First step towards explaining single bits

src/math/polysat/CMakeLists.txt

@@ -8,6 +8,7 @@ z3_add_component(polysat
     constraint.cpp
     constraint_manager.cpp
     eq_explain.cpp
+    fixed_bits.cpp
     forbidden_intervals.cpp
     inference_logger.cpp
     justification.cpp

src/math/polysat/constraint.h

@@ -17,6 +17,7 @@ Author:
 #include "math/polysat/interval.h"
 #include "math/polysat/assignment.h"
 #include "math/polysat/univariate/univariate_solver.h"
+#include "util/tbv.h"
 #include <iostream>
 
 namespace polysat {
@@ -84,6 +85,7 @@ namespace polysat {
         bool is_currently_false(solver const& s, bool is_positive) const { return is_currently_true(s, !is_positive); }
 
         virtual void narrow(solver& s, bool is_positive, bool first) = 0;
+        virtual void propagate_bits(solver& s, bool is_positive) {}
         /**
          * If possible, produce a lemma that contradicts the given assignment.
          * This method should not modify the solver's search state.

src/math/polysat/fixed_bits.cpp

@@ -0,0 +1,222 @@
+/*++
+Copyright (c) 2022 Microsoft Corporation
+
+Module Name:
+
+    fixed_bits
+
+Abstract:
+
+    Associates every pdd with the set of already fixed bits and justifications for this
+
+--*/
+
+#include "math/polysat/fixed_bits.h"
+#include "math/polysat/solver.h"
+
+namespace polysat {
+
+    tbv_manager& fixed_bits::get_manager(unsigned sz){
+          m_tbv_managers.reserve(sz + 1);
+          if (!m_tbv_managers[sz])
+              m_tbv_managers.set(sz, alloc(tbv_manager, sz));
+          return *m_tbv_managers[sz];
+    }
+
+    tbv_manager& fixed_bits::get_manager(const pdd& v) {
+          return get_manager(v.power_of_2());
+    }
+
+    tbv_ref& fixed_bits::get_tbv(pvar v, unsigned sz) {
+        if (m_var_to_tbv.size() <= v) {
+            m_var_to_tbv.reserve(v + 1);
+            auto& manager = get_manager(sz);
+            m_var_to_tbv[v] = tbv_ref(manager, manager.allocate());
+            return *m_var_to_tbv[v];
+        }
+        auto& old_manager = m_var_to_tbv[v]->manager();
+        if (old_manager.num_tbits() >= sz)
+            return *(m_var_to_tbv[v]);
+        tbv* old_tbv = m_var_to_tbv[v]->detach();
+        auto& new_manager = get_manager(sz);
+        tbv* new_tbv = new_manager.allocate();
+        old_manager.copy(*new_tbv, *old_tbv); // Copy the lower bits to the new (larger) tbv
+        old_manager.deallocate(old_tbv);
+        m_var_to_tbv[v] = tbv_ref(new_manager, new_tbv);
+        return *m_var_to_tbv[v];
+    }
+
+    tbv_ref& fixed_bits::get_tbv(const pdd& p) {
+        SASSERT(p.is_var());
+        return get_tbv(p.var(), p.power_of_2());
+    }
+
+    tbit fixed_bits::get_value(const pdd& p, unsigned idx) {
+        SASSERT(p.is_var());
+        return get_tbv(p)[idx];
+    }
+
+    bool fixed_bits::fix_value(solver& s, const pdd& p, unsigned idx, tbit val, constraint* c, bit_dependency& dep) {
+        SASSERT(val != BIT_x); // We don't use don't-cares
+        SASSERT(p.is_var());
+        if (val == BIT_z)
+            return true;
+        tbv_ref& tbv = get_tbv(p);
+        tbit curr_val = tbv[idx];
+
+        if (val == curr_val)
+            return true;
+
+        auto& m = tbv.manager();
+
+        if (curr_val == BIT_z) {
+            m.set(*tbv, idx, val);
+            m_tbv_to_justification[std::pair(tbv.get(), idx)] = bit_justication(c, (bit_dependency&&)std::move(dep));
+            return true;
+        }
+        SASSERT((curr_val == BIT_1 && val == BIT_0) || (curr_val == BIT_0 && val == BIT_1));
+
+        return false;
+
+    }
+
+    void fixed_bits::clear_value(const pdd& p, unsigned idx) {
+        SASSERT(p.is_var());
+        tbv_ref& tbv = get_tbv(p);
+        auto& m = tbv.manager();
+        m.set(*tbv, idx, BIT_z);
+
+        SASSERT(m_tbv_to_justification.contains(std::pair(tbv.get(), idx)));
+        m_tbv_to_justification[std::pair(tbv.get(), idx)] = bit_justication();
+    }
+
+#define COUNT(DOWN, TO_COUNT) \
+    do { \
+    unsigned sz = ref.num_tbits(); \
+    unsigned least = 0; \
+    for (; least < sz; least++) { \
+        if (ref[((DOWN) ? sz - least - 1 : least)] != (TO_COUNT)) \
+            break; \
+    } \
+    if (least == sz) \
+        return { sz, sz }; /* For sure TO_COUNT */ \
+    unsigned most = least; \
+    for (; most < sz; most++) { \
+        if (ref[((DOWN) ? sz - most - 1 : most)] == ((TO_COUNT) == BIT_0 ? BIT_1 : BIT_0)) \
+            break; \
+    } \
+    return { least, most }; /* There are between "least" and "most" leading/trailing TO_COUNT */ \
+    } while(false)
+
+    std::pair<unsigned, unsigned> fixed_bits::leading_zeros(const tbv_ref& ref) { COUNT(false, BIT_0); }
+    std::pair<unsigned, unsigned> fixed_bits::trailing_zeros(const tbv_ref& ref) { COUNT(true, BIT_0); }
+    std::pair<unsigned, unsigned> fixed_bits::leading_ones(const tbv_ref& ref) { COUNT(false, BIT_1); }
+    std::pair<unsigned, unsigned> fixed_bits::trailing_ones(const tbv_ref& ref) { COUNT(true, BIT_1); }
+
+    std::pair<rational, rational> fixed_bits::min_max(const tbv_ref& ref) {
+        unsigned sz = ref.num_tbits();
+        rational least(0);
+        rational most(0);
+
+        for (unsigned i = 0; i < sz; i++) {
+            tbit v = ref[i];
+            least *= 2;
+            most *= 2;
+            if (v == BIT_1) {
+                least++;
+                most++;
+            }
+            else if (v == BIT_z)
+                most++;
+        }
+
+        return { least, most };
+    }
+
+    // multiplication: (1*p0 + 2*p1 + 4*p2 + 8*p3 + ...) * (1*q0 + 2*q1 + 4*q2 + 8*q3 + ...) =
+    // = 1 * (p0 q0) + 2 * (p0 q1 + p1 q0) + 4 * (p0 q2 + p1 q1 + p2 q0) + 8 * (p0 q3 + p1 q2 + p2 q1 + p3 q0) + ...
+    // maintains
+    void fixed_bits::multiply(tbv_ref& in_out, const tbv_ref& in2) {
+        auto m= in_out.manager();
+        m_aux_values.reserve(m.num_tbits());
+
+        unsigned min_bit_value = 0; // The value of the current bit assuming all unknown bits are 0
+        unsigned max_bit_value = 0; // The value of the current bit assuming all unknown bits are 1
+
+        // TODO: Check: Is the performance too worse? It is O(k^2)
+        for (unsigned i = 0; i < m.num_tbits(); i++) {
+            for (unsigned x = 0, y = i; x <= i; x++, y--) {
+                tbit bit1 = in_out[x];
+                tbit bit2 = in2[y];
+
+                if (bit1 == BIT_1 && bit2 == BIT_1) {
+                    min_bit_value++; // we get two 1
+                    max_bit_value++;
+                }
+                else if (bit1 != BIT_0 && bit2 != BIT_0) {
+                    max_bit_value++; // we could get two 1
+                }
+            }
+            if (min_bit_value == max_bit_value) {
+                // We know the value of this bit
+                // As we might access in_out in some later iteration again we first write to aux-list
+                m_aux_values[i] = min_bit_value & 1 ? BIT_1 : BIT_0;
+            }
+            else {
+                m_aux_values[i] = BIT_z;
+            }
+            // Subtract one; shift this to the next higher bit as "carry value"
+            min_bit_value >>= 1;
+            max_bit_value >>= 1;
+        }
+
+        // Copy aux to result tbv
+        for (unsigned i = 0; i < m.num_tbits(); i++) {
+            m.set(*in_out, i, (tbit)m_aux_values[i]);
+        }
+    }
+
+    // similar to multiplying
+    void fixed_bits::add(tbv_ref& in_out, const tbv_ref& in2) {
+        auto m= in_out.manager();
+
+        unsigned min_bit_value = 0;
+        unsigned max_bit_value = 0;
+
+        for (unsigned i = 0; i < m.num_tbits(); i++) {
+            tbit bit1 = in_out[i];
+            tbit bit2 = in2[i];
+            if (bit1 == BIT_1 && bit2 == BIT_1) {
+                min_bit_value++;
+                max_bit_value++;
+            }
+            else if (bit1 != BIT_0 && bit2 != BIT_0) {
+                max_bit_value++;
+            }
+
+            if (min_bit_value == max_bit_value)
+                // for addition we don't need previous values so we can directly write to the output variable
+                m.set(*in_out, i, min_bit_value & 1 ? BIT_1 : BIT_0);
+            else
+                m.set(*in_out, i, BIT_z);
+
+            min_bit_value >>= 1;
+            max_bit_value >>= 1;
+        }
+    }
+
+    tbv_ref fixed_bits::eval(const pdd& p) {
+        tbv_manager m = get_manager(p);
+        unsigned sz = m.num_tbits();
+        tbv_ref ret = tbv_ref(m, m.allocate(0ull));
+        for (const dd::pdd_monomial& s : p) {
+            SASSERT(!s.coeff.is_zero());
+            tbv_ref sum = tbv_ref(m, m.allocate(s.coeff));
+            for (pvar fac : s.vars) {
+                multiply(sum, get_tbv(fac, sz));
+            }
+            add(ret, sum);
+        }
+        return ret;
+    }
+}

src/math/polysat/fixed_bits.h

@@ -0,0 +1,102 @@
+/*++
+Copyright (c) 2022 Microsoft Corporation
+
+Module Name:
+
+    fixed_bits
+
+Abstract:
+
+    Associates every pdd with the set of already fixed bits and justifications for this
+
+--*/
+#pragma once
+
+#include "types.h"
+#include "util/hash.h"
+#include "util/optional.h"
+#include "util/tbv.h"
+
+
+namespace polysat {
+
+    class solver;
+
+    using bit_dependency = vector<std::pair<pdd, unsigned>>;
+
+    struct bit_justication {
+        constraint* m_constraint = nullptr;
+
+        // variables + resp., bit-index
+        // (a variable might occur multiple times if more bits are relevant)
+        bit_dependency m_dependencies;
+
+    public:
+        bit_justication(constraint *pRaint, bit_dependency vector) = default;
+        bit_justication(constraint* c) : m_constraint(c) { }
+        bit_justication(constraint* c, bit_dependency&& dep) : m_constraint(c), m_dependencies(dep) { }
+    };
+
+    class fixed_bits {
+
+        solver& m_solver;
+
+        scoped_ptr_vector<tbv_manager> m_tbv_managers;
+
+        char_vector m_aux_values;
+
+        //using pdd_to_tbv_key = optional<pdd>;
+        //using pdd_to_tbv_eq = default_eq<pdd_to_tbv_key>;
+        //struct pdd_to_tbv_hash {
+        //    unsigned operator()(pdd_to_tbv_key const& args) const {
+        //        return args ? args->hash() : 0;
+        //    }
+        //};
+        //using pdd_to_tbv_map = map<pdd_to_tbv_key, tbv_ref, pdd_to_tbv_hash, pdd_to_tbv_eq>;
+
+        using tbv_to_justification_key = std::pair<tbv*, unsigned>;
+        using tbv_to_justification_eq = default_eq<tbv_to_justification_key>;
+        struct tbv_to_justification_hash {
+            unsigned operator()(tbv_to_justification_key const& args) const {
+                return combine_hash((unsigned)args.first, args.second);
+            }
+        };
+        using tbv_to_justification_map = map<tbv_to_justification_key, bit_justication, tbv_to_justification_hash, tbv_to_justification_eq>;
+
+        vector<optional<tbv_ref>> m_var_to_tbv;
+        tbv_to_justification_map m_tbv_to_justification;
+
+        tbv_manager& get_manager(const pdd& v);
+        tbv_manager& get_manager(unsigned sz);
+
+        void add(tbv_ref& in_out, const tbv_ref& in2);
+        void multiply(tbv_ref& in_out, const tbv_ref& in2);
+
+        tbv_ref& get_tbv(pvar v, unsigned sz);
+        tbv_ref& get_tbv(const pdd& p);
+
+    public:
+
+        fixed_bits(solver& s) : m_solver(s) {}
+
+        // #count [min; max]
+        static std::pair<unsigned, unsigned> leading_zeros(const tbv_ref& ref);
+        static std::pair<unsigned, unsigned> trailing_zeros(const tbv_ref& ref);
+        static std::pair<unsigned, unsigned> leading_ones(const tbv_ref& ref);
+        static std::pair<unsigned, unsigned> trailing_ones(const tbv_ref& ref);
+        static std::pair<rational, rational> min_max(const tbv_ref& ref);
+
+        tbit get_value(const pdd& p, unsigned idx); // More efficient than calling "eval" and accessing the returned tbv elements
+        bool fix_value(solver& s, const pdd& p, unsigned idx, tbit val, constraint* c, bit_dependency& dep);
+        bool fix_value(solver& s, const pdd& p, unsigned idx, tbit val, constraint* c, std::pair<pdd, unsigned> v1, std::pair<pdd, unsigned> v2) {
+            bit_dependency dep(2);
+            dep.push_back(v1);
+            dep.push_back(v2);
+            return fix_value(s, p, idx, val, c, dep);
+        }
+        void clear_value(const pdd& p, unsigned idx);
+
+        tbv_ref eval(const pdd& p);
+
+    };
+}

src/math/polysat/op_constraint.cpp

@@ -113,6 +113,9 @@ namespace polysat {
         if (first)
             activate(s);
 
+        if (!propagate_bits(s, is_positive))
+            return; // conflict
+
         if (clause_ref lemma = produce_lemma(s, s.assignment()))
             s.add_clause(*lemma);
         
@@ -120,6 +123,20 @@ namespace polysat {
             s.set_conflict(signed_constraint(this, is_positive));
     }
 
+    bool op_constraint::propagate_bits(solver& s, bool is_positive) {
+        switch (m_op) {
+        case code::lshr_op:
+            return propagate_bits_lshr(s, is_positive);
+        case code::shl_op:
+            return propagate_bits_shl(s, is_positive);
+        case code::and_op:
+            return propagate_bits_and(s, is_positive);
+        default:
+            NOT_IMPLEMENTED_YET();
+            return false;
+        }
+    }
+
     /**
      * Produce lemmas that contradict the given assignment.
      *
@@ -335,6 +352,39 @@ namespace polysat {
         return l_undef;
     }
 
+    bool op_constraint::propagate_bits_shl(solver& s, bool is_positive) {
+        tbv_ref p_val = s.m_fixed_bits.eval(m_p);
+        tbv_ref q_val = s.m_fixed_bits.eval(m_q);
+        tbv_ref r_val = s.m_fixed_bits.eval(m_r);
+        unsigned sz = m_p.power_of_2();
+
+        auto [shift_min, shift_max] = s.m_fixed_bits.min_max(q_val);
+
+        unsigned shift_min_u, shift_max_u;
+
+        if (!shift_min.is_unsigned() || shift_min.get_unsigned() > sz)
+            shift_min_u = sz;
+        else
+            shift_min_u = shift_min.get_unsigned();
+
+        if (!shift_max.is_unsigned() || shift_max.get_unsigned() > sz)
+            shift_max_u = sz;
+        else
+            shift_max_u = shift_max.get_unsigned();
+
+        SASSERT(shift_max_u <= sz);
+        SASSERT(shift_min_u <= shift_max_u);
+
+        for (unsigned i = 0; i < shift_min_u; i++) {
+            if (!s.m_fixed_bits.fix_value(s, m_r, i, BIT_0, this, s.))
+                return false;
+        }
+        for (unsigned i = shift_min_u; i < sz; i++) {
+            propagate_bit(s, m_r.var(), i, p_val[i - shift_min_u]);
+        }
+
+    }
+
     void op_constraint::activate_and(solver& s) {
         auto x = p(), y = q();
         if (x.is_val())
@@ -448,6 +498,31 @@ namespace polysat {
         return l_undef;
     }
 
+    bool op_constraint::propagate_bits_and(solver& s, bool is_positive){
+        tbv_ref p_val = s.m_fixed_bits.eval(m_p);
+        tbv_ref q_val = s.m_fixed_bits.eval(m_q);
+        tbv_ref r_val = s.m_fixed_bits.eval(m_r);
+        unsigned sz = m_p.power_of_2();
+
+        for (int i = 0; i < sz; i++) {
+            tbit bp = p_val[i];
+            tbit bq = q_val[i];
+            tbit br = r_val[i];
+
+            // TODO: Propagate from the result to the operands. e.g., 110... = xx1... & yyy...
+            // TODO: ==> x = 111..., y = 110...
+            if (bp == BIT_0 || bq == BIT_0) {
+                if (!s.m_fixed_bits.fix_value(s, m_r, i, BIT_0, this, std::pair(m_p, i), std::pair(m_q, i)))
+                    return false;
+            }
+            else if (bp == BIT_1 && bq == BIT_1) {
+                if (!s.m_fixed_bits.fix_value(s, m_r, i, BIT_1, this, std::pair(m_p, i), std::pair(m_q, i)))
+                    return false;
+            }
+        }
+        return true;
+    }
+
     void op_constraint::add_to_univariate_solver(solver& s, univariate_solver& us, unsigned dep, bool is_positive) const {
         auto p_coeff = s.subst(p()).get_univariate_coefficients();
         auto q_coeff = s.subst(q()).get_univariate_coefficients();

src/math/polysat/op_constraint.h

@@ -31,9 +31,9 @@ namespace polysat {
         friend class constraint_manager;
 
         code m_op;
-        pdd m_p;
+        pdd m_p; // operand1
-        pdd m_q;
+        pdd m_q; // operand2
-        pdd m_r;
+        pdd m_r; // result
 
         op_constraint(constraint_manager& m, code c, pdd const& p, pdd const& q, pdd const& r);
         lbool eval(pdd const& p, pdd const& q, pdd const& r) const;
@@ -41,12 +41,15 @@ namespace polysat {
 
         clause_ref lemma_lshr(solver& s, assignment const& a);
         static lbool eval_lshr(pdd const& p, pdd const& q, pdd const& r);
+        bool propagate_bits_lshr(solver& s, bool is_positive);
 
         clause_ref lemma_shl(solver& s, assignment const& a);
         static lbool eval_shl(pdd const& p, pdd const& q, pdd const& r);
+        bool propagate_bits_shl(solver& s, bool is_positive);
 
         clause_ref lemma_and(solver& s, assignment const& a);
         static lbool eval_and(pdd const& p, pdd const& q, pdd const& r);
+        bool propagate_bits_and(solver& s, bool is_positive);
 
         std::ostream& display(std::ostream& out, char const* eq) const;
 
@@ -64,6 +67,7 @@ namespace polysat {
         lbool eval() const override;
         lbool eval(assignment const& a) const override;
         void narrow(solver& s, bool is_positive, bool first) override;
+        bool propagate_bits(solver& s, bool is_positive) override;
         virtual clause_ref produce_lemma(solver& s, assignment const& a, bool is_positive) override;
         unsigned hash() const override;
         bool operator==(constraint const& other) const override;

src/math/polysat/solver.h

@@ -24,6 +24,7 @@ Author:
 #include "math/polysat/constraint.h"
 #include "math/polysat/constraint_manager.h"
 #include "math/polysat/clause_builder.h"
+#include "math/polysat/fixed_bits.h"
 #include "math/polysat/simplify_clause.h"
 #include "math/polysat/simplify.h"
 #include "math/polysat/restart.h"
@@ -146,6 +147,7 @@ namespace polysat {
         viable                   m_viable;   // viable sets per variable
         viable_fallback          m_viable_fallback;   // fallback for viable, using bitblasting over univariate constraints
         linear_solver            m_linear_solver;
+        fixed_bits               m_fixed_bits;
         conflict                 m_conflict;
         simplify_clause          m_simplify_clause;
         simplify                 m_simplify;

src/util/tbv.h

@@ -132,8 +132,9 @@ class tbv_ref {
     tbv_manager& mgr;
     tbv* d;
 public:
-    tbv_ref(tbv_manager& mgr):mgr(mgr),d(nullptr) {}
+    tbv_ref(tbv_manager& mgr) : mgr(mgr), d(nullptr) {}
-    tbv_ref(tbv_manager& mgr, tbv* d):mgr(mgr),d(d) {}
+    tbv_ref(tbv_manager& mgr, tbv* d) : mgr(mgr), d(d) {}
+    tbv_ref(tbv_ref&& d) : mgr(d.mgr), d(d.detach()) {}
     ~tbv_ref() {
         if (d) mgr.deallocate(d);
     }
@@ -144,8 +145,11 @@ public:
     }
     tbv& operator*() { return *d; }
     tbv* operator->() { return d; }
-    tbv* get() { return d; }
+    tbit operator[](unsigned idx) const { return (*d)[idx]; }
+    tbv* get() const { return d; }
     tbv* detach() { tbv* result = d; d = nullptr; return result; }
+    tbv_manager& manager() const { return mgr; }
+    unsigned num_tbits() const { return mgr.num_tbits(); }
 };