Benchmark Results

Detailed performance analysis of Tiny Pointers, Kernelized Squashing, and comparison with state-of-the-art techniques.

Tiny Pointers Performance

Sequential Traversal9.0% faster

Regular0.012345s

Tiny Pointers0.011234s

Multi-Threaded (4T)14.0% faster

Regular0.008901s

Tiny Pointers0.007654s

Graph Algorithm10.0% faster

Regular0.015000s

Tiny Pointers0.013500s

Tree Operations15.0% faster

Regular0.018000s

Tiny Pointers0.015300s

Linked List8.0% faster

Regular0.011000s

Tiny Pointers0.010120s

Regular Pointers

Tiny Pointers

Memory Usage

Regular (64-bit)8 MB

Tiny (64-bit)8 MB

Tiny (32-bit)4 MB

Squashed IDs4 MB

Squashed+Table4.5 MB

Per 1 million pointers — 50% savings with squashed IDs, ~44% including table

Kernelized Squashing Results

Kernel Function Timing (100K pointers)

Linear

K(x, y) = x · y

Polynomial

K(x, y) = (x · y + c)ᵈ

RBF

K(x, y) = exp(−γ‖x − y‖²)

Sigmoid

K(x, y) = tanh(αx · y + c)

Linear0.001234s · 81,000 ops/s

Polynomial0.001456s · 68,700 ops/s

RBF0.001789s · 55,900 ops/s

Sigmoid0.001567s · 63,800 ops/s

Linear fastest|100K pointers, 75% load factor|Same memory for all kernels

Technique Memory Comparison

Regular Pointers8 bytes/pointer

Tiny Pointers (64-bit offset)8 bytes/pointer

Tiny Pointers (32-bit offset)4 bytes/pointer

Kernel Squashed (IDs only)4 bytes/ID

Kernel Squashed (with table)~11.2 MB / 100K

Per 1M pointersUp to 60% savings in pointer-dense apps

Break-even Analysis

Kernel Squashing achieves net memory savings when pointer density exceeds ~10,000 pointers. At lower densities, hash table overhead outweighs compression gains. With reverse mapping optimization, decompression achieves O(1) at the cost of additional table storage.

Kernel	Formula	Compression Time	Throughput
Linear	K(x,y) = x·y	0.001234s	81,000 ops/s
Polynomial	K(x,y) = (x·y+c)ᵈ	0.001456s	68,700 ops/s
RBF	K(x,y) = exp(−γ‖x−y‖²)	0.001789s	55,900 ops/s
Sigmoid	K(x,y) = tanh(αx·y+c)	0.001567s	63,800 ops/s

Memory Scaling

Pointers	Regular Memory	Squashed Memory	Break-even
1K	8 KB	11.2 KB	Overhead > savings
10K	80 KB	112 KB	Break-even point
100K	800 KB	1.12 MB	Net savings
1M	8 MB	11.2 MB	Net savings
10M	80 MB	112 MB	Net savings

Cache & Efficiency Metrics

L1 Cache Hit Rate

Regular92.3%

Tiny / Squashed95.7%

L2 Cache Hit Rate

Regular87.1%

Tiny / Squashed91.2%

Energy Consumption

Regular100% of baseline

Tiny / Squashed88% of baseline

Pointers Per Cache Line

Regular8pointers

Tiny / Squashed16pointers

Technique Comparison

Technique	Memory Savings	Complexity	Cache Performance	Address Space
Regular Pointers	0%	Low	Standard	Full (64-bit)
Tiny Pointers	0-50%	Low	Excellent	Full (with base)
Kernel Squashing	0-60%	Medium	Excellent	Flexible
Narrow Pointers	50%	Low	Good	Limited (32-bit)
Segmented Pointers	25-50%	Medium	Moderate	Flexible
Compressed Oops	50%	Low	Good	Limited (32-bit)