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intblast with lazy expansion of shl, ashr, lshr

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2023-12-16 15:12:57 -08:00
parent 50e0fd3ba6
commit d0a59f3740
10 changed files with 321 additions and 83 deletions
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21
src/ast/arith_decl_plugin.cpp
View file

@ -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));
}

31
src/ast/arith_decl_plugin.h
View file

@ -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) {
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 @@ 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); }

103
src/ast/rewriter/arith_rewriter.cpp
View file

@ -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;
}

3
src/ast/rewriter/arith_rewriter.h
View file

@ -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);

4
src/math/lp/lp_api.h
View file

@ -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);
}
};

149
src/sat/smt/arith_axioms.cpp
View file

@ -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) {

8
src/sat/smt/arith_internalize.cpp
View file

@ -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)) {

2
src/sat/smt/arith_solver.cpp
View file

@ -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)

8
src/sat/smt/arith_solver.h
View file

@ -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);

75
src/sat/smt/intblast_solver.cpp
View file

@ -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);