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+Unicode ident
+=============
+
+[<img alt="github" src="https://img.shields.io/badge/github-dtolnay/unicode--ident-8da0cb?style=for-the-badge&labelColor=555555&logo=github" height="20">](https://github.com/dtolnay/unicode-ident)
+[<img alt="crates.io" src="https://img.shields.io/crates/v/unicode-ident.svg?style=for-the-badge&color=fc8d62&logo=rust" height="20">](https://crates.io/crates/unicode-ident)
+[<img alt="docs.rs" src="https://img.shields.io/badge/docs.rs-unicode--ident-66c2a5?style=for-the-badge&labelColor=555555&logo=docs.rs" height="20">](https://docs.rs/unicode-ident)
+[<img alt="build status" src="https://img.shields.io/github/actions/workflow/status/dtolnay/unicode-ident/ci.yml?branch=master&style=for-the-badge" height="20">](https://github.com/dtolnay/unicode-ident/actions?query=branch%3Amaster)
+
+Implementation of [Unicode Standard Annex #31][tr31] for determining which
+`char` values are valid in programming language identifiers.
+
+[tr31]: https://www.unicode.org/reports/tr31/
+
+This crate is a better optimized implementation of the older `unicode-xid`
+crate. This crate uses less static storage, and is able to classify both ASCII
+and non-ASCII codepoints with better performance, 2&ndash;10&times; faster than
+`unicode-xid`.
+
+<br>
+
+## Comparison of performance
+
+The following table shows a comparison between five Unicode identifier
+implementations.
+
+- `unicode-ident` is this crate;
+- [`unicode-xid`] is a widely used crate run by the "unicode-rs" org;
+- `ucd-trie` and `fst` are two data structures supported by the [`ucd-generate`] tool;
+- [`roaring`] is a Rust implementation of Roaring bitmap.
+
+The *static storage* column shows the total size of `static` tables that the
+crate bakes into your binary, measured in 1000s of bytes.
+
+The remaining columns show the **cost per call** to evaluate whether a single
+`char` has the XID\_Start or XID\_Continue Unicode property, comparing across
+different ratios of ASCII to non-ASCII codepoints in the input data.
+
+[`unicode-xid`]: https://github.com/unicode-rs/unicode-xid
+[`ucd-generate`]: https://github.com/BurntSushi/ucd-generate
+[`roaring`]: https://github.com/RoaringBitmap/roaring-rs
+
+| | static storage | 0% nonascii | 1% | 10% | 100% nonascii |
+|---|---|---|---|---|---|
+| **`unicode-ident`** | 10.1 K | 0.96 ns | 0.95 ns | 1.09 ns | 1.55 ns |
+| **`unicode-xid`** | 11.5 K | 1.88 ns | 2.14 ns | 3.48 ns | 15.63 ns |
+| **`ucd-trie`** | 10.2 K | 1.29 ns | 1.28 ns | 1.36 ns | 2.15 ns |
+| **`fst`** | 139 K | 55.1 ns | 54.9 ns | 53.2 ns | 28.5 ns |
+| **`roaring`** | 66.1 K | 2.78 ns | 3.09 ns | 3.37 ns | 4.70 ns |
+
+Source code for the benchmark is provided in the *bench* directory of this repo
+and may be repeated by running `cargo criterion`.
+
+<br>
+
+## Comparison of data structures
+
+#### unicode-xid
+
+They use a sorted array of character ranges, and do a binary search to look up
+whether a given character lands inside one of those ranges.
+
+```rust
+static XID_Continue_table: [(char, char); 763] = [
+ ('\u{30}', '\u{39}'), // 0-9
+ ('\u{41}', '\u{5a}'), // A-Z
+ …
+ ('\u{e0100}', '\u{e01ef}'),
+];
+```
+
+The static storage used by this data structure scales with the number of
+contiguous ranges of identifier codepoints in Unicode. Every table entry
+consumes 8 bytes, because it consists of a pair of 32-bit `char` values.
+
+In some ranges of the Unicode codepoint space, this is quite a sparse
+representation &ndash; there are some ranges where tens of thousands of adjacent
+codepoints are all valid identifier characters. In other places, the
+representation is quite inefficient. A characater like `µ` (U+00B5) which is
+surrounded by non-identifier codepoints consumes 64 bits in the table, while it
+would be just 1 bit in a dense bitmap.
+
+On a system with 64-byte cache lines, binary searching the table touches 7 cache
+lines on average. Each cache line fits only 8 table entries. Additionally, the
+branching performed during the binary search is probably mostly unpredictable to
+the branch predictor.
+
+Overall, the crate ends up being about 10&times; slower on non-ASCII input
+compared to the fastest crate.
+
+A potential improvement would be to pack the table entries more compactly.
+Rust's `char` type is a 21-bit integer padded to 32 bits, which means every
+table entry is holding 22 bits of wasted space, adding up to 3.9 K. They could
+instead fit every table entry into 6 bytes, leaving out some of the padding, for
+a 25% improvement in space used. With some cleverness it may be possible to fit
+in 5 bytes or even 4 bytes by storing a low char and an extent, instead of low
+char and high char. I don't expect that performance would improve much but this
+could be the most efficient for space across all the libraries, needing only
+about 7 K to store.
+
+#### ucd-trie
+
+Their data structure is a compressed trie set specifically tailored for Unicode
+codepoints. The design is credited to Raph Levien in [rust-lang/rust#33098].
+
+[rust-lang/rust#33098]: https://github.com/rust-lang/rust/pull/33098
+
+```rust
+pub struct TrieSet {
+ tree1_level1: &'static [u64; 32],
+ tree2_level1: &'static [u8; 992],
+ tree2_level2: &'static [u64],
+ tree3_level1: &'static [u8; 256],
+ tree3_level2: &'static [u8],
+ tree3_level3: &'static [u64],
+}
+```
+
+It represents codepoint sets using a trie to achieve prefix compression. The
+final states of the trie are embedded in leaves or "chunks", where each chunk is
+a 64-bit integer. Each bit position of the integer corresponds to whether a
+particular codepoint is in the set or not. These chunks are not just a compact
+representation of the final states of the trie, but are also a form of suffix
+compression. In particular, if multiple ranges of 64 contiguous codepoints have
+the same Unicode properties, then they all map to the same chunk in the final
+level of the trie.
+
+Being tailored for Unicode codepoints, this trie is partitioned into three
+disjoint sets: tree1, tree2, tree3. The first set corresponds to codepoints \[0,
+0x800), the second \[0x800, 0x10000) and the third \[0x10000, 0x110000). These
+partitions conveniently correspond to the space of 1 or 2 byte UTF-8 encoded
+codepoints, 3 byte UTF-8 encoded codepoints and 4 byte UTF-8 encoded codepoints,
+respectively.
+
+Lookups in this data structure are significantly more efficient than binary
+search. A lookup touches either 1, 2, or 3 cache lines based on which of the
+trie partitions is being accessed.
+
+One possible performance improvement would be for this crate to expose a way to
+query based on a UTF-8 encoded string, returning the Unicode property
+corresponding to the first character in the string. Without such an API, the
+caller is required to tokenize their UTF-8 encoded input data into `char`, hand
+the `char` into `ucd-trie`, only for `ucd-trie` to undo that work by converting
+back into the variable-length representation for trie traversal.
+
+#### fst
+
+Uses a [finite state transducer][fst]. This representation is built into
+[ucd-generate] but I am not aware of any advantage over the `ucd-trie`
+representation. In particular `ucd-trie` is optimized for storing Unicode
+properties while `fst` is not.
+
+[fst]: https://github.com/BurntSushi/fst
+[ucd-generate]: https://github.com/BurntSushi/ucd-generate
+
+As far as I can tell, the main thing that causes `fst` to have large size and
+slow lookups for this use case relative to `ucd-trie` is that it does not
+specialize for the fact that only 21 of the 32 bits in a `char` are meaningful.
+There are some dense arrays in the structure with large ranges that could never
+possibly be used.
+
+#### roaring
+
+This crate is a pure-Rust implementation of [Roaring Bitmap], a data structure
+designed for storing sets of 32-bit unsigned integers.
+
+[Roaring Bitmap]: https://roaringbitmap.org/about/
+
+Roaring bitmaps are compressed bitmaps which tend to outperform conventional
+compressed bitmaps such as WAH, EWAH or Concise. In some instances, they can be
+hundreds of times faster and they often offer significantly better compression.
+
+In this use case the performance was reasonably competitive but still
+substantially slower than the Unicode-optimized crates. Meanwhile the
+compression was significantly worse, requiring 6&times; as much storage for the
+data structure.
+
+I also benchmarked the [`croaring`] crate which is an FFI wrapper around the C
+reference implementation of Roaring Bitmap. This crate was consistently about
+15% slower than pure-Rust `roaring`, which could just be FFI overhead. I did not
+investigate further.
+
+[`croaring`]: https://crates.io/crates/croaring
+
+#### unicode-ident
+
+This crate is most similar to the `ucd-trie` library, in that it's based on
+bitmaps stored in the leafs of a trie representation, achieving both prefix
+compression and suffix compression.
+
+The key differences are:
+
+- Uses a single 2-level trie, rather than 3 disjoint partitions of different
+ depth each.
+- Uses significantly larger chunks: 512 bits rather than 64 bits.
+- Compresses the XID\_Start and XID\_Continue properties together
+ simultaneously, rather than duplicating identical trie leaf chunks across the
+ two.
+
+The following diagram show the XID\_Start and XID\_Continue Unicode boolean
+properties in uncompressed form, in row-major order:
+
+<table>
+<tr><th>XID_Start</th><th>XID_Continue</th></tr>
+<tr>
+<td><img alt="XID_Start bitmap" width="256" src="https://user-images.githubusercontent.com/1940490/168647353-c6eeb922-afec-49b2-9ef5-c03e9d1e0760.png"></td>
+<td><img alt="XID_Continue bitmap" width="256" src="https://user-images.githubusercontent.com/1940490/168647367-f447cca7-2362-4d7d-8cd7-d21c011d329b.png"></td>
+</tr>
+</table>
+
+Uncompressed, these would take 140 K to store, which is beyond what would be
+reasonable. However, as you can see there is a large degree of similarity
+between the two bitmaps and across the rows, which lends well to compression.
+
+This crate stores one 512-bit "row" of the above bitmaps in the leaf level of a
+trie, and a single additional level to index into the leafs. It turns out there
+are 124 unique 512-bit chunks across the two bitmaps so 7 bits are sufficient to
+index them.
+
+The chunk size of 512 bits is selected as the size that minimizes the total size
+of the data structure. A smaller chunk, like 256 or 128 bits, would achieve
+better deduplication but require a larger index. A larger chunk would increase
+redundancy in the leaf bitmaps. 512 bit chunks are the optimum for total size of
+the index plus leaf bitmaps.
+
+In fact since there are only 124 unique chunks, we can use an 8-bit index with a
+spare bit to index at the half-chunk level. This achieves an additional 8.5%
+compression by eliminating redundancies between the second half of any chunk and
+the first half of any other chunk. Note that this is not the same as using
+chunks which are half the size, because it does not necessitate raising the size
+of the trie's first level.
+
+In contrast to binary search or the `ucd-trie` crate, performing lookups in this
+data structure is straight-line code with no need for branching.
+
+```asm
+is_xid_start:
+ mov eax, edi
+ shr eax, 9
+ lea rcx, [rip + unicode_ident::tables::TRIE_START]
+ add rcx, rax
+ xor eax, eax
+ cmp edi, 201728
+ cmovb rax, rcx
+ test rax, rax
+ lea rcx, [rip + .L__unnamed_1]
+ cmovne rcx, rax
+ movzx eax, byte ptr [rcx]
+ shl rax, 5
+ mov ecx, edi
+ shr ecx, 3
+ and ecx, 63
+ add rcx, rax
+ lea rax, [rip + unicode_ident::tables::LEAF]
+ mov al, byte ptr [rax + rcx]
+ and dil, 7
+ mov ecx, edi
+ shr al, cl
+ and al, 1
+ ret
+```
+
+<br>
+
+## License
+
+Use of the Unicode Character Database, as this crate does, is governed by the <a
+href="LICENSE-UNICODE">Unicode License Agreement &ndash; Data Files and Software
+(2016)</a>.
+
+All intellectual property within this crate that is **not generated** using the
+Unicode Character Database as input is licensed under either of <a
+href="LICENSE-APACHE">Apache License, Version 2.0</a> or <a
+href="LICENSE-MIT">MIT license</a> at your option.
+
+The **generated** files incorporate tabular data derived from the Unicode
+Character Database, together with intellectual property from the original source
+code content of the crate. One must comply with the terms of both the Unicode
+License Agreement and either of the Apache license or MIT license when those
+generated files are involved.
+
+Unless you explicitly state otherwise, any contribution intentionally submitted
+for inclusion in this crate by you, as defined in the Apache-2.0 license, shall
+be licensed as just described, without any additional terms or conditions.