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authorJohannes Stoelp <johannes.stoelp@gmail.com>2024-12-04 20:16:35 +0100
committerJohannes Stoelp <johannes.stoelp@gmail.com>2024-12-04 20:40:03 +0100
commit888faa5f4f2b89c75f2dc2610fb5253120a028ce (patch)
treef95324aac581e3e2f9c947214fc7c7f952b8dae0 /src/arch
parentdeb4619a79deace26923e91a93b6d7bbfce40e78 (diff)
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cache: add notes about hw cachesHEADmaster
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# Arch
+- [cache](./cache.md)
- [x86_64](./x86_64.md)
- [armv8](./armv8.md)
- [arm64](./arm64.md)
diff --git a/src/arch/cache.md b/src/arch/cache.md
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+# cache
+
+Caches are organized by the following components
+- `sets`
+- `ways`
+- `entries`
+
+Each `set` consists of one or more `ways` and a `way` is a single slot which
+can hold an `entry`.
+```
+S-set / W-way cache
+
+ +----------------- .. -----------+
+SET 0 | WAY 0 | WAY 1 | | WAY W-1 |
+ +----------------- .. -----------+
+SET 1 | WAY 0 | WAY 1 | | WAY W-1 |
+ +----------------- .. -----------+
+.. | |
+ +----------------- .. -----------+
+SET S-1 | WAY 0 | WAY 1 | | WAY W-1 |
+ +----------------- .. -----------+
+```
+
+In general a cache is described by the number of `sets S` and the number of
+`ways W`. Depending on the values for `S` and `W` caches can be further
+classified.
+- `W=1` is a `direct-mapped` cache, which means that each entry can be placed
+ at exactly **ONE** location in the cache. It is also called a _one-way set
+ associative_ cache.
+- `S>1 & W>1` is a `W-way set associative` cache, which consists of S sets where
+ each set consists of W ways. Each entry maps to a **UNIQUE** set, but to
+ **ANY** way in that set.
+- `S=1` is a `fully-associative` cache, which means that each entry can be
+ placed at **ANY** location in the cache.
+
+To determine which set an entry falls into, a `hash function` is applied on the
+`key` which is associated with the entry. The set is then given by applying the
+modulo operation to the hash value `hash % num_sets`.
+
+The following figure illustrates the different cache classes and gives an
+example which entries the given hash value `5` can map to.
+```
+direct-mapped 2-way set associative fully-associative
+
+HASH=5 (IDX=5%4) HASH=5 (IDX=5%4) HASH=5 (only one IDX)
+| | |
+| S=4, W=1 | S=4, W=2 | S=1, W=4
+| +--------+ | +--------+--------+ | +--------+--------+--------+--------+
+| 0| | | 0| | | `->0| xxxxxx | xxxxxx | xxxxxx | xxxxxx |
+| +--------+ | +--------+--------+ +--------+--------+--------+--------+
+`- >1| xxxxxx | `->1| xxxxxx | xxxxxx |
+ +--------+ +--------+--------+
+ 2| | 2| | |
+ +--------+ +--------+--------+
+ 3| | 3| | |
+ +--------+ +--------+--------+
+```
+
+## CPU (hardware) caches
+The number of sets in a hardware cache is usually a power of two. The `address`
+acts as the key and some bits in the address are used to select the set in the
+cache. The hash function in this case is simple, as it just extracts the bits
+from the address which are used to select the set.
+
+The `address` is usually split up into the `{ TAG, IDX, OFF }` bits which are
+used to lookup an entry in the cache.
+
+The `IDX` bits are used to index into the corresponding set, where the `TAG`
+bits are then compared against the stored `TAG` bits in each way. If any way
+holds an entry with the matching `TAG` bits, the lookup is a `HIT`, else a
+`MISS`.
+
+In case the entry is in the cache, the `OFF` bits are used to index into the
+cache line. Hence, the number of offset bits available define the cache line
+size.
+
+The following gives an example for _64-bit addresses_ and a _direct-mapped_ cache.
+```
+ 63 0
+ +-----------------------+
+ADDR: | TAG | IDX | OFF |
+ +-----------------------+
+ | | `------------------,
+ | | |
+ | | CACHE |
+ | | +----------------+ |
+ | | | TAG | CACHE_LN | |
+ | | +----------------+ |
+ | | | TAG | CACHE_LN | |
+ | | +----------------+ |
+ | | | .. | |
+ | | +----------------+ |
+ | `--> | TAG | CACHE_LN | |
+ | +----------------+ |
+ | | | |
+ | v v |
+ `-------------> = + <----------`
+ | |
+ v v
+ HIT? DATA
+
+
+OFF bits: ln2 (cache_line_sz)
+IDX bits: ln2 (num_sets)
+TAG bits: 64 - IDX bits - OFF bits
+```
+
+The total size of a cache can be computed by `cache_line_sz * num_sets * num_ways`.
+```
+Example
+ SETS: 64 => 6 IDX bits
+ WAYS: 8
+ LINE: 64 bytes => 6 OFF bits
+
+ SIZE: 64 sets * 8 ways * 64 bytes => 32k bytes
+```
+
+## Hardware caches with virtual memory
+In the context of _virtual memory_, caches can be placed at different location
+in the memory path, either _before_ or _after_ the `virtual address (VA)` to
+`physical address (PA)` translation. Each placement has different properties
+discussed in the following.
+
+If the cache is placed _before_ the `VA -> PA` translation, it is called
+`virtually indexed virtually tagged (VIVT)` cache, as it is indexed by a virtual
+address and data in the cache is tagged with the virtual address as well.
+
+The benefit of VIVT caches is that lookups are very fast as there is no need to
+wait for the result of the address translation. However, VIVT caches may suffer
+from the following problems.
+- `synonyms`: different VAs map to the same PA. This can happen in a single
+ address space (same page table), if for example a process maps the same file
+ at different VAs (also commonly referred to as _aliasing_ or _cache-line
+ sharing_). This can also happen in different address spaces (different page
+ tables), if for example pages are shared between two processes.
+ ```
+ PT1
+ +-------+
+ | | PHYSMEM PT2
+ +-------+ +-------+ +-------+
+ | VA1 |---, | | | |
+ +-------+ | +-------+ +-------+
+ | | +--->| PA1 |<-------| VA3 |
+ +-------+ | +-------+ +-------+
+ | VA2 |---` | | | |
+ +-------+ +-------+ +-------+
+ | |
+ +-------+
+
+ Assume VA1 != VA2 != VA3
+
+ CACHE
+ TAG DATA
+ +-------+-------------+ Problems:
+ | VA1 | Copy of PA1 | * multiple copies of the same data.
+ | VA3 | Copy of PA1 | * write through one VA and read through a
+ | | | different VA results in reading stale data.
+ | VA2 | Copy of PA1 |
+ +-------+-------------+
+ ```
+- `homonyms`: same VA corresponds to different PAs. This is the standard case
+ between two different address spaces (eg in a multi-tasking os), for example
+ if the same VA is used in two different processes, but it maps to a different
+ PA for each process.
+ ```
+ PT1 PHYSMEM PT2
+ +-------+ +-------+ +-------+
+ | VA1 |------->| PA1 | ,---| VA2 |
+ +-------+ +-------+ | +-------+
+ | | | | | | |
+ | | +-------+ | | |
+ | | | PA2 |<---` | |
+ +-------+ +-------+ +-------+
+
+ Assume VA1 == VA2
+
+ CACHE
+ TAG DATA
+ +-------+-------------+ Problems:
+ | VA1 | Copy of PA1 | * same VA from different address spaces map to
+ | | | different PA
+ | | | * read thorugh VA2 returns data from PA1
+ +-------+-------------+ rather than from PA2
+ ```
+
+While `synonyms` may lead to accessing _stale_ data, if there is no hardware to
+guarantee coherency between aliased entries, `homonyms` may lead to accessing
+the _wrong_ data.
+
+On one hand there are multiple counter measures to avoid `homonyms`, for example
+physical tagging, tags could contain an address space identifier (ASID), or the
+cache could be flushed on context switches (changing the page table).
+Approaches like physical tagging and ASIDs work, as the same VA always maps to
+the same index in the cache, which would then result in a cache miss in case of
+the homonym.
+
+Preventing `synonyms` on the other hand is harder, as neither physical tagging
+nor ASIDs help in this case. Flushing the cache during context switches only
+helps with the case where different address spaces alias shared pages, but it
+won't help if the same PA is aliased by different VAs in a single address space.
+There are to alternative approaches, one is to have hardware support to detect
+synonyms and the other one is to have the operating system only allow shared
+mappings with VAs that have the same index bits for the cache. However, the
+latter only works for direct-mapped caches, as there is only a single location
+where those VAs could map to in the cache.
+
+If the cache is placed _after_ the `VA -> PA` translation, it is called
+`physically indexed physically tagged (PIPT)` cache, as it is indexed by a
+physical address and data in the cache is tagged with the physical address as
+well.
+
+Compared to VIVT caches, PIPT caches do not suffer from `synonyms` or
+`homonyms`. However, their major drawback is that the lookup depends on the
+result of the address translation, and hence the translation and the cache
+lookup happen sequentially which greatly decreases access latency.
+
+Between VIVT and PIPT caches there is also a hybrid approach called `virtually
+indexed physically tagged (VIPT)` cache, where the cache lookup is done with a
+virtual address and the data is tagged with the physical address.
+
+The benefit of this approach is that the cache lookup and the address
+translation can be done in parallel, and due to the physical tagging, `homonyms`
+are not possible.
+
+For VIPT caches, `synonyms` may still happen depending on how the cache is
+constructed.
+- if the `index` bits for the cache lookup, exceed the `page offset` in the
+ virtual address, then `synonyms` are still possible.
+- if all the `index` bits for the cache lookup fall into the `page offset` of
+ the virtual address, then the bits used for the cache lookup won't change
+ during the `VA -> PA` translation, and hence the cache effectively operates as
+ a PIPT cache. The only downside is that the number of sets in the cache is
+ limited by the page size.
+
+### VIPT as PIPT example
+The following example shows that for a system with `4k` pages and cache lines of
+`64 bytes` a VIPT cache can have at most `64 sets` to still act as PIPT cache.
+```
+ 63 12 0
+ +-----------------------+
+VA: | | PG_OFF |
+ +-----------------------+
+CACHE BITS: | C_IDX | C_OFF |
+ +---------------+
+
+PAGE SIZE : 4k
+PAGE OFFSET: ln (PAGE SIZE) = 12 bits
+
+CACHE LINE : 64 bytes
+CACHE OFFSET: ln (CACHE LINE) = 6 bits
+
+CACHE INDEX: PG_OFF - C_OFF = 6 bits
+CACHE SETS : 2^CACHE INDEX = 64 sets
+```
+The total cache size can be increased by adding additional ways, however that
+also has a practical upper limit, as adding more ways reduces the latency.
+
+## Cache info in Linux
+```sh
+# Info about different caches (size, ways, sets, type, ..).
+lscpu -C
+# NAME ONE-SIZE ALL-SIZE WAYS TYPE LEVEL SETS PHY-LINE COHERENCY-SIZE
+# L1d 32K 128K 8 Data 1 64 1 64
+# L1i 32K 128K 8 Instruction 1 64 1 64
+# L2 256K 1M 4 Unified 2 1024 1 64
+# L3 6M 6M 12 Unified 3 8192 1 64
+
+# Info about how caches are shared between cores / hw-threads. Identified by
+# the same cache ids on the same level.
+lscpu -e
+# CPU CORE L1d:L1i:L2:L3 ONLINE
+# 0 0 0:0:0:0 yes
+# 1 1 1:1:1:0 yes
+# 4 0 0:0:0:0 yes
+# 5 1 1:1:1:0 yes
+#
+# => CPU 0,4 share L1d, L1i, L2 caches (here two hw-threads of a core).
+```