Implementation of bitwise operations between BigInteger (#713)

Co-authored-by: Michele Orrù <michele.orru@berkeley.edu>

CHANGELOG.md

@@ -4,6 +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`.
 
 ### Breaking changes
 

ff/src/biginteger/mod.rs

@@ -1,3 +1,5 @@
+use core::ops::{BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Not};
+
 use crate::{
     bits::{BitIteratorBE, BitIteratorLE},
     const_for, UniformRand,
@@ -8,6 +10,7 @@ use ark_serialize::{
     CanonicalDeserialize, CanonicalSerialize, Compress, SerializationError, Valid, Validate,
 };
 use ark_std::{
+    borrow::Borrow,
     convert::TryFrom,
     fmt::{Debug, Display, UpperHex},
     io::{Read, Write},
@@ -681,6 +684,63 @@ impl<const N: usize> From<BigInt<N>> for BigUint {
     }
 }
 
+impl<B: Borrow<Self>, const N: usize> BitXorAssign<B> for BigInt<N> {
+    fn bitxor_assign(&mut self, rhs: B) {
+        (0..N).for_each(|i| self.0[i] ^= rhs.borrow().0[i])
+    }
+}
+
+impl<B: Borrow<Self>, const N: usize> BitXor<B> for BigInt<N> {
+    type Output = Self;
+
+    fn bitxor(mut self, rhs: B) -> Self::Output {
+        self ^= rhs;
+        self
+    }
+}
+
+impl<B: Borrow<Self>, const N: usize> BitAndAssign<B> for BigInt<N> {
+    fn bitand_assign(&mut self, rhs: B) {
+        (0..N).for_each(|i| self.0[i] &= rhs.borrow().0[i])
+    }
+}
+
+impl<B: Borrow<Self>, const N: usize> BitAnd<B> for BigInt<N> {
+    type Output = Self;
+
+    fn bitand(mut self, rhs: B) -> Self::Output {
+        self &= rhs;
+        self
+    }
+}
+
+impl<B: Borrow<Self>, const N: usize> BitOrAssign<B> for BigInt<N> {
+    fn bitor_assign(&mut self, rhs: B) {
+        (0..N).for_each(|i| self.0[i] |= rhs.borrow().0[i])
+    }
+}
+
+impl<B: Borrow<Self>, const N: usize> BitOr<B> for BigInt<N> {
+    type Output = Self;
+
+    fn bitor(mut self, rhs: B) -> Self::Output {
+        self |= rhs;
+        self
+    }
+}
+
+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
@@ -737,6 +797,18 @@ pub trait BigInteger:
     + From<u8>
     + TryFrom<BigUint, Error = ()>
     + Into<BigUint>
+    + BitXorAssign<Self>
+    + for<'a> BitXorAssign<&'a Self>
+    + BitXor<Self>
+    + for<'a> BitXor<&'a Self, Output = Self>
+    + BitAndAssign<Self>
+    + for<'a> BitAndAssign<&'a Self>
+    + BitAnd<Self>
+    + for<'a> BitAnd<&'a Self, Output = Self>
+    + BitOrAssign<Self>
+    + for<'a> BitOrAssign<&'a Self>
+    + BitOr<Self>
+    + for<'a> BitOr<&'a Self, Output = Self>
 {
     /// Number of 64-bit limbs representing `Self`.
     const NUM_LIMBS: usize;
@@ -949,7 +1021,7 @@ pub trait BigInteger:
     /// arr[63] = true;
     /// let mut one = B::from(1u64);
     /// assert_eq!(B::from_bits_be(&arr), one);
-    /// ```   
+    /// ```
     fn from_bits_be(bits: &[bool]) -> Self;
 
     /// Returns the big integer representation of a given little endian boolean
@@ -963,7 +1035,7 @@ pub trait BigInteger:
     /// arr[0] = true;
     /// let mut one = B::from(1u64);
     /// assert_eq!(B::from_bits_le(&arr), one);
-    /// ```   
+    /// ```
     fn from_bits_le(bits: &[bool]) -> Self;
 
     /// Returns the bit representation in a big endian boolean array,
@@ -978,7 +1050,7 @@ pub trait BigInteger:
     /// let mut vec = vec![false; 64];
     /// vec[63] = true;
     /// assert_eq!(arr, vec);
-    /// ```  
+    /// ```
     fn to_bits_be(&self) -> Vec<bool> {
         BitIteratorBE::new(self).collect::<Vec<_>>()
     }

ff/src/biginteger/tests.rs

@@ -1,4 +1,5 @@
-use crate::{biginteger::BigInteger, UniformRand};
+use crate::{biginteger::BigInteger, BigInt, UniformRand};
+use ark_std::rand::Rng;
 use num_bigint::BigUint;
 
 // Test elementary math operations for BigInteger.
@@ -51,6 +52,52 @@ fn biginteger_arithmetic_test<B: BigInteger>(a: B, b: B, zero: B) {
     assert_eq!(a_mul2, a_plus_a);
 }
 
+// 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> = UniformRand::rand(&mut rng);
+    assert_eq!(a ^ &a, BigInt::from(0_u64));
+
+    // Testing a xor b xor b
+    let a: BigInt<4> = UniformRand::rand(&mut rng);
+    let b: BigInt<4> = UniformRand::rand(&mut rng);
+    let xor_ab = a ^ b;
+    assert_eq!(xor_ab ^ b, a);
+
+    // Test OR
+    // a or a = a
+    let a = rng.gen::<BigInt<4>>();
+    assert_eq!(a | &a, a);
+
+    // Testing a or b or b
+    let a = rng.gen::<BigInt<4>>();
+    let b = rng.gen::<BigInt<4>>();
+    let or_ab = a | b;
+    assert_eq!(or_ab | &b, a | b);
+
+    // Test AND
+    // a and a = a
+    let a = rng.gen::<BigInt<4>>();
+    assert_eq!(a & (&a), a);
+
+    // Testing a and a and b.
+    let a = rng.gen::<BigInt<4>>();
+    let b = rng.gen::<BigInt<4>>();
+    let b_clone = b.clone();
+    let and_ab = a & b;
+    assert_eq!(and_ab & b_clone, a & b);
+
+    // Testing De Morgan's law
+    let a = rng.gen::<BigInt<4>>();
+    let b = rng.gen::<BigInt<4>>();
+    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
 fn biginteger_bits_test<B: BigInteger>() {
     let mut one = B::from(1u64);
@@ -93,6 +140,7 @@ fn test_biginteger<B: BigInteger>(zero: B) {
     biginteger_arithmetic_test(a, b, zero);
     biginteger_bits_test::<B>();
     biginteger_conversion_test::<B>();
+    biginteger_bitwise_ops_test::<B>()
 }
 
 #[test]