diff --git a/src/paging.rs b/src/paging.rs
index c552ef4..2689499 100644
--- a/src/paging.rs
+++ b/src/paging.rs
@@ -31,6 +31,11 @@ fn align_up(addr: u64, align: u64) -> u64 {
 pub struct PhysAddr(pub u64);
 
 impl PhysAddr {
+    #[inline]
+    pub const fn new(addr: u64) -> Self {
+        Self(addr)
+    }
+
     /// Convert to `u64`
     pub fn as_u64(self) -> u64 {
         self.0
@@ -113,14 +118,6 @@ impl Into<usize> for PhysAddr {
     }
 }
 
-impl ops::Add for PhysAddr {
-    type Output = PhysAddr;
-
-    fn add(self, rhs: PhysAddr) -> Self::Output {
-        PhysAddr(self.0 + rhs.0)
-    }
-}
-
 impl ops::Add<u64> for PhysAddr {
     type Output = PhysAddr;
 
@@ -129,20 +126,6 @@ impl ops::Add<u64> for PhysAddr {
     }
 }
 
-impl ops::Add<usize> for PhysAddr {
-    type Output = PhysAddr;
-
-    fn add(self, rhs: usize) -> Self::Output {
-        PhysAddr::from(self.0 + rhs as u64)
-    }
-}
-
-impl ops::AddAssign for PhysAddr {
-    fn add_assign(&mut self, other: PhysAddr) {
-        *self = PhysAddr::from(self.0 + other.0);
-    }
-}
-
 impl ops::AddAssign<u64> for PhysAddr {
     fn add_assign(&mut self, offset: u64) {
         *self = PhysAddr::from(self.0 + offset);
@@ -150,10 +133,10 @@ impl ops::AddAssign<u64> for PhysAddr {
 }
 
 impl ops::Sub for PhysAddr {
-    type Output = PhysAddr;
+    type Output = u64;
 
     fn sub(self, rhs: PhysAddr) -> Self::Output {
-        PhysAddr::from(self.0 - rhs.0)
+        self.as_u64().checked_sub(rhs.as_u64()).unwrap()
     }
 }
 
@@ -165,14 +148,6 @@ impl ops::Sub<u64> for PhysAddr {
     }
 }
 
-impl ops::Sub<usize> for PhysAddr {
-    type Output = PhysAddr;
-
-    fn sub(self, rhs: usize) -> Self::Output {
-        PhysAddr::from(self.0 - rhs as u64)
-    }
-}
-
 impl ops::Rem for PhysAddr {
     type Output = PhysAddr;
 
@@ -287,6 +262,11 @@ impl fmt::Pointer for PhysAddr {
 pub struct VirtAddr(pub u64);
 
 impl VirtAddr {
+    #[inline]
+    pub const fn new(addr: u64) -> Self {
+        Self(addr)
+    }
+
     /// Convert from `u64`
     pub const fn from_u64(v: u64) -> Self {
         VirtAddr(v)
@@ -429,14 +409,6 @@ impl Into<usize> for VirtAddr {
     }
 }
 
-impl ops::Add for VirtAddr {
-    type Output = VirtAddr;
-
-    fn add(self, rhs: VirtAddr) -> Self::Output {
-        VirtAddr(self.0 + rhs.0)
-    }
-}
-
 impl ops::Add<u64> for VirtAddr {
     type Output = VirtAddr;
 
@@ -445,37 +417,17 @@ impl ops::Add<u64> for VirtAddr {
     }
 }
 
-impl ops::Add<usize> for VirtAddr {
-    type Output = VirtAddr;
-
-    fn add(self, rhs: usize) -> Self::Output {
-        VirtAddr::from(self.0 + rhs as u64)
-    }
-}
-
-impl ops::AddAssign for VirtAddr {
-    fn add_assign(&mut self, other: VirtAddr) {
-        *self = VirtAddr::from(self.0 + other.0);
-    }
-}
-
 impl ops::AddAssign<u64> for VirtAddr {
     fn add_assign(&mut self, offset: u64) {
         *self = VirtAddr::from(self.0 + offset);
     }
 }
 
-impl ops::AddAssign<usize> for VirtAddr {
-    fn add_assign(&mut self, offset: usize) {
-        *self = VirtAddr::from(self.0 + offset as u64);
-    }
-}
-
 impl ops::Sub for VirtAddr {
-    type Output = VirtAddr;
+    type Output = u64;
 
     fn sub(self, rhs: VirtAddr) -> Self::Output {
-        VirtAddr::from(self.0 - rhs.0)
+        self.as_u64().checked_sub(rhs.as_u64()).unwrap()
     }
 }
 
@@ -487,14 +439,6 @@ impl ops::Sub<u64> for VirtAddr {
     }
 }
 
-impl ops::Sub<usize> for VirtAddr {
-    type Output = VirtAddr;
-
-    fn sub(self, rhs: usize) -> Self::Output {
-        VirtAddr::from(self.0 - rhs as u64)
-    }
-}
-
 impl ops::Rem for VirtAddr {
     type Output = VirtAddr;