diff --git a/rust-version b/rust-version
index 2115e482c6..ab6f899cd3 100644
--- a/rust-version
+++ b/rust-version
@@ -1 +1 @@
-0f806a9812b62c36bdab08d33c14cf2d3ecf4355
+4316d0c6252cb1f833e582dfa68adb98efd5ddfb
diff --git a/src/bin/miri.rs b/src/bin/miri.rs
index 9319877472..db4c4a28de 100644
--- a/src/bin/miri.rs
+++ b/src/bin/miri.rs
@@ -1,3 +1,4 @@
+#![feature(generic_nonzero)]
 #![feature(rustc_private, stmt_expr_attributes)]
 #![allow(
     clippy::manual_range_contains,
@@ -19,7 +20,7 @@ extern crate rustc_session;
 extern crate tracing;
 
 use std::env::{self, VarError};
-use std::num::NonZeroU64;
+use std::num::NonZero;
 use std::path::PathBuf;
 use std::str::FromStr;
 
@@ -524,7 +525,7 @@ fn main() {
                 }
             }
         } else if let Some(param) = arg.strip_prefix("-Zmiri-track-alloc-id=") {
-            let ids: Vec<miri::AllocId> = match parse_comma_list::<NonZeroU64>(param) {
+            let ids: Vec<miri::AllocId> = match parse_comma_list::<NonZero<u64>>(param) {
                 Ok(ids) => ids.into_iter().map(miri::AllocId).collect(),
                 Err(err) =>
                     show_error!(
diff --git a/src/borrow_tracker/mod.rs b/src/borrow_tracker/mod.rs
index f50aaa292f..711323b51c 100644
--- a/src/borrow_tracker/mod.rs
+++ b/src/borrow_tracker/mod.rs
@@ -1,6 +1,6 @@
 use std::cell::RefCell;
 use std::fmt;
-use std::num::NonZeroU64;
+use std::num::NonZero;
 
 use smallvec::SmallVec;
 
@@ -12,22 +12,22 @@ use crate::*;
 pub mod stacked_borrows;
 pub mod tree_borrows;
 
-pub type CallId = NonZeroU64;
+pub type CallId = NonZero<u64>;
 
 /// Tracking pointer provenance
 #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
-pub struct BorTag(NonZeroU64);
+pub struct BorTag(NonZero<u64>);
 
 impl BorTag {
     pub fn new(i: u64) -> Option<Self> {
-        NonZeroU64::new(i).map(BorTag)
+        NonZero::new(i).map(BorTag)
     }
 
     pub fn get(&self) -> u64 {
         self.0.get()
     }
 
-    pub fn inner(&self) -> NonZeroU64 {
+    pub fn inner(&self) -> NonZero<u64> {
         self.0
     }
 
@@ -183,7 +183,7 @@ impl GlobalStateInner {
             borrow_tracker_method,
             next_ptr_tag: BorTag::one(),
             base_ptr_tags: FxHashMap::default(),
-            next_call_id: NonZeroU64::new(1).unwrap(),
+            next_call_id: NonZero::new(1).unwrap(),
             protected_tags: FxHashMap::default(),
             tracked_pointer_tags,
             tracked_call_ids,
@@ -205,7 +205,7 @@ impl GlobalStateInner {
         if self.tracked_call_ids.contains(&call_id) {
             machine.emit_diagnostic(NonHaltingDiagnostic::CreatedCallId(call_id));
         }
-        self.next_call_id = NonZeroU64::new(call_id.get() + 1).unwrap();
+        self.next_call_id = NonZero::new(call_id.get() + 1).unwrap();
         FrameState { call_id, protected_tags: SmallVec::new() }
     }
 
diff --git a/src/concurrency/init_once.rs b/src/concurrency/init_once.rs
index 9a848d5034..35dcfecbbe 100644
--- a/src/concurrency/init_once.rs
+++ b/src/concurrency/init_once.rs
@@ -1,5 +1,4 @@
 use std::collections::VecDeque;
-use std::num::NonZeroU32;
 
 use rustc_index::Idx;
 use rustc_middle::ty::layout::TyAndLayout;
diff --git a/src/concurrency/sync.rs b/src/concurrency/sync.rs
index 6863119032..956a02ded0 100644
--- a/src/concurrency/sync.rs
+++ b/src/concurrency/sync.rs
@@ -1,5 +1,4 @@
 use std::collections::{hash_map::Entry, VecDeque};
-use std::num::NonZeroU32;
 use std::ops::Not;
 
 use rustc_data_structures::fx::FxHashMap;
@@ -24,12 +23,12 @@ macro_rules! declare_id {
         /// 0 is used to indicate that the id was not yet assigned and,
         /// therefore, is not a valid identifier.
         #[derive(Clone, Copy, Debug, PartialOrd, Ord, PartialEq, Eq, Hash)]
-        pub struct $name(NonZeroU32);
+        pub struct $name(std::num::NonZero<u32>);
 
         impl SyncId for $name {
             // Panics if `id == 0`.
             fn from_u32(id: u32) -> Self {
-                Self(NonZeroU32::new(id).unwrap())
+                Self(std::num::NonZero::new(id).unwrap())
             }
             fn to_u32(&self) -> u32 {
                 self.0.get()
@@ -42,11 +41,11 @@ macro_rules! declare_id {
                 // therefore, need to shift by one when converting from an index
                 // into a vector.
                 let shifted_idx = u32::try_from(idx).unwrap().checked_add(1).unwrap();
-                $name(NonZeroU32::new(shifted_idx).unwrap())
+                $name(std::num::NonZero::new(shifted_idx).unwrap())
             }
             fn index(self) -> usize {
                 // See the comment in `Self::new`.
-                // (This cannot underflow because self is NonZeroU32.)
+                // (This cannot underflow because `self.0` is `NonZero<u32>`.)
                 usize::try_from(self.0.get() - 1).unwrap()
             }
         }
diff --git a/src/diagnostics.rs b/src/diagnostics.rs
index 7825673db0..d47f446716 100644
--- a/src/diagnostics.rs
+++ b/src/diagnostics.rs
@@ -1,5 +1,5 @@
 use std::fmt::{self, Write};
-use std::num::NonZeroU64;
+use std::num::NonZero;
 
 use rustc_errors::{DiagnosticBuilder, DiagnosticMessage, Level};
 use rustc_span::{SpanData, Symbol, DUMMY_SP};
@@ -110,7 +110,7 @@ pub enum NonHaltingDiagnostic {
     /// (new_tag, new_perm, (alloc_id, base_offset, orig_tag))
     ///
     /// new_perm is `None` for base tags.
-    CreatedPointerTag(NonZeroU64, Option<String>, Option<(AllocId, AllocRange, ProvenanceExtra)>),
+    CreatedPointerTag(NonZero<u64>, Option<String>, Option<(AllocId, AllocRange, ProvenanceExtra)>),
     /// This `Item` was popped from the borrow stack. The string explains the reason.
     PoppedPointerTag(Item, String),
     CreatedCallId(CallId),
diff --git a/src/helpers.rs b/src/helpers.rs
index 932a35d9bf..d9b4363d60 100644
--- a/src/helpers.rs
+++ b/src/helpers.rs
@@ -1,6 +1,6 @@
 use std::cmp;
 use std::iter;
-use std::num::NonZeroUsize;
+use std::num::NonZero;
 use std::time::Duration;
 
 use rustc_apfloat::ieee::{Double, Single};
@@ -572,7 +572,7 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriInterpCxExt<'mir, 'tcx> {
             fn visit_union(
                 &mut self,
                 _v: &MPlaceTy<'tcx, Provenance>,
-                _fields: NonZeroUsize,
+                _fields: NonZero<usize>,
             ) -> InterpResult<'tcx> {
                 bug!("we should have already handled unions in `visit_value`")
             }
diff --git a/src/lib.rs b/src/lib.rs
index adc547aa6c..c567949102 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,6 +1,7 @@
 #![feature(rustc_private)]
 #![feature(cell_update)]
 #![feature(float_gamma)]
+#![feature(generic_nonzero)]
 #![feature(map_try_insert)]
 #![feature(never_type)]
 #![feature(try_blocks)]
diff --git a/src/shims/foreign_items.rs b/src/shims/foreign_items.rs
index f4d6905534..0645c1f176 100644
--- a/src/shims/foreign_items.rs
+++ b/src/shims/foreign_items.rs
@@ -475,7 +475,7 @@ trait EvalContextExtPriv<'mir, 'tcx: 'mir>: crate::MiriInterpCxExt<'mir, 'tcx> {
                 let [id, show_unnamed] = this.check_shim(abi, Abi::Rust, link_name, args)?;
                 let id = this.read_scalar(id)?.to_u64()?;
                 let show_unnamed = this.read_scalar(show_unnamed)?.to_bool()?;
-                if let Some(id) = std::num::NonZeroU64::new(id) {
+                if let Some(id) = std::num::NonZero::new(id) {
                     this.print_borrow_state(AllocId(id), show_unnamed)?;
                 }
             }
diff --git a/tests/pass/intrinsics.rs b/tests/pass/intrinsics.rs
index 8e46bd7ad4..0dda5aadce 100644
--- a/tests/pass/intrinsics.rs
+++ b/tests/pass/intrinsics.rs
@@ -37,7 +37,7 @@ fn main() {
     let mut saw_false = false;
 
     for _ in 0..50 {
-        if unsafe { intrinsics::is_val_statically_known(0) } {
+        if intrinsics::is_val_statically_known(0) {
             saw_true = true;
         } else {
             saw_false = true;