add smul over and underflow predicate

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/math/polysat/CMakeLists.txt

@@ -17,7 +17,7 @@ z3_add_component(polysat
     saturation.cpp
     search_state.cpp
     simplify.cpp
-    smul_ovfl_constraint.cpp
+    smul_fl_constraint.cpp
     solver.cpp
     ule_constraint.cpp
     viable.cpp

src/math/polysat/constraint.cpp

@@ -19,7 +19,7 @@ Author:
 #include "math/polysat/log_helper.h"
 #include "math/polysat/ule_constraint.h"
 #include "math/polysat/mul_ovfl_constraint.h"
-#include "math/polysat/smul_ovfl_constraint.h"
+#include "math/polysat/smul_fl_constraint.h"
 #include "math/polysat/op_constraint.h"
 
 namespace polysat {
@@ -239,7 +239,11 @@ namespace polysat {
     }
 
     signed_constraint constraint_manager::smul_ovfl(pdd const& a, pdd const& b) {
-        return { dedup(alloc(smul_ovfl_constraint, *this, a, b)), true };
+        return { dedup(alloc(smul_fl_constraint, *this, a, b, true)), true };
+    }
+    
+    signed_constraint constraint_manager::smul_udfl(pdd const& a, pdd const& b) {
+        return { dedup(alloc(smul_fl_constraint, *this, a, b, false)), true };
     }
 
     signed_constraint constraint_manager::lshr(pdd const& p, pdd const& q, pdd const& r) {
@@ -296,12 +300,12 @@ namespace polysat {
         return *dynamic_cast<mul_ovfl_constraint const*>(this);
     }
 
-    smul_ovfl_constraint& constraint::to_smul_ovfl() {
+    smul_fl_constraint& constraint::to_smul_fl() {
-        return *dynamic_cast<smul_ovfl_constraint*>(this);
+        return *dynamic_cast<smul_fl_constraint*>(this);
     }
 
-    smul_ovfl_constraint const& constraint::to_smul_ovfl() const {
+    smul_fl_constraint const& constraint::to_smul_fl() const {
-        return *dynamic_cast<smul_ovfl_constraint const*>(this);
+        return *dynamic_cast<smul_fl_constraint const*>(this);
     }
 
     op_constraint& constraint::to_op() {

src/math/polysat/constraint.h

@@ -20,12 +20,12 @@ Author:
 
 namespace polysat {
 
-    enum ckind_t { ule_t, mul_ovfl_t, smul_ovfl_t, op_t };
+    enum ckind_t { ule_t, mul_ovfl_t, smul_fl_t, op_t };
 
     class constraint;
     class ule_constraint;
     class mul_ovfl_constraint;
-    class smul_ovfl_constraint;
+    class smul_fl_constraint;
     class op_constraint;
     class signed_constraint;
 
@@ -100,6 +100,7 @@ namespace polysat {
         signed_constraint slt(pdd const& a, pdd const& b);
         signed_constraint mul_ovfl(pdd const& p, pdd const& q);
         signed_constraint smul_ovfl(pdd const& p, pdd const& q);
+        signed_constraint smul_udfl(pdd const& p, pdd const& q);
         signed_constraint bit(pdd const& p, unsigned i);
         signed_constraint lshr(pdd const& p, pdd const& q, pdd const& r);
         signed_constraint band(pdd const& p, pdd const& q, pdd const& r);
@@ -141,7 +142,7 @@ namespace polysat {
         friend class clause;
         friend class ule_constraint;
         friend class mul_ovfl_constraint;
-        friend class smul_ovfl_constraint;
+        friend class smul_fl_constraint;
         friend class op_constraint;
 
         // constraint_manager* m_manager;
@@ -170,7 +171,7 @@ namespace polysat {
         virtual bool is_diseq() const { return false; }
         bool is_ule() const { return m_kind == ckind_t::ule_t; }
         bool is_mul_ovfl() const { return m_kind == ckind_t::mul_ovfl_t; }
-        bool is_smul_ovfl() const { return m_kind == ckind_t::smul_ovfl_t; }
+        bool is_smul_fl() const { return m_kind == ckind_t::smul_fl_t; }
         bool is_op() const { return m_kind == ckind_t::op_t; }
         ckind_t kind() const { return m_kind; }
         virtual std::ostream& display(std::ostream& out, lbool status) const = 0;
@@ -190,8 +191,8 @@ namespace polysat {
         ule_constraint const& to_ule() const;
         mul_ovfl_constraint& to_mul_ovfl();
         mul_ovfl_constraint const& to_mul_ovfl() const;
-        smul_ovfl_constraint& to_smul_ovfl();
+        smul_fl_constraint& to_smul_fl();
-        smul_ovfl_constraint const& to_smul_ovfl() const;
+        smul_fl_constraint const& to_smul_fl() const;
         op_constraint& to_op();
         op_constraint const& to_op() const;
         unsigned_vector& vars() { return m_vars; }

src/math/polysat/smul_ovfl_constraint.cpp

@@ -15,8 +15,8 @@ Author:
 
 namespace polysat {
 
-    smul_ovfl_constraint::smul_ovfl_constraint(constraint_manager& m, pdd const& p, pdd const& q):
+    smul_ovfl_constraint::smul_ovfl_constraint(constraint_manager& m, pdd const& p, pdd const& q, bool is_overflow):
-        constraint(m, ckind_t::smul_ovfl_t), m_p(p), m_q(q) {
+        constraint(m, ckind_t::smul_ovfl_t), m_is_overflow(is_overflow), m_p(p), m_q(q) {
         simplify();
         m_vars.append(m_p.free_vars());
         for (auto v : m_q.free_vars())
@@ -45,13 +45,36 @@ namespace polysat {
     }
 
     std::ostream& smul_ovfl_constraint::display(std::ostream& out) const {
+        if (m_is_overflow)
             return out << "sovfl*(" << m_p << ", " << m_q << ")";
+        else
+            return out << "sudfl*(" << m_p << ", " << m_q << ")";            
     }
 
+    /**
+     * TODO - verify the rules for small bit-widths.
+     * 
+     *  sovfl(p,q) => p >= 2, q >= 2
+     *  sovfl(p,q) => p >s 0 <=> q >s 0
+     *  sovfl(p,q) & p >s 0 => p*q < 0 or ovfl(p,q)
+     *  sovfl(p,q) & p <s 0 => p*q < 0 or ovfl(-p,-q)
+
+     * ~sovfl(p,q) & p >s 0 = q >s 0 =>  q > 0 => ~ovfl(p,q) & p*q >=s 0
+     * smul_noovfl(p,q) => sign(p) != sign(q) or p'*q' < 2^{K-1}
+
+     * sudfl(p, q) => p >= 2, q >= 2
+     * sudfl(p, q) => p >s 0 xor q >s 0
+     * sudfl(p, q) & p >s 0 => p*q > 0 or ovfl(p, -q)
+     * sudfl(p, q) & q >s 0 => p*q > 0 or ovfl(-p, q)
+     *
+     * ~sudfl(p, q) & p >s 0 & q <s 0 => ~ovfl(p, -q) & p*q <s 0 
+     * ~sudfl(p, q) & p <s 0 & q >s 0 => ~ovfl(-p, q) & p*q <s 0 
+     */
     void smul_ovfl_constraint::narrow(solver& s, bool is_positive, bool first) {
         if (!first)
             return;
         signed_constraint sc(this, is_positive);
+        if (m_is_overflow) {
             if (is_positive) {
                 s.add_clause(~sc, s.ule(2, p()), false);
                 s.add_clause(~sc, s.ule(2, q()), false);
@@ -61,13 +84,29 @@ namespace polysat {
                 s.add_clause(~sc, s.sgt(p(), 0),  s.slt(p()*q(), 0), s.mul_ovfl(-p(), -q()), false);
             }
             else {
-            // smul_noovfl(p,q) => sign(p) != sign(q) or p'*q' < 2^{K-1}
                 s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), ~s.mul_ovfl(p(), q()), false);
                 s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), ~s.slt(p()*q(), 0), false);
                 s.add_clause(~sc, ~s.slt(p(), 0), ~s.slt(q(), 0), ~s.mul_ovfl(-p(), -q()), false);
                 s.add_clause(~sc, ~s.slt(p(), 0), ~s.slt(q(), 0), ~s.slt((-p())*(-q()), 0), false);
             }
         }
+        else {
+            if (is_positive) {
+                s.add_clause(~sc, s.ule(2, p()), false);
+                s.add_clause(~sc, s.ule(2, q()), false);
+                s.add_clause(~sc, ~s.sgt(p(), 0), ~s.sgt(q(), 0), false);
+                s.add_clause(~sc, s.sgt(q(), 0), s.sgt(p(), 0), false);
+                s.add_clause(~sc, ~s.sgt(p(), 0), s.sgt(p()*q(), 0), s.mul_ovfl(p(), -q()), false);
+                s.add_clause(~sc, ~s.sgt(q(), 0), s.sgt(p()*q(), 0), s.mul_ovfl(-p(), q()), false);
+            }
+            else {
+                s.add_clause(sc, ~s.sgt(p(), 0), ~s.slt(q(), 0), s.mul_ovfl(p(), -q()), false);
+                s.add_clause(sc, ~s.sgt(p(), 0), ~s.slt(q(), 0), s.slt(p()*q(), 0), false);
+                s.add_clause(sc, ~s.slt(p(), 0), ~s.sgt(q(), 0), s.mul_ovfl(-p(), q()), false);
+                s.add_clause(sc, ~s.slt(p(), 0), ~s.sgt(q(), 0), s.slt(p()*q(), 0), false);                
+            }                
+        }
+    }
 
     unsigned smul_ovfl_constraint::hash() const {
     	return mk_mix(p().hash(), q().hash(), kind());

src/math/polysat/smul_ovfl_constraint.h

@@ -20,11 +20,12 @@ namespace polysat {
     class smul_ovfl_constraint final : public constraint {
         friend class constraint_manager;
 
+        bool m_is_overflow;
         pdd  m_p;
         pdd  m_q;
 
         void simplify();
-        smul_ovfl_constraint(constraint_manager& m, pdd const& p, pdd const& q);
+        smul_ovfl_constraint(constraint_manager& m, pdd const& p, pdd const& q, bool is_overflow);
         
     public:
         ~smul_ovfl_constraint() override {}

src/math/polysat/solver.h

@@ -56,7 +56,7 @@ namespace polysat {
         friend class constraint;
         friend class ule_constraint;
         friend class mul_ovfl_constraint;
-        friend class smul_ovfl_constraint;
+        friend class smul_fl_constraint;
         friend class op_constraint;
         friend class signed_constraint;
         friend class clause;
@@ -344,6 +344,7 @@ namespace polysat {
         signed_constraint mul_ovfl(pdd const& p, pdd const& q) { return m_constraints.mul_ovfl(p, q); }
         signed_constraint mul_ovfl(rational const& p, pdd const& q) { return mul_ovfl(q.manager().mk_val(p), q); }
         signed_constraint smul_ovfl(pdd const& p, pdd const& q) { return m_constraints.smul_ovfl(p, q); }
+        signed_constraint smul_udfl(pdd const& p, pdd const& q) { return m_constraints.smul_udfl(p, q); }
         signed_constraint bit(pdd const& p, unsigned i) { return m_constraints.bit(p, i); }
 
         /** Create and activate polynomial constraints. */

src/sat/smt/bv_polysat.cpp

@@ -33,8 +33,10 @@ namespace bv {
     void solver::internalize_polysat(app* a) {
 
         std::function<polysat::pdd(polysat::pdd, polysat::pdd)> bin;
+        std::function<polysat::signed_constraint(polysat::pdd, polysat::pdd)> binc;
 
 #define mk_binary(a, fn) bin = fn; polysat_binary(a, bin);
+#define mk_binaryc(a, fn) binc = fn; polysat_binaryc(a, binc);
 
         switch (to_app(a)->get_decl_kind()) {
         case OP_BMUL:             mk_binary(a, [&](pdd const& p, pdd const& q) { return p * q; }); break;
@@ -56,8 +58,9 @@ namespace bv {
         case OP_UGT:              polysat_le<false, false, true>(a); break;
         case OP_SGT:              polysat_le<true,  false, true>(a); break;
 
-        case OP_BUMUL_NO_OVFL:    polysat_umul_noovfl(a); break;
+        case OP_BUMUL_NO_OVFL:    mk_binaryc(a, [&](pdd const& p, pdd const& q) { return m_polysat.mul_ovfl(p, q); }); break;            
-        case OP_BSMUL_NO_OVFL:    polysat_smul_noovfl(a); break;
+        case OP_BSMUL_NO_OVFL:    mk_binaryc(a, [&](pdd const& p, pdd const& q) { return m_polysat.smul_ovfl(p, q); }); break;
+        case OP_BSMUL_NO_UDFL:    mk_binaryc(a, [&](pdd const& p, pdd const& q) { return m_polysat.smul_udfl(p, q); }); break;
             
         case OP_BUDIV_I:          polysat_div_rem_i(a, true); break;       
         case OP_BUREM_I:          polysat_div_rem_i(a, false); break;
@@ -76,7 +79,6 @@ namespace bv {
         case OP_BSDIV:            
         case OP_BSREM:            
         case OP_BSMOD:     
-        case OP_BSMUL_NO_UDFL:    
         case OP_BSDIV_I:            
         case OP_BSREM_I:                        
         case OP_BSMOD_I:
@@ -102,19 +104,10 @@ namespace bv {
         }
     }
 
-    void solver::polysat_umul_noovfl(app* e) {
+    void solver::polysat_binaryc(app* e, std::function<polysat::signed_constraint(polysat::pdd, polysat::pdd)>& fn) {
         auto p = expr2pdd(e->get_arg(0));
         auto q = expr2pdd(e->get_arg(1));
-        auto sc = ~m_polysat.mul_ovfl(p, q);
+        auto sc = ~fn(p, q);
-        sat::literal lit = expr2literal(e);
-        atom* a = mk_atom(lit.var());
-        a->m_sc = sc;
-    }
-
-    void solver::polysat_smul_noovfl(app* e) {
-        auto p = expr2pdd(e->get_arg(0));
-        auto q = expr2pdd(e->get_arg(1));
-        auto sc = ~m_polysat.smul_ovfl(p, q);
         sat::literal lit = expr2literal(e);
         atom* a = mk_atom(lit.var());
         a->m_sc = sc;

src/sat/smt/bv_solver.h

@@ -280,8 +280,7 @@ namespace bv {
         void polysat_neg(app* a);
         void polysat_num(app* a);
         void polysat_mkbv(app* a);
-        void polysat_umul_noovfl(app* e);
+        void polysat_binaryc(app* e, std::function<polysat::signed_constraint(polysat::pdd, polysat::pdd)>& fn);
-        void polysat_smul_noovfl(app* e);
         void polysat_div_rem_i(app* e, bool is_div);
         void polysat_div_rem(app* e, bool is_div);
         void polysat_bit2bool(atom* a, expr* e, unsigned idx);