diff --git a/clippy_lints/src/consts.rs b/clippy_lints/src/consts.rs
index b4c8521a0a9f..aac9aa3e8ef1 100644
--- a/clippy_lints/src/consts.rs
+++ b/clippy_lints/src/consts.rs
@@ -92,7 +92,10 @@ impl PartialEq for Constant {
                 // we want `Fw32 == FwAny` and `FwAny == Fw64`, by transitivity we must have
                 // `Fw32 == Fw64` so don’t compare them
                 match (ls.parse::<f64>(), rs.parse::<f64>()) {
-                    (Ok(l), Ok(r)) => l.eq(&r),
+                    // mem::transmute is required to catch non-matching 0.0, -0.0, and NaNs
+                    (Ok(l), Ok(r)) => unsafe {
+                        mem::transmute::<f64, u64>(l) == mem::transmute::<f64, u64>(r)
+                    },
                     _ => false,
                 }
             }
@@ -159,7 +162,11 @@ impl PartialOrd for Constant {
             (&Constant::Int(l), &Constant::Int(r)) => Some(l.cmp(&r)),
             (&Constant::Float(ref ls, _), &Constant::Float(ref rs, _)) => {
                 match (ls.parse::<f64>(), rs.parse::<f64>()) {
-                    (Ok(ref l), Ok(ref r)) => l.partial_cmp(r),
+                    (Ok(ref l), Ok(ref r)) => match (l.partial_cmp(r), l.is_sign_positive() == r.is_sign_positive()) {
+                        // Check for comparison of -0.0 and 0.0
+                        (Some(Ordering::Equal), false) => None,
+                        (x, _) => x
+                    },
                     _ => None,
                 }
             }
diff --git a/tests/compile-fail/copies.rs b/tests/compile-fail/copies.rs
index a8d7157629b4..3c3e43931ed7 100644
--- a/tests/compile-fail/copies.rs
+++ b/tests/compile-fail/copies.rs
@@ -9,6 +9,7 @@
 #![allow(cyclomatic_complexity)]
 #![allow(blacklisted_name)]
 #![allow(collapsible_if)]
+#![allow(zero_divided_by_zero, eq_op)]
 
 fn bar<T>(_: T) {}
 fn foo() -> bool { unimplemented!() }
@@ -229,6 +230,46 @@ fn if_same_then_else() -> Result<&'static str, ()> {
         _ => 0,
     };
 
+    let _ = if true {
+        //~^NOTE same as this
+        0.0
+    } else { //~ERROR this `if` has identical blocks
+        0.0
+    };
+
+    let _ = if true {
+        //~^NOTE same as this
+        -0.0
+    } else { //~ERROR this `if` has identical blocks
+        -0.0
+    };
+
+    let _ = if true {
+        0.0
+    } else {
+        -0.0
+    };
+
+    // Different NaNs
+    let _ = if true {
+        0.0 / 0.0
+    } else {
+        std::f32::NAN
+    };
+
+    // Same NaNs
+    let _ = if true {
+        //~^NOTE same as this
+        std::f32::NAN
+    } else { //~ERROR this `if` has identical blocks
+        std::f32::NAN
+    };
+
+    let _ = match Some(()) {
+        Some(()) => 0.0,
+        None => -0.0
+    };
+
     match (Some(42), Some("")) {
         (Some(a), None) => bar(a),
         (None, Some(a)) => bar(a), // bindings have different types
diff --git a/tests/consts.rs b/tests/consts.rs
index 773b889ebff7..5f5f4cb47d0a 100644
--- a/tests/consts.rs
+++ b/tests/consts.rs
@@ -82,6 +82,12 @@ fn test_ops() {
     let half_any = Constant::Float("0.5".into(), FloatWidth::Any);
     let half32 = Constant::Float("0.5".into(), FloatWidth::F32);
     let half64 = Constant::Float("0.5".into(), FloatWidth::F64);
+    let pos_zero = Constant::Float("0.0".into(), FloatWidth::F64);
+    let neg_zero = Constant::Float("-0.0".into(), FloatWidth::F64);
+
+    assert_eq!(pos_zero, pos_zero);
+    assert_eq!(neg_zero, neg_zero);
+    assert_eq!(None, pos_zero.partial_cmp(&neg_zero));
 
     assert_eq!(half_any, half32);
     assert_eq!(half_any, half64);