/**
* A bunch of cases in which a geo expression is equivalent() to both itself or to another
* expression.
*/
TEST(ExpressionGeoTest, GeoEquivalent) {
{
BSONObj query = fromjson("{$within: {$box: [{x: 4, y: 4}, [6, 6]]}}");
std::unique_ptr<GeoMatchExpression> ge(makeGeoMatchExpression(query));
ASSERT(ge->equivalent(ge.get()));
}
{
BSONObj query = fromjson(
"{$within: {$geometry: {type: 'Polygon',"
"coordinates: [[[0, 0], [3, 6], [6, 1], [0, 0]]]}}}");
std::unique_ptr<GeoMatchExpression> ge(makeGeoMatchExpression(query));
ASSERT(ge->equivalent(ge.get()));
}
{
BSONObj query1 = fromjson(
"{$within: {$geometry: {type: 'Polygon',"
"coordinates: [[[0, 0], [3, 6], [6, 1], [0, 0]]]}}}"),
query2 = fromjson(
"{$within: {$geometry: {type: 'Polygon',"
"coordinates: [[[0, 0], [3, 6], [6, 1], [0, 0]]]}}}");
std::unique_ptr<GeoMatchExpression> ge1(makeGeoMatchExpression(query1)),
ge2(makeGeoMatchExpression(query2));
ASSERT(ge1->equivalent(ge2.get()));
}
}
template<typename Scalar> void trmm(int size,int /*othersize*/)
{
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixColMaj;
typedef Matrix<Scalar,Dynamic,Dynamic,RowMajor> MatrixRowMaj;
DenseIndex rows = size;
DenseIndex cols = ei_random<DenseIndex>(1,size);
MatrixColMaj triV(rows,cols), triH(cols,rows), upTri(cols,rows), loTri(rows,cols),
unitUpTri(cols,rows), unitLoTri(rows,cols), strictlyUpTri(cols,rows), strictlyLoTri(rows,cols);
MatrixColMaj ge1(rows,cols), ge2(cols,rows), ge3;
MatrixRowMaj rge3;
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>();
triV.setRandom();
triH.setRandom();
loTri = triV.template triangularView<Lower>();
upTri = triH.template triangularView<Upper>();
unitLoTri = triV.template triangularView<UnitLower>();
unitUpTri = triH.template triangularView<UnitUpper>();
strictlyLoTri = triV.template triangularView<StrictlyLower>();
strictlyUpTri = triH.template triangularView<StrictlyUpper>();
ge1.setRandom();
ge2.setRandom();
VERIFY_IS_APPROX( ge3 = triV.template triangularView<Lower>() * ge2, loTri * ge2);
VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<Lower>(), ge2 * loTri);
VERIFY_IS_APPROX( ge3 = triH.template triangularView<Upper>() * ge1, upTri * ge1);
VERIFY_IS_APPROX( ge3 = ge1 * triH.template triangularView<Upper>(), ge1 * upTri);
VERIFY_IS_APPROX( ge3 = (s1*triV.adjoint()).template triangularView<Upper>() * (s2*ge1), s1*loTri.adjoint() * (s2*ge1));
VERIFY_IS_APPROX( ge3 = ge1 * triV.adjoint().template triangularView<Upper>(), ge1 * loTri.adjoint());
VERIFY_IS_APPROX( ge3 = triH.adjoint().template triangularView<Lower>() * ge2, upTri.adjoint() * ge2);
VERIFY_IS_APPROX( ge3 = ge2 * triH.adjoint().template triangularView<Lower>(), ge2 * upTri.adjoint());
VERIFY_IS_APPROX( ge3 = triV.template triangularView<Lower>() * ge1.adjoint(), loTri * ge1.adjoint());
VERIFY_IS_APPROX( ge3 = ge1.adjoint() * triV.template triangularView<Lower>(), ge1.adjoint() * loTri);
VERIFY_IS_APPROX( ge3 = triH.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
VERIFY_IS_APPROX(rge3.noalias() = triH.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<Upper>() * ge2.adjoint(), ei_conj(s1) * loTri.adjoint() * ge2.adjoint());
VERIFY_IS_APPROX(rge3.noalias() = triV.adjoint().template triangularView<Upper>() * ge2.adjoint(), loTri.adjoint() * ge2.adjoint());
VERIFY_IS_APPROX( ge3 = triH.adjoint().template triangularView<Lower>() * ge1.adjoint(), upTri.adjoint() * ge1.adjoint());
VERIFY_IS_APPROX(rge3.noalias() = triH.adjoint().template triangularView<Lower>() * ge1.adjoint(), upTri.adjoint() * ge1.adjoint());
VERIFY_IS_APPROX( ge3 = triV.template triangularView<UnitLower>() * ge2, unitLoTri * ge2);
VERIFY_IS_APPROX( rge3.noalias() = ge2 * triV.template triangularView<UnitLower>(), ge2 * unitLoTri);
VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<UnitLower>(), ge2 * unitLoTri);
VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<UnitUpper>() * ge2.adjoint(), ei_conj(s1) * unitLoTri.adjoint() * ge2.adjoint());
VERIFY_IS_APPROX( ge3 = triV.template triangularView<StrictlyLower>() * ge2, strictlyLoTri * ge2);
VERIFY_IS_APPROX( rge3.noalias() = ge2 * triV.template triangularView<StrictlyLower>(), ge2 * strictlyLoTri);
VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<StrictlyLower>(), ge2 * strictlyLoTri);
VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<StrictlyUpper>() * ge2.adjoint(), ei_conj(s1) * strictlyLoTri.adjoint() * ge2.adjoint());
}
smt_astt
smt_convt::overflow_arith(const expr2tc &expr)
{
// If in integer mode, this is completely pointless. Return false.
if (int_encoding)
return mk_smt_bool(false);
const overflow2t &overflow = to_overflow2t(expr);
const arith_2ops &opers = static_cast<const arith_2ops &>(*overflow.operand);
assert(opers.side_1->type == opers.side_2->type);
constant_int2tc zero(opers.side_1->type, BigInt(0));
lessthan2tc op1neg(opers.side_1, zero);
lessthan2tc op2neg(opers.side_2, zero);
equality2tc op1iszero(opers.side_1, zero);
equality2tc op2iszero(opers.side_2, zero);
or2tc containszero(op1iszero, op2iszero);
// Guess whether we're performing a signed or unsigned comparison.
bool is_signed = (is_signedbv_type(opers.side_1) ||
is_signedbv_type(opers.side_2));
if (is_add2t(overflow.operand)) {
if (is_signed) {
// Two cases: pos/pos, and neg/neg, which can over and underflow resp.
// In pos/neg cases, no overflow or underflow is possible, for any value.
constant_int2tc zero(opers.side_1->type, BigInt(0));
lessthan2tc op1pos(zero, opers.side_1);
lessthan2tc op2pos(zero, opers.side_2);
and2tc both_pos(op1pos, op2pos);
not2tc negop1(op1pos);
not2tc negop2(op2pos);
and2tc both_neg(negop1, negop2);
implies2tc nooverflow(both_pos,
greaterthanequal2tc(overflow.operand, zero));
implies2tc nounderflow(both_neg,
lessthanequal2tc(overflow.operand, zero));
return convert_ast(not2tc(and2tc(nooverflow, nounderflow)));
} else {
// Just ensure the result is >= both operands.
greaterthanequal2tc ge1(overflow.operand, opers.side_1);
greaterthanequal2tc ge2(overflow.operand, opers.side_2);
and2tc res(ge1, ge2);
not2tc inv(res);
return convert_ast(inv);
}
} else if (is_sub2t(overflow.operand)) {
if (is_signed) {
// Convert to be an addition
neg2tc negop2(opers.side_2->type, opers.side_2);
add2tc anadd(opers.side_1->type, opers.side_1, negop2);
expr2tc add_overflows(new overflow2t(anadd));
// Corner case: subtracting MIN_INT from many things overflows. The result
// should always be positive.
constant_int2tc zero(opers.side_1->type, BigInt(0));
uint64_t topbit = 1ULL << (opers.side_1->type->get_width() - 1);
constant_int2tc min_int(opers.side_1->type, BigInt(topbit));
equality2tc is_min_int(min_int, opers.side_2);
implies2tc imp(is_min_int, greaterthan2tc(overflow.operand, zero));
return convert_ast(or2tc(add_overflows, is_min_int));
} else {
// Just ensure the result is >= the operands.
lessthanequal2tc le1(overflow.operand, opers.side_1);
lessthanequal2tc le2(overflow.operand, opers.side_2);
and2tc res(le1, le2);
not2tc inv(res);
return convert_ast(inv);
}
} else {
assert(is_mul2t(overflow.operand) && "unexpected overflow_arith operand");
// Zero extend; multiply; Make a decision based on the top half.
unsigned int sz = zero->type->get_width();
smt_sortt boolsort = boolean_sort;
smt_sortt normalsort = mk_sort(SMT_SORT_BV, sz, false);
smt_sortt bigsort = mk_sort(SMT_SORT_BV, sz * 2, false);
// All one bit vector is tricky, might be 64 bits wide for all we know.
constant_int2tc allonesexpr(zero->type, BigInt((sz == 64)
? 0xFFFFFFFFFFFFFFFFULL
: ((1ULL << sz) - 1)));
smt_astt allonesvector = convert_ast(allonesexpr);
smt_astt arg1_ext, arg2_ext;
if (is_signed) {
// sign extend top bits.
arg1_ext = convert_ast(opers.side_1);
arg1_ext = convert_sign_ext(arg1_ext, bigsort, sz - 1, sz);
arg2_ext = convert_ast(opers.side_2);
arg2_ext = convert_sign_ext(arg2_ext, bigsort, sz - 1, sz);
} else {
// Zero extend the top parts
arg1_ext = convert_ast(opers.side_1);
arg1_ext = convert_zero_ext(arg1_ext, bigsort, sz);
arg2_ext = convert_ast(opers.side_2);
arg2_ext = convert_zero_ext(arg2_ext, bigsort, sz);
}
smt_astt result = mk_func_app(bigsort, SMT_FUNC_BVMUL, arg1_ext, arg2_ext);
// Extract top half.
smt_astt toppart = mk_extract(result, (sz * 2) - 1, sz, normalsort);
if (is_signed) {
// It should either be zero or all one's; which depends on what
// configuration of signs it had. If both pos / both neg, then the top
// should all be zeros, otherwise all ones. Implement with xor.
smt_astt op1neg_ast = convert_ast(op1neg);
smt_astt op2neg_ast = convert_ast(op2neg);
smt_astt allonescond =
mk_func_app(boolsort, SMT_FUNC_XOR, op1neg_ast, op2neg_ast);
smt_astt zerovector = convert_ast(zero);
smt_astt initial_switch =
mk_func_app(normalsort, SMT_FUNC_ITE, allonescond,
allonesvector, zerovector);
// either value being zero means the top must be zero.
smt_astt contains_zero_ast = convert_ast(containszero);
smt_astt second_switch = mk_func_app(normalsort, SMT_FUNC_ITE,
contains_zero_ast,
zerovector,
initial_switch);
smt_astt is_eq =
mk_func_app(boolsort, SMT_FUNC_EQ, second_switch, toppart);
return mk_func_app(boolsort, SMT_FUNC_NOT, &is_eq, 1);
} else {
// It should be zero; if not, overflow
smt_astt iseq =
mk_func_app(boolsort, SMT_FUNC_EQ, toppart, convert_ast(zero));
return mk_func_app(boolsort, SMT_FUNC_NOT, &iseq, 1);
}
}
return NULL;
}
