From f97b7cad87f23b5dc8d234a4af0795296a8406b9 Mon Sep 17 00:00:00 2001
From: miguelis <miguelis@ucm.es>
Date: Wed, 25 Sep 2024 18:28:56 +0200
Subject: [PATCH] Complement function depends on the number of bits of the
 prime number

---
 circom_algebra/src/algebra.rs                  |  4 ++--
 circom_algebra/src/modular_arithmetic.rs       | 13 ++++++-------
 constraint_generation/src/execute.rs           |  2 +-
 mkdocs/docs/circom-language/basic-operators.md |  8 ++++----
 4 files changed, 13 insertions(+), 14 deletions(-)

diff --git a/circom_algebra/src/algebra.rs b/circom_algebra/src/algebra.rs
index bb3a47b46..235b7e951 100644
--- a/circom_algebra/src/algebra.rs
+++ b/circom_algebra/src/algebra.rs
@@ -554,13 +554,13 @@ impl<C: Default + Clone + Display + Hash + Eq> ArithmeticExpression<C> {
     }
 
     // Bit operations
-    pub fn complement_254(
+    pub fn complement(
         elem: &ArithmeticExpression<C>,
         field: &BigInt,
     ) -> ArithmeticExpression<C> {
         use ArithmeticExpression::*;
         if let Number { value } = elem {
-            Number { value: modular_arithmetic::complement_254(value, field) }
+            Number { value: modular_arithmetic::complement(value, field) }
         } else {
             NonQuadratic
         }
diff --git a/circom_algebra/src/modular_arithmetic.rs b/circom_algebra/src/modular_arithmetic.rs
index f1d5790f2..60c386c05 100644
--- a/circom_algebra/src/modular_arithmetic.rs
+++ b/circom_algebra/src/modular_arithmetic.rs
@@ -91,15 +91,14 @@ pub fn multi_inv(values: &Vec<BigInt>, field: &BigInt) -> Vec<BigInt>{
 }
 
 //Bit operations
-
-// 254 bit complement
-pub fn complement_254(elem: &BigInt, field: &BigInt) -> BigInt {
+pub fn complement(elem: &BigInt, field: &BigInt) -> BigInt {
     let (sign, mut bit_repr) = bit_representation(elem);
     let new_sign = if elem == &BigInt::from(0) { Sign::Plus } else { sign};
-    while bit_repr.len() > 254 {
+    let nbits = field.bits();
+    while bit_repr.len() > nbits {
         bit_repr.pop();
     }
-    for _i in bit_repr.len()..254 {
+    for _i in bit_repr.len()..nbits {
         bit_repr.push(0);
     }
     for bit in &mut bit_repr {
@@ -253,8 +252,8 @@ mod tests {
             .expect("generating the big int was not possible");
         let big_num = BigInt::parse_bytes("1234".as_bytes(), 10)
             .expect("generating the big int was not possible");
-        let big_num_complement = complement_254(&big_num, &field);
-        let big_num_complement_complement = complement_254(&big_num_complement, &field);
+        let big_num_complement = complement(&big_num, &field);
+        let big_num_complement_complement = complement(&big_num_complement, &field);
         let big_num_modulus = modulus(&big_num, &field);
         assert_eq!(big_num_complement_complement, big_num_modulus);
     }
diff --git a/constraint_generation/src/execute.rs b/constraint_generation/src/execute.rs
index 887d52c38..1a4a3061a 100644
--- a/constraint_generation/src/execute.rs
+++ b/constraint_generation/src/execute.rs
@@ -2079,7 +2079,7 @@ fn execute_prefix_op(
     let result = match prefix_op {
         BoolNot => AExpr::not(value, field),
         Sub => AExpr::prefix_sub(value, field),
-        Complement => AExpr::complement_254(value, field),
+        Complement => AExpr::complement(value, field),
     };
     Result::Ok(result)
 }
diff --git a/mkdocs/docs/circom-language/basic-operators.md b/mkdocs/docs/circom-language/basic-operators.md
index 7ff89ffec..c2940bc7f 100644
--- a/mkdocs/docs/circom-language/basic-operators.md
+++ b/mkdocs/docs/circom-language/basic-operators.md
@@ -95,8 +95,8 @@ All bitwise operators are performed modulo p.
 | :--- | :--- | :--- |
 | & | a & b | Bitwise AND |
 | \| | a \| b | Bitwise OR |
-| ~ | ~a | Complement 254 bits |
-| ^ | a ^ b | XOR  254 bits |
+| ~ | ~a | Complement to the number of bits of the prime number |
+| ^ | a ^ b | Bitwise XOR |
 | &gt;&gt; | a &gt;&gt; 4 | Right shift operator |
 | &lt;&lt; | a &lt;&lt; 4 | Left shift operator |
 
@@ -122,8 +122,8 @@ There are operators that combine bitwise operators with a final assignment.
 | :--- | :--- | :--- |
 | &= | a &= b | Bitwise AND and assignment |
 | \|= | a \|= b | Bitwise OR and assignment |
-| ~= | ~=a | Complement 254 bits and assignment |
-| ^= | a ^= b | XOR  254 bits and assignment |
+| ~= | ~=a | Complement to the number of bits of the prime number and assignment |
+| ^= | a ^= b | Bitwise XOR and assignment |
 | &gt;&gt;= | a &gt;&gt;= 4 | Right shift operator and assignment |
 | &lt;&lt;= | a &lt;&lt;= 4 | Left shift operator and assignment |