diff --git a/src/lib.rs b/src/lib.rs
index d17ce5a..5a512e7 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -41,7 +41,14 @@ const MAN_MASK: u64 = 0x000fffffffffffffu64;
 
 // canonical raw bit patterns (for hashing)
 const CANONICAL_NAN_BITS: u64 = 0x7ff8000000000000u64;
-const CANONICAL_ZERO_BITS: u64 = 0x0u64;
+
+#[inline(always)]
+fn canonicalize_signed_zero<T: FloatCore>(x: T) -> T {
+    // -0.0 + 0.0 == +0.0 under IEEE754 roundTiesToEven rounding mode,
+    // which Rust guarantees. Thus by adding a positive zero we
+    // canonicalize signed zero without any branches in one instruction.
+    x + T::zero()
+}
 
 /// A wrapper around floats providing implementations of `Eq`, `Ord`, and `Hash`.
 ///
@@ -116,25 +123,43 @@ impl<T: FloatCore> PartialOrd for OrderedFloat<T> {
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
         Some(self.cmp(other))
     }
+
+    #[inline]
+    fn lt(&self, other: &Self) -> bool {
+        !self.ge(other)
+    }
+
+    #[inline]
+    fn le(&self, other: &Self) -> bool {
+        other.ge(self)
+    }
+
+    #[inline]
+    fn gt(&self, other: &Self) -> bool {
+        !other.ge(self)
+    }
+
+    #[inline]
+    fn ge(&self, other: &Self) -> bool {
+        // We consider all NaNs equal, and NaN is the largest possible
+        // value. Thus if self is NaN we always return true. Otherwise
+        // self >= other is correct. If other is also not NaN it is trivially
+        // correct, and if it is we note that nothing can be greater or
+        // equal to NaN except NaN itself, which we already handled earlier.
+        self.0.is_nan() | (self.0 >= other.0)
+    }
 }
 
 impl<T: FloatCore> Ord for OrderedFloat<T> {
+    #[inline]
     fn cmp(&self, other: &Self) -> Ordering {
-        let lhs = &self.0;
-        let rhs = &other.0;
-        match lhs.partial_cmp(rhs) {
-            Some(ordering) => ordering,
-            None => {
-                if lhs.is_nan() {
-                    if rhs.is_nan() {
-                        Ordering::Equal
-                    } else {
-                        Ordering::Greater
-                    }
-                } else {
-                    Ordering::Less
-                }
-            }
+        #[allow(clippy::comparison_chain)]
+        if self < other {
+            Ordering::Less
+        } else if self > other {
+            Ordering::Greater
+        } else {
+            Ordering::Equal
         }
     }
 }
@@ -161,10 +186,8 @@ impl<T: FloatCore> Hash for OrderedFloat<T> {
     fn hash<H: Hasher>(&self, state: &mut H) {
         let bits = if self.is_nan() {
             CANONICAL_NAN_BITS
-        } else if self.is_zero() {
-            CANONICAL_ZERO_BITS
         } else {
-            raw_double_bits(&self.0)
+            raw_double_bits(&canonicalize_signed_zero(self.0))
         };
 
         bits.hash(state)
@@ -1150,12 +1173,7 @@ impl<T: FloatCore> Ord for NotNan<T> {
 impl<T: FloatCore> Hash for NotNan<T> {
     #[inline]
     fn hash<H: Hasher>(&self, state: &mut H) {
-        let bits = if self.is_zero() {
-            CANONICAL_ZERO_BITS
-        } else {
-            raw_double_bits(&self.0)
-        };
-
+        let bits = raw_double_bits(&canonicalize_signed_zero(self.0));
         bits.hash(state)
     }
 }
diff --git a/tests/test.rs b/tests/test.rs
index 69dfd6d..5626d1c 100644
--- a/tests/test.rs
+++ b/tests/test.rs
@@ -21,6 +21,32 @@ fn not_nan<T: FloatCore>(x: T) -> NotNan<T> {
     NotNan::new(x).unwrap()
 }
 
+#[test]
+fn test_total_order() {
+    let numberline = [
+        (-f32::INFINITY, 0),
+        (-1.0, 1),
+        (-0.0, 2),
+        (0.0, 2),
+        (1.0, 3),
+        (f32::INFINITY, 4),
+        (f32::NAN, 5),
+        (-f32::NAN, 5),
+    ];
+
+    for &(fi, i) in &numberline {
+        for &(fj, j) in &numberline {
+            assert_eq!(OrderedFloat(fi) < OrderedFloat(fj), i < j);
+            assert_eq!(OrderedFloat(fi) > OrderedFloat(fj), i > j);
+            assert_eq!(OrderedFloat(fi) <= OrderedFloat(fj), i <= j);
+            assert_eq!(OrderedFloat(fi) >= OrderedFloat(fj), i >= j);
+            assert_eq!(OrderedFloat(fi) == OrderedFloat(fj), i == j);
+            assert_eq!(OrderedFloat(fi) != OrderedFloat(fj), i != j);
+            assert_eq!(OrderedFloat(fi).cmp(&OrderedFloat(fj)), i.cmp(&j));
+        }
+    }
+}
+
 #[test]
 fn ordered_f32_compare_regular_floats() {
     assert_eq!(OrderedFloat(7.0f32).cmp(&OrderedFloat(7.0)), Equal);