diff --git a/compiler/rustc_const_eval/src/interpret/operand.rs b/compiler/rustc_const_eval/src/interpret/operand.rs
index 36da9037e43d9..39755169e6cae 100644
--- a/compiler/rustc_const_eval/src/interpret/operand.rs
+++ b/compiler/rustc_const_eval/src/interpret/operand.rs
@@ -310,7 +310,7 @@ impl<'tcx, Prov: Provenance> ImmTy<'tcx, Prov> {
         let ty = tcx.ty_ordering_enum(None);
         let layout =
             tcx.layout_of(ty::TypingEnv::fully_monomorphized().as_query_input(ty)).unwrap();
-        Self::from_scalar(Scalar::from_i8(c as i8), layout)
+        Self::from_scalar(Scalar::Int(c.into()), layout)
     }
 
     pub fn from_pair(a: Self, b: Self, cx: &(impl HasTypingEnv<'tcx> + HasTyCtxt<'tcx>)) -> Self {
diff --git a/compiler/rustc_middle/src/mir/interpret/value.rs b/compiler/rustc_middle/src/mir/interpret/value.rs
index 9d462093b9ea1..7ba0e5b5e07e5 100644
--- a/compiler/rustc_middle/src/mir/interpret/value.rs
+++ b/compiler/rustc_middle/src/mir/interpret/value.rs
@@ -180,27 +180,27 @@ impl<Prov> Scalar<Prov> {
 
     #[inline]
     pub fn from_i8(i: i8) -> Self {
-        Self::from_int(i, Size::from_bits(8))
+        Self::Int(i.into())
     }
 
     #[inline]
     pub fn from_i16(i: i16) -> Self {
-        Self::from_int(i, Size::from_bits(16))
+        Self::Int(i.into())
     }
 
     #[inline]
     pub fn from_i32(i: i32) -> Self {
-        Self::from_int(i, Size::from_bits(32))
+        Self::Int(i.into())
     }
 
     #[inline]
     pub fn from_i64(i: i64) -> Self {
-        Self::from_int(i, Size::from_bits(64))
+        Self::Int(i.into())
     }
 
     #[inline]
     pub fn from_i128(i: i128) -> Self {
-        Self::from_int(i, Size::from_bits(128))
+        Self::Int(i.into())
     }
 
     #[inline]
diff --git a/compiler/rustc_middle/src/ty/consts/int.rs b/compiler/rustc_middle/src/ty/consts/int.rs
index 9f5e31d894cb3..9c9cd6953392a 100644
--- a/compiler/rustc_middle/src/ty/consts/int.rs
+++ b/compiler/rustc_middle/src/ty/consts/int.rs
@@ -422,9 +422,9 @@ macro_rules! from_scalar_int_for_x {
             impl From<ScalarInt> for $ty {
                 #[inline]
                 fn from(int: ScalarInt) -> Self {
-                    // The `unwrap` cannot fail because to_bits (if it succeeds)
+                    // The `unwrap` cannot fail because to_uint (if it succeeds)
                     // is guaranteed to return a value that fits into the size.
-                    int.to_bits(Size::from_bytes(size_of::<$ty>()))
+                    int.to_uint(Size::from_bytes(size_of::<$ty>()))
                        .try_into().unwrap()
                 }
             }
@@ -450,6 +450,49 @@ impl From<char> for ScalarInt {
     }
 }
 
+macro_rules! from_x_for_scalar_int_signed {
+    ($($ty:ty),*) => {
+        $(
+            impl From<$ty> for ScalarInt {
+                #[inline]
+                fn from(u: $ty) -> Self {
+                    Self {
+                        data: u128::from(u.cast_unsigned()), // go via the unsigned type of the same size
+                        size: NonZero::new(size_of::<$ty>() as u8).unwrap(),
+                    }
+                }
+            }
+        )*
+    }
+}
+
+macro_rules! from_scalar_int_for_x_signed {
+    ($($ty:ty),*) => {
+        $(
+            impl From<ScalarInt> for $ty {
+                #[inline]
+                fn from(int: ScalarInt) -> Self {
+                    // The `unwrap` cannot fail because to_int (if it succeeds)
+                    // is guaranteed to return a value that fits into the size.
+                    int.to_int(Size::from_bytes(size_of::<$ty>()))
+                       .try_into().unwrap()
+                }
+            }
+        )*
+    }
+}
+
+from_x_for_scalar_int_signed!(i8, i16, i32, i64, i128);
+from_scalar_int_for_x_signed!(i8, i16, i32, i64, i128);
+
+impl From<std::cmp::Ordering> for ScalarInt {
+    #[inline]
+    fn from(c: std::cmp::Ordering) -> Self {
+        // Here we rely on `Ordering` having the same values in host and target!
+        ScalarInt::from(c as i8)
+    }
+}
+
 /// Error returned when a conversion from ScalarInt to char fails.
 #[derive(Debug)]
 pub struct CharTryFromScalarInt;
diff --git a/library/core/src/intrinsics/mod.rs b/library/core/src/intrinsics/mod.rs
index 23bafa778bc6b..439c8c1f9a1e6 100644
--- a/library/core/src/intrinsics/mod.rs
+++ b/library/core/src/intrinsics/mod.rs
@@ -1,7 +1,10 @@
 //! Compiler intrinsics.
 //!
-//! The corresponding definitions are in <https://github.com/rust-lang/rust/blob/master/compiler/rustc_codegen_llvm/src/intrinsic.rs>.
-//! The corresponding const implementations are in <https://github.com/rust-lang/rust/blob/master/compiler/rustc_const_eval/src/interpret/intrinsics.rs>.
+//! These are the imports making intrinsics available to Rust code. The actual implementations live in the compiler.
+//! Some of these intrinsics are lowered to MIR in <https://github.com/rust-lang/rust/blob/master/compiler/rustc_mir_transform/src/lower_intrinsics.rs>.
+//! The remaining intrinsics are implemented for the LLVM backend in <https://github.com/rust-lang/rust/blob/master/compiler/rustc_codegen_ssa/src/mir/intrinsic.rs>
+//! and <https://github.com/rust-lang/rust/blob/master/compiler/rustc_codegen_llvm/src/intrinsic.rs>,
+//! and for const evaluation in <https://github.com/rust-lang/rust/blob/master/compiler/rustc_const_eval/src/interpret/intrinsics.rs>.
 //!
 //! # Const intrinsics
 //!
@@ -20,28 +23,14 @@
 //!
 //! The volatile intrinsics provide operations intended to act on I/O
 //! memory, which are guaranteed to not be reordered by the compiler
-//! across other volatile intrinsics. See the LLVM documentation on
-//! [[volatile]].
-//!
-//! [volatile]: https://llvm.org/docs/LangRef.html#volatile-memory-accesses
+//! across other volatile intrinsics. See [`read_volatile`][ptr::read_volatile]
+//! and [`write_volatile`][ptr::write_volatile].
 //!
 //! # Atomics
 //!
 //! The atomic intrinsics provide common atomic operations on machine
-//! words, with multiple possible memory orderings. They obey the same
-//! semantics as C++11. See the LLVM documentation on [[atomics]].
-//!
-//! [atomics]: https://llvm.org/docs/Atomics.html
-//!
-//! A quick refresher on memory ordering:
-//!
-//! * Acquire - a barrier for acquiring a lock. Subsequent reads and writes
-//!   take place after the barrier.
-//! * Release - a barrier for releasing a lock. Preceding reads and writes
-//!   take place before the barrier.
-//! * Sequentially consistent - sequentially consistent operations are
-//!   guaranteed to happen in order. This is the standard mode for working
-//!   with atomic types and is equivalent to Java's `volatile`.
+//! words, with multiple possible memory orderings. See the
+//! [atomic types][crate::sync::atomic] docs for details.
 //!
 //! # Unwinding
 //!