Implemented NOT and improved tests

CHANGELOG.md

@@ -4,7 +4,7 @@
 
 - [\#689](https://github.com/arkworks-rs/algebra/pull/689) (`ark-serialize`) Add `CanonicalSerialize` and `CanonicalDeserialize` impls for `VecDeque` and `LinkedList`.
 - [\#693](https://github.com/arkworks-rs/algebra/pull/693) (`ark-serialize`) Add `serialize_to_vec!` convenience macro.
-- [\#713](https://github.com/arkworks-rs/algebra/pull/713) (`ark-ff`) Add support for bitwise operations AND, OR and XOR between `BigInteger`.
+- [\#713](https://github.com/arkworks-rs/algebra/pull/713) (`ark-ff`) Add support for bitwise operations AND, OR, NOT, and XOR between `BigInteger`.
 
 ### Breaking changes
 

ff/src/biginteger/mod.rs

@@ -1,4 +1,4 @@
-use core::ops::{BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign};
+use core::ops::{BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Not};
 
 use crate::{
     bits::{BitIteratorBE, BitIteratorLE},
@@ -738,6 +738,18 @@ impl<const N: usize> BitOr for BigInt<N> {
     }
 }
 
+impl<const N: usize> Not for BigInt<N> {
+    type Output = Self;
+
+    fn not(self) -> Self::Output {
+        let mut result = Self::zero();
+        for i in 0..N {
+            result.0[i] = !self.0[i];
+        }
+        result
+    }
+}
+
 /// Compute the signed modulo operation on a u64 representation, returning the result.
 /// If n % modulus > modulus / 2, return modulus - n
 /// # Example
@@ -800,6 +812,7 @@ pub trait BigInteger:
     + BitAnd<Self>
     + BitOrAssign<Self>
     + BitOr<Self>
+    + Not
 {
     /// Number of 64-bit limbs representing `Self`.
     const NUM_LIMBS: usize;

ff/src/biginteger/tests.rs

@@ -53,44 +53,54 @@ fn biginteger_arithmetic_test<B: BigInteger>(a: B, b: B, zero: B) {
 
 // Test for BigInt's bitwise operations
 fn biginteger_bitwise_ops_test<B: BigInteger>() {
+    let mut rng = ark_std::test_rng();
+
     // Test XOR
     // a xor a = 0
-    let a: BigInt<4> = BigInt::from(4_u64);
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
     let a_clone = a.clone();
     assert_eq!(a ^ a_clone, BigInt::from(0_u64));
 
     // Testing a xor b xor b
-    let a: BigInt<4> = BigInt::from(4_u64);
-    let b = BigInt::from(5_u64);
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
+    let b: BigInt<4> = UniformRand::rand(&mut rng);
+    let a_clone = a.clone();
     let b_clone = b.clone();
     let xor_ab = a ^ b;
-    assert_eq!(xor_ab ^ b_clone, BigInt::from(4_u64));
+    assert_eq!(xor_ab ^ b_clone, a_clone);
 
     // Test OR
-    // 1 or 1 = 1
-    let a: BigInt<4> = BigInt::from(1_u64);
+    // a or a = a
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
     let a_clone = a.clone();
-    assert_eq!(a | a_clone, BigInt::from(1_u64));
+    assert_eq!(a | a_clone, a);
 
     // Testing a or b or b
-    let a: BigInt<4> = BigInt::from(4_u64);
-    let b = BigInt::from(5_u64);
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
+    let b: BigInt<4> = UniformRand::rand(&mut rng);
     let b_clone = b.clone();
     let or_ab = a | b;
-    assert_eq!(or_ab | b_clone, BigInt::from(5_u64));
+    assert_eq!(or_ab | b_clone, a | b);
 
     // Test AND
     // a and a = a
-    let a: BigInt<4> = BigInt::from(2_u64);
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
     let a_clone = a.clone();
-    assert_eq!(a & a_clone, BigInt::from(2_u64));
+    assert_eq!(a & a_clone, a);
 
     // Testing a and a and b.
-    let a: BigInt<4> = BigInt::from(4_u64);
-    let b = BigInt::from(5_u64);
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
+    let b: BigInt<4> = UniformRand::rand(&mut rng);
     let b_clone = b.clone();
     let and_ab = a & b;
-    assert_eq!(and_ab & b_clone, BigInt::from(4_u64));
+    assert_eq!(and_ab & b_clone, a & b);
+
+    // Testing De Morgan's law
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
+    let b = UniformRand::rand(&mut rng);
+    let de_morgan_lhs = !(a | b);
+    let de_morgan_rhs = (!a) & (!b);
+    assert_eq!(de_morgan_lhs, de_morgan_rhs);
 }
 
 // Test correctness of BigInteger's bit values