Static search trees: 40x faster than binary search

Wed, 18 Dec 2024 00:00:00 +0100

Table of Contents

1 Introduction
- 1.1 Problem statement
- 1.2 Motivation
- 1.3 Recommended reading
- 1.4 Binary search and Eytzinger layout
- 1.5 Hugepages
- 1.6 A note on benchmarking
- 1.7 Cache lines
- 1.8 S-trees and B-trees
2 Optimizing find
- 2.1 Linear
- 2.2 Auto-vectorization
- 2.3 Trailing zeros
- 2.4 Popcount
- 2.5 Manual SIMD
3 Optimizing the search
- 3.1 Batching
- 3.2 Prefetching
- 3.3 Pointer arithmetic
  - 3.3.1 Up-front splat
  - 3.3.2 Byte-based pointers
  - 3.3.3 The final version
- 3.4 Skip prefetch
- 3.5 Interleave
4 Optimizing the tree layout
- 4.1 Left-tree
- 4.2 Memory layouts
- 4.3 Node size \(B=15\)
  - 4.3.1 Data structure size
- 4.4 Summary
5 Prefix partitioning
- 5.1 Full layout
- 5.2 Compact subtrees
- 5.3 The best of both: compact first level
- 5.4 Overlapping trees
- 5.5 Human data
- 5.6 Prefix map
- 5.7 Summary
6 Multi-threaded comparison
7 Conclusion
- 7.1 Future work
  - 7.1.1 Branchy search
  - 7.1.2 Interpolation search
  - 7.1.3 Packing data smaller
  - 7.1.4 Returning indices in original data
  - 7.1.5 Range queries
  - 7.1.6 Sorting queries
  - 7.1.7 Suffix array searching

In this post, we will implement a static search tree (S+ tree) for high-throughput searching of sorted data, as introduced on Algorithmica. We’ll mostly take the code presented there as a starting point, and optimize it to its limits. For a large part, I’m simply taking the ‘future work’ ideas of that post and implementing them. And then there will be a bunch of looking at assembly code to shave off all the instructions we can. Lastly, there will be one big addition to optimize throughput: batching.

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