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Last active Aug 28, 2019
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Twisting Pool Allocator
Twisting Pool Allocator
written by Leonard Ritter (
This file is in the public domain
I don't know if I was the first one to stumble upon this technique, so
I can't guarantee there's no patent on it, but let's hope there's not,
then this counts as prior art.
This is a proof of concept implementation for a pool allocator that guarantees
compactness (unsorted gapless iteration without indirections) while preserving
element ids (using one order-optimized indirection), with insertion, deletion
and lookup in O(1) time.
Because all id <-> index assignments are symmetric swaps (either
identity-mapped or twisted), only a single table is required to resolve
index from id and id from index.
Insertion and deletion is a self-sorting process. Both operations attempt
to untwist identifiers that share the same status (obtained/released) and
so, regardless of deallocation order, only few entries are accessed and
fragmentation is generally low; in my random allocation test, the average number
of fragmented entries appeared to be ~log2(capacity)); It is possible to produce
a worst case by obtaining all id's, then releasing every other id. The upper
bound on fragmented entries appears to be capacity/3.
The data being managed must be allocated separately, and the user must
copy at least none, at most one element after a call to obtain/release.
With this implementation, the memory requirement is
sizeof(unsigned int) * capacity, typically 4 bytes per entry.
It might however possible to implement the map with a compact sorted array or
hashtable, storing only twisted entries, which should tremendously reduce memory
usage and therefore notably improve cache efficiency.
#include <stdbool.h>
#include <assert.h>
// use whatever size you prefer; this implementation operates directly on
// global memory; a productive implementation would probably use the heap.
#define CAPACITY 10000
#define N (CAPACITY+1)
/* index: offset of element in data array; elements are moved
to keep the array compact and contiguous
id: numerical name assigned to a data element; never changes.
therefore, elements should typically be referenced by their id,
not their index.
id 0 and index 0 are synonymous with no element
/* symmetrical map
maps index -> id; compact, gapless
last index == count
happens to also map id -> index; has gaps
unsigned int map[N];
/* all ids are mapped, even the unused ones;
the ideal mapping is id == index
the first free index is count+1
if count == capacity, the pool is full.
unsigned int count;
// pool constructor
void construct () {
unsigned int i;
// initially no elements
count = 0;
for (i = 0; i < N; ++i) {
// start out with identity mapping;
// all unused ids are mapped
map[i] = i;
// lookup index from id or id from index
unsigned int resolve(unsigned int id_or_index) {
return map[id_or_index];
bool is_index_valid (unsigned int index) {
return (index > 0) && (index <= count);
bool is_id_valid (unsigned int id) {
return (id > 0) && (id <= CAPACITY) && is_index_valid(resolve(id));
bool is_identity (unsigned int id_or_index) {
return (map[id_or_index] == id_or_index);
// swap the ids of two indices (or the indices of two ids)
void swap (unsigned int a, unsigned int b) {
// ids can only be twisted or untwisted, map must not be shuffled any further
assert((a == b)
|| ((map[a] == a) && (map[b] == b))
|| ((map[a] == b) && (map[b] == a)));
unsigned int t = map[a];
map[a] = map[b];
map[b] = t;
typedef struct _pair {
unsigned int _0;
unsigned int _1;
} pair;
/* allocate a new id from the pool
user must copy slot[index(id)] to slot[count] after
allocation. obtain() returns a { src, dst } tuple indicating
how data must be moved; if (dst == src), then no move is necessary.
src is also identical to the newly obtained id
if the pool is full, obtain returns { 0, 0 }
pair obtain () {
if (count < CAPACITY) {
unsigned int index;
unsigned int id;
// increase number of elements
// index of new last element
index = count;
// id of new last element
id = map[index];
// if id not identical to index (is twisted)
if (id != index) {
// swap with index that matches this id,
// so that index(id) == id
swap(index, id);
// return new id/index and index of moved item
pair result = { id, index };
return result;
} else {
// out of space
pair result = { 0, 0 };
return result;
/* release an obtained id to the pool
user must copy slot[count] to slot[index(id)] after
deletion. (release id) returns a (src dst) tuple indicating
how data must be moved; if (src == dst), then no move is necessary.
pair release (unsigned int id) {
unsigned int index;
unsigned int last_index;
unsigned int last_id;
// index of element to be deleted
index = map[id];
// if element is twisted, then untwist
if (id > count)
swap(index, id);
// index and id of element to take its place
last_index = count;
last_id = map[last_index];
// swap indices so that tailing element fills the gap (twist)
// if last element is twisted, then untwist first
if (last_id > count) {
swap(last_index, last_id);
swap(index, last_id);
} else {
swap(index, last_index);
// decrease number of elements
// return index of element to be moved and index of gap
pair result = { last_index, index };
return result;
// ----------------------------------------------------------------------------
// test
#include <stdlib.h>
#include <stdio.h>
// our "data array", which just stores the id again, so we can easily verify
// if an id still matches its assigned content
unsigned int data[N];
void dump() {
unsigned int i;
printf("index -> ID:\n");
for (i = 1; i <= CAPACITY; ++i) {
if (i == (count + 1))
unsigned int id = resolve(i);
unsigned int ri = resolve(id);
printf("%u\t%u\t%s\n", i, id, ((i != ri)?"!":""));
printf("%i used elements\n\n", count);
void move(pair k) {
if (k._0 != k._1) {
data[k._1] = data[k._0];
unsigned int verify_data () {
unsigned int i;
unsigned int twisted = 0;
for (i = 1; i <= count; ++i) {
unsigned int id = resolve(i);
assert(data[i] == id);
assert(resolve(id) == i);
if (!is_identity(i))
return twisted;
unsigned int test_obtain () {
pair k = obtain();
data[k._0] = k._0;
return k._0;
unsigned int test_release (unsigned int id) {
assert(id != 0);
pair k = release(id);
#include <memory.h>
#include <stdio.h>
// array of ids in use
unsigned int used[CAPACITY];
int main (int argc, void** argv) {
int i;
unsigned int mintwisted = N;
unsigned int maxtwisted = 0;
unsigned int total = 0;
unsigned int steps = 0;
unsigned int used_count = 0;
memset(used, 0, sizeof(used));
#if 1
// do random obtains/releases, see if something breaks
for (i = 0; i < 100000; ++i) {
if (((rand() % 100) < 50) && (used_count > 0)) {
unsigned int used_index = rand() % used_count;
unsigned int id = used[used_index];
// remove from used array and fill
used[used_index] = used[used_count];
used[used_count] = 0;
unsigned int t = verify_data();
mintwisted = (mintwisted < t)?mintwisted:t;
maxtwisted = (maxtwisted > t)?maxtwisted:t;
total += t;
} else {
unsigned int k = test_obtain();
if (k != 0) {
assert(used_count < CAPACITY);
used[used_count] = k;
// attempt to fabricate a worst case
for (i = 0; i < CAPACITY; ++i) {
for (i = 1; i <= CAPACITY; i += 2) {
unsigned int t = verify_data();
mintwisted = (mintwisted < t)?mintwisted:t;
maxtwisted = (maxtwisted > t)?maxtwisted:t;
total += t;
printf("releases: %u\nmin twisted: %u\nmax twisted: %u\ntotal twisted: %u\naverage: %f\n",
steps, mintwisted, maxtwisted, total, (double)total / (double)steps);
return 0;
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