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simplification.cpp
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#include "z3_utils/simplification.h"
#include "hal_core/netlist/boolean_function.h"
#include "hal_core/utilities/log.h"
#include "z3_utils/z3_utils.h"
#include <deque>
namespace hal
{
namespace BV_ConstantPropagation
{
/**
* Helper function to simplify a constant AND operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction And(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
std::vector<BooleanFunction::Value> simplified;
simplified.reserve(p0.size());
for (auto i = 0u; i < p0.size(); i++)
{
if ((p0[i] == 0) || (p1[i] == 0))
{
simplified.emplace_back(BooleanFunction::Value::ZERO);
}
else if ((p0[i] == 1) && (p1[i] == 1))
{
simplified.emplace_back(BooleanFunction::Value::ONE);
}
else
{
simplified.emplace_back(BooleanFunction::Value::X);
}
}
return BooleanFunction::Const(simplified);
}
/**
* Helper function to simplify a constant OR operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Or(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
std::vector<BooleanFunction::Value> simplified;
simplified.reserve(p0.size());
for (auto i = 0u; i < p0.size(); i++)
{
if ((p0[i] == 0) && (p1[i] == 0))
{
simplified.emplace_back(BooleanFunction::Value::ZERO);
}
else if ((p0[i] == 1) || (p1[i] == 1))
{
simplified.emplace_back(BooleanFunction::Value::ONE);
}
else
{
simplified.emplace_back(BooleanFunction::Value::X);
}
}
return BooleanFunction::Const(simplified);
}
/**
* Helper function to simplify a constant NOT operation.
*
* @param[in] p - Boolean function parameter.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Not(const std::vector<BooleanFunction::Value>& p)
{
std::vector<BooleanFunction::Value> simplified;
simplified.reserve(p.size());
for (const auto& value : p)
{
if (value == BooleanFunction::Value::ZERO)
{
simplified.emplace_back(BooleanFunction::Value::ONE);
}
else if (value == BooleanFunction::Value::ONE)
{
simplified.emplace_back(BooleanFunction::Value::ZERO);
}
else
{
simplified.emplace_back(value);
}
}
return BooleanFunction::Const(simplified);
}
/**
* Helper function to simplify a constant XOR operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Xor(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
std::vector<BooleanFunction::Value> simplified;
simplified.reserve(p0.size());
for (auto i = 0u; i < p0.size(); i++)
{
if (((p0[i] == 0) && (p1[i] == 1)) || ((p0[i] == 1) && (p1[i] == 0)))
{
simplified.emplace_back(BooleanFunction::Value::ONE);
}
else if (((p0[i] == 0) && (p1[i] == 0)) || ((p0[i] == 1) && (p1[i] == 1)))
{
simplified.emplace_back(BooleanFunction::Value::ZERO);
}
else
{
simplified.emplace_back(BooleanFunction::Value::X);
}
}
return BooleanFunction::Const(simplified);
}
/**
* Helper function to simplify a constant ADD operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Add(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
if (std::any_of(p0.begin(), p0.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; })
|| std::any_of(p1.begin(), p1.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; }))
{
return BooleanFunction::Const(std::vector<BooleanFunction::Value>(p0.size(), BooleanFunction::Value::X));
}
std::vector<BooleanFunction::Value> simplified;
simplified.reserve(p0.size());
auto carry = BooleanFunction::Value::ZERO;
for (auto i = 0u; i < p0.size(); i++)
{
auto res = p0[i] + p1[i] + carry;
simplified.emplace_back(static_cast<BooleanFunction::Value>(res & 0x1));
carry = static_cast<BooleanFunction::Value>(res >> 1);
}
return BooleanFunction::Const(simplified);
}
/**
* Helper function to simplify a constant SUB operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Sub(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
if (std::any_of(p0.begin(), p0.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; })
|| std::any_of(p1.begin(), p1.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; }))
{
return BooleanFunction::Const(std::vector<BooleanFunction::Value>(p0.size(), BooleanFunction::Value::X));
}
std::vector<BooleanFunction::Value> simplified;
simplified.reserve(p0.size());
auto carry = BooleanFunction::Value::ONE;
for (auto i = 0u; i < p0.size(); i++)
{
auto res = p0[i] + !(p1[i]) + carry;
simplified.emplace_back(static_cast<BooleanFunction::Value>(res & 0x1));
carry = static_cast<BooleanFunction::Value>(res >> 1);
}
return BooleanFunction::Const(simplified);
}
/**
* Helper function to simplify a constant MUL operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Mul(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
if (std::any_of(p0.begin(), p0.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; })
|| std::any_of(p1.begin(), p1.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; }))
{
return BooleanFunction::Const(std::vector<BooleanFunction::Value>(p0.size(), BooleanFunction::Value::X));
}
auto bitsize = p0.size();
std::vector<BooleanFunction::Value> simplified(bitsize, BooleanFunction::Value::ZERO);
for (auto i = 0u; i < bitsize; i++)
{
auto carry = BooleanFunction::Value::ZERO;
for (auto j = 0u; j < bitsize - i; j++)
{
auto res = simplified[i + j] + (p0[i] & p1[j]) + carry;
simplified[i + j] = static_cast<BooleanFunction::Value>(res & 0x1);
carry = static_cast<BooleanFunction::Value>(res >> 1);
}
}
return BooleanFunction::Const(simplified);
}
/**
* Helper function to simplify a constant SLE operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Sle(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
if (std::any_of(p0.begin(), p0.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; })
|| std::any_of(p1.begin(), p1.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; }))
{
return BooleanFunction::Const({BooleanFunction::Value::X});
}
auto msb_p0 = p0.back();
auto msb_p1 = p1.back();
if (msb_p0 == BooleanFunction::Value::ONE && msb_p1 == BooleanFunction::Value::ZERO)
{
return BooleanFunction::Const(1, 1);
}
else if (msb_p0 == BooleanFunction::Value::ZERO && msb_p1 == BooleanFunction::Value::ONE)
{
return BooleanFunction::Const(0, 1);
}
std::vector<BooleanFunction::Value> simplified;
u8 carry = 1;
u8 neq = 0;
u8 res = 0;
for (auto i = 0u; i < p0.size(); i++)
{
res = p0[i] + !(p1[i]) + carry;
carry = res >> 1;
neq |= res & 1;
}
return BooleanFunction::Const({static_cast<BooleanFunction::Value>((res & 1) | !neq)});
}
/**
* Helper function to simplify a constant SLT operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Slt(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
if (std::any_of(p0.begin(), p0.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; })
|| std::any_of(p1.begin(), p1.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; }))
{
return BooleanFunction::Const({BooleanFunction::Value::X});
}
auto msb_p0 = p0.back();
auto msb_p1 = p1.back();
if (msb_p0 == BooleanFunction::Value::ONE && msb_p1 == BooleanFunction::Value::ZERO)
{
return BooleanFunction::Const(1, 1);
}
else if (msb_p0 == BooleanFunction::Value::ZERO && msb_p1 == BooleanFunction::Value::ONE)
{
return BooleanFunction::Const(0, 1);
}
std::vector<BooleanFunction::Value> simplified;
u8 res = 0;
u8 carry = 1;
for (auto i = 0u; i < p0.size(); i++)
{
res = p0[i] + !(p1[i]) + carry;
carry = (res >> 1) & 1;
}
return BooleanFunction::Const({static_cast<BooleanFunction::Value>(res & 1)});
}
/**
* Helper function to simplify a constant ULE operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Ule(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
if (std::any_of(p0.begin(), p0.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; })
|| std::any_of(p1.begin(), p1.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; }))
{
return BooleanFunction::Const({BooleanFunction::Value::X});
}
for (i32 i = p0.size() - 1; i >= 0; i--)
{
if (p0[i] == BooleanFunction::Value::ONE && p1[i] == BooleanFunction::Value::ZERO)
{
return BooleanFunction::Const(0, 1);
}
else if (p0[i] == BooleanFunction::Value::ZERO && p1[i] == BooleanFunction::Value::ONE)
{
return BooleanFunction::Const(1, 1);
}
}
return BooleanFunction::Const(1, 1);
}
/**
* Helper function to simplify a constant ULT operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Ult(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1)
{
if (std::any_of(p0.begin(), p0.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; })
|| std::any_of(p1.begin(), p1.end(), [](auto val) { return val == BooleanFunction::Value::X || val == BooleanFunction::Value::Z; }))
{
return BooleanFunction::Const({BooleanFunction::Value::X});
}
for (i32 i = p0.size() - 1; i >= 0; i--)
{
if (p0[i] == BooleanFunction::Value::ONE && p1[i] == BooleanFunction::Value::ZERO)
{
return BooleanFunction::Const(0, 1);
}
else if (p0[i] == BooleanFunction::Value::ZERO && p1[i] == BooleanFunction::Value::ONE)
{
return BooleanFunction::Const(1, 1);
}
}
return BooleanFunction::Const(0, 1);
}
/**
* Helper function to simplify a constant ITE operation.
*
* @param[in] p0 - Boolean function parameter 0.
* @param[in] p1 - Boolean function parameter 1.
* @param[in] p2 - Boolean function parameter 2.
* @returns Boolean function with a simplified constant value.
*/
BooleanFunction Ite(const std::vector<BooleanFunction::Value>& p0, const std::vector<BooleanFunction::Value>& p1, const std::vector<BooleanFunction::Value>& p2)
{
if (p0.front() == BooleanFunction::Value::ONE)
{
return BooleanFunction::Const(p1);
}
else if (p0.front() == BooleanFunction::Value::ZERO)
{
return BooleanFunction::Const(p2);
}
else
{
return BooleanFunction::Const(std::vector<BooleanFunction::Value>(p0.size(), BooleanFunction::Value::X));
}
}
/**
* Applies constant propagation for the node operation and the constant parameters
*
* @param[in] node - Boolean function node that specifies the operation type
* @param[in] p - The parameters as a vector of constant Boolean functions
* @return Constant Boolean fucntion as the result of the operation.
*/
Result<BooleanFunction> constant_propagation(const BooleanFunction::Node& node, std::vector<BooleanFunction>&& p)
{
std::vector<std::vector<BooleanFunction::Value>> values;
for (const auto& parameter : p)
{
values.emplace_back(parameter.get_top_level_node().constant);
}
switch (node.type)
{
case BooleanFunction::NodeType::And:
return OK(And(values[0], values[1]));
case BooleanFunction::NodeType::Or:
return OK(Or(values[0], values[1]));
case BooleanFunction::NodeType::Not:
return OK(Not(values[0]));
case BooleanFunction::NodeType::Xor:
return OK(Xor(values[0], values[1]));
case BooleanFunction::NodeType::Add:
return OK(Add(values[0], values[1]));
case BooleanFunction::NodeType::Sub:
return OK(Sub(values[0], values[1]));
case BooleanFunction::NodeType::Mul:
return OK(Mul(values[0], values[1]));
case BooleanFunction::NodeType::Sle:
// TODO implement for z3 where Boolean and bitvector sort exist
return OK(BooleanFunction());
case BooleanFunction::NodeType::Slt:
// TODO implement for z3 where Boolean and bitvector sort exist
return OK(BooleanFunction());
case BooleanFunction::NodeType::Ule:
// TODO implement for z3 where Boolean and bitvector sort exist
return OK(BooleanFunction());
case BooleanFunction::NodeType::Ult:
// TODO implement for z3 where Boolean and bitvector sort exist
return OK(BooleanFunction());
case BooleanFunction::NodeType::Ite:
// TODO implement for z3 where Boolean and bitvector sort exist
return OK(BooleanFunction());
case BooleanFunction::NodeType::Eq:
// TODO implement for z3 where Boolean and bitvector sort exist
return OK(BooleanFunction());
case BooleanFunction::NodeType::Zext:
// TODO implement for z3 where indices are not part of the parameters
return OK(BooleanFunction());
case BooleanFunction::NodeType::Sext:
// TODO implement for z3 where indices are not part of the parameters
return OK(BooleanFunction());
case BooleanFunction::NodeType::Slice:
// TODO implement for z3 where indices are not part of the parameters
return OK(BooleanFunction());
case BooleanFunction::NodeType::Concat:
// TODO implement for z3 where indices are not part of the parameters
return OK(BooleanFunction());
case BooleanFunction::NodeType::Sdiv:
// TODO implement
case BooleanFunction::NodeType::Udiv:
// TODO implement
case BooleanFunction::NodeType::Srem:
// TODO implement
case BooleanFunction::NodeType::Urem:
// TODO implement
default:
return ERR("could not propagate constants: not implemented for given node type");
}
}
} // namespace BV_ConstantPropagation
namespace
{
/**
* Helper function that checks two expressions for syntactical equality.
*/
bool is_x_y(const z3::expr& x, const z3::expr& y)
{
if (x.id() == y.id())
{
return true;
}
if (z3::eq(x, y))
{
return true;
}
return false;
}
/**
* Helper function to check whether one of the two expressions is just the other function negated.
*/
bool is_x_not_y(const z3::expr& x, const z3::expr& y)
{
const auto x_kind = x.decl().decl_kind();
const auto y_kind = y.decl().decl_kind();
if (x_kind == Z3_OP_BNOT || x_kind == Z3_OP_NOT)
{
if (is_x_y(x.arg(0), y))
{
return true;
}
}
if (y_kind == Z3_OP_BNOT || y_kind == Z3_OP_NOT)
{
if (is_x_y(y.arg(0), x))
{
return true;
}
}
return false;
}
/**
* Helper function to get the parameters of an expression formatted as a vector of expressions.
*/
std::vector<z3::expr> get_parameters(const z3::expr& e)
{
std::vector<z3::expr> p;
for (u32 i = 0; i < e.num_args(); i++)
{
p.push_back(e.arg(i));
}
return p;
}
/**
* Helper function to check whether an expression is numeral and all bits are one.
*/
bool is_ones(const z3::expr& e)
{
if (!e.is_numeral())
{
return false;
}
const std::string val_str = Z3_get_numeral_binary_string(e.ctx(), e);
// Check if the binary representation consists only of '1's
return val_str.find('0') == std::string::npos;
}
/**
* Helper function to check whether an expression is numeral and all bits are zero.
*/
bool is_zero(const z3::expr& e)
{
if (!e.is_numeral())
{
return false;
}
const std::string val_str = Z3_get_numeral_binary_string(e.ctx(), e);
// Check if the binary representation consists only of '0's
return val_str.find('1') == std::string::npos;
}
/**
* Helper function to check whether an expression is numeral and is equal to a specific value.
* Only works for numerals < 64 bit.
*/
bool has_constant_value(const z3::expr& e, const u64& val)
{
if (!e.is_numeral())
{
return false;
}
if (e.get_sort().bv_size() > 64)
{
return false;
}
return e.get_numeral_uint64() == val;
}
/**
* Helper function to check whether an expression is of a specific type.
*/
bool is_kind(const z3::expr& e, const Z3_decl_kind& t)
{
return e.decl().decl_kind() == t;
}
/**
* Helper function to determine whether an operation is commutative or not.
*/
bool is_commutative(const Z3_decl_kind& t)
{
switch (t)
{
case Z3_OP_TRUE:
case Z3_OP_FALSE:
case Z3_OP_AND:
case Z3_OP_OR:
case Z3_OP_NOT:
case Z3_OP_BAND:
case Z3_OP_BNOT:
case Z3_OP_BOR:
case Z3_OP_BXOR:
case Z3_OP_BADD:
return true;
case Z3_OP_BNEG:
case Z3_OP_BSUB:
return false;
case Z3_OP_BMUL:
return true;
case Z3_OP_BSDIV:
case Z3_OP_BUDIV:
case Z3_OP_BSREM:
case Z3_OP_BUREM:
return false;
case Z3_OP_EXTRACT:
return true;
case Z3_OP_CONCAT:
return false;
case Z3_OP_ZERO_EXT:
case Z3_OP_SIGN_EXT:
case Z3_OP_EQ:
return true;
case Z3_OP_SLEQ:
case Z3_OP_SLT:
case Z3_OP_ULEQ:
case Z3_OP_ULT:
case Z3_OP_ITE:
return false;
default: {
log_error("z3_utils", "commutative check not implemeted for type {}!", static_cast<std::size_t>(t));
return false;
}
}
}
/**
* Helper function to normalize a vector of parameters by sorting them based on their declaration.
*/
std::vector<z3::expr> normalize(std::vector<z3::expr>&& p)
{
if (p.size() <= 1ul)
{
return std::move(p);
}
std::sort(p.begin(), p.end(), [](const auto& lhs, const auto& rhs) { return lhs.decl().decl_kind() > rhs.decl().decl_kind(); });
return std::move(p);
}
/**
* Helper function to check whether the orignal version of an expression and its simplification are still semantically equivalent
*/
bool check_simplification_for_correctness(const z3::expr& org, const z3::expr& smp)
{
log_warning("z3_utils", "Checking simplification for correctness. This is slow and expensive!");
z3::solver s(org.ctx());
s.add(org != smp);
const auto r = s.check();
if (r != z3::unsat)
{
std::cout << "Correctness Check failed!!!" << std::endl;
std::cout << "ORG: " << org << std::endl;
std::cout << "NEW: " << smp << std::endl;
return false;
}
return true;
}
/**
* Helper function to simplfy two expressions that are conactinated together
*/
std::vector<z3::expr> simplify_concat(z3::context& ctx, const z3::expr& p0, const z3::expr& p1)
{
const u64 p0_size = p0.get_sort().bv_size();
const u64 p1_size = p1.get_sort().bv_size();
// TODO make this able to handle more than 64 bits
// CONCAT(CONST(X), CONST(Y)) => CONST(X || Y)
if (p0.is_numeral() && p1.is_numeral())
{
if ((p0_size + p1_size) <= 64)
{
return {ctx.bv_val((p1.get_numeral_uint64() << p0_size) + p0.get_numeral_uint64(), p0_size + p1_size)};
}
}
if (is_kind(p0, Z3_OP_EXTRACT) && is_kind(p1, Z3_OP_EXTRACT))
{
auto p0_parameter = get_parameters(p0);
auto p1_parameter = get_parameters(p1);
if (is_x_y(p0_parameter[0], p1_parameter[0]))
{
// CONCAT(SLICE(X, j+1, k), SLICE(X, i, j)) => SLICE(X, i, k)
if (p1.lo() == (p0.hi() + 1))
{
const auto res = p0_parameter[0].extract(p1.hi(), p0.lo());
return {res};
}
// CONCAT(SLICE(X, j, j), SLICE(X, j, i)) => SEXT(SLICE(X, j, i), 1)
if ((p1.lo() == p1.hi()) && (p1.lo() == p0.hi()))
{
const auto res = z3::expr(ctx, Z3_mk_sign_ext(ctx, 1, p0));
return {res};
}
}
}
if (is_kind(p0, Z3_OP_EXTRACT) && p1.is_numeral())
{
// CONCAT(00..00, SLICE(X, i, j)) => ZEXT(SLICE(X, i, k), n)
if (is_zero(p1))
{
const auto res = z3::expr(ctx, Z3_mk_zero_ext(ctx, p1_size, p0));
return {res};
}
}
if (is_kind(p0, Z3_OP_SIGN_EXT) && is_kind(p1, Z3_OP_EXTRACT))
{
auto p0_parameter = get_parameters(p0);
auto p1_parameter = get_parameters(p1);
auto p00_parameter = get_parameters(p0_parameter[0]);
if (is_x_y(p00_parameter[0], p1_parameter[0]))
{
// CONCAT(SLICE(X, j, j), SEXT(SLICE(X, j, i), n)) => SEXT(SLICE(X, j, i), n + 1)
if ((p1.lo() == p1.hi()) && (p1.lo() == p0_parameter[0].hi()))
{
const u32 extend_by = p0.get_sort().bv_size() - p0_parameter[0].get_sort().bv_size() + 1;
auto res = z3::expr(ctx, Z3_mk_sign_ext(ctx, extend_by, p0_parameter[0]));
return {res};
}
}
}
if (is_kind(p0, Z3_OP_ZERO_EXT) && p1.is_numeral())
{
auto p0_parameter = get_parameters(p0);
// CONCAT(00..00, ZEXT(SLICE(X, j, i), n)) => ZEXT(SLICE(X, j, i), n + m))
if (is_zero(p1))
{
const u32 extend_by = p0.get_sort().bv_size() - p0_parameter[0].get_sort().bv_size() + p1_size;
const auto res = z3::expr(ctx, Z3_mk_zero_ext(ctx, extend_by, p0_parameter[0]));
return {res};
}
}
return {p0, p1};
}
/**
* Internal simplification function that is called recursively on the expression and its parameters to simplfy teh whole AST of the expression.
*/
Result<z3::expr> simplify_internal(const z3::expr& e, std::unordered_map<u32, z3::expr>& cache, const bool check_correctness)
{
if (const auto it = cache.find(e.id()); it != cache.end())
{
return OK(it->second);
}
u64 size;
if (e.is_bv())
{
if (e.is_numeral())
{
return OK(e);
}
else if (e.is_const())
{
return OK(e);
}
else if (e.is_var())
{
return OK(e);
}
size = e.get_sort().bv_size();
}
auto& ctx = e.ctx();
// 1. Simplify all parameters of the function recursively
const auto op = e.decl().decl_kind();
std::vector<z3::expr> p;
for (u32 i = 0; i < e.num_args(); i++)
{
const auto arg = e.arg(i);
const auto res = simplify_internal(arg, cache, check_correctness);
if (res.is_ok())
{
if (check_correctness && !check_simplification_for_correctness(arg, res.get()))
{
return ERR("simplification failed correctness check!");
}
const auto [it, _] = cache.insert({arg.id(), res.get()});
p.push_back(it->second);
}
else
{
return ERR(res.get_error());
}
}
// 2. If all simplified parameters are constants apply constant propagation
if (!p.empty() && std::all_of(p.begin(), p.end(), [](const auto& p_e) { return p_e.is_numeral() && p_e.is_bv(); }))
{
const auto bf = z3_utils::to_bf(e).get();
std::vector<BooleanFunction> p_bf;
for (const auto& p_e : p)
{
const auto t = z3_utils::to_bf(p_e).get();
p_bf.push_back(t);
}
auto res = BV_ConstantPropagation::constant_propagation(bf.get_top_level_node(), std::move(p_bf));
if (res.is_error())
{
return ERR_APPEND(res.get_error(), "could not simplify sub-expression in abstract syntax tree: constant propagation failed");
}
auto bf_c = res.get();
if (!bf_c.is_empty())
{
const auto bf_z3 = z3_utils::from_bf(bf_c, ctx);
return OK(bf_z3);
}
}
// 3. If the operation is commutative normalize the order of operands
if (is_commutative(op))
{
p = normalize(std::move(p));
}
// 4. Apply various simplifcation rules based on the operation
switch (op)
{
case Z3_OP_TRUE: {
return OK(e);
}
case Z3_OP_FALSE: {
return OK(e);
}
case Z3_OP_AND: {
// X & False => False
if (p[1].is_bool() && p[1].is_false())
{
return OK(ctx.bool_val(false));
}
// X & True => X
if (p[1].is_bool() && p[1].is_true())
{
return OK(p[0]);
}
// X & X => X
if (is_x_y(p[0], p[1]))
{
return OK(p[0]);
}
// X & ~X => False
if (is_x_not_y(p[0], p[1]))
{
return OK(ctx.bool_val(false));
}
if (p[0].is_or() && p[1].is_or())
{
auto p0_parameter = get_parameters(p[0]);
auto p1_parameter = get_parameters(p[1]);
// (X | Y) & (X | Z) => X | (Y & Z)
if (is_x_y(p0_parameter[0], p1_parameter[0]))
{
return OK(p0_parameter[0] | (p0_parameter[1] & p1_parameter[1]));
}
// (X | Y) & (Z | X) => X | (Y & Z)
if (is_x_y(p0_parameter[0], p1_parameter[1]))
{
return OK(p0_parameter[0] | (p0_parameter[1] & p1_parameter[0]));
}
// (X | Y) & (Y | Z) => Y | (X & Z)
if (is_x_y(p0_parameter[1], p1_parameter[0]))
{
return OK(p0_parameter[1] | (p0_parameter[0] & p1_parameter[1]));
}
// (X | Y) & (Z | Y) => Y | (X & Z)
if (is_x_y(p0_parameter[1], p1_parameter[1]))
{
return OK(p0_parameter[1] | (p0_parameter[0] & p1_parameter[0]));
}
}
if (p[1].is_and())
{
auto p1_parameter = get_parameters(p[1]);
// X & (X & Y) => (X & Y)
if (is_x_y(p[0], p1_parameter[1]))
{
return OK(p[1]);
}
// X & (Y & X) => (Y & X)
if (is_x_y(p[0], p1_parameter[0]))
{
return OK(p[1]);
}
// X & (~X & Y) => 0
if (is_x_not_y(p1_parameter[0], p[0]))
{
return OK(ctx.bool_val(false));
}
// X & (Y & ~X) => 0
if (is_x_not_y(p1_parameter[1], p[0]))
{
return OK(ctx.bool_val(false));
}
}
if (p[1].is_or())
{
auto p1_parameter = get_parameters(p[1]);
// X & (X | Y) => X
if (is_x_y(p1_parameter[0], p[0]))
{
return OK(p[0]);
}
// X & (Y | X) => X
if (is_x_y(p1_parameter[1], p[0]))
{
return OK(p[0]);
}
// X & (~X | Y) => X & Y
if (is_x_not_y(p1_parameter[0], p[0]))
{
return OK(p[0] & p1_parameter[1]);
}
// X & (Y | ~X) => X & Y
if (is_x_not_y(p1_parameter[1], p[0]))
{
return OK(p[0] & p1_parameter[0]);
}
}
if (p[0].is_and())
{
auto p0_parameter = get_parameters(p[0]);
// (X & Y) & X => X & Y
if (is_x_y(p0_parameter[0], p[1]))
{
return OK(p[0]);
}
// (Y & X) & X => Y & X
if (is_x_y(p0_parameter[1], p[1]))
{
return OK(p[0]);
}
// (~X & Y) & X => 0
if (is_x_not_y(p0_parameter[0], p[1]))
{
return OK(ctx.bool_val(false));
}
// (Y & ~X) & X => 0
if (is_x_not_y(p0_parameter[1], p[1]))
{
return OK(ctx.bool_val(false));
}
}
if (p[0].is_or())
{
auto p0_parameter = get_parameters(p[0]);
// (X | Y) & X => X
if (is_x_y(p0_parameter[0], p[1]))
{
return OK(p[1]);
}
// (Y | X) & X => X
if (is_x_y(p0_parameter[1], p[1]))
{
return OK(p[1]);
}
// (~X | Y) & X => X & Y
if (is_x_not_y(p0_parameter[0], p[1]))
{
return OK(p[1] & p0_parameter[1]);
}
// (Y | ~X) & X => X & Y
if (is_x_not_y(p0_parameter[1], p[1]))
{
return OK(p[1] & p0_parameter[0]);
}
}