diff --git a/src/ast/arith_decl_plugin.cpp b/src/ast/arith_decl_plugin.cpp
index 8317b37c39b..f09daaf7541 100644
--- a/src/ast/arith_decl_plugin.cpp
+++ b/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));
}
diff --git a/src/ast/arith_decl_plugin.h b/src/ast/arith_decl_plugin.h
index 25c4977e9f2..308bc1326aa 100644
--- a/src/ast/arith_decl_plugin.h
+++ b/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 @@ class arith_decl_plugin : public decl_plugin {
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 @@ class arith_decl_plugin : public decl_plugin {
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 @@ class arith_recognizers {
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) {
- if (!is_band(n))
- 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;
- }
+ bool is_band(expr const* n, unsigned& sz, expr*& x, expr*& y) { return is_arith_op(n, OP_ARITH_BAND, sz, x, y); }
+ bool is_shl(expr const* n) const { return is_app_of(n, arith_family_id, OP_ARITH_SHL); }
+ bool is_shl(expr const* n, unsigned& sz, expr*& x, expr*& y) { return is_arith_op(n, OP_ARITH_SHL, sz, x, y); }
+ bool is_lshr(expr const* n) const { return is_app_of(n, arith_family_id, OP_ARITH_LSHR); }
+ bool is_lshr(expr const* n, unsigned& sz, expr*& x, expr*& y) { return is_arith_op(n, OP_ARITH_LSHR, sz, x, y); }
+ bool is_ashr(expr const* n) const { return is_app_of(n, arith_family_id, OP_ARITH_ASHR); }
+ 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 @@ class arith_util : public arith_recognizers {
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); }
diff --git a/src/ast/rewriter/arith_rewriter.cpp b/src/ast/rewriter/arith_rewriter.cpp
index ddfabed8380..d8a06ada65b 100644
--- a/src/ast/rewriter/arith_rewriter.cpp
+++ b/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;
}
diff --git a/src/ast/rewriter/arith_rewriter.h b/src/ast/rewriter/arith_rewriter.h
index 548ab80dbed..6066c9eb419 100644
--- a/src/ast/rewriter/arith_rewriter.h
+++ b/src/ast/rewriter/arith_rewriter.h
@@ -160,6 +160,9 @@ class arith_rewriter : public poly_rewriter<arith_rewriter_core> {
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);
diff --git a/src/math/lp/lp_api.h b/src/math/lp/lp_api.h
index 0eb8b6b3713..021501ecd25 100644
--- a/src/math/lp/lp_api.h
+++ b/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);
}
};
diff --git a/src/sat/smt/arith_axioms.cpp b/src/sat/smt/arith_axioms.cpp
index f004422a652..ae67783ebd8 100644
--- a/src/sat/smt/arith_axioms.cpp
+++ b/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);
- bool yb = valy.get_bit(i);
- bool nb = valn.get_bit(i);
- if (xb && yb && !nb)
- add_clause(~bitof(x, i), ~bitof(y, i), bitof(n, i));
- else if (nb && !xb)
- add_clause(~bitof(n, i), bitof(x, i));
- else if (nb && !yb)
- add_clause(~bitof(n, i), bitof(y, i));
- else
- continue;
+
+ if (a.is_band(n)) {
+ IF_VERBOSE(2, verbose_stream() << "band: " << mk_bounded_pp(n, m) << " " << valn << " := " << valx << "&" << valy << "\n");
+ for (unsigned i = 0; i < sz; ++i) {
+ bool xb = valx.get_bit(i);
+ bool yb = valy.get_bit(i);
+ bool nb = valn.get_bit(i);
+ if (xb && yb && !nb)
+ add_clause(~bitof(x, i), ~bitof(y, i), bitof(n, i));
+ else if (nb && !xb)
+ add_clause(~bitof(n, i), bitof(x, i));
+ 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() {
- for (app* n : m_band_terms) {
- if (!check_band_term(n)) {
- ++m_stats.m_band_axioms;
+ bool solver::check_bv_terms() {
+ for (app* n : m_bv_terms) {
+ if (!check_bv_term(n)) {
+ ++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;
- VERIFY(a.is_band(n, sz, x, y));
+ expr* _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))));
- add_clause(mk_literal(a.mk_le(n, a.mk_int(N - 1))));
- 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)))));
+ expr_ref x(a.mk_mod(_x, a.mk_int(N)), m);
+ expr_ref y(a.mk_mod(_y, a.mk_int(N)), m);
+
+ 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) {
diff --git a/src/sat/smt/arith_internalize.cpp b/src/sat/smt/arith_internalize.cpp
index decd49019e4..ed49092fd6a 100644
--- a/src/sat/smt/arith_internalize.cpp
+++ 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)) {
- m_band_terms.push_back(to_app(n));
- mk_band_axiom(to_app(n));
- ctx.push(push_back_vector(m_band_terms));
+ else if (a.is_band(n) || a.is_shl(n) || a.is_ashr(n) || a.is_lshr(n)) {
+ m_bv_terms.push_back(to_app(n));
+ ctx.push(push_back_vector(m_bv_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)) {
diff --git a/src/sat/smt/arith_solver.cpp b/src/sat/smt/arith_solver.cpp
index eff25bc4a3b..078515184c1 100644
--- a/src/sat/smt/arith_solver.cpp
+++ b/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)
diff --git a/src/sat/smt/arith_solver.h b/src/sat/smt/arith_solver.h
index 022dbeaead6..cbf4206a9cf 100644
--- a/src/sat/smt/arith_solver.h
+++ b/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_band_term(app* n);
+ bool check_bv_terms();
+ bool check_bv_term(app* n);
void add_lemmas();
void propagate_nla();
void add_equality(lpvar v, rational const& k, lp::explanation const& exp);
diff --git a/src/sat/smt/intblast_solver.cpp b/src/sat/smt/intblast_solver.cpp
index 9d03d0ad086..fed43e2173c 100644
--- a/src/sat/smt/intblast_solver.cpp
+++ b/src/sat/smt/intblast_solver.cpp
@@ -656,24 +656,58 @@ namespace intblast {
break;
}
case OP_BSHL: {
- expr* x = arg(0), * y = umod(e, 1);
- r = a.mk_int(0);
- 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);
+ if (!a.is_numeral(arg(0)) && !a.is_numeral(arg(1)))
+ r = a.mk_shl(bv.get_bv_size(e), arg(0),arg(1));
+ else {
+ 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: {
- expr* x = arg(0), * y = umod(e, 1);
- r = a.mk_int(0);
- 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);
+ case OP_BLSHR:
+ if (!a.is_numeral(arg(0)) && !a.is_numeral(arg(1)))
+ r = a.mk_lshr(bv.get_bv_size(e), arg(0), arg(1));
+ else {
+ 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);