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fix(r1cs): lower unsafe wide arithmetic bitwise #253

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126 changes: 94 additions & 32 deletions src/target/r1cs/trans.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -644,6 +644,37 @@ impl<'cfg> ToR1cs<'cfg> {
acc
}

/// Add equally sized, least-significant-bit-first bit vectors modulo their width.
fn bv_add_bits(&mut self, xs: &[TermLc], ys: &[TermLc]) -> Vec<TermLc> {
assert_eq!(xs.len(), ys.len());
let mut carry = self.zero.clone();
let mut sum = Vec::with_capacity(xs.len());
for (x, y) in xs.iter().zip(ys) {
sum.push(self.nary_xor(vec![x.clone(), y.clone(), carry.clone()].into_iter()));

// Majority(x, y, carry) = xy + carry * (x + y - 2xy).
let xy = self.mul(x.clone(), y.clone());
carry = self.mul(carry, x.clone() + y - &(xy.clone() * 2)) + &xy;
}
sum
}

/// Multiply equally sized bit vectors modulo their width without packing an oversized
/// intermediate into the scalar field.
fn bv_mul_bits(&mut self, xs: &[TermLc], ys: &[TermLc]) -> Vec<TermLc> {
assert_eq!(xs.len(), ys.len());
let width = xs.len();
let mut product = vec![self.zero.clone(); width];
for (shift, y) in ys.iter().enumerate() {
let mut partial = vec![self.zero.clone(); width];
for i in shift..width {
partial[i] = self.mul(xs[i - shift].clone(), y.clone());
}
product = self.bv_add_bits(&product, &partial);
}
product
}

/// Shift `x` left by `2^(2^y)`, if bit-valued `c` is true.
fn const_pow_shift_bv_lit(&mut self, x: &TermLc, y: usize, c: TermLc) -> TermLc {
let two_to_the_y = 1usize.checked_shl(y as u32).unwrap();
Expand Down Expand Up @@ -792,42 +823,55 @@ impl<'cfg> ToR1cs<'cfg> {
let res = bits_bv_idx.into_iter().map(f).collect();
self.set_bv_bits(bv, res);
}
BvNaryOp::Add | BvNaryOp::Mul => {
BvNaryOp::Add => {
let f_width = self.r1cs.modulus().significant_bits() as usize - 1;
let values = bv
.cs()
.iter()
.map(|c| self.get_bv_uint(c))
.collect::<Vec<_>>();
let (res, width) = match o {
BvNaryOp::Add => {
let sum =
values.into_iter().fold(self.zero.clone(), |s, v| s + &v);
let extra_width = bitsize(bv.cs().len().saturating_sub(1));
(sum, n + extra_width)
let extra_width = bitsize(bv.cs().len().saturating_sub(1));
let bits = if n + extra_width <= f_width {
let values = bv
.cs()
.iter()
.map(|c| self.get_bv_uint(c))
.collect::<Vec<_>>();
let sum = values.into_iter().fold(self.zero.clone(), |s, v| s + &v);
let mut bits = self.bitify("arith", &sum, n + extra_width, false);
bits.truncate(n);
bits
} else {
let mut sum = vec![self.zero.clone(); n];
for child in bv.cs() {
let bits = self.get_bv_bits(child);
sum = self.bv_add_bits(&sum, &bits);
}
BvNaryOp::Mul => {
if bv.cs().len() * n < f_width {
let z = self.zero.clone() + 1;
(
values.into_iter().fold(z, |acc, v| self.mul(acc, v)),
bv.cs().len() * n,
)
} else {
let z = self.zero.clone() + 1;
let p = values.into_iter().fold(z, |acc, v| {
let p = self.mul(acc, v);
let mut bits = self.bitify("binMul", &p, 2 * n, false);
bits.truncate(n);
self.debitify(bits.into_iter(), false)
});
(p, n)
}
sum
};
self.set_bv_bits(bv, bits);
}
BvNaryOp::Mul => {
let f_width = self.r1cs.modulus().significant_bits() as usize - 1;
let bits = if bv.cs().len() * n < f_width {
let values = bv
.cs()
.iter()
.map(|c| self.get_bv_uint(c))
.collect::<Vec<_>>();
let one = self.zero.clone() + 1;
let product =
values.into_iter().fold(one, |acc, v| self.mul(acc, v));
let mut bits =
self.bitify("arith", &product, bv.cs().len() * n, false);
bits.truncate(n);
bits
} else {
let mut children = bv.cs().iter();
let mut product = self.get_bv_bits(
children.next().expect("bit-vector multiplication is empty"),
);
for child in children {
let bits = self.get_bv_bits(child);
product = self.bv_mul_bits(&product, &bits);
}
_ => unreachable!(),
product
};
let mut bits = self.bitify("arith", &res, width, false);
bits.truncate(n);
self.set_bv_bits(bv, bits);
}
},
Expand Down Expand Up @@ -1539,6 +1583,24 @@ pub mod test {
add_test_instance(&[0b11, 0b11, 0b11, 0b11, 0b11], 0b11, 2);
}

#[test]
fn wide_arithmetic_test() {
init();
let u128_max: Integer = (Integer::from(1) << 128) - 1;
const_test(term![
Op::Eq;
term![BV_MUL; bv_lit(u128_max.clone(), 128), bv_lit(u128_max, 128)],
bv_lit(1, 128)
]);

let high_u255: Integer = Integer::from(1) << 254;
const_test(term![
Op::Eq;
term![BV_ADD; bv_lit(high_u255.clone(), 255), bv_lit(high_u255, 255)],
bv_lit(0, 255)
]);
}

#[test]
fn concat_test() {
init();
Expand Down