diff --git a/src/byteorder.rs b/src/byteorder.rs
index adcfb3a6079..fd38cc3e02b 100644
--- a/src/byteorder.rs
+++ b/src/byteorder.rs
@@ -171,6 +171,28 @@ macro_rules! impl_fmt_trait {
     };
 }
 
+trait GetFallback: Sized {
+    #[inline(always)]
+    fn get(self) -> Self {
+        self
+    }
+}
+
+impl GetFallback for f32 {}
+impl GetFallback for f64 {}
+impl GetFallback for i8 {}
+impl GetFallback for i16 {}
+impl GetFallback for i32 {}
+impl GetFallback for i64 {}
+impl GetFallback for i128 {}
+impl GetFallback for isize {}
+impl GetFallback for u8 {}
+impl GetFallback for u16 {}
+impl GetFallback for u32 {}
+impl GetFallback for u64 {}
+impl GetFallback for u128 {}
+impl GetFallback for usize {}
+
 macro_rules! impl_fmt_traits {
     ($name:ident, $native:ident, "floating point number") => {
         impl_fmt_trait!($name, $native, Display);
@@ -215,8 +237,8 @@ macro_rules! impl_ops_traits {
         impl_ops_traits!(@without_byteorder_swap $name, $native, BitAnd, bitand, BitAndAssign, bitand_assign);
         impl_ops_traits!(@without_byteorder_swap $name, $native, BitOr, bitor, BitOrAssign, bitor_assign);
         impl_ops_traits!(@without_byteorder_swap $name, $native, BitXor, bitxor, BitXorAssign, bitxor_assign);
-        impl_ops_traits!(@with_byteorder_swap $name, $native, Shl, shl, ShlAssign, shl_assign);
-        impl_ops_traits!(@with_byteorder_swap $name, $native, Shr, shr, ShrAssign, shr_assign);
+        impl_ops_traits!(@with_byteorder_swap $name, $native, Shl, <{Self}>, shl, ShlAssign, shl_assign);
+        impl_ops_traits!(@with_byteorder_swap $name, $native, Shr, <{Self}>, shr, ShrAssign, shr_assign);
 
         impl<O> core::ops::Not for $name<O> {
             type Output = $name<O>;
@@ -235,7 +257,7 @@ macro_rules! impl_ops_traits {
             }
         }
 
-        impl<O: ByteOrder> Ord for $name<O> {
+        impl<O: ByteOrder> Ord<$native> for $name<O> {
             #[inline(always)]
             fn cmp(&self, other: &Self) -> Ordering {
                 self.get().cmp(&other.get())
@@ -255,31 +277,33 @@ macro_rules! impl_ops_traits {
         }
     };
     ($name:ident, $native:ident, @all_types) => {
-        impl_ops_traits!(@with_byteorder_swap $name, $native, Add, add, AddAssign, add_assign);
-        impl_ops_traits!(@with_byteorder_swap $name, $native, Div, div, DivAssign, div_assign);
-        impl_ops_traits!(@with_byteorder_swap $name, $native, Mul, mul, MulAssign, mul_assign);
-        impl_ops_traits!(@with_byteorder_swap $name, $native, Rem, rem, RemAssign, rem_assign);
-        impl_ops_traits!(@with_byteorder_swap $name, $native, Sub, sub, SubAssign, sub_assign);
+        impl_ops_traits!(@with_byteorder_swap $name, $native, Add, <{Self, $native}>, add, AddAssign, add_assign);
+        impl_ops_traits!(@with_byteorder_swap $name, $native, Div, <{Self, $native}>, div, DivAssign, div_assign);
+        impl_ops_traits!(@with_byteorder_swap $name, $native, Mul, <{Self, $native}>, mul, MulAssign, mul_assign);
+        impl_ops_traits!(@with_byteorder_swap $name, $native, Rem, <{Self, $native}>, rem, RemAssign, rem_assign);
+        impl_ops_traits!(@with_byteorder_swap $name, $native, Sub, <{Self, $native}>, sub, SubAssign, sub_assign);
     };
-    (@with_byteorder_swap $name:ident, $native:ident, $trait:ident, $method:ident, $trait_assign:ident, $method_assign:ident) => {
-        impl<O: ByteOrder> core::ops::$trait for $name<O> {
-            type Output = $name<O>;
+    (@with_byteorder_swap $name:ident, $native:ident, $trait:ident, <{$($rhs:ident),*}>, $method:ident, $trait_assign:ident, $method_assign:ident) => {
+        $(
+            impl<O: ByteOrder> core::ops::$trait<$rhs> for $name<O> {
+                type Output = $name<O>;
 
-            #[inline(always)]
-            fn $method(self, rhs: $name<O>) -> $name<O> {
-                let self_native: $native = self.get();
-                let rhs_native: $native = rhs.get();
-                let result_native = core::ops::$trait::$method(self_native, rhs_native);
-                $name::<O>::new(result_native)
+                #[inline(always)]
+                fn $method(self, rhs: $rhs) -> $name<O> {
+                    let self_native: $native = self.get();
+                    let rhs_native: $native = rhs.get();
+                    let result_native = core::ops::$trait::$method(self_native, rhs_native);
+                    $name::<O>::new(result_native)
+                }
             }
-        }
 
-        impl<O: ByteOrder> core::ops::$trait_assign for $name<O> {
-            #[inline(always)]
-            fn $method_assign(&mut self, rhs: $name<O>) {
-                *self = core::ops::$trait::$method(*self, rhs);
+            impl<O: ByteOrder> core::ops::$trait_assign<$rhs> for $name<O> {
+                #[inline(always)]
+                fn $method_assign(&mut self, rhs: $rhs) {
+                    *self = core::ops::$trait::$method(*self, rhs);
+                }
             }
-        }
+        )*
     };
     // Implement traits in terms of the same trait on the native type, but
     // without performing a byte order swap. This only works for bitwise