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Fix solver cond val #157

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Fix solver cond val #157

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06de1b4
fix: essential input selection, updating assigment for inputs only
saraseidl Aug 3, 2021
88cb4ec
fix: changes in IV computation for MUL, REMU, DIVU
saraseidl Aug 3, 2021
c830015
fix: changes in CV computations for MUL, REMU, DIVU
saraseidl Aug 3, 2021
70f6c02
fix: add/fix testcases for consistent value computation for REMU
saraseidl Aug 9, 2021
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4 changes: 4 additions & 0 deletions src/engine/symbolic_state.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -411,6 +411,10 @@ impl<'a> Formula for FormulaView<'a> {
!matches!(self.data_flow[NodeIndex::new(sym)], Symbol::Operator(_))
}

fn is_input(&self, sym: SymbolId) -> bool {
matches!(self.data_flow[NodeIndex::new(sym)], Symbol::Input(_))
}

fn traverse<V, R>(&self, n: SymbolId, visit_map: &mut HashMap<SymbolId, R>, v: &mut V) -> R
where
V: FormulaVisitor<R>,
Expand Down
2 changes: 2 additions & 0 deletions src/solver/mod.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -155,6 +155,8 @@ pub trait Formula: Index<SymbolId, Output = Symbol> {

fn is_operand(&self, sym: SymbolId) -> bool;

fn is_input(&self, sym: SymbolId) -> bool;

fn traverse<V, R>(&self, n: SymbolId, visit_map: &mut HashMap<SymbolId, R>, v: &mut V) -> R
where
V: FormulaVisitor<R>,
Expand Down
185 changes: 120 additions & 65 deletions src/solver/monster.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -77,7 +77,7 @@ fn is_invertible(op: BVOperator, s: BitVector, t: BitVector, d: OperandSide) ->
}
},
BVOperator::Remu => match d {
OperandSide::Lhs => !(s <= t),
OperandSide::Lhs => !(-s) >= t,
OperandSide::Rhs => {
if s == t {
true
Expand Down Expand Up @@ -154,9 +154,9 @@ fn select<F: Formula>(
(rhs, lhs, OperandSide::Rhs)
} else if is_constant(f, rhs) {
(lhs, rhs, OperandSide::Lhs)
} else if is_essential(f, lhs, OperandSide::Lhs, rhs, t, ab) {
} else if is_essential(f, idx, lhs, OperandSide::Lhs, t, ab) {
(lhs, rhs, OperandSide::Lhs)
} else if is_essential(f, rhs, OperandSide::Rhs, lhs, t, ab) {
} else if is_essential(f, idx, rhs, OperandSide::Rhs, t, ab) {
(rhs, lhs, OperandSide::Rhs)
} else if random() {
(rhs, lhs, OperandSide::Rhs)
Expand All @@ -176,25 +176,29 @@ fn compute_inverse_value(op: BVOperator, s: BitVector, t: BitVector, d: OperandS
OperandSide::Rhs => s - t,
},
BVOperator::Mul => {
let y = s >> s.ctz();
if s == BitVector(0) {
BitVector(random::<u64>())
} else {
let y = s >> s.ctz();

let y_inv = y
.modinverse()
.expect("a modular inverse has to exist iff operator is invertible");
let y_inv = y
.modinverse()
.expect("a modular inverse has to exist iff operator is invertible");

let result = (t >> s.ctz()) * y_inv;
let result = (t >> s.ctz()) * y_inv;

let to_shift = 64 - s.ctz();
let to_shift = 64 - s.ctz();

let arbitrary_bit_mask = if to_shift == 64 {
BitVector(0)
} else {
BitVector::ones() << to_shift
};
let arbitrary_bit_mask = if to_shift == 64 {
BitVector(0)
} else {
BitVector::ones() << to_shift
};

let arbitrary_bits = BitVector(random::<u64>()) & arbitrary_bit_mask;
let arbitrary_bits = BitVector(random::<u64>()) & arbitrary_bit_mask;

result | arbitrary_bits
result | arbitrary_bits
}
}
BVOperator::Sltu => match d {
OperandSide::Lhs => {
Expand Down Expand Up @@ -223,34 +227,23 @@ fn compute_inverse_value(op: BVOperator, s: BitVector, t: BitVector, d: OperandS
if (t == BitVector::ones()) && (s == BitVector(1)) {
BitVector::ones()
} else {
let range_start = t * s;
if range_start.0.overflowing_add(s.0 - 1).1 {
BitVector(
thread_rng()
.sample(Uniform::new_inclusive(range_start.0, u64::max_value())),
)
} else {
BitVector(thread_rng().sample(Uniform::new_inclusive(
range_start.0,
range_start.0 + (s.0 - 1),
)))
}
let range_start = (t * s).0;
let range_end = range_start.saturating_add(s.0 - 1);

BitVector(thread_rng().sample(Uniform::new_inclusive(range_start, range_end)))
}
}
OperandSide::Rhs => {
if (t == s) && t == BitVector::ones() {
BitVector(thread_rng().sample(Uniform::new_inclusive(0, 1)))
} else if (t == BitVector::ones()) && (s != BitVector::ones()) {
BitVector(0)
} else {
s / t
}
let range_start = s / (t + BitVector(1)) + BitVector(1);
let range_end = s / t;

BitVector(thread_rng().sample(Uniform::new_inclusive(range_start.0, range_end.0)))
}
},
BVOperator::Remu => match d {
OperandSide::Lhs => {
let y = BitVector(
thread_rng().sample(Uniform::new_inclusive(1, ((BitVector::ones() - t) / s).0)),
thread_rng().sample(Uniform::new_inclusive(0, ((BitVector::ones() - t) / s).0)),
);
// below computation cannot overflow due to how `y` was chosen
assert!(
Expand Down Expand Up @@ -305,7 +298,7 @@ fn compute_consistent_value(op: BVOperator, t: BitVector, d: OperandSide) -> Bit
BVOperator::Add | BVOperator::Sub | BVOperator::Equals => BitVector(random::<u64>()),
BVOperator::Mul => BitVector({
if t == BitVector(0) {
0
random::<u64>()
} else {
let mut r;
loop {
Expand All @@ -323,17 +316,19 @@ fn compute_consistent_value(op: BVOperator, t: BitVector, d: OperandSide) -> Bit
}),
BVOperator::Divu => match d {
OperandSide::Lhs => {
if (t == BitVector::ones()) || (t == BitVector(0)) {
if t == BitVector::ones() {
BitVector(random::<u64>())
} else if t == BitVector(0) {
BitVector(thread_rng().sample(Uniform::new_inclusive(0, u64::max_value() - 1)))
} else {
let mut y = BitVector(0);
while !(y != BitVector(0)) && !(y.mulo(t)) {
y = BitVector(
thread_rng().sample(Uniform::new_inclusive(0, u64::max_value())),
);
}
let y = BitVector(
thread_rng().sample(Uniform::new_inclusive(1, u64::max_value() / t.0)),
);

let range_start = (t * y).0;
let range_end = range_start.saturating_add(y.0 - 1);

y * t
BitVector(thread_rng().sample(Uniform::new_inclusive(range_start, range_end)))
}
}
OperandSide::Rhs => {
Expand Down Expand Up @@ -368,10 +363,16 @@ fn compute_consistent_value(op: BVOperator, t: BitVector, d: OperandSide) -> Bit
},
BVOperator::Remu => match d {
OperandSide::Lhs => {
if t == BitVector::ones() {
BitVector::ones()
if t == BitVector::ones() || t > BitVector::ones() - t {
t
} else {
BitVector(thread_rng().sample(Uniform::new_inclusive(t.0, BitVector::ones().0)))
let r = thread_rng().sample(Uniform::new_inclusive(2 * t.0, u64::max_value()));

if r == 2 * t.0 {
t
} else {
BitVector(r)
}
}
}
OperandSide::Rhs => {
Expand Down Expand Up @@ -440,15 +441,15 @@ fn value<F: Formula>(

fn is_essential<F: Formula>(
formula: &F,
n: SymbolId,
this: SymbolId,
on_side: OperandSide,
other: SymbolId,
t: BitVector,
ab: &[BitVector],
) -> bool {
let ab_nx = ab[this];

match &formula[other] {
match &formula[n] {
Symbol::Operator(op) => !is_invertible(*op, ab_nx, t, on_side.other()),
// TODO: not mentioned in paper => improvised. is that really true?
Symbol::Constant(_) | Symbol::Input(_) => false,
Expand Down Expand Up @@ -637,7 +638,9 @@ fn sat<F: Formula>(
n = nx;
}

update_assignment(formula, &mut ab, n, t);
if formula.is_input(n) {
update_assignment(formula, &mut ab, n, t);
}
}

let assignment: Assignment = formula.symbol_ids().map(|i| (i, ab[i])).collect();
Expand Down Expand Up @@ -821,42 +824,64 @@ mod tests {
// prove: Ey.(computed <> y == t) where <> is the binary bit vector operator
//

// compute inverse value for other operand
let inverse = match op {
BVOperator::Add => t - computed,
BVOperator::Add => {
assert!(
is_invertible(op, computed, t, d.other()),
"consistent value has an inverse"
);
compute_inverse_value(op, computed, t, d.other())
}
BVOperator::Mul => {
assert!(
is_invertible(op, computed, t, d),
"choose values which are invertible..."
is_invertible(op, computed, t, d.other()),
"consistent value has an inverse"
);

compute_inverse_value(op, computed, t, d)
compute_inverse_value(op, computed, t, d.other())
}
BVOperator::Sltu => {
assert!(
is_invertible(op, computed, t, d.other()),
"consistent value has an inverse"
);
compute_inverse_value(op, computed, t, d.other())
}
BVOperator::Sltu => compute_inverse_value(op, computed, t, d),
BVOperator::Divu => {
assert!(is_invertible(op, computed, t, d));
compute_inverse_value(op, computed, t, d)
assert!(
is_invertible(op, computed, t, d.other()),
"consistent value has an inverse"
);
compute_inverse_value(op, computed, t, d.other())
}
BVOperator::Remu => {
assert!(
is_invertible(op, computed, t, d.other()),
"consistent value has an inverse"
);
compute_inverse_value(op, computed, t, d.other())
}
_ => unimplemented!(),
};

if d == OperandSide::Lhs {
assert_eq!(
f(inverse, computed),
f(computed, inverse),
t,
"{:?} {:?} {:?} == {:?}",
inverse,
op,
computed,
op,
inverse,
t
);
} else {
assert_eq!(
f(computed, inverse),
f(inverse, computed),
t,
"{:?} {:?} {:?} == {:?}",
computed,
op,
inverse,
op,
computed,
t
);
}
Expand Down Expand Up @@ -890,6 +915,15 @@ mod tests {
let side = OperandSide::Lhs;

test_invertibility(MUL, 0b1, 0b1, side, true, "trivial multiplication");
test_invertibility(
MUL,
0b0,
0b0,
side,
true,
"trivial multiplication, t == s == 0",
);
test_invertibility(MUL, 0b10, 0b0, side, true, "trivial multiplication, t == 0");
test_invertibility(MUL, 0b10, 0b1, side, false, "operand bigger than result");
test_invertibility(
MUL,
Expand Down Expand Up @@ -989,6 +1023,8 @@ mod tests {
test_inverse_value_computation(MUL, 0b10, 0b10, side, f);
test_inverse_value_computation(MUL, 0b100, 0b100, side, f);
test_inverse_value_computation(MUL, 0b10, 0b1100, side, f);
test_inverse_value_computation(MUL, 0b0, 0b0, side, f);
test_inverse_value_computation(MUL, 0b10, 0b0, side, f);
}

#[test]
Expand Down Expand Up @@ -1101,4 +1137,23 @@ mod tests {
test_consistent_value_computation(SLTU, 0, side, f);
test_consistent_value_computation(SLTU, 1, side, f);
}

#[test]
fn compute_consistent_values_for_remu() {
let mut side = OperandSide::Lhs;

fn f(l: BitVector, r: BitVector) -> BitVector {
l % r
}

// test only for values which actually have a consistent value
test_consistent_value_computation(REMU, u64::max_value(), side, f);
test_consistent_value_computation(REMU, u64::max_value() / 2 + 7, side, f);
test_consistent_value_computation(REMU, 0, side, f);
test_consistent_value_computation(REMU, 7, side, f);

side = OperandSide::Rhs;
test_consistent_value_computation(REMU, u64::max_value(), side, f);
test_consistent_value_computation(REMU, 7, side, f);
}
}