Add further integer ring examples

applied-crypto-references/aleo-cryptography/src/algebra.rs

@@ -1,29 +1,58 @@
 ///! This module explores Aleo's basic algebraic structures and their properties
 
-//Field and Ring elements
-use snarkvm::utilities::{
-    BigInteger384, BigInteger
-};
-
 #[cfg(test)]
 mod tests {
-    use super::*;
+    //Field and Ring elements
+    use snarkvm::utilities::{
+        BigInteger384, BigInteger
+    };
 
     #[test]
     fn additions_overflow() {
         let mut a = BigInteger384::new([u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX]);
-        let mut b = BigInteger384::from(7);
-        a.add_nocarry(&b);
+        let b = BigInteger384::from(7);
+        let add_overflowed = a.add_nocarry(&b);
         let d = BigInteger384::from(6);
         assert_eq!(a, d);
+        assert!(add_overflowed);
+
     }
 
     #[test]
     fn subs_overflow() {
         let mut a = BigInteger384::from(0);
-        let mut b = BigInteger384::from(1);
-        a.sub_noborrow(&b);
+        let b = BigInteger384::from(1);
+        let sub_overflowed = a.sub_noborrow(&b);
         let d = BigInteger384::new([u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX]);
         assert_eq!(a, d);
+        assert!(sub_overflowed);
+    }
+
+    #[test]
+    fn mul_test() {
+        let mut a = BigInteger384::from(2000000);
+        a.muln(1);
+        let mut b = BigInteger384::from(2000000);
+        b.muln(2);
+        let mut c = BigInteger384::from(2000000);
+        c.muln(4);
+        assert_eq!(a, BigInteger384::from(4000000));
+        assert_eq!(b, BigInteger384::from(8000000));
+        assert_eq!(c, BigInteger384::from(32000000));
+
+        let mut c = BigInteger384::from(2000000);
+        c.mul2();
+        assert_eq!(c, BigInteger384::from(4000000));
+
+    }
+
+    #[test]
+    fn mul_saturation() {
+        // Create a number that is within 1 multiplication of overflowing
+        let mut a = BigInteger384::new([u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX - 4]);
+        let u384_max = BigInteger384::new([u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX, u64::MAX]);
+        a.mul2();
+        println!("a: {}", a);
+        println!("u384_max: {}", u384_max);
     }
 }