dw-cache

Dual Window Cache

Dual window cache adaptively coordinates the ratio of LRU to LFU using the two sliding windows.

Maintenance

The source code is maintained on the next source repository.

https://github.com/falsandtru/spica

Abstract

The highest performance constant complexity cache algorithm.

Strategies

• Dynamic partition
• Sliding window
• Transitive wide MRU with cyclic replacement
  • Omittable if loop resistance is unnecessary.
• Weighted aging
  • Omittable if low inter-reference accesses are present.

Properties

Generally superior and almost flawless.

• High performance
  • High hit ratio (DS1, S3, OLTP, GLI)
    • Highest hit ratio among all the general-purpose cache algorithms.
    • Near ARC (S3, OLTP).
    • Significantly higher than ARC (DS1, GLI).
  • Low overhead (High throughput)
    • Constant time complexity overhead decreasing in linear time.
    • Use of only two lists.
  • Low latency
    • Constant time complexity.
    • No batch processing like LIRS and TinyLFU.
  • Parallel suitable
    • Separated lists are suitable for lock-free processing.
• Efficient
  • Low memory usage
    • Constant extra space complexity.
    • Retain only keys of resident entries (No history).
  • Immediate release of evicted keys
    • Primary cache algorithm in the standard library must release memory immediately.
• High resistance
  • Scan, loop, and burst resistance
• Few tradeoffs
  • Not the highest hit ratio
  • Significantly small cache size can degrade hit ratio
• Upward compatible with ARC
  • Comprehensively higher performance
• Upward compatible with Segmented LRU
  • Totally higher performance
  • Suitable for TinyLFU
    • Better for (W-)TinyLFU's eviction algorithm.

Efficiency

Some different cache algorithms require extra memory space to retain evicted keys. Linear time complexity indicates the existence of batch processing. Note that admission algorithm doesn't work without eviction algorithm.

Algorithm	Type	Time complexity (Worst case)	Space complexity (Extra)	Key size	Data structures
LRU	Evict	Constant	Constant	1x	1 list
DWC	Evict	Constant	Constant	1x	2 lists
ARC	Evict	Constant	Linear	2x	4 lists
LIRS	Evict	Linear	Linear	3-2500x	2 lists
TinyLFU	Admit	Linear	Linear	8bit * 10N * 4	5 arrays
W-TinyLFU	Admit	Linear	Linear	8bit * 10N * 4	1 list 4 arrays

https://github.com/ben-manes/caffeine/wiki/Efficiency
https://github.com/zhongch4g/LIRS2/blob/master/src/replace_lirs_base.cc

Resistance

LIRS's burst resistance means resistance to continuous cache miss.

Algorithm	Type	Scan	Loop	Burst
LRU	Evict			✓
DWC	Evict	✓	✓	✓
ARC	Evict	✓		✓
LIRS	Evict	✓	✓
TinyLFU	Admit	✓	✓
W-TinyLFU	Admit	✓	✓	✓

Tradeoffs

Note that LIRS and TinyLFU are risky cache algorithms.

• LRU
  • Low performance
  • No resistance
    • Scan access clears all entries.
• DWC
  • Not the highest hit ratio
  • Significantly small cache size can degrade hit ratio
• ARC
  • Middle performance
  • Inefficient
    • 2x key size.
  • High overhead
    • 4 lists.
  • Few resistance
    • No loop resistance.
• LIRS
  • Extremely inefficient
    • 3-2500x key size.
  • Spike latency
    • Bulk deletion of low-frequency entries takes linear time.
  • Vulnerable algorithm
    • Continuous cache misses at the last of LIR and of HIR entries explode key size.
      • https://issues.redhat.com/browse/ISPN-7171
      • https://issues.redhat.com/browse/ISPN-7246
• TinyLFU
  • Unreliable performance
    • Burst access degrades performance.
    • Lower hit ratio than LRU at OLTP.
    • Many major benchmarks are lacking in the paper despite performance of TinyLFU is significantly worse than W-TinyLFU.
  • Restricted delete operation
    • Bloom filters don't support delete operation.
    • Frequent delete operations degrade performance.
  • Spike latency
    • Whole reset of Bloom filters takes linear time.
  • Vulnerable algorithm
    • Burst access saturates Bloom filters.
• W-TinyLFU
  • Restricted delete operation
    • Bloom filters don't support delete operation.
    • Frequent delete operations degrade performance.
  • Spike latency
    • Whole reset of Bloom filters takes linear time.

Hit ratio

Note that another cache algorithm sometimes changes the parameter values per workload to get a favorite result as the paper of TinyLFU has changed the window size of W-TinyLFU. All the results of DWC are measured by the same default parameter values. Graphs are approximate.

1. Set the datasets to ./benchmark/trace (See ./benchmark/ratio.ts).
2. Run npm i
3. Run npm run bench
4. Click the DEBUG button to open a debug tab.
5. Close the previous tab.
6. Press F12 key to open devtools.
7. Select the console tab.

https://github.com/ben-manes/caffeine/wiki/Efficiency
https://github.com/dgraph-io/ristretto
https://github.com/dgraph-io/benchmarks

DS1

W-TinyLFU > (LIRS) > DWC > (TinyLFU) > ARC > LRU

• DWC is significantly better than ARC.

DS1 1,000,000
LRU hit ratio 3.08%
DWC hit ratio 11.32%
DWC - LRU hit ratio delta 8.24%
DWC / LRU hit ratio rate  367%

DS1 2,000,000
LRU hit ratio 10.74%
DWC hit ratio 26.35%
DWC - LRU hit ratio delta 15.61%
DWC / LRU hit ratio rate  245%

DS1 3,000,000
LRU hit ratio 18.59%
DWC hit ratio 38.56%
DWC - LRU hit ratio delta 19.97%
DWC / LRU hit ratio rate  207%

DS1 4,000,000
LRU hit ratio 20.24%
DWC hit ratio 42.73%
DWC - LRU hit ratio delta 22.48%
DWC / LRU hit ratio rate  211%

DS1 5,000,000
LRU hit ratio 21.03%
DWC hit ratio 48.16%
DWC - LRU hit ratio delta 27.13%
DWC / LRU hit ratio rate  229%

DS1 6,000,000
LRU hit ratio 33.95%
DWC hit ratio 56.03%
DWC - LRU hit ratio delta 22.08%
DWC / LRU hit ratio rate  165%

DS1 7,000,000
LRU hit ratio 38.89%
DWC hit ratio 57.15%
DWC - LRU hit ratio delta 18.25%
DWC / LRU hit ratio rate  146%

DS1 8,000,000
LRU hit ratio 43.03%
DWC hit ratio 63.82%
DWC - LRU hit ratio delta 20.78%
DWC / LRU hit ratio rate  148%

S3

W-TinyLFU > (TinyLFU) > (LIRS) > ARC, DWC > LRU

• DWC is an approximation of ARC.

S3 100,000
LRU hit ratio 2.32%
DWC hit ratio 10.53%
DWC - LRU hit ratio delta 8.21%
DWC / LRU hit ratio rate  452%

S3 200,000
LRU hit ratio 4.63%
DWC hit ratio 18.88%
DWC - LRU hit ratio delta 14.24%
DWC / LRU hit ratio rate  407%

S3 300,000
LRU hit ratio 7.58%
DWC hit ratio 24.56%
DWC - LRU hit ratio delta 16.97%
DWC / LRU hit ratio rate  323%

S3 400,000
LRU hit ratio 12.03%
DWC hit ratio 29.59%
DWC - LRU hit ratio delta 17.55%
DWC / LRU hit ratio rate  245%

S3 500,000
LRU hit ratio 22.76%
DWC hit ratio 37.48%
DWC - LRU hit ratio delta 14.71%
DWC / LRU hit ratio rate  164%

S3 600,000
LRU hit ratio 34.63%
DWC hit ratio 46.12%
DWC - LRU hit ratio delta 11.49%
DWC / LRU hit ratio rate  133%

S3 700,000
LRU hit ratio 46.04%
DWC hit ratio 55.26%
DWC - LRU hit ratio delta 9.22%
DWC / LRU hit ratio rate  120%

S3 800,000
LRU hit ratio 56.59%
DWC hit ratio 63.74%
DWC - LRU hit ratio delta 7.14%
DWC / LRU hit ratio rate  112%

OLTP

W-TinyLFU > ARC, DWC > (LIRS) > LRU > (TinyLFU)

• DWC is an approximation of ARC.

OLTP 250
LRU hit ratio 16.47%
DWC hit ratio 18.19%
DWC - LRU hit ratio delta 1.72%
DWC / LRU hit ratio rate  110%

OLTP 500
LRU hit ratio 23.44%
DWC hit ratio 28.78%
DWC - LRU hit ratio delta 5.34%
DWC / LRU hit ratio rate  122%

OLTP 750
LRU hit ratio 28.28%
DWC hit ratio 34.63%
DWC - LRU hit ratio delta 6.35%
DWC / LRU hit ratio rate  122%

OLTP 1,000
LRU hit ratio 32.83%
DWC hit ratio 37.98%
DWC - LRU hit ratio delta 5.15%
DWC / LRU hit ratio rate  115%

OLTP 1,250
LRU hit ratio 36.20%
DWC hit ratio 40.11%
DWC - LRU hit ratio delta 3.90%
DWC / LRU hit ratio rate  110%

OLTP 1,500
LRU hit ratio 38.69%
DWC hit ratio 41.79%
DWC - LRU hit ratio delta 3.09%
DWC / LRU hit ratio rate  108%

OLTP 1,750
LRU hit ratio 40.78%
DWC hit ratio 43.27%
DWC - LRU hit ratio delta 2.49%
DWC / LRU hit ratio rate  106%

OLTP 2,000
LRU hit ratio 42.46%
DWC hit ratio 44.55%
DWC - LRU hit ratio delta 2.08%
DWC / LRU hit ratio rate  104%

GLI

W-TinyLFU, (LIRS) > DWC > (TinyLFU) >> ARC > LRU

• DWC is significantly better than ARC.

GLI 250
LRU hit ratio 0.93%
DWC hit ratio 15.89%
DWC - LRU hit ratio delta 14.96%
DWC / LRU hit ratio rate  1707%

GLI 500
LRU hit ratio 0.96%
DWC hit ratio 31.48%
DWC - LRU hit ratio delta 30.51%
DWC / LRU hit ratio rate  3265%

GLI 750
LRU hit ratio 1.16%
DWC hit ratio 41.93%
DWC - LRU hit ratio delta 40.77%
DWC / LRU hit ratio rate  3604%

GLI 1,000
LRU hit ratio 11.22%
DWC hit ratio 48.90%
DWC - LRU hit ratio delta 37.68%
DWC / LRU hit ratio rate  435%

GLI 1,250
LRU hit ratio 21.25%
DWC hit ratio 52.17%
DWC - LRU hit ratio delta 30.91%
DWC / LRU hit ratio rate  245%

GLI 1,500
LRU hit ratio 36.56%
DWC hit ratio 53.93%
DWC - LRU hit ratio delta 17.37%
DWC / LRU hit ratio rate  147%

GLI 1,750
LRU hit ratio 45.04%
DWC hit ratio 55.06%
DWC - LRU hit ratio delta 10.02%
DWC / LRU hit ratio rate  122%

GLI 2,000
LRU hit ratio 57.41%
DWC hit ratio 57.41%
DWC - LRU hit ratio delta 0.00%
DWC / LRU hit ratio rate  100%

LOOP

LOOP 100
LRU hit ratio 0.00%
DWC hit ratio 8.68%
DWC - LRU hit ratio delta 8.68%
DWC / LRU hit ratio rate  Infinity%

LOOP 250
LRU hit ratio 0.00%
DWC hit ratio 23.29%
DWC - LRU hit ratio delta 23.29%
DWC / LRU hit ratio rate  Infinity%

LOOP 500
LRU hit ratio 0.00%
DWC hit ratio 46.88%
DWC - LRU hit ratio delta 46.88%
DWC / LRU hit ratio rate  Infinity%

LOOP 750
LRU hit ratio 0.00%
DWC hit ratio 70.34%
DWC - LRU hit ratio delta 70.34%
DWC / LRU hit ratio rate  Infinity%

LOOP 1,000
LRU hit ratio 0.00%
DWC hit ratio 95.14%
DWC - LRU hit ratio delta 95.14%
DWC / LRU hit ratio rate  Infinity%

LOOP 1,250
LRU hit ratio 99.80%
DWC hit ratio 99.80%
DWC - LRU hit ratio delta 0.00%
DWC / LRU hit ratio rate  100%

Throughput

75-95% of lru-cache.

Note that the number of trials per capacity for simulation 1,000,000 is insufficient.

No result with 10,000,000 because lru-cache crushes with the next error on the next machine of GitHub Actions. It is verified that the error was thrown also when benchmarking only lru-cache. Of course it is verified that DWC works fine under the same condition.

Error: Uncaught RangeError: Map maximum size exceeded

System:
OS: Linux 5.15 Ubuntu 20.04.5 LTS (Focal Fossa)
CPU: (2) x64 Intel(R) Xeon(R) Platinum 8370C CPU @ 2.80GHz
Memory: 5.88 GB / 6.78 GB

'LRUCache new x 11,379 ops/sec ±0.63% (68 runs sampled)'

'DW-Cache new x 4,731,010 ops/sec ±0.34% (68 runs sampled)'

'LRUCache simulation 10 x 8,215,381 ops/sec ±0.31% (68 runs sampled)'

'DW-Cache simulation 10 x 6,723,681 ops/sec ±0.54% (68 runs sampled)'

'LRUCache simulation 100 x 8,376,085 ops/sec ±0.43% (68 runs sampled)'

'DW-Cache simulation 100 x 6,178,399 ops/sec ±0.29% (68 runs sampled)'

'LRUCache simulation 1,000 x 7,448,487 ops/sec ±0.42% (68 runs sampled)'

'DW-Cache simulation 1,000 x 5,965,094 ops/sec ±0.42% (68 runs sampled)'

'LRUCache simulation 10,000 x 6,671,862 ops/sec ±0.38% (68 runs sampled)'

'DW-Cache simulation 10,000 x 5,214,870 ops/sec ±0.60% (68 runs sampled)'

'LRUCache simulation 100,000 x 3,229,658 ops/sec ±0.84% (67 runs sampled)'

'DW-Cache simulation 100,000 x 2,973,754 ops/sec ±1.56% (67 runs sampled)'

'LRUCache simulation 1,000,000 x 1,506,821 ops/sec ±1.38% (66 runs sampled)'

'DW-Cache simulation 1,000,000 x 1,348,542 ops/sec ±1.84% (67 runs sampled)'

const key = random() < 0.8
  ? random() * capacity * 1 | 0
  : random() * capacity * 9 + capacity | 0;
cache.get(key) ?? cache.set(key, {});

Comprehensive evaluation

Hit ratio

Rank	Algorithms
Very high	W-TinyLFU
Hight	(LIRS) > DWC
Middle	ARC, (TinyLFU)
Low	LRU

Efficiency

Extra space	Algorithms
Constant	LRU, DWC
Linear (< 1)	W-TinyLFU > (TinyLFU)
Linear (1)	ARC
Linear (> 1)	(LIRS)

Resistance

Rank	Algorithms
High	W-TinyLFU > (LIRS)
Middle	(TinyLFU) >= DWC
Low	ARC
None	LRU

Throughput

Class	Algorithms
Bloom filter + Static list	(TinyLFU)
Multiple lists (Lock-free)	DWC > (LIRS) > ARC
Dynamic list + Bloom filter	W-TinyLFU
Static list	LRU

Latency

Time	Algorithms
Constant	LRU, DWC, ARC
Linear (1)	W-TinyLFU > (TinyLFU)
Linear (> 1)	(LIRS)

Vulnerability

Class	Algorithms
Degrade	(TinyLFU)
Crush	(LIRS)

API

export namespace Cache {
  export interface Options<K, V = undefined> {
    // Max entries.
    readonly capacity?: number;
    readonly window?: number;
    readonly resource?: number;
    readonly age?: number;
    readonly earlyExpiring?: boolean;
    readonly disposer?: (value: V, key: K) => void;
    readonly capture?: {
      readonly delete?: boolean;
      readonly clear?: boolean;
    };
    // Mainly for experiments.
    readonly resolution?: number;
    readonly offset?: number;
    readonly entrance?: number;
    readonly sweep?: {
      readonly threshold?: number;
      readonly window?: number;
      readonly range?: number;
      readonly shift?: number;
    };
    readonly life?: {
      readonly LRU: number;
      readonly LFU: number;
    };
  }
}
export class Cache<K, V = undefined> {
  constructor(capacity: number, opts?: Cache.Options<K, V>);
  constructor(opts: Cache.Options<K, V>);
  put(key: K, value: V, opts?: { size?: number; age?: number; }): boolean;
  put(this: Cache<K, undefined>, key: K, value?: V, opts?: { size?: number; age?: number; }): boolean;
  set(key: K, value: V, opts?: { size?: number; age?: number; }): this;
  set(this: Cache<K, undefined>, key: K, value?: V, opts?: { size?: number; age?: number; }): this;
  get(key: K): V | undefined;
  has(key: K): boolean;
  delete(key: K): boolean;
  clear(): void;
  resize(capacity: number, resource?: number): void;
  readonly length: number;
  readonly size: number;
  [Symbol.iterator](): Iterator<[K, V], undefined, undefined>;
}