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[markdown] Index footnote definitions and labels on Document for O(1) lookup - #2760

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markdown_footnote_index
Oct 30, 2026
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[markdown] Index footnote definitions and labels on Document for O(1) lookup#2760
jonasfj merged 2 commits into
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markdown_footnote_index

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@jonasfj jonasfj commented Oct 29, 2026 •
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Cache a case-folded footnote definition key map (_footnoteKeyByLower) and a
0-based footnote label index map (_footnoteLabelIndex) on Document, exposed
to FootnoteRefSyntax via a package-private DocumentFootnotes extension (with
lib/markdown.dart exporting show Document, LinkReference from
src/document.dart).

Why this change is necessary

Even after fast-rejecting empty footnoteReferences and non-[^...] brackets,
FootnoteRefSyntax.tryCreateFootnoteLink still performed two linear O(D) scans
whenever a document contained D footnote definitions ([^1]: a, ..., [^D]: a)
and R footnote-shaped references ([^...]):

  1. Linear scan of footnoteReferences.keys (O(D * R) = O(n^2)):
    Because Document.footnoteReferences stores case-sensitive keys (used when
    rendering href="#fn-$id"), FootnoteRefSyntax looked up each lowercase
    key via: 
    final label = refs.keys.firstWhere(
  (k) => k.toLowerCase() == key,
  orElse: () => '',
);
    On a 64 KB input with D = 4,000 footnote definitions followed by R = 8,000
    footnote references (such as [^x] * 8,000), firstWhere linearly scanned
    all 4,000 keys and called k.toLowerCase() 3.2 * 10^7 times.
  2. Linear scan of footnoteLabels (O(D * R) = O(n^2)):
    When a footnote reference matched, var pos = labels.indexOf(key); linearly
    scanned document.footnoteLabels on every reference to find or assign its
    1-based footnote number.

How this change works

  1. Document holds two private fields:
    • Map<String, String>? _footnoteKeyByLower;: lazily built once on the first
      footnote lookup after block parsing has populated footnoteReferences.
      Iterating footnoteReferences.keys.toList().reversed ensures that if two
      definitions share the same lowercase key, the earliest definition wins—
      matching refs.keys.firstWhere((k) => k.toLowerCase() == key) semantics.
    • final _footnoteLabelIndex = <String, int>{};: maps each referenced
      lowercase key to its 0-based index in footnoteLabels, appending to
      footnoteLabels via putIfAbsent when key is referenced for the first
      time.
  2. DocumentFootnotes exposes findFootnoteLabel(String key) and
    footnoteLabelOrdinal(String key) inside lib/src/, while
    export 'src/document.dart' show Document, LinkReference; in
    lib/markdown.dart keeps DocumentFootnotes package-private so the public
    API of package:markdown is unchanged.

Differential testing

Rendered every input with origin/main and with this branch (GFM extension
set, 30 s per-file timeout) and compared the HTML. Sources:

  • pub.dev: 367,926 Markdown files from 93,452 packages
  • Real-world docs: 116,231 files from mdn/content, github/docs,
    kubernetes/website, freeCodeCamp, tldr, flutter/website,
    dart-lang/site-www, microsoft/vscode-docs, withastro/docs,
    rust-lang/book, GitHub READMEs, and Wikipedia
  • Parser test suites: 6,458 cases from cmark, cmark-gfm, commonmark.js,
    pulldown-cmark, md4c, goldmark, markdown-it, comrak, marked,
    pandoc, and pathological generators
  • OSS-Fuzz: 57,716 inputs from the cmark, md4c, and markdown-it-py fuzzers

OSS-Fuzz inputs that sit at the 30 s timeout or the stack limit flip between
runs; every one reported as a new failure was re-run standalone on both trees.

Results:

  • No HTML differences and no new exceptions across all four sources.
  • 1 OSS-Fuzz timeout resolved; cumulative parse time −0.4%.

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Breaking changes ✔️
Package Change Current Version New Version Needed Version Looking good?
markdown Non-Breaking 7.3.1 7.4.1-wip 7.4.1-wip ✔️

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Coverage ⚠️
File Coverage
pkgs/markdown/lib/markdown.dart 💔 Not covered
pkgs/markdown/lib/src/document.dart 💚 96 % ⬆️ 1 %
pkgs/markdown/lib/src/inline_syntaxes/footnote_ref_syntax.dart 💚 100 %

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License Headers ✔️ 
// Copyright (c) 2026, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.
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gemini-code-assist[bot]
gemini-code-assist Bot reviewed Oct 29, 2026
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Code Review

This pull request optimizes footnote reference lookups from O(N) to O(1) by caching footnote keys and label ordinals in the Document class, and adds tests for reusing documents and handling case-insensitive duplicate footnote definitions. The review feedback suggests optimizing the findFootnoteLabel implementation to avoid list allocations by iterating forward, adding proper DartDoc documentation to the new extension, and simplifying the null-checking logic in footnote_ref_syntax.dart.

Comment thread pkgs/markdown/lib/src/document.dart
Comment on lines +241 to +253
extension DocumentFootnotes on Document {
String? findFootnoteLabel(String key) => (_footnoteKeyByLower ??= {
for (final k in footnoteReferences.keys.toList().reversed)
k.toLowerCase(): k,
})[key];

int footnoteLabelOrdinal(String key) =>
_footnoteLabelIndex.putIfAbsent(key, () {
final index = footnoteLabels.length;
footnoteLabels.add(key);
return index;
});
}

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medium

The current implementation of findFootnoteLabel allocates a temporary list of keys and reverses it (footnoteReferences.keys.toList().reversed) to ensure that the first duplicate definition wins. We can achieve the same result more efficiently without any list allocations by iterating forward and using map[lower] ??= k. Additionally, adding documentation to this extension and its methods improves maintainability. Note that DartDoc comments should describe what the function does on the first line, rather than starting with 'Returns'.

/// Internal extension to provide O(1) footnote lookups on Document.
extension DocumentFootnotes on Document {
  /// Finds the case-sensitive footnote label for the given lowercase key.
  ///
  /// This is null if no such footnote reference exists.
  String? findFootnoteLabel(String key) {
    if (_footnoteKeyByLower == null) {
      final map = <String, String>{};
      for (final k in footnoteReferences.keys) {
        map[k.toLowerCase()] ??= k;
      }
      _footnoteKeyByLower = map;
    }
    return _footnoteKeyByLower![key];
  }

  /// Obtains the 0-based ordinal index for the given footnote key.
  int footnoteLabelOrdinal(String key) =>
      _footnoteLabelIndex.putIfAbsent(key, () {
        final index = footnoteLabels.length;
        footnoteLabels.add(key);
        return index;
      });
}
References
  1. At least all public members should have documentation, answering the why. (link)
  2. DartDoc comments should not start with "Returns" if it's not the first line of the DartDoc. The first line should describe what the function does, and subsequent lines can describe the return value.

Comment thread pkgs/markdown/lib/src/inline_syntaxes/footnote_ref_syntax.dart
Comment on lines 43 to 50
// `label` is what footnoteReferences stored, it is case sensitive.
final label = refs.keys.firstWhere(
(k) => k.toLowerCase() == key,
orElse: () => '',
);
final label = parser.document.findFootnoteLabel(key);
// `count != null` means footnote was valid.
var count = refs[label];
var count = label == null ? null : refs[label];
// And then check if footnote was matched.
if (count == null) {
if (label == null || count == null) {
return null;
}

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medium

The null checks and ternary operators here can be simplified. Since label can be null, checking label == null first allows us to safely look up refs[label] and perform a single check on count without redundant conditions.

    // label is what footnoteReferences stored, it is case sensitive.
    final label = parser.document.findFootnoteLabel(key);
    if (label == null) {
      return null;
    }
    var count = refs[label];
    if (count == null) {
      return null;
    }

@jonasfj
jonasfj force-pushed the markdown_footnote_index branch from 12ff205 to 9773032 Compare October 30, 2026 07:57
@jonasfj
[markdown] Index footnote definitions and labels on Document for O(1)…
5ae4b2a 
… lookup

Cache a case-folded footnote definition key map (`_footnoteKeyByLower`) and a
0-based footnote label index map (`_footnoteLabelIndex`) on `Document`, exposed
to `FootnoteRefSyntax` via a package-private `DocumentFootnotes` extension (with
`lib/markdown.dart` exporting `show Document, LinkReference` from
`src/document.dart`).

----

### Why this change is necessary

Even after fast-rejecting empty `footnoteReferences` and non-`[^...]` brackets,
`FootnoteRefSyntax.tryCreateFootnoteLink` still performed two linear O(D) scans
whenever a document contained D footnote definitions (`[^1]: a`, ..., `[^D]: a`)
and R footnote-shaped references (`[^...]`):

1. **Linear scan of `footnoteReferences.keys` (`O(D * R) = O(n^2)`)**:
   Because `Document.footnoteReferences` stores case-sensitive keys (used when
   rendering `href="#fn-$id"`), `FootnoteRefSyntax` looked up each lowercase
   `key` via:
   ```dart
   final label = refs.keys.firstWhere(
     (k) => k.toLowerCase() == key,
     orElse: () => '',
   );
   ```
   On a 64 KB input with D = 4,000 footnote definitions followed by R = 8,000
   footnote references (such as `[^x]` * 8,000), `firstWhere` linearly scanned
   all 4,000 keys and called `k.toLowerCase()` 3.2 * 10^7 times.
2. **Linear scan of `footnoteLabels` (`O(D * R) = O(n^2)`)**:
   When a footnote reference matched, `var pos = labels.indexOf(key);` linearly
   scanned `document.footnoteLabels` on every reference to find or assign its
   1-based footnote number.

### How this change works

1. `Document` holds two private fields:
   - `Map<String, String>? _footnoteKeyByLower;`: lazily built once on the first
     footnote lookup after block parsing has populated `footnoteReferences`.
     Iterating `footnoteReferences.keys.toList().reversed` ensures that if two
     definitions share the same lowercase key, the earliest definition wins—
     matching `refs.keys.firstWhere((k) => k.toLowerCase() == key)` semantics.
   - `final _footnoteLabelIndex = <String, int>{};`: maps each referenced
     lowercase `key` to its 0-based index in `footnoteLabels`, appending to
     `footnoteLabels` via `putIfAbsent` when `key` is referenced for the first
     time.
2. `DocumentFootnotes` exposes `findFootnoteLabel(String key)` and
   `footnoteLabelOrdinal(String key)` inside `lib/src/`, while
   `export 'src/document.dart' show Document, LinkReference;` in
   `lib/markdown.dart` keeps `DocumentFootnotes` package-private so the public
   API of `package:markdown` is unchanged.
@jonasfj
[markdown] Build the footnote key index without copying the key list
0e850f2 
Iterate `footnoteReferences.keys` forward and keep the first label per
lower-cased key with `??=` instead of reversing a copy of the keys, document
the `DocumentFootnotes` extension, and return early when no definition
matches.
@jonasfj
jonasfj force-pushed the markdown_footnote_index branch from 9773032 to 0e850f2 Compare October 30, 2026 09:22
@jonasfj
jonasfj requested a review from szakarias October 30, 2026 10:15
@jonasfj
jonasfj marked this pull request as ready for review October 30, 2026 10:15
@jonasfj
jonasfj requested a review from srawlins as a code owner October 30, 2026 10:15
@jonasfj jonasfj changed the title [WIP] [markdown] Index footnote definitions and labels on Document for O(1) lookup [markdown] Index footnote definitions and labels on Document for O(1) lookup Oct 30, 2026
szakarias
szakarias approved these changes Oct 30, 2026
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LGTM

@jonasfj
jonasfj merged commit 3671d33 into main Oct 30, 2026
31 of 33 checks passed
@jonasfj
jonasfj deleted the markdown_footnote_index branch October 30, 2026 11:56
copybara-service Bot pushed a commit to dart-lang/sdk that referenced this pull request Nov 3, 2026
@natebosch dart-scoped@luci-project-accounts.iam.gserviceaccount.com
[deps] rev core, ecosystem, http, i18n, shelf, test, tools
c48ebb8 
Revisions updated by `dart tools/rev_sdk_deps.dart`.

core (https://github.com/dart-lang/core/compare/d7bd45c..24e09c4):
  24e09c4c  Sun Nov 1 21:12:19 2026 +0000  dependabot[bot]  Bump the github-actions group with 4 updates (dart-lang/core#1037)
  87ac1b4c  Fri Oct 30 16:02:43 2026 +0100  Michael Thomsen  [os_detect] Deprecate package:os_detect in favor of package:platform (dart-lang/core#1003)
  8debf335  Fri Oct 30 01:57:36 2026 +0530  Sahaja Pallapothula  Clarify Characters equality and Unicode normalization (dart-lang/core#1031)

ecosystem (https://github.com/dart-lang/ecosystem/compare/24b9ba8..f8faabf):
  f8faabf  Sun Nov 1 18:16:20 2026 +0000  dependabot[bot]  Bump the github-actions group with 2 updates (dart-lang/ecosystem#481)
  27c2fc8  Sat Oct 31 12:36:53 2026 +0100  Moritz  Fix publish workflow pins, add tag_prefix to health, and update docs (dart-lang/ecosystem#480)
  05641a9  Sat Oct 31 09:56:42 2026 +0100  Moritz  Restore deprecated publish.yaml workflow and firehose CLI entrypoint (dart-lang/ecosystem#479)
  78abf72  Fri Oct 30 08:24:07 2026 -0700  Kevin Moore  fix(repo_manage): use pub_semver for changelog -wip transitions (dart-lang/ecosystem#475)
  0bfa654  Fri Oct 30 09:33:57 2026 +0100  Moritz  Move publish check to health workflow and use individual package publishing workflows from `setup-dart` (dart-lang/ecosystem#454)
  adf7979  Thu Oct 29 23:46:49 2026 -0700  Kevin Moore  test(firehose): use hasLength, containsPair, and isFalse (dart-lang/ecosystem#477)

http (https://github.com/dart-lang/http/compare/c76dfb3..8c0d66a):
  8c0d66a  Fri Oct 30 09:54:41 2026 -0700  Brian Quinlan  chore(cupertino_http): check ffigen generation (dart-lang/http#2044)
  c8737d1  Fri Oct 30 09:11:46 2026 +0100  Moritz  chore(http): run Firefox tests with -headless instead of xvfb-run (dart-lang/http#2033)
  05d0b18  Fri Oct 30 07:08:19 2026 +0100  Moritz  fix(http2): make StreamException a StreamTransportException and forward ALPN errors to onError (dart-lang/http#2009)

i18n (https://github.com/dart-lang/i18n/compare/4c7b4ad..7475ce6):
  7475ce64  Sat Oct 31 02:49:28 2026 +0100  Moritz  [intl4x] Fix NumberFormat.percent ignoring digits (dart-lang/i18n#1115)

shelf (https://github.com/dart-lang/shelf/compare/62d3e4e..9946de5):
  9946de5  Sun Nov 1 12:27:59 2026 +0000  dependabot[bot]  build(deps): bump the github-actions group with 3 updates (dart-lang/shelf#554)

test (https://github.com/dart-lang/test/compare/6d74720..2a9e017):
  2a9e0175  Sun Nov 1 03:47:24 2026 +0000  dependabot[bot]  Bump the github-actions group with 6 updates (dart-lang/test#2813)
  55cd5cd5  Fri Oct 30 13:43:47 2026 -0700  Nate Bosch  Migrate publishing workflows from firehose to setup-dart (dart-lang/test#2812)
  10dc78c0  Fri Oct 30 11:21:53 2026 -0700  Nate Bosch  [checks] Describe what the stream did in failures (dart-lang/test#2811)
  c11ad06d  Fri Oct 30 08:59:57 2026 -0700  Nate Bosch  [checks] Add CheckFailure.describeNested (dart-lang/test#2793)
  0137b43e  Fri Oct 30 05:40:43 2026 +0530  Shriraj Jadhav  [checks] Use the Iterable.last member for the last expectation (dart-lang/test#2807)
  50c9f454  Thu Oct 29 15:11:39 2026 -0700  Nate Bosch  [checks] Collapse clauses for described conditions (dart-lang/test#2794)

tools (https://github.com/dart-lang/tools/compare/3980dca..1579f8d):
  1579f8d69  Mon Nov 2 02:44:58 2026 +0530  Joshua  fix(coverage): reject package: and dart: URIs outside known roots in Resolver (dart-lang/tools#2764)
  f869fdca4  Sun Nov 1 10:26:34 2026 +0100  dart-ecosystem-bot[bot]  [boring] Update BoringSSL to ed9209cf (dart-lang/tools#2774)
  d10e2b87f  Sun Nov 1 10:26:11 2026 +0100  dart-ecosystem-bot[bot]  [boring] Pin the prebuilt binaries of boring-binaries-20261101-33e9e69722af (dart-lang/tools#2777)
  33e9e6972  Sun Nov 1 05:56:30 2026 +0000  dependabot[bot]  build(deps): bump the github-actions group with 4 updates (dart-lang/tools#2775)
  f84d0d0d2  Sun Nov 1 05:36:12 2026 +0000  dependabot[bot]  build(deps): bump ffigen from 22.0.0 to 23.0.0 in /pkgs/boring (dart-lang/tools#2776)
  14ad5e515  Fri Oct 30 10:48:58 2026 -0700  Kevin Moore  [mime] Harden BoundMultipartStream error routing, headers, and epilogue (dart-lang/tools#2629)
  7a780d48c  Fri Oct 30 12:57:03 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid rescanning failed plain-text runs in InlineParser (dart-lang/tools#2757)
  3671d33a9  Fri Oct 30 12:56:48 2026 +0100  Jonas Finnemann Jensen  [markdown] Index footnote definitions and labels on Document for O(1) lookup (dart-lang/tools#2760)
  6f38e9fda  Fri Oct 30 12:56:09 2026 +0100  Jonas Finnemann Jensen  [markdown] Bound the domain of extended URL autolinks to DNS limits (dart-lang/tools#2759)
  aa0c38544  Fri Oct 30 12:20:40 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid quadratic removeRange in _combineAdjacentText (dart-lang/tools#2758)
  f425baf46  Fri Oct 30 11:16:28 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid rescanning failed space runs in LineBreakSyntax (dart-lang/tools#2756)
  c7eafbec3  Fri Oct 30 11:09:45 2026 +0100  Jonas Finnemann Jensen  [markdown] Reject '<' in AutolinkSyntax (dart-lang/tools#2755)
  86ed0f902  Fri Oct 30 11:08:25 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid quadratic backtracking in headerPattern (dart-lang/tools#2754)
  8ea07517f  Fri Oct 30 07:45:42 2026 +0100  Moritz  [boring] Regenerate the x509-limbo expected failures in the refresh job (dart-lang/tools#2712)
  40235c365  Thu Oct 29 14:46:17 2026 +0100  Jonas Finnemann Jensen  [markdown] Make HtmlBlockSyntax.parseChildLines iterative (dart-lang/tools#2749)
  0ff03f643  Thu Oct 29 14:41:33 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid re-escaping nested image alt text in ImageSyntax.createNode (dart-lang/tools#2752)
  784654d01  Thu Oct 29 14:37:11 2026 +0100  Jonas Finnemann Jensen  [markdown] Add test cases covering parser and renderer edge cases (dart-lang/tools#2753)
  4f2718ad8  Thu Oct 29 14:36:52 2026 +0100  Jonas Finnemann Jensen  [markdown] Make Document._parseInlineContent iterative (dart-lang/tools#2750)
  cac1421d5  Thu Oct 29 14:17:06 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid quadratic duplicate heading ID probing in HtmlRenderer (dart-lang/tools#2748)
  66880bcd3  Thu Oct 29 14:11:27 2026 +0100  Jonas Finnemann Jensen  [markdown] Check footnote label and empty map before scanning footnote keys (dart-lang/tools#2751)
  7f8696523  Thu Oct 29 14:07:06 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid quadratic blank-line lookahead in CodeBlockSyntax (dart-lang/tools#2747)
  9da6bb291  Thu Oct 29 14:03:04 2026 +0100  Jonas Finnemann Jensen  [markdown] Avoid exponential and quadratic backtracking in tablePattern (dart-lang/tools#2746)

dartdoc is held back at db94437, before dart-lang/dartdoc#4312, because its
mock SDK version changes conflict in the google3 3-way merge with the hotfix
in cl/1005963642.

native is held back at e0ca7c6, before dart-lang/native#3742, because
deprecating `MacOSCodeConfig(targetVersion: ...)` causes a fatal
`deprecated_member_use` diagnostic in `pkg/dartdev/lib/src/native_assets.dart`.

web is held back at 4e60e61, before dart-lang/web#596, because it changes
`package:web` signatures (e.g. `innerHTML=`, `parseFromString`, `Worker()`)
from `JSAny` to `String` in ways that break callers in google3.

Change-Id: I53d2cbde741c45b8fd33bca42742549819dd332b
Reviewed-on: https://dart-review.googlesource.com/c/sdk/+/572780
Reviewed-by: Brian Quinlan <[email protected]>
Commit-Queue: Nate Bosch <[email protected]>
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