational& val) {
-        if (m_fixed_slices.empty())
-            return true;
-        unsigned sz = c.size(m_var);
-        for (unsigned i = 0; i < sz; ++i)
-            m_bits[i] = val.get_bit(i);
-        unsigned i = sz;
-        for (; i-- > 0; )
-            if (m_fixed[i] != l_undef && m_fixed[i] != to_lbool(m_bits[i]))
-                break;
-        if (i == 0)       
-            return true;
-
-        for (unsigned j = 0; j < sz; ++j) {
-            if (m_fixed[j] != l_undef)
-                m_bits[j] = m_fixed[j] == l_true;
-            else if (j < i)
-                m_bits[j] = false;
-        }
-
-        if (m_fixed[i] == l_false) {
-            for (; i < sz; ++i) {
-                if (m_fixed[i] != l_undef)
-                    continue;
-                if (m_bits[i])
-                    m_bits[i] = false;
-                else {
-                    m_bits[i] = true;
-                    break;
-                }
-            }
-
-
-            CTRACE("bv", i == sz, display(tout << "overflow\n"));
-            // overflow
-            if (i == sz)
                 return false;
+            }
         }
-        val = 0;
-        for (unsigned i = sz; i-- > 0;)
-            val = val * 2 + rational(m_bits[i]);    
         return true;
     }
 
-    // explain the fixed bits ranges.
-    dependency_vector fixed_bits::explain() {
-        dependency_vector result;
-        for (auto const& slice : m_fixed_slices) 
-            result.push_back(dependency({ m_var, slice }));
-        return result;
-    }
-
     std::ostream& fixed_bits::display(std::ostream& out) const {
-        return out << "fixed bits: v" << m_var << " " << m_fixed << "\n";
+        for (auto const& s : m_fixed_slices)
+            out << s.hi << " " << s.lo << " " << s.value << "\n";  
+        return out;
     }
 
     /**

src/sat/smt/polysat/fixed_bits.h

@@ -13,6 +13,7 @@ Author:
 #pragma once
 #include "sat/smt/polysat/types.h"
 #include "sat/smt/polysat/constraints.h"
+#include "sat/smt/polysat/forbidden_intervals.h"
 #include "util/vector.h"
 
 namespace polysat {
@@ -31,9 +32,7 @@ namespace polysat {
     class fixed_bits {
         core& c;
         pvar m_var = null_var;
-        vector<fixed_slice> m_fixed_slices;
+        fixed_bits_vector m_fixed_slices;
-        svector<lbool> m_fixed;
-        bool_vector m_bits;
     public:
         fixed_bits(core& c) : c(c) {}
 
@@ -41,13 +40,9 @@ namespace polysat {
         void reset();
 
         // reset with fixed bits information for variable v
-        void reset(pvar v);
+        void init(pvar v);
 
-        // find then next value >= val that agrees with fixed bits, or false if none exists within the maximal value for val.
+        bool check(rational const& val, fi_record& fi);
-        bool next(rational& val);
-
-        // explain the fixed bits ranges.
-        dependency_vector explain();
 
         std::ostream& display(std::ostream& out) const;
     };

src/sat/smt/polysat/forbidden_intervals.h

@@ -26,6 +26,7 @@ namespace polysat {
         eval_interval               interval;
         vector<signed_constraint>   side_cond;
         vector<signed_constraint>   src;        // only units may have multiple src (as they can consist of contracted bit constraints)
+        vector<dependency>          deps;
         rational                    coeff;
         unsigned                    bit_width = 0;  // number of lower bits; TODO: should move this to viable::entry; where the coeff/bit-width is adapted accordingly
 
@@ -37,6 +38,7 @@ namespace polysat {
             side_cond.reset();
             src.reset();
             coeff.reset();
+            deps.reset();
             bit_width = 0;
         }
 

src/sat/smt/polysat/types.h

@@ -116,7 +116,7 @@ namespace polysat {
         return out << "v" << js.v << " at offset " << js.offset;
     }
 
-    using fixed_bits_vector = svector<fixed_slice>;
+    using fixed_bits_vector = vector<fixed_slice>;
 
     using dependency_vector = vector<dependency>;
     using constraint_or_dependency = std::variant<signed_constraint, dependency>;

src/sat/smt/polysat/viable.cpp

@@ -87,7 +87,7 @@ namespace polysat {
         m_explain.reset();
         m_var = v;
         m_num_bits = c.size(v);
-        m_fixed_bits.reset(v);
+        m_fixed_bits.init(v);
         init_overlaps(v);
         m_conflict = false;       
 
@@ -101,8 +101,9 @@ namespace polysat {
                 return find_t::empty;
 
             if (!n) {
-                if (refine_disequal_lin(v, lo) &&
+                if (check_fixed_bits(v, lo) && 
-                    refine_equal_lin(v, lo))
+                    check_disequal_lin(v, lo) &&
+                    check_equal_lin(v, lo))
                     return find_t::multiple;
                 ++rounds;
             }                      
@@ -128,11 +129,6 @@ namespace polysat {
     // 
 
     viable::entry* viable::find_overlap(rational& val) {
-        // disable fixed-bits until added to explanation trail.
-        if (false && !m_fixed_bits.next(val)) {
-            val = 0;
-            VERIFY(m_fixed_bits.next(val));
-        }
 
         entry* last = nullptr;
         for (auto const& [w, offset] : m_overlaps) {
@@ -217,7 +213,7 @@ namespace polysat {
         return nullptr;
     }
 
-    bool viable::refine_equal_lin(pvar v, rational const& val) {
+    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)
@@ -357,7 +353,22 @@ namespace polysat {
         return true;
     }
 
-    bool viable::refine_disequal_lin(pvar v, rational const& val) {
+    bool viable::check_fixed_bits(pvar v, rational const& val) {
+        // disable fixed bits for now
+        return true;
+
+        auto e = alloc_entry(v, constraint_id::null());
+        if (m_fixed_bits.check(val, *e)) {
+            m_alloc.push_back(e);
+            return true;
+        }
+        else {
+            intersect(v, e);
+            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)
@@ -490,14 +501,13 @@ namespace polysat {
 
         TRACE("bv", display_explain(tout));
 
-        result.append(m_fixed_bits.explain());
-
         if (last.e->interval.is_full()) {
             if (m_var != last.e->var)
                 result.push_back(offset_claim(m_var, { last.e->var, 0 }));
             for (auto const& sc : last.e->side_cond)
                 result.push_back(c.propagate(sc, c.explain_weak_eval(sc)));
-            result.push_back(c.get_dependency(last.e->constraint_index));
+            if (!last.e->constraint_index.is_null())
+                result.push_back(c.get_dependency(last.e->constraint_index));
             SASSERT(m_explain.size() == 1);
         }
 
@@ -506,14 +516,17 @@ namespace polysat {
             auto index = e.e->constraint_index;
             explain_overlap(e, after, result);
             after = e;
-            if (seen.contains(index.id))
+            if (!index.is_null() && seen.contains(index.id))
                 continue;
-            seen.insert(index.id);
+            if (!index.is_null())
+                seen.insert(index.id);
             if (m_var != e.e->var)
                 result.push_back(offset_claim(m_var, { e.e->var, 0 }));            
             for (auto const& sc : e.e->side_cond)
                 result.push_back(c.propagate(sc, c.explain_weak_eval(sc)));
-            result.push_back(c.get_dependency(index));
+            result.append(e.e->deps);
+            if (!index.is_null())
+                result.push_back(c.get_dependency(index));            
             if (e.e == last.e)
                 break;
         }

src/sat/smt/polysat/viable.h

@@ -128,9 +128,11 @@ namespace polysat {
 
         viable::entry* find_overlap(rational const& val, entry* entries);
 
-        bool refine_disequal_lin(pvar v, rational const& val);
+        bool check_disequal_lin(pvar v, rational const& val);
 
-        bool refine_equal_lin(pvar v, rational const& val);
+        bool check_equal_lin(pvar v, rational const& val);
+
+        bool check_fixed_bits(pvar v, rational const& val);
 
         
 

src/sat/smt/polysat_model.cpp

@@ -75,6 +75,9 @@ namespace polysat {
     void solver::collect_statistics(statistics& st) const {
         m_intblast.collect_statistics(st);
         m_core.collect_statistics(st);
+        st.update("polysat-conflicts", m_stats.m_num_conflicts);
+        st.update("polysat-axioms", m_stats.m_num_axioms);
+        st.update("polysat-propagations", m_stats.m_num_propagations);            
     }
 
     std::ostream& solver::display_justification(std::ostream& out, sat::ext_justification_idx idx) const {

src/sat/smt/polysat_solver.cpp

@@ -119,6 +119,7 @@ namespace polysat {
     }
 
     void solver::set_conflict(dependency_vector const& deps, char const* hint_info) {
+        ++m_stats.m_num_conflicts;
         if (inconsistent())
             return;
         auto [lits, eqs] = explain_deps(deps);
@@ -127,8 +128,8 @@ namespace polysat {
             hint = mk_proof_hint(hint_info, lits, eqs);
         auto ex = euf::th_explain::conflict(*this, lits, eqs, hint);
         TRACE("bv", tout << "conflict: " << lits << " ";
-        for (auto [a, b] : eqs) tout << ctx.bpp(a) << " == " << ctx.bpp(b) << " "; 
+                    for (auto [a, b] : eqs) tout << ctx.bpp(a) << " == " << ctx.bpp(b) << " "; 
-        tout << "\n"; s().display(tout));
+                    tout << "\n"; s().display(tout));
         validate_conflict(lits, eqs);
         ctx.set_conflict(ex);
     }
@@ -182,7 +183,6 @@ namespace polysat {
                 SASSERT(n1->get_root() == n2->get_root());
             });
         
-
         return { core, eqs };
     }
 
@@ -248,6 +248,7 @@ namespace polysat {
     // Everything goes over expressions/literals. polysat::core is not responsible for replaying expressions. 
     
     dependency solver::propagate(signed_constraint sc, dependency_vector const& deps, char const* hint_info) {
+        ++m_stats.m_num_propagations;
         TRACE("bv", sc.display(tout << "propagate ") << "\n");
         sat::literal lit = ctx.mk_literal(constraint2expr(sc));        
         if (s().value(lit) == l_true)
@@ -280,6 +281,7 @@ namespace polysat {
     }
 
     void solver::propagate(dependency const& d, bool sign, dependency_vector const& deps, char const* hint_info) {
+        ++m_stats.m_num_propagations;
         TRACE("bv", tout << "propagate " << d << " " << sign << "\n");
         auto [core, eqs] = explain_deps(deps);
         SASSERT(d.is_bool_var() || d.is_eq());
@@ -322,6 +324,7 @@ namespace polysat {
     }
 
     bool solver::add_axiom(char const* name, constraint_or_dependency const* begin, constraint_or_dependency const* end, bool is_redundant) {
+        ++m_stats.m_num_axioms;
         if (inconsistent())
             return false;
         TRACE("bv", tout << "add " << name << "\n");
@@ -357,6 +360,7 @@ namespace polysat {
     }
 
     void solver::add_axiom(char const* name, std::initializer_list<sat::literal> const& clause) {
+        ++m_stats.m_num_axioms;
         bool is_redundant = false;
         sat::literal_vector lits;
         proof_hint* hint = nullptr;

src/sat/smt/polysat_solver.h

@@ -74,6 +74,9 @@ namespace polysat {
 
         struct stats {
             void reset() { memset(this, 0, sizeof(stats)); }
+            unsigned m_num_conflicts;
+            unsigned m_num_propagations;
+            unsigned m_num_axioms;
             stats() { reset(); }
         };