diff --git a/Cargo.toml b/Cargo.toml
index 8ee6b32..b78bde6 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -4,4 +4,4 @@ version = "0.1.0"
 authors = ["awick"]
 
 [dependencies]
-quickcheck = "0.7.1"
\ No newline at end of file
+quickcheck = "^0.7.2"
\ No newline at end of file
diff --git a/generate.hs b/generate.hs
index a973125..fe53152 100644
--- a/generate.hs
+++ b/generate.hs
@@ -135,7 +135,7 @@ needs = [ Need RSA         (\ size -> [Req (size `div` 2) Sub,
                                        Req (size + 64) SignedAdd,
                                        Req (size + 64) SignedSub,
                                        Req (size + 64) SignedCmp
-                                       ])
+                                      ])
         , Need ModInv      (\ size -> [Req size BaseOps,
                                        Req (size + 64) SignedBase,
                                        Req (size + 64) BaseOps,
@@ -143,7 +143,7 @@ needs = [ Need RSA         (\ size -> [Req (size `div` 2) Sub,
                                        Req size EGCD,
                                        Req (size + 64) SignedAdd,
                                        Req size Barretts
-                                       ])
+                                      ])
         ]
 -- needs = [ Need ModExp      (\ size -> [Req size ModMul
 --                                       ,Req size ModSq
@@ -219,6 +219,9 @@ rsaSizes =  [512,1024,2048,3072,4096,8192,15360]
 
 baseRequirements :: [Requirement]
 baseRequirements = concatMap (\ x -> [Req x RSA]) rsaSizes
+                ++ [Req 192 Add, Req 256 Add, Req 384 Add] -- used for testing
+                ++ [Req 192 Mul, Req 384 Mul] -- used for testing
+                ++ [Req 448 (Convert 512)] -- used for testing
 
 requirements :: [Requirement]
 requirements = go baseRequirements
diff --git a/src/lib.rs b/src/lib.rs
index 6c685a6..b0db1ce 100644
--- a/src/lib.rs
+++ b/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;
\ No newline at end of file
+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))
+        }
+    } 
+}
\ No newline at end of file
diff --git a/src/signed/add.rs b/src/signed/add.rs
index a9f8cfc..17d3687 100644
--- a/src/signed/add.rs
+++ b/src/signed/add.rs
@@ -60,16 +60,19 @@ macro_rules! add_impls
                         value: &self.value + &rhs.value
                     }
                 } else {
-                    if self.value > rhs.value {
-                        $bigger {
-                            negative: self.negative,
-                            value: $ubigger::from(&self.value - &rhs.value)
-                        }
-                    } else {
-                        $bigger {
-                            negative: rhs.negative,
-                            value: $ubigger::from(&rhs.value - &self.value)
-                        }
+                    match self.value.cmp(&rhs.value) {
+                        Ordering::Greater =>
+                            $bigger {
+                                negative: self.negative,
+                                value: $ubigger::from(&self.value - &rhs.value)
+                            },
+                        Ordering::Less =>
+                            $bigger {
+                                negative: rhs.negative,
+                                value: $ubigger::from(&rhs.value - &self.value)
+                            },
+                        Ordering::Equal =>
+                            $bigger::zero()
                     }
                 }
             }
diff --git a/src/signed/base.rs b/src/signed/base.rs
index f3a1d3b..f8116f3 100644
--- a/src/signed/base.rs
+++ b/src/signed/base.rs
@@ -85,16 +85,18 @@ macro_rules! signed_impls {
             }
         }
 
-//        #[cfg(test)]
-//        impl Arbitrary for $sname {
-//            fn arbitrary<G: Gen>(g: &mut G) -> $name {
-//                let neg = g.gen::<bool>();
-//                let val = g.gen::<$name>();
-//                $sname{ negative: neg, value: val }
-//            }
-//        }
-
         #[cfg(test)]
+        impl Arbitrary for $sname {
+            fn arbitrary<G>(g: &mut G) -> $sname
+              where G: Gen
+            {
+                let neg = bool::arbitrary(g);
+                let val = $name::arbitrary(g);
+                let neg2 = if val.is_zero() { false } else { neg };
+                $sname{ negative: neg2, value: val }
+            }
+        }
+
         impl fmt::Debug for $sname {
             fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
                 if self.negative {
diff --git a/src/signed/mod.rs b/src/signed/mod.rs
index 37cf770..14b90e8 100644
--- a/src/signed/mod.rs
+++ b/src/signed/mod.rs
@@ -26,6 +26,8 @@ mod shift;
 #[macro_use]
 mod subtraction;
 
+#[cfg(test)]
+use quickcheck::{Arbitrary,Gen};
 use std::cmp::{Ord,Ordering,PartialOrd};
 use std::fmt;
 use std::ops::{Add,AddAssign};