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fix: Field comparisons #4704

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Apr 3, 2024
Merged

fix: Field comparisons #4704

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37 changes: 19 additions & 18 deletions noir_stdlib/src/field/bn254.nr
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Original file line number Diff line number Diff line change
Expand Up @@ -21,11 +21,23 @@ unconstrained fn decompose_unsafe(x: Field) -> (Field, Field) {
(low, high)
}

// Assert that (alo > blo && ahi >= bhi) || (alo <= blo && ahi > bhi)
fn assert_gt_limbs(a: (Field, Field), b: (Field, Field)) {
let (alo, ahi) = a;
let (blo, bhi) = b;
let borrow = lte_unsafe(alo, blo, 16);

let rlo = alo - blo - 1 + (borrow as Field) * TWO_POW_128;
let rhi = ahi - bhi - (borrow as Field);

rlo.assert_max_bit_size(128);
rhi.assert_max_bit_size(128);
}

/// Decompose a single field into two 16 byte fields.
pub fn decompose(x: Field) -> (Field, Field) {
// Take hints of the decomposition
let (xlo, xhi) = decompose_unsafe(x);
let borrow = lt_unsafe(PLO, xlo, 16);

// Range check the limbs
xlo.assert_max_bit_size(128);
Expand All @@ -34,13 +46,8 @@ pub fn decompose(x: Field) -> (Field, Field) {
// Check that the decomposition is correct
assert_eq(x, xlo + TWO_POW_128 * xhi);

// Check that (xlo < plo && xhi <= phi) || (xlo >= plo && xhi < phi)
let rlo = PLO - xlo + (borrow as Field) * TWO_POW_128;
let rhi = PHI - xhi - (borrow as Field);

rlo.assert_max_bit_size(128);
rhi.assert_max_bit_size(128);

// Assert that the decomposition of P is greater than the decomposition of x
assert_gt_limbs((PLO, PHI), (xlo, xhi));
(xlo, xhi)
}

Expand Down Expand Up @@ -69,17 +76,11 @@ unconstrained fn lte_unsafe(x: Field, y: Field, num_bytes: u32) -> bool {

pub fn assert_gt(a: Field, b: Field) {
// Decompose a and b
let (alo, ahi) = decompose(a);
let (blo, bhi) = decompose(b);

let borrow = lte_unsafe(alo, blo, 16);
let a_limbs = decompose(a);
let b_limbs = decompose(b);

// Assert that (alo > blo && ahi >= bhi) || (alo <= blo && ahi > bhi)
let rlo = alo - blo - 1 + (borrow as Field) * TWO_POW_128;
let rhi = ahi - bhi - (borrow as Field);

rlo.assert_max_bit_size(128);
rhi.assert_max_bit_size(128);
// Assert that a_limbs is greater than b_limbs
assert_gt_limbs(a_limbs, b_limbs)
}

pub fn assert_lt(a: Field, b: Field) {
Expand Down
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