diff --git a/src/libcore/num/mod.rs b/src/libcore/num/mod.rs
index 6fb67ea9c9a..5b7d5f45d92 100644
--- a/src/libcore/num/mod.rs
+++ b/src/libcore/num/mod.rs
@@ -1215,7 +1215,7 @@ $EndFeature, "
 ```"),
             #[stable(feature = "num_wrapping", since = "1.2.0")]
             #[inline]
-            pub fn wrapping_neg(self) -> Self {
+            pub const fn wrapping_neg(self) -> Self {
                 self.overflowing_neg().0
             }
         }
@@ -1569,12 +1569,8 @@ assert_eq!(", stringify!($SelfT), "::MIN.overflowing_neg(), (", stringify!($Self
 ```"),
             #[inline]
             #[stable(feature = "wrapping", since = "1.7.0")]
-            pub fn overflowing_neg(self) -> (Self, bool) {
-                if self == Self::min_value() {
-                    (Self::min_value(), true)
-                } else {
-                    (-self, false)
-                }
+            pub const fn overflowing_neg(self) -> (Self, bool) {
+                ((!self).wrapping_add(1), self == Self::min_value())
             }
         }
 
@@ -3092,7 +3088,7 @@ assert_eq!(100", stringify!($SelfT), ".wrapping_rem_euclid(10), 0);
         /// ```
         #[stable(feature = "num_wrapping", since = "1.2.0")]
         #[inline]
-        pub fn wrapping_neg(self) -> Self {
+        pub const fn wrapping_neg(self) -> Self {
             self.overflowing_neg().0
         }
 
@@ -3397,7 +3393,7 @@ assert_eq!(2", stringify!($SelfT), ".overflowing_neg(), (-2i32 as ", stringify!(
 ```"),
             #[inline]
             #[stable(feature = "wrapping", since = "1.7.0")]
-            pub fn overflowing_neg(self) -> (Self, bool) {
+            pub const fn overflowing_neg(self) -> (Self, bool) {
                 ((!self).wrapping_add(1), self != 0)
             }
         }
diff --git a/src/test/run-pass/const-int-overflowing.rs b/src/test/run-pass/const-int-overflowing.rs
index 289b1236cf1..82057868b73 100644
--- a/src/test/run-pass/const-int-overflowing.rs
+++ b/src/test/run-pass/const-int-overflowing.rs
@@ -13,6 +13,9 @@ const SHL_B: (u32, bool) = 0x1u32.overflowing_shl(132);
 const SHR_A: (u32, bool) = 0x10u32.overflowing_shr(4);
 const SHR_B: (u32, bool) = 0x10u32.overflowing_shr(132);
 
+const NEG_A: (u32, bool) = 0u32.overflowing_neg();
+const NEG_B: (u32, bool) = core::u32::MAX.overflowing_neg();
+
 fn ident<T>(ident: T) -> T {
     ident
 }
@@ -32,4 +35,7 @@ fn main() {
 
     assert_eq!(SHR_A, ident((0x1, false)));
     assert_eq!(SHR_B, ident((0x1, true)));
+
+    assert_eq!(NEG_A, ident((0, false)));
+    assert_eq!(NEG_B, ident((1, true)));
 }
diff --git a/src/test/run-pass/const-int-wrapping.rs b/src/test/run-pass/const-int-wrapping.rs
index 5ab712015df..140fd57ecb8 100644
--- a/src/test/run-pass/const-int-wrapping.rs
+++ b/src/test/run-pass/const-int-wrapping.rs
@@ -13,6 +13,9 @@ const SHL_B: u32 = 1u32.wrapping_shl(128);
 const SHR_A: u32 = 128u32.wrapping_shr(7);
 const SHR_B: u32 = 128u32.wrapping_shr(128);
 
+const NEG_A: u32 = 5u32.wrapping_neg();
+const NEG_B: u32 = 1234567890u32.wrapping_neg();
+
 fn ident<T>(ident: T) -> T {
     ident
 }
@@ -32,4 +35,7 @@ fn main() {
 
     assert_eq!(SHR_A, ident(1));
     assert_eq!(SHR_B, ident(128));
+
+    assert_eq!(NEG_A, ident(4294967291));
+    assert_eq!(NEG_B, ident(3060399406));
 }