Add some property testing, and fix a bug it found.

src/lib.rs

@@ -1,5 +1,3 @@
-#![recursion_limit="1024"]
-
 #[cfg(test)]
 #[macro_use]
 extern crate quickcheck;
@@ -7,4 +5,46 @@ extern crate quickcheck;
 pub mod signed;
 pub mod unsigned;
 #[cfg(test)]
-pub mod testing;
+pub mod testing;
+
+#[cfg(test)]
+mod arithmetic {
+    use super::signed::*;
+    use super::unsigned::*;
+
+    quickcheck! {
+        fn commutivity_signed_add(x: I576, y: I576) -> bool {
+            (&x + &y) == (&y + &x)
+        }
+        fn commutivity_unsigned_add(x: U576, y: U576) -> bool {
+            (&x + &y) == (&y + &x)
+        }
+        fn commutivity_unsigned_mul(x: U192, y: U192) -> bool {
+            (&x * &y) == (&y * &x)
+        }
+
+        fn associativity_unsigned_add(x: U192, y: U192, z: U192) -> bool {
+            (U256::from(&x) + (&y + &z)) == ((&x + &y) + U256::from(&z))
+        }
+        fn associativity_unsigned_mul(x: U192, y: U192, z: U192) -> bool {
+            (U384::from(&x) * (&y * &z)) == ((&x * &y) * U384::from(&z))
+        }
+
+        fn identity_signed_add(x: I576) -> bool {
+            (&x + I576::zero()) == I640::from(&x)
+        }
+        fn identity_unsigned_add(x: U576) -> bool {
+            (&x + U576::zero()) == U640::from(&x)
+        }
+        fn identity_unsigned_mul(x: U192) -> bool {
+            (&x * U192::from(1u64)) == U384::from(&x)
+        }
+
+        fn additive_inverse(x: I576) -> bool {
+            (&x + x.negate()) == I640::zero()
+        }
+        fn distribution(x: U192, y: U192, z: U192) -> bool {
+            (U256::from(&x) * (&y + &z)) == U512::from((&x * &y) + (&x * &z))
+        }
+    } 
+}