Auto merge of #124780 - Mark-Simulacrum:lockless-cache, r=lcnr

Improve VecCache under parallel frontend

This replaces the single Vec allocation with a series of progressively larger buckets. With the cfg for parallel enabled but with -Zthreads=1, this looks like a slight regression in i-count and cycle counts (~1%).

With the parallel frontend at -Zthreads=4, this is an improvement (-5% wall-time from 5.788 to 5.4688 on libcore) than our current Lock-based approach, likely due to reducing the bouncing of the cache line holding the lock. At -Zthreads=32 it's a huge improvement (-46%: 8.829 -> 4.7319 seconds).

try-job: i686-gnu-nopt
try-job: dist-x86_64-linux

compiler/rustc_data_structures/src/lib.rs

@@ -21,6 +21,7 @@
 #![feature(auto_traits)]
 #![feature(cfg_match)]
 #![feature(core_intrinsics)]
+#![feature(dropck_eyepatch)]
 #![feature(extend_one)]
 #![feature(file_buffered)]
 #![feature(hash_raw_entry)]
@@ -78,6 +79,7 @@ pub mod thinvec;
 pub mod transitive_relation;
 pub mod unhash;
 pub mod unord;
+pub mod vec_cache;
 pub mod work_queue;
 
 mod atomic_ref;

compiler/rustc_data_structures/src/vec_cache.rs

@@ -0,0 +1,324 @@
+//! VecCache maintains a mapping from K -> (V, I) pairing. K and I must be roughly u32-sized, and V
+//! must be Copy.
+//!
+//! VecCache supports efficient concurrent put/get across the key space, with write-once semantics
+//! (i.e., a given key can only be put once). Subsequent puts will panic.
+//!
+//! This is currently used for query caching.
+
+use std::fmt::Debug;
+use std::marker::PhantomData;
+use std::sync::atomic::{AtomicPtr, AtomicU32, AtomicUsize, Ordering};
+
+use rustc_index::Idx;
+
+struct Slot<V> {
+    // We never construct &Slot<V> so it's fine for this to not be in an UnsafeCell.
+    value: V,
+    // This is both an index and a once-lock.
+    //
+    // 0: not yet initialized.
+    // 1: lock held, initializing.
+    // 2..u32::MAX - 2: initialized.
+    index_and_lock: AtomicU32,
+}
+
+/// This uniquely identifies a single `Slot<V>` entry in the buckets map, and provides accessors for
+/// either getting the value or putting a value.
+#[derive(Copy, Clone, Debug)]
+struct SlotIndex {
+    // the index of the bucket in VecCache (0 to 20)
+    bucket_idx: usize,
+    // number of entries in that bucket
+    entries: usize,
+    // the index of the slot within the bucket
+    index_in_bucket: usize,
+}
+
+// This makes sure the counts are consistent with what we allocate, precomputing each bucket a
+// compile-time. Visiting all powers of two is enough to hit all the buckets.
+//
+// We confirm counts are accurate in the slot_index_exhaustive test.
+const ENTRIES_BY_BUCKET: [usize; 21] = {
+    let mut entries = [0; 21];
+    let mut key = 0;
+    loop {
+        let si = SlotIndex::from_index(key);
+        entries[si.bucket_idx] = si.entries;
+        if key == 0 {
+            key = 1;
+        } else if key == (1 << 31) {
+            break;
+        } else {
+            key <<= 1;
+        }
+    }
+    entries
+};
+
+impl SlotIndex {
+    // This unpacks a flat u32 index into identifying which bucket it belongs to and the offset
+    // within that bucket. As noted in the VecCache docs, buckets double in size with each index.
+    // Typically that would mean 31 buckets (2^0 + 2^1 ... + 2^31 = u32::MAX - 1), but to reduce
+    // the size of the VecCache struct and avoid uselessly small allocations, we instead have the
+    // first bucket have 2**12 entries. To simplify the math, the second bucket also 2**12 entries,
+    // and buckets double from there.
+    //
+    // We assert that [0, 2**32 - 1] uniquely map through this function to individual, consecutive
+    // slots (see `slot_index_exhaustive` in tests).
+    #[inline]
+    const fn from_index(idx: u32) -> Self {
+        let mut bucket = match idx.checked_ilog2() {
+            Some(x) => x as usize,
+            None => 0,
+        };
+        let entries;
+        let running_sum;
+        if bucket <= 11 {
+            entries = 1 << 12;
+            running_sum = 0;
+            bucket = 0;
+        } else {
+            entries = 1 << bucket;
+            running_sum = entries;
+            bucket = bucket - 11;
+        }
+        SlotIndex { bucket_idx: bucket, entries, index_in_bucket: idx as usize - running_sum }
+    }
+
+    // SAFETY: Buckets must be managed solely by functions here (i.e., get/put on SlotIndex) and
+    // `self` comes from SlotIndex::from_index
+    #[inline]
+    unsafe fn get<V: Copy>(&self, buckets: &[AtomicPtr<Slot<V>>; 21]) -> Option<(V, u32)> {
+        // SAFETY: `bucket_idx` is ilog2(u32).saturating_sub(11), which is at most 21, i.e.,
+        // in-bounds of buckets. See `from_index` for computation.
+        let bucket = unsafe { buckets.get_unchecked(self.bucket_idx) };
+        let ptr = bucket.load(Ordering::Acquire);
+        // Bucket is not yet initialized: then we obviously won't find this entry in that bucket.
+        if ptr.is_null() {
+            return None;
+        }
+        assert!(self.index_in_bucket < self.entries);
+        // SAFETY: `bucket` was allocated (so <= isize in total bytes) to hold `entries`, so this
+        // must be inbounds.
+        let slot = unsafe { ptr.add(self.index_in_bucket) };
+
+        // SAFETY: initialized bucket has zeroed all memory within the bucket, so we are valid for
+        // AtomicU32 access.
+        let index_and_lock = unsafe { &(*slot).index_and_lock };
+        let current = index_and_lock.load(Ordering::Acquire);
+        let index = match current {
+            0 => return None,
+            // Treat "initializing" as actually just not initialized at all.
+            // The only reason this is a separate state is that `complete` calls could race and
+            // we can't allow that, but from load perspective there's no difference.
+            1 => return None,
+            _ => current - 2,
+        };
+
+        // SAFETY:
+        // * slot is a valid pointer (buckets are always valid for the index we get).
+        // * value is initialized since we saw a >= 2 index above.
+        // * `V: Copy`, so safe to read.
+        let value = unsafe { (*slot).value };
+        Some((value, index))
+    }
+
+    fn bucket_ptr<V>(&self, bucket: &AtomicPtr<Slot<V>>) -> *mut Slot<V> {
+        let ptr = bucket.load(Ordering::Acquire);
+        if ptr.is_null() { self.initialize_bucket(bucket) } else { ptr }
+    }
+
+    #[cold]
+    fn initialize_bucket<V>(&self, bucket: &AtomicPtr<Slot<V>>) -> *mut Slot<V> {
+        static LOCK: std::sync::Mutex<()> = std::sync::Mutex::new(());
+
+        // If we are initializing the bucket, then acquire a global lock.
+        //
+        // This path is quite cold, so it's cheap to use a global lock. This ensures that we never
+        // have multiple allocations for the same bucket.
+        let _allocator_guard = LOCK.lock().unwrap_or_else(|e| e.into_inner());
+
+        let ptr = bucket.load(Ordering::Acquire);
+
+        // OK, now under the allocator lock, if we're still null then it's definitely us that will
+        // initialize this bucket.
+        if ptr.is_null() {
+            let bucket_layout =
+                std::alloc::Layout::array::<Slot<V>>(self.entries as usize).unwrap();
+            // This is more of a sanity check -- this code is very cold, so it's safe to pay a
+            // little extra cost here.
+            assert!(bucket_layout.size() > 0);
+            // SAFETY: Just checked that size is non-zero.
+            let allocated = unsafe { std::alloc::alloc_zeroed(bucket_layout).cast::<Slot<V>>() };
+            if allocated.is_null() {
+                std::alloc::handle_alloc_error(bucket_layout);
+            }
+            bucket.store(allocated, Ordering::Release);
+            allocated
+        } else {
+            // Otherwise some other thread initialized this bucket after we took the lock. In that
+            // case, just return early.
+            ptr
+        }
+    }
+
+    /// Returns true if this successfully put into the map.
+    #[inline]
+    fn put<V>(&self, buckets: &[AtomicPtr<Slot<V>>; 21], value: V, extra: u32) -> bool {
+        // SAFETY: `bucket_idx` is ilog2(u32).saturating_sub(11), which is at most 21, i.e.,
+        // in-bounds of buckets.
+        let bucket = unsafe { buckets.get_unchecked(self.bucket_idx) };
+        let ptr = self.bucket_ptr(bucket);
+
+        assert!(self.index_in_bucket < self.entries);
+        // SAFETY: `bucket` was allocated (so <= isize in total bytes) to hold `entries`, so this
+        // must be inbounds.
+        let slot = unsafe { ptr.add(self.index_in_bucket) };
+
+        // SAFETY: initialized bucket has zeroed all memory within the bucket, so we are valid for
+        // AtomicU32 access.
+        let index_and_lock = unsafe { &(*slot).index_and_lock };
+        match index_and_lock.compare_exchange(0, 1, Ordering::AcqRel, Ordering::Acquire) {
+            Ok(_) => {
+                // We have acquired the initialization lock. It is our job to write `value` and
+                // then set the lock to the real index.
+
+                unsafe {
+                    (&raw mut (*slot).value).write(value);
+                }
+
+                index_and_lock.store(extra.checked_add(2).unwrap(), Ordering::Release);
+
+                true
+            }
+
+            // Treat "initializing" as the caller's fault. Callers are responsible for ensuring that
+            // there are no races on initialization. In the compiler's current usage for query
+            // caches, that's the "active query map" which ensures each query actually runs once
+            // (even if concurrently started).
+            Err(1) => panic!("caller raced calls to put()"),
+
+            // This slot was already populated. Also ignore, currently this is the same as
+            // "initializing".
+            Err(_) => false,
+        }
+    }
+}
+
+pub struct VecCache<K: Idx, V, I> {
+    // Entries per bucket:
+    // Bucket  0:       4096 2^12
+    // Bucket  1:       4096 2^12
+    // Bucket  2:       8192
+    // Bucket  3:      16384
+    // ...
+    // Bucket 19: 1073741824
+    // Bucket 20: 2147483648
+    // The total number of entries if all buckets are initialized is u32::MAX-1.
+    buckets: [AtomicPtr<Slot<V>>; 21],
+
+    // In the compiler's current usage these are only *read* during incremental and self-profiling.
+    // They are an optimization over iterating the full buckets array.
+    present: [AtomicPtr<Slot<()>>; 21],
+    len: AtomicUsize,
+
+    key: PhantomData<(K, I)>,
+}
+
+impl<K: Idx, V, I> Default for VecCache<K, V, I> {
+    fn default() -> Self {
+        VecCache {
+            buckets: Default::default(),
+            key: PhantomData,
+            len: Default::default(),
+            present: Default::default(),
+        }
+    }
+}
+
+// SAFETY: No access to `V` is made.
+unsafe impl<K: Idx, #[may_dangle] V, I> Drop for VecCache<K, V, I> {
+    fn drop(&mut self) {
+        // We have unique ownership, so no locks etc. are needed. Since `K` and `V` are both `Copy`,
+        // we are also guaranteed to just need to deallocate any large arrays (not iterate over
+        // contents).
+        //
+        // Confirm no need to deallocate invidual entries. Note that `V: Copy` is asserted on
+        // insert/lookup but not necessarily construction, primarily to avoid annoyingly propagating
+        // the bounds into struct definitions everywhere.
+        assert!(!std::mem::needs_drop::<K>());
+        assert!(!std::mem::needs_drop::<V>());
+
+        for (idx, bucket) in self.buckets.iter().enumerate() {
+            let bucket = bucket.load(Ordering::Acquire);
+            if !bucket.is_null() {
+                let layout = std::alloc::Layout::array::<Slot<V>>(ENTRIES_BY_BUCKET[idx]).unwrap();
+                unsafe {
+                    std::alloc::dealloc(bucket.cast(), layout);
+                }
+            }
+        }
+
+        for (idx, bucket) in self.present.iter().enumerate() {
+            let bucket = bucket.load(Ordering::Acquire);
+            if !bucket.is_null() {
+                let layout = std::alloc::Layout::array::<Slot<()>>(ENTRIES_BY_BUCKET[idx]).unwrap();
+                unsafe {
+                    std::alloc::dealloc(bucket.cast(), layout);
+                }
+            }
+        }
+    }
+}
+
+impl<K, V, I> VecCache<K, V, I>
+where
+    K: Eq + Idx + Copy + Debug,
+    V: Copy,
+    I: Idx + Copy,
+{
+    #[inline(always)]
+    pub fn lookup(&self, key: &K) -> Option<(V, I)> {
+        let key = u32::try_from(key.index()).unwrap();
+        let slot_idx = SlotIndex::from_index(key);
+        match unsafe { slot_idx.get(&self.buckets) } {
+            Some((value, idx)) => Some((value, I::new(idx as usize))),
+            None => None,
+        }
+    }
+
+    #[inline]
+    pub fn complete(&self, key: K, value: V, index: I) {
+        let key = u32::try_from(key.index()).unwrap();
+        let slot_idx = SlotIndex::from_index(key);
+        if slot_idx.put(&self.buckets, value, index.index() as u32) {
+            let present_idx = self.len.fetch_add(1, Ordering::Relaxed);
+            let slot = SlotIndex::from_index(present_idx as u32);
+            // We should always be uniquely putting due to `len` fetch_add returning unique values.
+            assert!(slot.put(&self.present, (), key));
+        }
+    }
+
+    pub fn iter(&self, f: &mut dyn FnMut(&K, &V, I)) {
+        for idx in 0..self.len.load(Ordering::Acquire) {
+            let key = SlotIndex::from_index(idx as u32);
+            match unsafe { key.get(&self.present) } {
+                // This shouldn't happen in our current usage (iter is really only
+                // used long after queries are done running), but if we hit this in practice it's
+                // probably fine to just break early.
+                None => unreachable!(),
+                Some(((), key)) => {
+                    let key = K::new(key as usize);
+                    // unwrap() is OK: present entries are always written only after we put the real
+                    // entry.
+                    let value = self.lookup(&key).unwrap();
+                    f(&key, &value.0, value.1);
+                }
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests;

compiler/rustc_data_structures/src/vec_cache/tests.rs

@@ -0,0 +1,95 @@
+use super::*;
+
+#[test]
+#[cfg(not(miri))]
+fn vec_cache_empty() {
+    let cache: VecCache<u32, u32, u32> = VecCache::default();
+    for key in 0..u32::MAX {
+        assert!(cache.lookup(&key).is_none());
+    }
+}
+
+#[test]
+fn vec_cache_insert_and_check() {
+    let cache: VecCache<u32, u32, u32> = VecCache::default();
+    cache.complete(0, 1, 2);
+    assert_eq!(cache.lookup(&0), Some((1, 2)));
+}
+
+#[test]
+fn sparse_inserts() {
+    let cache: VecCache<u32, u8, u32> = VecCache::default();
+    let end = if cfg!(target_pointer_width = "64") && cfg!(target_os = "linux") {
+        // For paged memory, 64-bit systems we should be able to sparsely allocate all of the pages
+        // needed for these inserts cheaply (without needing to actually have gigabytes of resident
+        // memory).
+        31
+    } else {
+        // Otherwise, still run the test but scaled back:
+        //
+        // Each slot is 5 bytes, so 2^25 entries (on non-virtual memory systems, like e.g. Windows) will
+        // mean 160 megabytes of allocated memory. Going beyond that is probably not reasonable for
+        // tests.
+        25
+    };
+    for shift in 0..end {
+        let key = 1u32 << shift;
+        cache.complete(key, shift, key);
+        assert_eq!(cache.lookup(&key), Some((shift, key)));
+    }
+}
+
+#[test]
+fn concurrent_stress_check() {
+    let cache: VecCache<u32, u32, u32> = VecCache::default();
+    std::thread::scope(|s| {
+        for idx in 0..100 {
+            let cache = &cache;
+            s.spawn(move || {
+                cache.complete(idx, idx, idx);
+            });
+        }
+    });
+
+    for idx in 0..100 {
+        assert_eq!(cache.lookup(&idx), Some((idx, idx)));
+    }
+}
+
+#[test]
+fn slot_entries_table() {
+    assert_eq!(ENTRIES_BY_BUCKET, [
+        4096, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304,
+        8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824,
+        2147483648
+    ]);
+}
+
+#[test]
+#[cfg(not(miri))]
+fn slot_index_exhaustive() {
+    let mut buckets = [0u32; 21];
+    for idx in 0..=u32::MAX {
+        buckets[SlotIndex::from_index(idx).bucket_idx] += 1;
+    }
+    let mut prev = None::<SlotIndex>;
+    for idx in 0..=u32::MAX {
+        let slot_idx = SlotIndex::from_index(idx);
+        if let Some(p) = prev {
+            if p.bucket_idx == slot_idx.bucket_idx {
+                assert_eq!(p.index_in_bucket + 1, slot_idx.index_in_bucket);
+            } else {
+                assert_eq!(slot_idx.index_in_bucket, 0);
+            }
+        } else {
+            assert_eq!(idx, 0);
+            assert_eq!(slot_idx.index_in_bucket, 0);
+            assert_eq!(slot_idx.bucket_idx, 0);
+        }
+
+        assert_eq!(buckets[slot_idx.bucket_idx], slot_idx.entries as u32);
+        assert_eq!(ENTRIES_BY_BUCKET[slot_idx.bucket_idx], slot_idx.entries, "{}", idx);
+
+        prev = Some(slot_idx);
+    }
+}

compiler/rustc_middle/src/query/keys.rs

@@ -2,6 +2,7 @@
 
 use rustc_hir::def_id::{CrateNum, DefId, LOCAL_CRATE, LocalDefId, LocalModDefId, ModDefId};
 use rustc_hir::hir_id::{HirId, OwnerId};
+use rustc_query_system::dep_graph::DepNodeIndex;
 use rustc_query_system::query::{DefIdCache, DefaultCache, SingleCache, VecCache};
 use rustc_span::symbol::{Ident, Symbol};
 use rustc_span::{DUMMY_SP, Span};
@@ -111,7 +112,7 @@ impl<'tcx> Key for mir::interpret::LitToConstInput<'tcx> {
 }
 
 impl Key for CrateNum {
-    type Cache<V> = VecCache<Self, V>;
+    type Cache<V> = VecCache<Self, V, DepNodeIndex>;
 
     fn default_span(&self, _: TyCtxt<'_>) -> Span {
         DUMMY_SP
@@ -128,7 +129,7 @@ impl AsLocalKey for CrateNum {
 }
 
 impl Key for OwnerId {
-    type Cache<V> = VecCache<Self, V>;
+    type Cache<V> = VecCache<Self, V, DepNodeIndex>;
 
     fn default_span(&self, tcx: TyCtxt<'_>) -> Span {
         self.to_def_id().default_span(tcx)
@@ -140,7 +141,7 @@ impl Key for OwnerId {
 }
 
 impl Key for LocalDefId {
-    type Cache<V> = VecCache<Self, V>;
+    type Cache<V> = VecCache<Self, V, DepNodeIndex>;
 
     fn default_span(&self, tcx: TyCtxt<'_>) -> Span {
         self.to_def_id().default_span(tcx)

compiler/rustc_query_system/src/lib.rs

@@ -2,6 +2,7 @@
 #![allow(rustc::potential_query_instability, internal_features)]
 #![feature(assert_matches)]
 #![feature(core_intrinsics)]
+#![feature(dropck_eyepatch)]
 #![feature(hash_raw_entry)]
 #![feature(let_chains)]
 #![feature(min_specialization)]

compiler/rustc_query_system/src/query/caches.rs

@@ -3,9 +3,10 @@ use std::hash::Hash;
 
 use rustc_data_structures::fx::FxHashMap;
 use rustc_data_structures::sharded::{self, Sharded};
-use rustc_data_structures::sync::{Lock, OnceLock};
+use rustc_data_structures::sync::OnceLock;
+pub use rustc_data_structures::vec_cache::VecCache;
 use rustc_hir::def_id::LOCAL_CRATE;
-use rustc_index::{Idx, IndexVec};
+use rustc_index::Idx;
 use rustc_span::def_id::{DefId, DefIndex};
 
 use crate::dep_graph::DepNodeIndex;
@@ -100,52 +101,10 @@ where
     }
 }
 
-pub struct VecCache<K: Idx, V> {
-    cache: Lock<IndexVec<K, Option<(V, DepNodeIndex)>>>,
-}
-
-impl<K: Idx, V> Default for VecCache<K, V> {
-    fn default() -> Self {
-        VecCache { cache: Default::default() }
-    }
-}
-
-impl<K, V> QueryCache for VecCache<K, V>
-where
-    K: Eq + Idx + Copy + Debug,
-    V: Copy,
-{
-    type Key = K;
-    type Value = V;
-
-    #[inline(always)]
-    fn lookup(&self, key: &K) -> Option<(V, DepNodeIndex)> {
-        let lock = self.cache.lock();
-        if let Some(Some(value)) = lock.get(*key) { Some(*value) } else { None }
-    }
-
-    #[inline]
-    fn complete(&self, key: K, value: V, index: DepNodeIndex) {
-        let mut lock = self.cache.lock();
-        lock.insert(key, (value, index));
-    }
-
-    fn iter(&self, f: &mut dyn FnMut(&Self::Key, &Self::Value, DepNodeIndex)) {
-        for (k, v) in self.cache.lock().iter_enumerated() {
-            if let Some(v) = v {
-                f(&k, &v.0, v.1);
-            }
-        }
-    }
-}
-
 pub struct DefIdCache<V> {
     /// Stores the local DefIds in a dense map. Local queries are much more often dense, so this is
     /// a win over hashing query keys at marginal memory cost (~5% at most) compared to FxHashMap.
-    ///
+    local: VecCache<DefIndex, V, DepNodeIndex>,
-    /// The second element of the tuple is the set of keys actually present in the IndexVec, used
-    /// for faster iteration in `iter()`.
-    local: Lock<(IndexVec<DefIndex, Option<(V, DepNodeIndex)>>, Vec<DefIndex>)>,
     foreign: DefaultCache<DefId, V>,
 }
 
@@ -165,8 +124,7 @@ where
     #[inline(always)]
     fn lookup(&self, key: &DefId) -> Option<(V, DepNodeIndex)> {
         if key.krate == LOCAL_CRATE {
-            let cache = self.local.lock();
+            self.local.lookup(&key.index)
-            cache.0.get(key.index).and_then(|v| *v)
         } else {
             self.foreign.lookup(key)
         }
@@ -175,27 +133,39 @@ where
     #[inline]
     fn complete(&self, key: DefId, value: V, index: DepNodeIndex) {
         if key.krate == LOCAL_CRATE {
-            let mut cache = self.local.lock();
+            self.local.complete(key.index, value, index)
-            let (cache, present) = &mut *cache;
-            let slot = cache.ensure_contains_elem(key.index, Default::default);
-            if slot.is_none() {
-                // FIXME: Only store the present set when running in incremental mode. `iter` is not
-                // used outside of saving caches to disk and self-profile.
-                present.push(key.index);
-            }
-            *slot = Some((value, index));
         } else {
             self.foreign.complete(key, value, index)
         }
     }
 
     fn iter(&self, f: &mut dyn FnMut(&Self::Key, &Self::Value, DepNodeIndex)) {
-        let guard = self.local.lock();
+        self.local.iter(&mut |key, value, index| {
-        let (cache, present) = &*guard;
+            f(&DefId { krate: LOCAL_CRATE, index: *key }, value, index);
-        for &idx in present.iter() {
+        });
-            let value = cache[idx].unwrap();
-            f(&DefId { krate: LOCAL_CRATE, index: idx }, &value.0, value.1);
-        }
         self.foreign.iter(f);
     }
 }
+
+impl<K, V> QueryCache for VecCache<K, V, DepNodeIndex>
+where
+    K: Idx + Eq + Hash + Copy + Debug,
+    V: Copy,
+{
+    type Key = K;
+    type Value = V;
+
+    #[inline(always)]
+    fn lookup(&self, key: &K) -> Option<(V, DepNodeIndex)> {
+        self.lookup(key)
+    }
+
+    #[inline]
+    fn complete(&self, key: K, value: V, index: DepNodeIndex) {
+        self.complete(key, value, index)
+    }
+
+    fn iter(&self, f: &mut dyn FnMut(&Self::Key, &Self::Value, DepNodeIndex)) {
+        self.iter(f)
+    }
+}