Folded Trie: Efficient Data Structure for All of Unicode

1. Folded Trie: Efficient Data Structure for All of Unicode Vladimir Weinstein vweinste@us.ibm.com Globalization Center of Competency, San Jose, CA

2. Introduction • A lot of data for each code point • Need appropriate data structures • Unicode version 3.1 introduced code points into supplementary space – addressable range grew to more than a million • Repetitive data • Sparsely populated range, especially the supplementary space

3. Data Structures • Arrays • Advantages: very fast access time, fast write time • Disadvantage: Unacceptable memory consumption • Hash tables • Advantages: Easy to use, Reasonably fast, General • Disadvantages: High overhead, complicated sequential access, slower than array lookup, data within ranges is not shared

4. Data Structures (continued) • Inversion Maps • Advantages: simple, very compact, fast boolean operations • Disadvantages: worse access time than arrays and possibly hash tables • For more details see “Bits of Unicode” at http://www.macchiato.com/slides/Bits_of_Unicode.ppt

5. Tries • A trie is a structure with one or more indexes and one data storage. • Name comes from “Information Retrieval” • Shares repetitive data • Good compaction • Not appropriate for frequently changing data

6. Single-Index Trie • A trie structure with an index array and a data array. • Advantages • Excellent size • Very good access performance (two array accesses, shift, mask and addition) • Disadvantages • Not appropriate for frequently changing data • Index array gets too big when dealing with supplementary code points

7. UPPER_WIDTH LOWER_WIDTH LOWER_MASK BMP code point Upper Lower 15 0 Data Array Index 0 Block Data 0 Block Single-Index Trie Diagram

8. Double-Index Trie • Two index arrays and a data block • Compared to single-index trie: • Provides better compression of the index array • Worse performance, but still very fast • Feasible for supplementary code points

9. UPPER_WIDTH MIDDLE_WIDTH LOWER_WIDTH MIDDLE_MASK LOWER_MASK Code point Lower Upper Middle 0 20 Data Index 1 Index 2 0 Index1 0 Index2 Block Data Double-Index Trie Diagram

10. Folded Trie • Fast access for BMP code points • Slower access for supplementary code points, but far less frequent • Compacts supplementary index • Needs additional build time processing • Fast address with UTF-16 code units • no need to construct code point

11. Lead Surrogate 15 0 1 Same for the surrogate block 110110.. 3 Has data for surrogate block? 2 Folded Trie Data No Trail Surrogate Yes 0 15 9 110111.. Lead Surrogate Data 4 4 5 Pseudo Code Point 6 Index + Data Folded Trie – Supplementary Access Diagram • BMP code points access same as with single-index Final Data

12. ICU Implementation: UTrie • ICU implementation is called UTrie • Stores either 16 bit or 32 bit wide data (extensible in the future) • Up to 256K different data elements • Can be frozen and reused as memory mapped image for fast startup • Using UTrie requires custom code More about ICU at the end of presentation

13. start-1 Element 1 start Element 2 Element 2 Element 2 Element 2 Element 2 Element 2 limit-1 Element 3 limit Range Enumeration • Allows enumerating over a set of contiguous maximal ranges of same data elements • Elements can be preprocessed by additional callback • Saves time when processing the whole Unicode range by efficiently walking the trie structure

14. Latin-1 Fast Path • Build time option • Allows direct array access for the Latin-1 range (0x00-0xFF) • Latin-1 range is not compressed if this option is used • Appropriate when access for Latin-1 range is critical • collation

15. Example: Normalization Data • Normalization data is stored using UTries • For example, main data has the following format 31 15 7 6 5 3 0 Extra data index Combining class BCK FWD QC_MAYBE QC_NO • Can be either: • index to variable length data • first part of supplementary lookup value • Special handling indicator (Hangul, Jamo) Combines back Values for normalization quick check Combines forward • Variable-length data contains composition and decomposition info

16. Data Index Example: Character Properties Data • The result of UTrie lookup is an index • Double indexing allows for even better compression, since many code points have the same property value • UTrie data width is 16 bit (thousands of data entries), while the property data width is 32 bits (few hundred unique data words). Folded Trie Property data 32 bits 16 bits

17. International Components for Unicode • International Components for Unicode(ICU) is a library that provides robust and full-featured Unicode support • Several library services use the common UTrie implementation • Wide variety of supported platforms • open source (X license – non-viral) • C/C++ and Java versions • http://oss.software.ibm.com/icu/

18. Conclusion • UTrie data structure provides good compression with fast access • The main constraint for usage is the nature of the data that needs to be stored • Designed for repetitive and sparse data

19. Q & A

20. Folding and Surrogate Access • Folding process compacts the index for supplementaries and moves it right above the BMP index • Access in ICU4C: • Define a C callback, invoked when special lead surrogate is detected • Manually detect special lead surrogates • In ICU4J, provide a subclass with a method that detects special lead surrogates

21. Summary • Introduction: Storing Unicode data • Types of data structures • Tries • Single-index trie • Double-index trie • Folded trie • Usage of folded trie in normalization • Usage of folded trie for character properties