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MINOR: [C++] Fix typos in key_map doc and comment (#45104)
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### Rationale for this change

### What changes are included in this PR?

### Are these changes tested?

### Are there any user-facing changes?

Authored-by: Rossi Sun <zanmato1984@gmail.com>
Signed-off-by: Rossi Sun <zanmato1984@gmail.com>
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zanmato1984 authored Dec 24, 2024
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2 changes: 1 addition & 1 deletion cpp/src/arrow/acero/doc/key_map.md
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Expand Up @@ -65,7 +65,7 @@ Every slot can either be **empty** or store data related to a single inserted ke

Status byte, as the name suggests, stores 8 bits. The highest bit indicates if the slot is empty (the highest bit is set) or corresponds to one of inserted keys (the highest bit is zero). The remaining 7 bits contain 7 bits of key hash that we call a **stamp**. The stamp is used to eliminate some false positives when searching for a matching key for a given input. Slot also stores **key id**, which is a non-negative integer smaller than the number of inserted keys, that is used as a reference to the actual inserted key. The last piece of information related to an inserted key is its **hash** value. We store hashes for all keys, so that they never need to be re-computed. That greatly simplifies some operations, like resizing of a hash table, that may not even need to look at the keys at all. For an empty slot, the status byte is 0x80, key id is zero and the hash is not used and can be set to any number.

A single block contains 8 slots and can be viewed as a micro-stack of up to 8 inserted keys. When the first key is inserted into an empty block, it will occupy a slot with local id 0. The second inserted key will go into slot number 1 and so on. We use N highest bits of hash to get an index of a **start block**, when searching for a match or an empty slot to insert a previously not seen key when that is the case. If the start block contains any empty slots, then the search for either a match or place to insert a key will end at that block. We will call such a block an **open block**. A block that is not open is a full block. In the case of full block, the input key related search may continue in the next block module the number of blocks. If the key is not inserted into its start block, we will refer to it as an **overflow** entry, other entries being **non-overflow**. Overflow entries are slower to process, since they require visiting more than one block, so we want to keep their percentage low. This is done by choosing the right **load factor** (percentage of occupied slots in the hash table) at which the hash table gets resized and the number of blocks gets doubled. By tuning this value we can control the probability of encountering an overflow entry.
A single block contains 8 slots and can be viewed as a micro-stack of up to 8 inserted keys. When the first key is inserted into an empty block, it will occupy a slot with local id 0. The second inserted key will go into slot number 1 and so on. We use N highest bits of hash to get an index of a **start block**, when searching for a match or an empty slot to insert a previously not seen key when that is the case. If the start block contains any empty slots, then the search for either a match or place to insert a key will end at that block. We will call such a block an **open block**. A block that is not open is a full block. In the case of full block, the input key related search may continue in the next block modulo the number of blocks. If the key is not inserted into its start block, we will refer to it as an **overflow** entry, other entries being **non-overflow**. Overflow entries are slower to process, since they require visiting more than one block, so we want to keep their percentage low. This is done by choosing the right **load factor** (percentage of occupied slots in the hash table) at which the hash table gets resized and the number of blocks gets doubled. By tuning this value we can control the probability of encountering an overflow entry.

The most interesting part of each block is the set of status bytes of its slots, which is simply a single 64-bit word. The implementation of efficient searches across these bytes during lookups require using either leading zero count or trailing zero count intrinsic. Since there are cases when only the first one is available, in order to take advantage of it, we order the bytes in the 64-bit status word so that the first slot within a block uses the highest byte and the last one uses the lowest byte (slots are in reversed bytes order). The diagram below shows how the information about slots is stored within a 64-bit status word:

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2 changes: 1 addition & 1 deletion cpp/src/arrow/compute/key_map_internal.cc
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Expand Up @@ -281,7 +281,7 @@ void SwissTable::early_filter_imp(const int num_keys, const uint32_t* hashes,
// When we reach this limit, we need to break processing of any further rows and resize.
//
uint64_t SwissTable::num_groups_for_resize() const {
// Resize small hash tables when 50% full (up to 12KB).
// Resize small hash tables when 50% full (up to 32KB).
// Resize large hash tables when 75% full.
constexpr int log_blocks_small_ = 9;
uint64_t num_slots = 1ULL << (log_blocks_ + 3);
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