intblast with lazy expansion of shl, ashr, lshr

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

src/ast/arith_decl_plugin.cpp

@@ -508,6 +508,19 @@ static bool is_const_op(decl_kind k) {
         //k == OP_0_PW_0_REAL;
 }
 
+symbol arith_decl_plugin::bv_symbol(decl_kind k) const {
+    switch (k) {
+    case OP_ARITH_BAND: return symbol("band");
+    case OP_ARITH_SHL: return symbol("shl");
+    case OP_ARITH_ASHR: return symbol("ashr");
+    case OP_ARITH_LSHR: return symbol("lshr");
+    default:
+        UNREACHABLE();
+    }
+    return symbol();
+}
+
+
 func_decl * arith_decl_plugin::mk_func_decl(decl_kind k, unsigned num_parameters, parameter const * parameters,
                                           unsigned arity, sort * const * domain, sort * range) {
     if (k == OP_NUM)
@@ -523,10 +536,10 @@ func_decl * arith_decl_plugin::mk_func_decl(decl_kind k, unsigned num_parameters
         return m_manager->mk_func_decl(symbol("divisible"), 1, &m_int_decl, m_manager->mk_bool_sort(), 
                                        func_decl_info(m_family_id, k, num_parameters, parameters));
     }
-    if (k == OP_ARITH_BAND) {
+    if (k == OP_ARITH_BAND || k == OP_ARITH_SHL || k == OP_ARITH_ASHR || k == OP_ARITH_LSHR) {
         if (arity != 2 || domain[0] != m_int_decl || domain[1] != m_int_decl || num_parameters != 1 || !parameters[0].is_int()) 
             m_manager->raise_exception("invalid bitwise and application. Expects integer parameter and two arguments of sort integer");
-        return m_manager->mk_func_decl(symbol("band"), 2, domain, m_int_decl,
+        return m_manager->mk_func_decl(bv_symbol(k), 2, domain, m_int_decl,
             func_decl_info(m_family_id, k, num_parameters, parameters));
     }
 
@@ -554,11 +567,11 @@ func_decl * arith_decl_plugin::mk_func_decl(decl_kind k, unsigned num_parameters
         return m_manager->mk_func_decl(symbol("divisible"), 1, &m_int_decl, m_manager->mk_bool_sort(), 
                                        func_decl_info(m_family_id, k, num_parameters, parameters));
     }
-    if (k == OP_ARITH_BAND) {
+    if (k == OP_ARITH_BAND  || k == OP_ARITH_SHL || k == OP_ARITH_ASHR || k == OP_ARITH_LSHR) {
         if (num_args != 2 || args[0]->get_sort() != m_int_decl || args[1]->get_sort() != m_int_decl || num_parameters != 1 || !parameters[0].is_int())
             m_manager->raise_exception("invalid bitwise and application. Expects integer parameter and two arguments of sort integer");
         sort* domain[2] = { m_int_decl, m_int_decl };
-        return m_manager->mk_func_decl(symbol("band"), 2, domain, m_int_decl,
+        return m_manager->mk_func_decl(bv_symbol(k), 2, domain, m_int_decl,
             func_decl_info(m_family_id, k, num_parameters, parameters));
     }
 

src/ast/arith_decl_plugin.h

@@ -72,6 +72,9 @@ enum arith_op_kind {
     OP_ATANH,
     // Bit-vector functions
     OP_ARITH_BAND,
+    OP_ARITH_SHL,
+    OP_ARITH_ASHR,
+    OP_ARITH_LSHR,
     // constants
     OP_PI,
     OP_E,
@@ -150,6 +153,8 @@ protected:
 
     bool        m_convert_int_numerals_to_real;
 
+    symbol bv_symbol(decl_kind k) const;
+
     func_decl * mk_func_decl(decl_kind k, bool is_real);
     void set_manager(ast_manager * m, family_id id) override;
     decl_kind fix_kind(decl_kind k, unsigned arity);
@@ -233,6 +238,14 @@ public:
    executed in different threads.
 */
 class arith_recognizers {
+    bool is_arith_op(expr const* n, decl_kind k, unsigned& sz, expr*& x, expr*& y) {
+        if (!is_app_of(n, arith_family_id, k))
+            return false;
+        x = to_app(n)->get_arg(0);
+        y = to_app(n)->get_arg(1);
+        sz = to_app(n)->get_parameter(0).get_int();
+        return true;
+    }
 public:
     family_id get_family_id() const { return arith_family_id; }
 
@@ -296,14 +309,13 @@ public:
     bool is_int_real(expr const * n) const { return is_int_real(n->get_sort()); }
 
     bool is_band(expr const* n) const { return is_app_of(n, arith_family_id, OP_ARITH_BAND); }
-    bool is_band(expr const* n, unsigned& sz, expr*& x, expr*& y) {
+    bool is_band(expr const* n, unsigned& sz, expr*& x, expr*& y) { return is_arith_op(n, OP_ARITH_BAND, sz, x, y); }
-        if (!is_band(n))
+    bool is_shl(expr const* n) const { return is_app_of(n, arith_family_id, OP_ARITH_SHL); }
-            return false;
+    bool is_shl(expr const* n, unsigned& sz, expr*& x, expr*& y) { return is_arith_op(n, OP_ARITH_SHL, sz, x, y); }
-        x = to_app(n)->get_arg(0);
+    bool is_lshr(expr const* n) const { return is_app_of(n, arith_family_id, OP_ARITH_LSHR); }
-        y = to_app(n)->get_arg(1);
+    bool is_lshr(expr const* n, unsigned& sz, expr*& x, expr*& y) { return is_arith_op(n, OP_ARITH_LSHR, sz, x, y); }
-        sz = to_app(n)->get_parameter(0).get_int();
+    bool is_ashr(expr const* n) const { return is_app_of(n, arith_family_id, OP_ARITH_ASHR); }
-        return true;
+    bool is_ashr(expr const* n, unsigned& sz, expr*& x, expr*& y) { return is_arith_op(n, OP_ARITH_ASHR, sz, x, y); }
-    }
 
     bool is_sin(expr const* n) const { return is_app_of(n, arith_family_id, OP_SIN); }
     bool is_cos(expr const* n) const { return is_app_of(n, arith_family_id, OP_COS); }
@@ -487,6 +499,9 @@ public:
     app * mk_power0(expr* arg1, expr* arg2) { return m_manager.mk_app(arith_family_id, OP_POWER0, arg1, arg2); }
 
     app* mk_band(unsigned n, expr* arg1, expr* arg2) { parameter p(n); expr* args[2] = { arg1, arg2 }; return m_manager.mk_app(arith_family_id, OP_ARITH_BAND, 1, &p, 2, args); }
+    app* mk_shl(unsigned n, expr* arg1, expr* arg2) { parameter p(n); expr* args[2] = { arg1, arg2 }; return m_manager.mk_app(arith_family_id, OP_ARITH_SHL, 1, &p, 2, args); }
+    app* mk_ashr(unsigned n, expr* arg1, expr* arg2) { parameter p(n); expr* args[2] = { arg1, arg2 }; return m_manager.mk_app(arith_family_id, OP_ARITH_ASHR, 1, &p, 2, args); }
+    app* mk_lshr(unsigned n, expr* arg1, expr* arg2) { parameter p(n); expr* args[2] = { arg1, arg2 }; return m_manager.mk_app(arith_family_id, OP_ARITH_LSHR, 1, &p, 2, args); }
 
     app * mk_sin(expr * arg) { return m_manager.mk_app(arith_family_id, OP_SIN, arg); }
     app * mk_cos(expr * arg) { return m_manager.mk_app(arith_family_id, OP_COS, arg); }

src/ast/rewriter/arith_rewriter.cpp

@@ -92,6 +92,9 @@ br_status arith_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * c
     case OP_COSH: SASSERT(num_args == 1); st = mk_cosh_core(args[0], result); break;
     case OP_TANH: SASSERT(num_args == 1); st = mk_tanh_core(args[0], result); break;
     case OP_ARITH_BAND: SASSERT(num_args == 2);  st = mk_band_core(f->get_parameter(0).get_int(), args[0], args[1], result); break;
+    case OP_ARITH_SHL: SASSERT(num_args == 2);  st = mk_shl_core(f->get_parameter(0).get_int(), args[0], args[1], result); break;
+    case OP_ARITH_ASHR: SASSERT(num_args == 2);  st = mk_ashr_core(f->get_parameter(0).get_int(), args[0], args[1], result); break;
+    case OP_ARITH_LSHR: SASSERT(num_args == 2);  st = mk_lshr_core(f->get_parameter(0).get_int(), args[0], args[1], result); break;
     default: st = BR_FAILED; break;
     }
     CTRACE("arith_rewriter", st != BR_FAILED, tout << st << ": " << mk_pp(f, m);
@@ -1350,6 +1353,98 @@ app* arith_rewriter_core::mk_power(expr* x, rational const& r, sort* s) {
     return y;
 }
 
+br_status arith_rewriter::mk_shl_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result) {
+    numeral x, y, N;
+    bool is_num_x = m_util.is_numeral(arg1, x);
+    bool is_num_y = m_util.is_numeral(arg2, y);
+    N = rational::power_of_two(sz);
+    if (is_num_x) 
+        x = mod(x, N);
+    if (is_num_y)
+        y = mod(y, N);
+    if (is_num_x && is_num_y) {
+        if (y >= sz) 
+            result = m_util.mk_int(0);
+        else 
+            result = m_util.mk_int(mod(x * rational::power_of_two(y.get_unsigned()), N));
+        return BR_DONE;
+    }
+    if (is_num_y) {
+        if (y >= sz) 
+            result = m_util.mk_int(0);
+        else 
+            result = m_util.mk_mod(m_util.mk_mul(arg1, m_util.mk_int(rational::power_of_two(y.get_unsigned()))), m_util.mk_int(N));
+        return BR_REWRITE1;
+    }
+    if (is_num_x && x == 0) {
+        result = m_util.mk_int(0);
+        return BR_DONE;
+    }        
+    return BR_FAILED;
+}
+br_status arith_rewriter::mk_ashr_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result) {
+    numeral x, y, N;
+    bool is_num_x = m_util.is_numeral(arg1, x);
+    bool is_num_y = m_util.is_numeral(arg2, y);
+    N = rational::power_of_two(sz);
+    if (is_num_x) 
+        x = mod(x, N);
+    if (is_num_y)
+        y = mod(y, N);
+    if (is_num_x && x == 0) {
+        result = m_util.mk_int(0);
+        return BR_DONE;
+    }
+    if (is_num_x && is_num_y) {
+        bool signx = x >= N/2;
+        rational d = div(x, rational::power_of_two(y.get_unsigned()));
+        SASSERT(y >= 0);
+        if (signx) {
+            if (y >= sz)
+                result = m_util.mk_int(N-1);
+            else
+                result = m_util.mk_int(d);
+        }
+        else {
+            if (y >= sz) 
+                result = m_util.mk_int(0);
+            else 
+                result = m_util.mk_int(mod(d - rational::power_of_two(sz - y.get_unsigned()), N));
+        }
+        return BR_DONE;
+    }
+    return BR_FAILED;
+}
+
+br_status arith_rewriter::mk_lshr_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result) {
+    numeral x, y, N;
+    bool is_num_x = m_util.is_numeral(arg1, x);
+    bool is_num_y = m_util.is_numeral(arg2, y);
+    N = rational::power_of_two(sz);
+    if (is_num_x) 
+        x = mod(x, N);
+    if (is_num_y)
+        y = mod(y, N);
+    if (is_num_x && x == 0) {
+        result = m_util.mk_int(0);
+        return BR_DONE;
+    }
+    if (is_num_y && y == 0) {
+        result = arg1;
+        return BR_DONE;
+    }
+    if (is_num_x && is_num_y) {
+        if (y >= sz)
+            result = m_util.mk_int(N-1);
+        else {
+            rational d = div(x, rational::power_of_two(y.get_unsigned()));
+            result = m_util.mk_int(d);
+        }
+        return BR_DONE;
+    }
+    return BR_FAILED;
+}
+
 br_status arith_rewriter::mk_band_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result) {
     numeral x, y, N;
     bool is_num_x = m_util.is_numeral(arg1, x);
@@ -1375,6 +1470,14 @@ br_status arith_rewriter::mk_band_core(unsigned sz, expr* arg1, expr* arg2, expr
         result = m_util.mk_int(r);
         return BR_DONE;
     }
+    if (is_num_x && (x + 1).is_power_of_two()) {
+        result = m_util.mk_mod(arg2, m_util.mk_int(x + 1));
+        return BR_REWRITE1;
+    }
+    if (is_num_y && (y + 1).is_power_of_two()) {
+        result = m_util.mk_mod(arg1, m_util.mk_int(y + 1));
+        return BR_REWRITE1;
+    }
     return BR_FAILED;
 }
 

src/ast/rewriter/arith_rewriter.h

@@ -160,6 +160,9 @@ public:
     br_status mk_rem_core(expr * arg1, expr * arg2, expr_ref & result);
     br_status mk_power_core(expr* arg1, expr* arg2, expr_ref & result);
     br_status mk_band_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result);
+    br_status mk_shl_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result);
+    br_status mk_lshr_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result);
+    br_status mk_ashr_core(unsigned sz, expr* arg1, expr* arg2, expr_ref& result);
     void mk_div(expr * arg1, expr * arg2, expr_ref & result) {
         if (mk_div_core(arg1, arg2, result) == BR_FAILED)
             result = m.mk_app(get_fid(), OP_DIV, arg1, arg2);

src/math/lp/lp_api.h

@@ -108,7 +108,7 @@ namespace lp_api {
         unsigned m_gomory_cuts;
         unsigned m_assume_eqs;
         unsigned m_branch;
-        unsigned m_band_axioms;
+        unsigned m_bv_axioms;
         stats() { reset(); }
         void reset() {
             memset(this, 0, sizeof(*this));
@@ -129,7 +129,7 @@ namespace lp_api {
             st.update("arith-gomory-cuts", m_gomory_cuts);
             st.update("arith-assume-eqs", m_assume_eqs);
             st.update("arith-branch", m_branch);
-            st.update("arith-band-axioms", m_band_axioms);
+            st.update("arith-bv-axioms", m_bv_axioms);
         }
     };
 

src/sat/smt/arith_axioms.cpp

@@ -205,58 +205,117 @@ namespace arith {
         add_clause(dgez, neg);
     }
 
-    bool solver::check_band_term(app* n) {
+    bool solver::check_bv_term(app* n) {
         unsigned sz;
-        expr* x, * y;
+        expr* _x, * _y;
         if (!ctx.is_relevant(expr2enode(n)))
             return true;
-        VERIFY(a.is_band(n, sz, x, y));
         expr_ref vx(m), vy(m),vn(m);
-        if (!get_value(expr2enode(x), vx) || !get_value(expr2enode(y), vy) || !get_value(expr2enode(n), vn)) {
+        rational valn, valx, valy;
+        bool is_int;
+        VERIFY(a.is_band(n, sz, _x, _y) || a.is_shl(n, sz, _x, _y) || a.is_ashr(n, sz, _x, _y) || a.is_lshr(n, sz, _x, _y));
+        if (!get_value(expr2enode(_x), vx) || !get_value(expr2enode(_y), vy) || !get_value(expr2enode(n), vn)) {
             IF_VERBOSE(2, verbose_stream() << "could not get value of " << mk_pp(n, m) << "\n");
             found_unsupported(n);
             return true;
         }
-        rational valn, valx, valy;
-        bool is_int;
         if (!a.is_numeral(vn, valn, is_int) || !is_int || !a.is_numeral(vx, valx, is_int) || !is_int || !a.is_numeral(vy, valy, is_int) || !is_int) {
             IF_VERBOSE(2, verbose_stream() << "could not get value of " << mk_pp(n, m) << "\n");
             found_unsupported(n);
             return true;
         }
-        // verbose_stream() << "band: " << mk_pp(n, m) << " " << valn << " := " << valx << "&" << valy << "\n";
         rational N = rational::power_of_two(sz);
         valx = mod(valx, N);
         valy = mod(valy, N);
+        expr_ref x(a.mk_mod(_x, a.mk_int(N)), m);
+        expr_ref y(a.mk_mod(_y, a.mk_int(N)), m);
         SASSERT(0 <= valn && valn < N);
-
+        
         // x mod 2^{i + 1} >= 2^i means the i'th bit is 1.
         auto bitof = [&](expr* x, unsigned i) { 
             expr_ref r(m);
             r = a.mk_ge(a.mk_mod(x, a.mk_int(rational::power_of_two(i+1))), a.mk_int(rational::power_of_two(i)));
             return mk_literal(r);
         };
-        for (unsigned i = 0; i < sz; ++i) {
+
-            bool xb = valx.get_bit(i);
+        if (a.is_band(n)) {
-            bool yb = valy.get_bit(i);
+            IF_VERBOSE(2, verbose_stream() << "band: " << mk_bounded_pp(n, m) << " " << valn << " := " << valx << "&" << valy << "\n");
-            bool nb = valn.get_bit(i);
+            for (unsigned i = 0; i < sz; ++i) {
-            if (xb && yb && !nb)
+                bool xb = valx.get_bit(i);
-                add_clause(~bitof(x, i), ~bitof(y, i), bitof(n, i));
+                bool yb = valy.get_bit(i);
-            else if (nb && !xb)
+                bool nb = valn.get_bit(i);
-                add_clause(~bitof(n, i), bitof(x, i));
+                if (xb && yb && !nb)
-            else if (nb && !yb)
+                    add_clause(~bitof(x, i), ~bitof(y, i), bitof(n, i));
-                add_clause(~bitof(n, i), bitof(y, i));
+                else if (nb && !xb)
-            else
+                    add_clause(~bitof(n, i), bitof(x, i));
-                continue;
+                else if (nb && !yb)
+                    add_clause(~bitof(n, i), bitof(y, i));
+                else
+                    continue;
+                return false;
+            }
+        }
+        if (a.is_shl(n)) {
+            SASSERT(valy >= 0);
+            if (valy >= sz || valy == 0)
+                return true;
+            unsigned k = valy.get_unsigned();
+            sat::literal eq = eq_internalize(n, a.mk_mod(a.mk_mul(_x, a.mk_int(rational::power_of_two(k))), a.mk_int(N)));
+            if (s().value(eq) == l_true)
+                return true;            
+            add_clause(~eq_internalize(y, a.mk_int(k)), eq);
+            IF_VERBOSE(2, verbose_stream() << "shl: " << mk_bounded_pp(n, m) << " " << valn << " := " << valx << " << " << valy << "\n");
+            return false;
+        }
+        if (a.is_lshr(n)) {
+            SASSERT(valy >= 0);
+            if (valy >= sz || valy == 0)
+                return true;
+            unsigned k = valy.get_unsigned();
+            sat::literal eq = eq_internalize(n, a.mk_idiv(x, a.mk_int(rational::power_of_two(k))));
+            if (s().value(eq) == l_true)
+                return true;            
+            add_clause(~eq_internalize(y, a.mk_int(k)), eq);
+            IF_VERBOSE(2, verbose_stream() << "lshr: " << mk_bounded_pp(n, m) << " " << valn << " := " << valx << " >>l " << valy << "\n");
+            return false;
+        }
+        if (a.is_ashr(n)) {
+            SASSERT(valy >= 0);
+            if (valy >= sz || valy == 0)
+                return true;
+            unsigned k = valy.get_unsigned();
+            sat::literal signx = mk_literal(a.mk_ge(x, a.mk_int(N/2)));
+            sat::literal eq;
+            expr* xdiv2k;
+            switch (s().value(signx)) {
+            case l_true:
+                // x < 0 & y = k -> n = (x div 2^k - 2^{N-k}) mod 2^N
+                xdiv2k = a.mk_idiv(x, a.mk_int(rational::power_of_two(k)));
+                eq = eq_internalize(n, a.mk_mod(a.mk_add(xdiv2k, a.mk_int(-rational::power_of_two(sz - k))), a.mk_int(N)));
+                if (s().value(eq) == l_true)
+                    return true;
+                break;
+            case l_false:
+                // x >= 0 & y = k -> n = x div 2^k
+                xdiv2k = a.mk_idiv(x, a.mk_int(rational::power_of_two(k)));
+                eq = eq_internalize(n, xdiv2k);
+                if (s().value(eq) == l_true)
+                    return true;
+                break;
+            case l_undef:
+                ctx.mark_relevant(signx);
+                return false;
+            }
+            add_clause(~eq_internalize(y, a.mk_int(k)), ~signx, eq); 
             return false;
         }
         return true;
     }
 
-    bool solver::check_band_terms() {
+    bool solver::check_bv_terms() {
-        for (app* n : m_band_terms) {
+        for (app* n : m_bv_terms) {
-            if (!check_band_term(n)) {
+            if (!check_bv_term(n)) {
-                ++m_stats.m_band_axioms;
+                ++m_stats.m_bv_axioms;
                 return false;
             }
         }
@@ -268,15 +327,43 @@ namespace arith {
     * x&y <= x
     * x&y <= y
     */
-    void solver::mk_band_axiom(app* n) {
+    void solver::mk_bv_axiom(app* n) {
         unsigned sz;
-        expr* x, * y;
+        expr* _x, * _y;
-        VERIFY(a.is_band(n, sz, x, y));
+        VERIFY(a.is_band(n, sz, _x, _y) || a.is_shl(n, sz, _x, _y) || a.is_ashr(n, sz, _x, _y) || a.is_lshr(n, sz, _x, _y));
         rational N = rational::power_of_two(sz);
-        add_clause(mk_literal(a.mk_ge(n, a.mk_int(0))));
+        expr_ref x(a.mk_mod(_x, a.mk_int(N)), m);
-        add_clause(mk_literal(a.mk_le(n, a.mk_int(N - 1))));
+        expr_ref y(a.mk_mod(_y, a.mk_int(N)), m);
-        add_clause(mk_literal(a.mk_le(n, a.mk_mod(x, a.mk_int(N)))));
+
-        add_clause(mk_literal(a.mk_le(n, a.mk_mod(y, a.mk_int(N)))));
+        if (a.is_band(n)) {
+            add_clause(mk_literal(a.mk_ge(n, a.mk_int(0))));
+            add_clause(mk_literal(a.mk_le(n, a.mk_int(N - 1))));
+            add_clause(mk_literal(a.mk_le(n, x)));
+            add_clause(mk_literal(a.mk_le(n, y)));
+        }
+        else if (a.is_shl(n)) {
+            // y >= sz => n = 0
+            // y = 0 => n = x
+            add_clause(~mk_literal(a.mk_ge(y, a.mk_int(sz))), mk_literal(m.mk_eq(n, a.mk_int(0))));
+            add_clause(~mk_literal(a.mk_eq(y, a.mk_int(0))), mk_literal(m.mk_eq(n, x)));
+        }
+        else if (a.is_lshr(n)) {
+            // y >= sz => n = 0
+            // y = 0 => n = x
+            add_clause(~mk_literal(a.mk_ge(y, a.mk_int(sz))), mk_literal(m.mk_eq(n, a.mk_int(0))));
+            add_clause(~mk_literal(a.mk_eq(y, a.mk_int(0))), mk_literal(m.mk_eq(n, x)));
+        }
+        else if (a.is_ashr(n)) {
+            // y >= sz & x < 2^{sz-1} => n = 0
+            // y >= sz & x >= 2^{sz-1} => n = -1
+            // y = 0 => n = x
+            auto signx = mk_literal(a.mk_ge(x, a.mk_int(N/2)));
+            add_clause(~mk_literal(a.mk_ge(a.mk_mod(y, a.mk_int(N)), a.mk_int(sz))), signx, mk_literal(m.mk_eq(n, a.mk_int(0))));
+            add_clause(~mk_literal(a.mk_ge(a.mk_mod(y, a.mk_int(N)), a.mk_int(sz))), ~signx, mk_literal(m.mk_eq(n, a.mk_int(N-1))));
+            add_clause(~mk_literal(a.mk_eq(a.mk_mod(y, a.mk_int(N)), a.mk_int(0))), mk_literal(m.mk_eq(n, x)));            
+        }
+        else
+            UNREACHABLE();
     }
 
     void solver::mk_bound_axioms(api_bound& b) {

src/sat/smt/arith_internalize.cpp

@@ -252,10 +252,10 @@ namespace arith {
                     st.to_ensure_var().push_back(n1);
                     st.to_ensure_var().push_back(n2);
                 }
-                else if (a.is_band(n)) {
+                else if (a.is_band(n) || a.is_shl(n) || a.is_ashr(n) || a.is_lshr(n)) {
-                    m_band_terms.push_back(to_app(n));
+                    m_bv_terms.push_back(to_app(n));
-                    mk_band_axiom(to_app(n));
+                    ctx.push(push_back_vector(m_bv_terms));
-                    ctx.push(push_back_vector(m_band_terms));
+                    mk_bv_axiom(to_app(n));
                     ensure_arg_vars(to_app(n));
                 }
                 else if (!a.is_div0(n) && !a.is_mod0(n) && !a.is_idiv0(n) && !a.is_rem0(n) && !a.is_power0(n)) {

src/sat/smt/arith_solver.cpp

@@ -1053,7 +1053,7 @@ namespace arith {
         if (!check_delayed_eqs()) 
             return sat::check_result::CR_CONTINUE;
 
-        if (!int_undef && !check_band_terms())
+        if (!int_undef && !check_bv_terms())
             return sat::check_result::CR_CONTINUE;
 
         if (ctx.get_config().m_arith_ignore_int && int_undef)

src/sat/smt/arith_solver.h

@@ -214,7 +214,7 @@ namespace arith {
         expr* m_not_handled = nullptr;
         ptr_vector<app>        m_underspecified;
         ptr_vector<expr>       m_idiv_terms;
-        ptr_vector<app>        m_band_terms;
+        ptr_vector<app>        m_bv_terms;
         vector<ptr_vector<api_bound> > m_use_list;        // bounds where variables are used.
 
         // attributes for incremental version:
@@ -318,7 +318,7 @@ namespace arith {
         void mk_bound_axioms(api_bound& b);
         void mk_bound_axiom(api_bound& b1, api_bound& b2);
         void mk_power0_axioms(app* t, app* n);
-        void mk_band_axiom(app* n);
+        void mk_bv_axiom(app* n);
         void flush_bound_axioms();
         void add_farkas_clause(sat::literal l1, sat::literal l2);
 
@@ -410,8 +410,8 @@ namespace arith {
         bool  check_delayed_eqs();
         lbool check_lia();
         lbool check_nla();
-        bool check_band_terms();
+        bool check_bv_terms();
-        bool check_band_term(app* n);
+        bool check_bv_term(app* n);
         void add_lemmas();
         void propagate_nla();
         void add_equality(lpvar v, rational const& k, lp::explanation const& exp);

src/sat/smt/intblast_solver.cpp

@@ -656,24 +656,58 @@ namespace intblast {
             break;
         }
         case OP_BSHL: {
-            expr* x = arg(0), * y = umod(e, 1);
+            if (!a.is_numeral(arg(0)) && !a.is_numeral(arg(1))) 
-            r = a.mk_int(0);
+                r = a.mk_shl(bv.get_bv_size(e), arg(0),arg(1));
-            for (unsigned i = 0; i < bv.get_bv_size(e); ++i)
+            else {
-                r = m.mk_ite(m.mk_eq(y, a.mk_int(i)), a.mk_mul(x, a.mk_int(rational::power_of_two(i))), r);            
+                expr* x = arg(0), * y = umod(e, 1);
+                r = a.mk_int(0);
+                IF_VERBOSE(2, verbose_stream() << "shl " << mk_bounded_pp(e, m) << " " << bv.get_bv_size(e) << "\n");
+                for (unsigned i = 0; i < bv.get_bv_size(e); ++i)
+                    r = m.mk_ite(m.mk_eq(y, a.mk_int(i)), a.mk_mul(x, a.mk_int(rational::power_of_two(i))), r);   
+            }
             break;
         }
         case OP_BNOT:
             r = bnot(arg(0));
             break;
-        case OP_BLSHR: {
+        case OP_BLSHR: 
-            expr* x = arg(0), * y = umod(e, 1);
+            if (!a.is_numeral(arg(0)) && !a.is_numeral(arg(1)))  
-            r = a.mk_int(0);
+                r = a.mk_lshr(bv.get_bv_size(e), arg(0), arg(1));
-            for (unsigned i = 0; i < bv.get_bv_size(e); ++i)
+            else {
-                r = m.mk_ite(m.mk_eq(y, a.mk_int(i)), a.mk_idiv(x, a.mk_int(rational::power_of_two(i))), r);
+                expr* x = arg(0), * y = umod(e, 1);
+                r = a.mk_int(0);
+                IF_VERBOSE(2, verbose_stream() << "lshr " << mk_bounded_pp(e, m) << " " << bv.get_bv_size(e) << "\n");
+                for (unsigned i = 0; i < bv.get_bv_size(e); ++i)
+                    r = m.mk_ite(m.mk_eq(y, a.mk_int(i)), a.mk_idiv(x, a.mk_int(rational::power_of_two(i))), r);
+            }
+            break;
+        case OP_BASHR: 
+            if (!a.is_numeral(arg(1)))
+                r = a.mk_ashr(bv.get_bv_size(e), arg(0), arg(1));
+            else {
+                
+                //
+                // ashr(x, y)
+                // if y = k & x >= 0 -> x / 2^k   
+                // if y = k & x < 0  -> (x / 2^k) - 2^{N-k}
+                //
+                unsigned sz = bv.get_bv_size(e);
+                rational N = bv_size(e);
+                expr* x = umod(e, 0), *y = umod(e, 1);
+                expr* signx = a.mk_ge(x, a.mk_int(N / 2));
+                r = m.mk_ite(signx, a.mk_int(- 1), a.mk_int(0));
+                IF_VERBOSE(1, verbose_stream() << "ashr " << mk_bounded_pp(e, m) << " " << bv.get_bv_size(e) << "\n");
+                for (unsigned i = 0; i < sz; ++i) {
+                    expr* d = a.mk_idiv(x, a.mk_int(rational::power_of_two(i)));              
+                    r = m.mk_ite(m.mk_eq(y, a.mk_int(i)),
+                                 m.mk_ite(signx, a.mk_add(d, a.mk_int(- rational::power_of_two(sz-i))), d),
+                                 r);
+                }
+            }
             break;
-        }                     
         case OP_BOR: {
             // p | q := (p + q) - band(p, q)
+            IF_VERBOSE(2, verbose_stream() << "bor " << mk_bounded_pp(e, m) << " " << bv.get_bv_size(e) << "\n");
             r = arg(0);
             for (unsigned i = 1; i < args.size(); ++i)
                 r = a.mk_sub(a.mk_add(r, arg(i)), a.mk_band(bv.get_bv_size(e), r, arg(i)));
@@ -683,12 +717,14 @@ namespace intblast {
             r = bnot(band(args));
             break;
         case OP_BAND:
+            IF_VERBOSE(2, verbose_stream() << "band " << mk_bounded_pp(e, m) << " " << bv.get_bv_size(e) << "\n");
             r = band(args);
             break;
         case OP_BXNOR:
         case OP_BXOR: {
             // p ^ q := (p + q) - 2*band(p, q);
             unsigned sz = bv.get_bv_size(e);
+            IF_VERBOSE(2, verbose_stream() << "bxor " << bv.get_bv_size(e) << "\n");
             r = arg(0);
             for (unsigned i = 1; i < args.size(); ++i) {
                 expr* q = arg(i);
@@ -698,25 +734,6 @@ namespace intblast {
                 r = bnot(r);
             break;
         }
-        case OP_BASHR: {
-            //
-            // ashr(x, y)
-            // if y = k & x >= 0 -> x / 2^k   
-            // if y = k & x < 0  -> (x / 2^k) - 1 + 2^{N-k}
-            //
-            unsigned sz = bv.get_bv_size(e);
-            rational N = bv_size(e);
-            expr* x = umod(e, 0), *y = umod(e, 1);
-            expr* signx = a.mk_ge(x, a.mk_int(N / 2));
-            r = m.mk_ite(signx, a.mk_int(- 1), a.mk_int(0));
-            for (unsigned i = 0; i < sz; ++i) {
-                expr* d = a.mk_idiv(x, a.mk_int(rational::power_of_two(i)));              
-                r = m.mk_ite(m.mk_eq(y, a.mk_int(i)),
-                    m.mk_ite(signx, a.mk_add(d, a.mk_int(- rational::power_of_two(sz-i))), d),
-                    r);
-            }
-            break;
-        }
         case OP_ZERO_EXT:
             bv_expr = e->get_arg(0);
             r = umod(bv_expr, 0);