chore: removing the last element of the borrow flags as it's not needed (#139)

Co-authored-by: Khashayar Barooti <[email protected]>

Author: kashbrti

src/fns/expressions.nr

@@ -40,7 +40,7 @@ unconstrained fn __compute_quadratic_expression_with_borrow_flags<let N: u32, le
     rhs_flags: [[bool; RHS_N]; NUM_PRODUCTS],
     linear_terms: [[u128; N]; ADD_N],
     linear_flags: [bool; ADD_N],
-) -> ([u128; N], [u128; N], [Field; 2 * N]) {
+) -> ([u128; N], [u128; N], [Field; 2 * N - 2]) {
     // TODO, validate we do not overflow N2 when multiplying and N when adding
     let mut mulout_p = __compute_quadratic_expression_product(
         params,
@@ -65,7 +65,7 @@ unconstrained fn __compute_quadratic_expression_with_borrow_flags<let N: u32, le
     }
 
     // compute borrow flags from mulout_p and mulout_n
-    let mut borrow_flags: [Field; 2 * N] = [0; 2 * N];
+    let mut borrow_flags: [Field; 2 * N - 2] = [0; 2 * N - 2];
     let borrow_shift: Field = TWO_POW_246; // 2^{246}
     let borrow_carry: Field = TWO_POW_126; // 2^{246 - 120} = 2^{126}
     let downshift: Field = 1 / (TWO_POW_120 as Field);
@@ -254,7 +254,7 @@ pub(crate) fn evaluate_quadratic_expression<let N: u32, let MOD_BITS: u32, let L
     linear_flags: [bool; ADD_N],
 ) {
     // use an unconstrained function to compute the value of the quotient
-    let (quotient, _, borrow_flags): ([u128; N], [u128; N], [Field; 2 * N]) = unsafe {
+    let (quotient, _, borrow_flags): ([u128; N], [u128; N], [Field; 2 * N - 2]) = unsafe {
         __compute_quadratic_expression_with_borrow_flags::<_, MOD_BITS, _, _, _, _>(
             params,
             lhs_terms,

src/fns/unconstrained_helpers.nr

@@ -83,18 +83,20 @@ pub(crate) unconstrained fn __validate_gt_remainder<let N: u32>(
 pub(crate) unconstrained fn __neg_with_flags<let N: u32, let MOD_BITS: u32>(
     params: P<N, MOD_BITS>,
     val: [u128; N],
-) -> ([u128; N], [bool; N]) {
+) -> ([u128; N], [bool; N - 1]) {
     let mut result: [u128; N] = [0; N];
     let mut borrow_in: u128 = 0;
 
-    let mut borrow_flags: [bool; N] = [false; N];
+    let mut borrow_flags: [bool; N - 1] = [false; N - 1];
     for i in 0..N {
         let sub_term = val[i] + borrow_in;
         let borrow = (sub_term > params.modulus[i]) as u128;
         result[i] = borrow * TWO_POW_120 + params.modulus[i] - sub_term;
 
         borrow_in = borrow;
-        borrow_flags[i] = borrow as bool;
+        if (i < N - 1) {
+            borrow_flags[i] = borrow as bool;
+        }
     }
     (result, borrow_flags)
 }
@@ -103,7 +105,7 @@ pub(crate) unconstrained fn __add_with_flags<let N: u32, let MOD_BITS: u32>(
     params: P<N, MOD_BITS>,
     lhs: [u128; N],
     rhs: [u128; N],
-) -> ([u128; N], [bool; N], [bool; N], bool) {
+) -> ([u128; N], [bool; N], [bool; N - 1], bool) {
     let add_res = __helper_add(lhs, rhs);
     let overflow = __gte(add_res, params.modulus);
 
@@ -116,7 +118,7 @@ pub(crate) unconstrained fn __add_with_flags<let N: u32, let MOD_BITS: u32>(
 
     let mut carry_in: u128 = 0;
     let mut borrow_in: u128 = 0;
-    let mut borrow_flags: [bool; N] = [false; N];
+    let mut borrow_flags: [bool; N - 1] = [false; N - 1];
     let mut carry_flags: [bool; N] = [false; N];
     for i in 0..N {
         let mut add_term = lhs[i] + rhs[i] + carry_in;
@@ -133,7 +135,9 @@ pub(crate) unconstrained fn __add_with_flags<let N: u32, let MOD_BITS: u32>(
         // Only set `borrow` and `carry` if they differ
         if (carry != borrow) {
             carry_flags[i] = carry as bool;
-            borrow_flags[i] = borrow as bool;
+            if (i < N - 1) {
+                borrow_flags[i] = borrow as bool;
+            }
         }
     }
     (result, carry_flags, borrow_flags, overflow)
@@ -143,7 +147,7 @@ pub(crate) unconstrained fn __sub_with_flags<let N: u32, let MOD_BITS: u32>(
     params: P<N, MOD_BITS>,
     lhs: [u128; N],
     rhs: [u128; N],
-) -> ([u128; N], [bool; N], [bool; N], bool) {
+) -> ([u128; N], [bool; N], [bool; N - 1], bool) {
     let mut one: [u128; N] = [0; N];
     one[0] = 1;
     let underflow = !__gte(lhs, rhs);
@@ -152,7 +156,7 @@ pub(crate) unconstrained fn __sub_with_flags<let N: u32, let MOD_BITS: u32>(
 
     let mut carry_in: u128 = 0;
     let mut borrow_in: u128 = 0;
-    let mut borrow_flags: [bool; N] = [false; N];
+    let mut borrow_flags: [bool; N - 1] = [false; N - 1];
     let mut carry_flags: [bool; N] = [false; N];
     for i in 0..N {
         let mut add_term: u128 = lhs[i] + addend[i] + carry_in;
@@ -168,7 +172,9 @@ pub(crate) unconstrained fn __sub_with_flags<let N: u32, let MOD_BITS: u32>(
         // Only set `borrow` and `carry` if they differ
         if (carry != borrow) {
             carry_flags[i] = carry as bool;
-            borrow_flags[i] = borrow as bool;
+            if (i < N - 1) {
+                borrow_flags[i] = borrow as bool;
+            }
         }
     }
     (result, carry_flags, borrow_flags, underflow)