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intblast with lazy expansion of shl, ashr, lshr
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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
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@NikolajBjorner
NikolajBjorner committed Dec 16, 2023
1 parent 50e0fd3 commit d0a59f3
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Showing 10 changed files with 321 additions and 83 deletions.
21 changes: 17 additions & 4 deletions src/ast/arith_decl_plugin.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -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)
Expand All @@ -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));
}

Expand Down Expand Up @@ -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));
}

Expand Down
31 changes: 23 additions & 8 deletions src/ast/arith_decl_plugin.h
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Original file line number Diff line number Diff line change
Expand Up @@ -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,
Expand Down Expand Up @@ -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);
Expand Down Expand Up @@ -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; }

Expand Down Expand Up @@ -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); }
Expand Down Expand Up @@ -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); }
Expand Down
103 changes: 103 additions & 0 deletions src/ast/rewriter/arith_rewriter.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -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);
Expand Down Expand Up @@ -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);
Expand All @@ -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;
}

Expand Down
3 changes: 3 additions & 0 deletions src/ast/rewriter/arith_rewriter.h
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Original file line number Diff line number Diff line change
Expand Up @@ -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);
Expand Down
4 changes: 2 additions & 2 deletions src/math/lp/lp_api.h
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Original file line number Diff line number Diff line change
Expand Up @@ -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));
Expand All @@ -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);
}
};

Expand Down

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