Walkthrough on CuriousCoding

Binary search variants and the effects of batching

Wed, 12 Feb 2025 00:00:00 +0100

Table of Contents

1 Optimizing Binary Search And Interpolation Search
- 1.1 Problem statement
- 1.2 Inspiration and background
- 1.3 Benchmarking setup
2 Binary search
- 2.1 Branchless search
- 2.2 Explicit prefetching
- 2.3 Batching
- 2.4 A note on power-of-two array sizes
3 Eytzinger
- 3.1 Naive implementation
- 3.2 Prefetching
- 3.3 Branchless Eytzinger
- 3.4 Batched Eytzinger
  - 3.4.1 Non-prefetched
  - 3.4.2 Prefetched
4 Eytzinger or BinSearch?
5 Memory efficiency – parallel search and comparison to S-trees
6 Interpolation search
7 Conclusion and takeaways

1 Optimizing Binary Search And Interpolation Search Link to heading

This blogpost is a preliminary of the post on static search trees. We will be looking into binary search and how it can be optimized using different memory layouts (Eytzinger), branchless techniques and careful use of prefetching. In addition, we will explore batching. Our language of choice will be Rust.

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.

SimdMinimizers: Computing random minimizers, fast

Fri, 12 Jul 2024 00:00:00 +0200

Table of Contents

1 Introduction
- 1.1 Results
2 Random minimizers
3 Algorithms
4 Analysing what we have so far
5 Rolling our own hash
6 SIMD sliding window
- 6.1 Results
  - Human genome results
7 Extending into something useful
- 7.1 Collecting minimizer positions
- 7.2 Deduplicating the minimizer positions
- 7.3 Super-k-mers
- 7.4 Canonical k-mers
- 7.5 AntiLex hash
8 Conclusion
- 8.1 Future work

SimdMinimizers has been published as a paper: DOI, PDF:

28000x speedup with Numba.CUDA

Mon, 24 May 2021 00:00:00 +0200

Backlinks: r/CUDA, Numba discourse