diff --git a/.all-contributorsrc b/.all-contributorsrc
index fa1796ec..b33d332f 100644
--- a/.all-contributorsrc
+++ b/.all-contributorsrc
@@ -4,7 +4,8 @@
   "repoType": "github",
   "repoHost": "https://github.com",
   "files": [
-    "README.md", "CONTRIBUTORS.md"
+    "README.md",
+    "CONTRIBUTORS.md"
   ],
   "imageSize": 100,
   "commitType": "docs",
@@ -25,7 +26,9 @@
         "maintenance",
         "tool",
         "test",
-        "bug"
+        "bug",
+        "platform",
+        "review"
       ]
     },
     {
@@ -35,7 +38,8 @@
       "profile": "https://github.com/mdhaber",
       "contributions": [
         "code",
-        "ideas"
+        "ideas",
+        "test"
       ]
     },
     {
@@ -45,7 +49,8 @@
       "profile": "https://github.com/j-bowhay",
       "contributions": [
         "code",
-        "review"
+        "review",
+        "tool"
       ]
     },
     {
@@ -88,14 +93,20 @@
       ]
     },
     {
-      "login": "rgommers",
-      "name": "Ralf Gommers",
-      "avatar_url": "https://avatars.githubusercontent.com/u/98330?v=4",
-      "profile": "https://github.com/rgommers/",
+      "login": "crusaderky",
+      "name": "Guido Imperiale",
+      "avatar_url": "https://avatars.githubusercontent.com/u/6213168?v=4",
+      "profile": "https://github.com/crusaderky",
       "contributions": [
+        "code",
+        "doc",
+        "tool",
+        "test",
+        "example",
+        "bug",
         "ideas",
-        "infra",
-        "review"
+        "review",
+        "maintenance"
       ]
     },
     {
@@ -143,6 +154,101 @@
       "contributions": [
         "code"
       ]
+    },
+    {
+      "login": "OmarManzoor",
+      "name": "Omar Salman",
+      "avatar_url": "https://avatars.githubusercontent.com/u/17495884?v=4",
+      "profile": "https://github.com/OmarManzoor",
+      "contributions": [
+        "code"
+      ]
+    },
+    {
+      "login": "rgommers",
+      "name": "Ralf Gommers",
+      "avatar_url": "https://avatars.githubusercontent.com/u/98330?v=4",
+      "profile": "https://github.com/rgommers/",
+      "contributions": [
+        "ideas",
+        "infra",
+        "review"
+      ]
+    },
+    {
+      "login": "ogrisel",
+      "name": "Olivier Grisel",
+      "avatar_url": "https://avatars.githubusercontent.com/u/89061?v=4",
+      "profile": "https://ogrisel.com",
+      "contributions": [
+        "code"
+      ]
+    },
+    {
+      "login": "ev-br",
+      "name": "Evgeni Burovski",
+      "avatar_url": "https://avatars.githubusercontent.com/u/2133832?v=4",
+      "profile": "https://github.com/ev-br",
+      "contributions": [
+        "code",
+        "doc"
+      ]
+    },
+    {
+      "login": "jakevdp",
+      "name": "Jake Vanderplas",
+      "avatar_url": "https://avatars.githubusercontent.com/u/781659?v=4",
+      "profile": "http://www.vanderplas.com/",
+      "contributions": [
+        "review"
+      ]
+    },
+    {
+      "login": "kotlinisland",
+      "name": "kotlinisland",
+      "avatar_url": "https://avatars.githubusercontent.com/u/65446343?v=4",
+      "profile": "https://github.com/KotlinIsland",
+      "contributions": [
+        "review"
+      ]
+    },
+    {
+      "login": "detachhead",
+      "name": "detachhead",
+      "avatar_url": "https://avatars.githubusercontent.com/u/57028336?v=4",
+      "profile": "https://github.com/DetachHead",
+      "contributions": [
+        "review"
+      ]
+    },
+    {
+      "login": "NeilGirdhar",
+      "name": "Neil Girdhar",
+      "avatar_url": "https://avatars.githubusercontent.com/u/730137?v=4",
+      "profile": "https://github.com/NeilGirdhar",
+      "contributions": [
+        "code",
+        "test"
+      ]
+    },
+    {
+      "login": "lithomas1",
+      "name": "Thomas Li",
+      "avatar_url": "https://avatars.githubusercontent.com/u/47963215?v=4",
+      "profile": "https://github.com/lithomas1",
+      "contributions": [
+        "bug",
+        "tool"
+      ]
+    },
+    {
+      "login": "pearu",
+      "name": "Pearu Peterson",
+      "avatar_url": "https://avatars.githubusercontent.com/u/402156?v=4",
+      "profile": "https://github.com/pearu",
+      "contributions": [
+        "review"
+      ]
     }
   ]
 }
diff --git a/.dprint.jsonc b/.dprint.jsonc
new file mode 100644
index 00000000..c3642905
--- /dev/null
+++ b/.dprint.jsonc
@@ -0,0 +1,25 @@
+{
+  "json": {
+    "lineWidth": 100,
+    "array.preferSingleLine": true,
+  },
+  "markdown": {
+    "lineWidth": 200,
+    "emphasisKind": "asterisks",
+  },
+  "toml": {
+    "lineWidth": 100,
+  },
+  "yaml": {
+    "printWidth": 100,
+    "formatComments": true,
+    "braceSpacing": false,
+  },
+  "excludes": ["**/*-lock.json", "**/*.lock", "**/node_modules/", "dist/"],
+  "plugins": [
+    "https://plugins.dprint.dev/g-plane/pretty_yaml-v0.5.1.wasm",
+    "https://plugins.dprint.dev/json-0.20.0.wasm",
+    "https://plugins.dprint.dev/markdown-0.19.0.wasm",
+    "https://plugins.dprint.dev/toml-0.7.0.wasm",
+  ],
+}
diff --git a/.editorconfig b/.editorconfig
new file mode 100644
index 00000000..46f23570
--- /dev/null
+++ b/.editorconfig
@@ -0,0 +1,14 @@
+root = true
+
+[*.{py,md}]
+indent_style = space
+end_of_line = lf
+trim_trailing_whitespace = true
+insert_final_newline = true
+
+[*.py]
+max_line_length = 88
+indent_size = 4
+
+[*.md]
+max_line_length = 80
diff --git a/.github/dependabot.yml b/.github/dependabot.yml
deleted file mode 100644
index 6c4b3695..00000000
--- a/.github/dependabot.yml
+++ /dev/null
@@ -1,11 +0,0 @@
-version: 2
-updates:
-  # Maintain dependencies for GitHub Actions
-  - package-ecosystem: "github-actions"
-    directory: "/"
-    schedule:
-      interval: "weekly"
-    groups:
-      actions:
-        patterns:
-          - "*"
diff --git a/.github/pull_request_template.md b/.github/pull_request_template.md
new file mode 100644
index 00000000..014064f0
--- /dev/null
+++ b/.github/pull_request_template.md
@@ -0,0 +1,5 @@
+<!--
+Thanks for contributing a pull request!
+
+Please check out the contributor guidance at https://data-apis.org/array-api-extra/contributing.html.
+-->
diff --git a/.github/workflows/cd.yml b/.github/workflows/cd.yml
index e00708a5..68bd3738 100644
--- a/.github/workflows/cd.yml
+++ b/.github/workflows/cd.yml
@@ -1,5 +1,8 @@
 name: CD
 
+permissions:
+  contents: read
+
 on:
   workflow_dispatch:
   pull_request:
@@ -14,11 +17,11 @@ jobs:
   dist:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
         with:
           fetch-depth: 0
 
-      - uses: hynek/build-and-inspect-python-package@v2
+      - uses: hynek/build-and-inspect-python-package@c52c3a4710070b50470d903818a7b25115dcd076 # v2.13.0
 
   publish:
     needs: [dist]
@@ -31,14 +34,14 @@ jobs:
     if: github.event_name == 'release' && github.event.action == 'published'
 
     steps:
-      - uses: actions/download-artifact@v4
+      - uses: actions/download-artifact@d3f86a106a0bac45b974a628896c90dbdf5c8093 # v4.3.0
         with:
           name: Packages
           path: dist
 
       - name: Generate artifact attestation for sdist and wheel
-        uses: actions/attest-build-provenance@v1.4.4
+        uses: actions/attest-build-provenance@e8998f949152b193b063cb0ec769d69d929409be # v2.4.0
         with:
           subject-path: "dist/*"
 
-      - uses: pypa/gh-action-pypi-publish@release/v1
+      - uses: pypa/gh-action-pypi-publish@76f52bc884231f62b9a034ebfe128415bbaabdfc # v1.12.4
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index ff8d1a07..e92e284c 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -1,5 +1,8 @@
 name: CI
 
+permissions:
+  contents: read
+
 on:
   workflow_dispatch:
   pull_request:
@@ -17,53 +20,59 @@ env:
   FORCE_COLOR: 3
 
 jobs:
-  pre-commit-and-lint:
-    name: Format
+  lint:
+    name: Lint
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
         with:
           fetch-depth: 0
-      - uses: actions/setup-python@v5
-        with:
-          python-version: "3.x"
-      - uses: pre-commit/action@v3.0.1
-        with:
-          extra_args: --hook-stage manual --all-files
-      - uses: prefix-dev/setup-pixi@v0.8.1
+
+      - uses: prefix-dev/setup-pixi@14c8aabd75893f83f4ab30c03e7cf853c8208961 # v0.8.10
         with:
-          pixi-version: v0.37.0
+          pixi-version: v0.50.2
           cache: true
-      - name: Run Pylint & Mypy
-        run: |
-          pixi run -e lint pylint
-          pixi run -e lint mypy
+          environments: lint
+
+      - name: Lint (if this step fails, please 'pixi run lint' locally and push the changes)
+        run: pixi run -e lint lint
 
   checks:
-    name: Check ${{ matrix.environment }}
+    name: Test ${{ matrix.environment }}
     runs-on: ${{ matrix.runs-on }}
-    needs: [pre-commit-and-lint]
     strategy:
       fail-fast: false
       matrix:
-        environment: [ci-py310, ci-py313]
+        environment:
+          - tests-py310
+          - tests-py313
+          - tests-numpy1
+          - tests-backends
+          - tests-nogil
         runs-on: [ubuntu-latest]
 
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
         with:
           fetch-depth: 0
 
-      - uses: prefix-dev/setup-pixi@v0.8.1
+      - uses: prefix-dev/setup-pixi@14c8aabd75893f83f4ab30c03e7cf853c8208961 # v0.8.10
         with:
-          pixi-version: v0.37.0
+          pixi-version: v0.50.2
           cache: true
           environments: ${{ matrix.environment }}
 
       - name: Test package
+        # Save some time; also at the moment of writing coverage crashes on python 3.13t
+        if: ${{ matrix.environment != 'tests-nogil' }}
         run: pixi run -e ${{ matrix.environment }} tests-ci
 
+      - name: Test free-threading
+        if: ${{ matrix.environment == 'tests-nogil' }}
+        run: pixi run -e tests-nogil tests --parallel-threads=4
+
       - name: Upload coverage report
-        uses: codecov/codecov-action@v4.5.0
+        if: ${{ matrix.environment != 'tests-nogil' }}
+        uses: codecov/codecov-action@18283e04ce6e62d37312384ff67231eb8fd56d24 # v5.4.3
         with:
           token: ${{ secrets.CODECOV_TOKEN }}
diff --git a/.github/workflows/dependabot-auto-merge.yml b/.github/workflows/dependabot-auto-merge.yml
deleted file mode 100644
index bd29e25b..00000000
--- a/.github/workflows/dependabot-auto-merge.yml
+++ /dev/null
@@ -1,23 +0,0 @@
-# https://docs.github.com/en/code-security/dependabot/working-with-dependabot/automating-dependabot-with-github-actions#approve-a-pull-request
-name: Dependabot auto-merge
-on: pull_request
-
-permissions:
-  contents: write
-  pull-requests: write
-
-jobs:
-  dependabot:
-    runs-on: ubuntu-latest
-    if: github.actor == 'dependabot[bot]'
-    steps:
-      - name: Dependabot metadata
-        id: metadata
-        uses: dependabot/fetch-metadata@v2
-        with:
-          github-token: "${{ secrets.GITHUB_TOKEN }}"
-      - name: Enable auto-merge for Dependabot PRs
-        run: gh pr merge --auto --merge "$PR_URL"
-        env:
-          PR_URL: ${{github.event.pull_request.html_url}}
-          GH_TOKEN: ${{secrets.GITHUB_TOKEN}}
diff --git a/.github/workflows/docs-build.yml b/.github/workflows/docs-build.yml
index 1cdf221e..95340c82 100644
--- a/.github/workflows/docs-build.yml
+++ b/.github/workflows/docs-build.yml
@@ -1,20 +1,27 @@
 name: Docs Build
 
+permissions:
+  contents: read
+
 on: [push, pull_request]
 
 jobs:
   docs-build:
     runs-on: ubuntu-latest
     steps:
-      - uses: actions/checkout@v4
-      - uses: prefix-dev/setup-pixi@v0.8.1
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
+
+      - uses: prefix-dev/setup-pixi@14c8aabd75893f83f4ab30c03e7cf853c8208961 # v0.8.10
         with:
-          pixi-version: v0.37.0
+          pixi-version: v0.50.2
           cache: true
+          environments: docs
+
       - name: Build Docs
         run: pixi run -e docs docs
+
       - name: Upload Artifact
-        uses: actions/upload-artifact@v4
+        uses: actions/upload-artifact@ea165f8d65b6e75b540449e92b4886f43607fa02 # v4.6.2
         with:
           name: docs-build
           path: docs/build/
diff --git a/.github/workflows/docs-deploy.yml b/.github/workflows/docs-deploy.yml
index 5ba6577d..844031bd 100644
--- a/.github/workflows/docs-deploy.yml
+++ b/.github/workflows/docs-deploy.yml
@@ -1,5 +1,8 @@
 name: Docs Deploy
 
+permissions:
+  contents: write # needed for the deploy step
+
 on:
   workflow_run:
     workflows: ["Docs Build"]
@@ -14,9 +17,10 @@ jobs:
     environment:
       name: docs-deploy
     steps:
-      - uses: actions/checkout@v4
+      - uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
+
       - name: Download Artifact
-        uses: dawidd6/action-download-artifact@v6
+        uses: dawidd6/action-download-artifact@ac66b43f0e6a346234dd65d4d0c8fbb31cb316e5 # v11
         with:
           workflow: docs-build.yml
           name: docs-build
@@ -26,7 +30,7 @@ jobs:
       # See
       # https://github.com/JamesIves/github-pages-deploy-action/tree/dev#using-an-ssh-deploy-key-
       - name: Deploy
-        uses: JamesIves/github-pages-deploy-action@v4
+        uses: JamesIves/github-pages-deploy-action@6c2d9db40f9296374acc17b90404b6e8864128c8 # v4.7.3
         with:
           folder: docs/build/
           ssh-key: ${{ secrets.DEPLOY_KEY }}
diff --git a/.gitignore b/.gitignore
index eccba9dc..0b377833 100644
--- a/.gitignore
+++ b/.gitignore
@@ -114,9 +114,11 @@ ENV/
 env.bak/
 venv.bak/
 
-# Spyder project settings
+# IDE project settings
+.idea/
 .spyderproject
 .spyproject
+.vscode/
 
 # Rope project settings
 .ropeproject
@@ -160,3 +162,12 @@ Thumbs.db
 # pixi environments
 .pixi
 *.egg-info
+
+# Vendor tests
+vendor_tests/array_api_compat/
+vendor_tests/array_api_extra/
+
+# all-contributors
+node_modules
+package.json
+yarn.lock
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
deleted file mode 100644
index 41beb381..00000000
--- a/.pre-commit-config.yaml
+++ /dev/null
@@ -1,80 +0,0 @@
-ci:
-  autoupdate_commit_msg: "chore: update pre-commit hooks"
-  autofix_commit_msg: "style: pre-commit fixes"
-
-exclude: ^.cruft.json|.copier-answers.yml$
-
-repos:
-  - repo: https://github.com/adamchainz/blacken-docs
-    rev: "1.18.0"
-    hooks:
-      - id: blacken-docs
-        additional_dependencies: [black==24.*]
-
-  - repo: https://github.com/pre-commit/pre-commit-hooks
-    rev: "v4.6.0"
-    hooks:
-      - id: check-added-large-files
-      - id: check-case-conflict
-      - id: check-merge-conflict
-      - id: check-symlinks
-      - id: check-yaml
-      - id: debug-statements
-      - id: end-of-file-fixer
-      - id: mixed-line-ending
-      - id: name-tests-test
-        args: ["--pytest-test-first"]
-      - id: requirements-txt-fixer
-      - id: trailing-whitespace
-
-  - repo: https://github.com/pre-commit/pygrep-hooks
-    rev: "v1.10.0"
-    hooks:
-      - id: rst-backticks
-      - id: rst-directive-colons
-      - id: rst-inline-touching-normal
-
-  - repo: https://github.com/rbubley/mirrors-prettier
-    rev: "v3.3.3"
-    hooks:
-      - id: prettier
-        types_or: [yaml, markdown, html, css, scss, javascript, json]
-        args: [--prose-wrap=always]
-
-  - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: "v0.6.1"
-    hooks:
-      - id: ruff
-        args: ["--fix", "--show-fixes"]
-      - id: ruff-format
-
-  - repo: https://github.com/codespell-project/codespell
-    rev: "v2.3.0"
-    hooks:
-      - id: codespell
-        exclude: pixi.lock
-
-  - repo: https://github.com/shellcheck-py/shellcheck-py
-    rev: "v0.10.0.1"
-    hooks:
-      - id: shellcheck
-
-  - repo: local
-    hooks:
-      - id: disallow-caps
-        name: Disallow improper capitalization
-        language: pygrep
-        entry: PyBind|Numpy|Cmake|CCache|Github|PyTest
-        exclude: .pre-commit-config.yaml
-
-  - repo: https://github.com/abravalheri/validate-pyproject
-    rev: "v0.19"
-    hooks:
-      - id: validate-pyproject
-        additional_dependencies: ["validate-pyproject-schema-store[all]"]
-
-  - repo: https://github.com/python-jsonschema/check-jsonschema
-    rev: "0.29.1"
-    hooks:
-      - id: check-dependabot
-      - id: check-github-workflows
diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md
index 2d20fe70..cc93de44 100644
--- a/CONTRIBUTORS.md
+++ b/CONTRIBUTORS.md
@@ -1,4 +1,7 @@
-## Contributors
+# Contributors
+
+This project exists thanks to the following contributors
+([emoji key](https://allcontributors.org/docs/en/emoji-key)):
 
 <!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
 <!-- prettier-ignore-start -->
@@ -6,21 +9,35 @@
 <table>
   <tbody>
     <tr>
-      <td align="center" valign="top" width="14.28%"><a href="https://lucascolley.github.io/"><img src="https://avatars.githubusercontent.com/u/51488791?v=4?s=100" width="100px;" alt="Lucas Colley"/><br /><sub><b>Lucas Colley</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Documentation">📖</a> <a href="#example-lucascolley" title="Examples">💡</a> <a href="#ideas-lucascolley" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-lucascolley" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="#maintenance-lucascolley" title="Maintenance">🚧</a> <a href="#tool-lucascolley" title="Tools">🔧</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Tests">⚠️</a> <a href="/data-apis/array-api-extra/issues?q=author%3Alucascolley" title="Bug reports">🐛</a></td>
-      <td align="center" valign="top" width="14.28%"><a href="/mdhaber"><img src="https://avatars.githubusercontent.com/u/6570539?v=4?s=100" width="100px;" alt="Matt Haberland"/><br /><sub><b>Matt Haberland</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=mdhaber" title="Code">💻</a> <a href="#ideas-mdhaber" title="Ideas, Planning, & Feedback">🤔</a></td>
-      <td align="center" valign="top" width="14.28%"><a href="/j-bowhay"><img src="https://avatars.githubusercontent.com/u/60778417?v=4?s=100" width="100px;" alt="Jake Bowhay"/><br /><sub><b>Jake Bowhay</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=j-bowhay" title="Code">💻</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Aj-bowhay" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://lucascolley.github.io/"><img src="https://avatars.githubusercontent.com/u/51488791?v=4?s=100" width="100px;" alt="Lucas Colley"/><br /><sub><b>Lucas Colley</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Documentation">📖</a> <a href="#example-lucascolley" title="Examples">💡</a> <a href="#ideas-lucascolley" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-lucascolley" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="#maintenance-lucascolley" title="Maintenance">🚧</a> <a href="#tool-lucascolley" title="Tools">🔧</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Tests">⚠️</a> <a href="/data-apis/array-api-extra/issues?q=author%3Alucascolley" title="Bug reports">🐛</a> <a href="#platform-lucascolley" title="Packaging/porting to new platform">📦</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Alucascolley" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/mdhaber"><img src="https://avatars.githubusercontent.com/u/6570539?v=4?s=100" width="100px;" alt="Matt Haberland"/><br /><sub><b>Matt Haberland</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=mdhaber" title="Code">💻</a> <a href="#ideas-mdhaber" title="Ideas, Planning, & Feedback">🤔</a> <a href="/data-apis/array-api-extra/commits?author=mdhaber" title="Tests">⚠️</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/j-bowhay"><img src="https://avatars.githubusercontent.com/u/60778417?v=4?s=100" width="100px;" alt="Jake Bowhay"/><br /><sub><b>Jake Bowhay</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=j-bowhay" title="Code">💻</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Aj-bowhay" title="Reviewed Pull Requests">👀</a> <a href="#tool-j-bowhay" title="Tools">🔧</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/asmeurer"><img src="https://avatars.githubusercontent.com/u/71486?v=4?s=100" width="100px;" alt="Aaron Meurer"/><br /><sub><b>Aaron Meurer</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Aasmeurer" title="Reviewed Pull Requests">👀</a> <a href="#ideas-asmeurer" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-asmeurer" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/betatim"><img src="https://avatars.githubusercontent.com/u/1448859?v=4?s=100" width="100px;" alt="Tim Head"/><br /><sub><b>Tim Head</b></sub></a><br /><a href="#ideas-betatim" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/stdlib-js/stdlib"><img src="https://avatars.githubusercontent.com/u/2643044?v=4?s=100" width="100px;" alt="Athan"/><br /><sub><b>Athan</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Akgryte" title="Reviewed Pull Requests">👀</a> <a href="#ideas-kgryte" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/vnmabus"><img src="https://avatars.githubusercontent.com/u/2364173?v=4?s=100" width="100px;" alt="Carlos Ramos Carreño"/><br /><sub><b>Carlos Ramos Carreño</b></sub></a><br /><a href="#ideas-vnmabus" title="Ideas, Planning, & Feedback">🤔</a></td>
     </tr>
     <tr>
-      <td align="center" valign="top" width="14.28%"><a href="/rgommers/"><img src="https://avatars.githubusercontent.com/u/98330?v=4?s=100" width="100px;" alt="Ralf Gommers"/><br /><sub><b>Ralf Gommers</b></sub></a><br /><a href="#ideas-rgommers" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-rgommers" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Argommers" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/crusaderky"><img src="https://avatars.githubusercontent.com/u/6213168?v=4?s=100" width="100px;" alt="Guido Imperiale"/><br /><sub><b>Guido Imperiale</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=crusaderky" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=crusaderky" title="Documentation">📖</a> <a href="#tool-crusaderky" title="Tools">🔧</a> <a href="/data-apis/array-api-extra/commits?author=crusaderky" title="Tests">⚠️</a> <a href="#example-crusaderky" title="Examples">💡</a> <a href="/data-apis/array-api-extra/issues?q=author%3Acrusaderky" title="Bug reports">🐛</a> <a href="#ideas-crusaderky" title="Ideas, Planning, & Feedback">🤔</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Acrusaderky" title="Reviewed Pull Requests">👀</a> <a href="#maintenance-crusaderky" title="Maintenance">🚧</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/jorenham"><img src="https://avatars.githubusercontent.com/u/6208662?v=4?s=100" width="100px;" alt="Joren Hammudoglu"/><br /><sub><b>Joren Hammudoglu</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Ajorenham" title="Reviewed Pull Requests">👀</a></td>
       <td align="center" valign="top" width="14.28%"><a href="https://www.thomasjpfan.com/"><img src="https://avatars.githubusercontent.com/u/5402633?v=4?s=100" width="100px;" alt="Thomas J. Fan"/><br /><sub><b>Thomas J. Fan</b></sub></a><br /><a href="#ideas-thomasjpfan" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/izaid"><img src="https://avatars.githubusercontent.com/u/482179?v=4?s=100" width="100px;" alt="Irwin Zaid"/><br /><sub><b>Irwin Zaid</b></sub></a><br /><a href="#ideas-izaid" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/jakirkham"><img src="https://avatars.githubusercontent.com/u/3019665?v=4?s=100" width="100px;" alt="jakirkham"/><br /><sub><b>jakirkham</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=jakirkham" title="Code">💻</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Ajakirkham" title="Reviewed Pull Requests">👀</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/tupui"><img src="https://avatars.githubusercontent.com/u/23188539?v=4?s=100" width="100px;" alt="Pamphile Roy"/><br /><sub><b>Pamphile Roy</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=tupui" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/OmarManzoor"><img src="https://avatars.githubusercontent.com/u/17495884?v=4?s=100" width="100px;" alt="Omar Salman"/><br /><sub><b>Omar Salman</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=OmarManzoor" title="Code">💻</a></td>
+    </tr>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="/rgommers/"><img src="https://avatars.githubusercontent.com/u/98330?v=4?s=100" width="100px;" alt="Ralf Gommers"/><br /><sub><b>Ralf Gommers</b></sub></a><br /><a href="#ideas-rgommers" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-rgommers" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Argommers" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://ogrisel.com"><img src="https://avatars.githubusercontent.com/u/89061?v=4?s=100" width="100px;" alt="Olivier Grisel"/><br /><sub><b>Olivier Grisel</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=ogrisel" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/ev-br"><img src="https://avatars.githubusercontent.com/u/2133832?v=4?s=100" width="100px;" alt="Evgeni Burovski"/><br /><sub><b>Evgeni Burovski</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=ev-br" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=ev-br" title="Documentation">📖</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="http://www.vanderplas.com/"><img src="https://avatars.githubusercontent.com/u/781659?v=4?s=100" width="100px;" alt="Jake Vanderplas"/><br /><sub><b>Jake Vanderplas</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Ajakevdp" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/KotlinIsland"><img src="https://avatars.githubusercontent.com/u/65446343?v=4?s=100" width="100px;" alt="kotlinisland"/><br /><sub><b>kotlinisland</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Akotlinisland" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/DetachHead"><img src="https://avatars.githubusercontent.com/u/57028336?v=4?s=100" width="100px;" alt="detachhead"/><br /><sub><b>detachhead</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Adetachhead" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/NeilGirdhar"><img src="https://avatars.githubusercontent.com/u/730137?v=4?s=100" width="100px;" alt="Neil Girdhar"/><br /><sub><b>Neil Girdhar</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=NeilGirdhar" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=NeilGirdhar" title="Tests">⚠️</a></td>
+    </tr>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="/lithomas1"><img src="https://avatars.githubusercontent.com/u/47963215?v=4?s=100" width="100px;" alt="Thomas Li"/><br /><sub><b>Thomas Li</b></sub></a><br /><a href="/data-apis/array-api-extra/issues?q=author%3Alithomas1" title="Bug reports">🐛</a> <a href="#tool-lithomas1" title="Tools">🔧</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/pearu"><img src="https://avatars.githubusercontent.com/u/402156?v=4?s=100" width="100px;" alt="Pearu Peterson"/><br /><sub><b>Pearu Peterson</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Apearu" title="Reviewed Pull Requests">👀</a></td>
     </tr>
   </tbody>
 </table>
@@ -29,3 +46,7 @@
 <!-- prettier-ignore-end -->
 
 <!-- ALL-CONTRIBUTORS-LIST:END -->
+
+We follow the
+[all-contributors](https://github.com/all-contributors/all-contributors)
+specification. Contributions of any kind welcome!
diff --git a/README.md b/README.md
index 07e97409..1b33322a 100644
--- a/README.md
+++ b/README.md
@@ -1,56 +1,98 @@
 # array-api-extra
 
-[![Actions Status][actions-badge]][actions-link]
 [![docs - here!][docs-badge]][docs-link]
-[![Pixi Badge](https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/prefix-dev/pixi/main/assets/badge/v0.json)](https://pixi.sh)
-[![All Contributors](https://img.shields.io/github/all-contributors/data-apis/array-api-extra?color=ee8449&style=flat-square)](#contributors)
-
 [![PyPI version][pypi-version]][pypi-link]
 [![Conda-Forge][conda-badge]][conda-link]
 [![PyPI platforms][pypi-platforms]][pypi-link]
+[![All Contributors](https://img.shields.io/github/all-contributors/data-apis/array-api-extra?color=ee8449&style=flat-square)](#contributors)
+
+[![Pixi Badge](https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/prefix-dev/pixi/main/assets/badge/v0.json)](https://pixi.sh)
+[![Typing](https://img.shields.io/pypi/types/array-api-extra)](https://typing.python.org/)
+[![codecov](https://codecov.io/github/data-apis/array-api-extra/graph/badge.svg)](https://codecov.io/github/data-apis/array-api-extra)
+[![EffVer Versioning](https://img.shields.io/badge/version_scheme-EffVer-0097a7)](https://jacobtomlinson.dev/effver)
+[![SPEC 8 — Securing the Release Process](https://img.shields.io/badge/SPEC-8-green?labelColor=%23004811&color=%235CA038)](https://scientific-python.org/specs/spec-0008/)
 
 <!-- SPHINX-START -->
 
 <!-- prettier-ignore-start -->
-[actions-badge]:            https://github.com/data-apis/array-api-extra/workflows/CI/badge.svg
-[actions-link]:             https://github.com/data-apis/array-api-extra/actions
-[conda-badge]:              https://img.shields.io/conda/vn/conda-forge/array-api-extra
-[conda-link]:               https://github.com/conda-forge/array-api-extra-feedstock
+
+[actions-badge]: https://github.com/data-apis/array-api-extra/workflows/CI/badge.svg
+[actions-link]: https://github.com/data-apis/array-api-extra/actions
+[conda-badge]: https://img.shields.io/conda/vn/conda-forge/array-api-extra
+[conda-link]: https://github.com/conda-forge/array-api-extra-feedstock
 [github-discussions-badge]: https://img.shields.io/static/v1?label=Discussions&message=Ask&color=blue&logo=github
-[github-discussions-link]:  https://github.com/data-apis/array-api-extra/discussions
-[pypi-link]:                https://pypi.org/project/array-api-extra/
-[pypi-platforms]:           https://img.shields.io/pypi/pyversions/array-api-extra
-[pypi-version]:             https://img.shields.io/pypi/v/array-api-extra
-[docs-badge]:               https://img.shields.io/badge/docs-here!-2ea44f
-[docs-link]:                https://data-apis.org/array-api-extra/index.html
+[github-discussions-link]: https://github.com/data-apis/array-api-extra/discussions
+[pypi-link]: https://pypi.org/project/array-api-extra/
+[pypi-platforms]: https://img.shields.io/pypi/pyversions/array-api-extra
+[pypi-version]: https://img.shields.io/pypi/v/array-api-extra
+[docs-badge]: https://img.shields.io/badge/docs-here!-2ea44f
+[docs-link]: https://data-apis.org/array-api-extra/index.html
 
 <!-- prettier-ignore-end -->
 
 Extra array functions built on top of the array API standard.
 
+Used by:
+
+- [SciPy](https://github.com/scipy/scipy) — Fundamental algorithms for
+  scientific computing.
+- [scikit-learn](https://github.com/scikit-learn/scikit-learn) — Machine
+  Learning in Python.
+- *your library? Let us know!*
+
+## Installation
+
+See https://data-apis.org/array-api-extra/#installation.
+
+## Versioning
+
+This project uses [EffVer](https://jacobtomlinson.dev/effver/). TL;DR:
+
+- To bump from version `x.y.z` to `x.(y+1).0` of array-api-extra, expect that
+  you may need to put in some work.
+- To bump from version `x.y.z` to `x.y.(z+1)`, any work needed on your side
+  should be minimal. Please open an issue if this is not the case!
+
 ## Contributors
 
+This project exists thanks to the following contributors
+([emoji key](https://allcontributors.org/docs/en/emoji-key)):
+
 <!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->
 <!-- prettier-ignore-start -->
 <!-- markdownlint-disable -->
 <table>
   <tbody>
     <tr>
-      <td align="center" valign="top" width="14.28%"><a href="https://lucascolley.github.io/"><img src="https://avatars.githubusercontent.com/u/51488791?v=4?s=100" width="100px;" alt="Lucas Colley"/><br /><sub><b>Lucas Colley</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Documentation">📖</a> <a href="#example-lucascolley" title="Examples">💡</a> <a href="#ideas-lucascolley" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-lucascolley" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="#maintenance-lucascolley" title="Maintenance">🚧</a> <a href="#tool-lucascolley" title="Tools">🔧</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Tests">⚠️</a> <a href="/data-apis/array-api-extra/issues?q=author%3Alucascolley" title="Bug reports">🐛</a></td>
-      <td align="center" valign="top" width="14.28%"><a href="/mdhaber"><img src="https://avatars.githubusercontent.com/u/6570539?v=4?s=100" width="100px;" alt="Matt Haberland"/><br /><sub><b>Matt Haberland</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=mdhaber" title="Code">💻</a> <a href="#ideas-mdhaber" title="Ideas, Planning, & Feedback">🤔</a></td>
-      <td align="center" valign="top" width="14.28%"><a href="/j-bowhay"><img src="https://avatars.githubusercontent.com/u/60778417?v=4?s=100" width="100px;" alt="Jake Bowhay"/><br /><sub><b>Jake Bowhay</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=j-bowhay" title="Code">💻</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Aj-bowhay" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://lucascolley.github.io/"><img src="https://avatars.githubusercontent.com/u/51488791?v=4?s=100" width="100px;" alt="Lucas Colley"/><br /><sub><b>Lucas Colley</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Documentation">📖</a> <a href="#example-lucascolley" title="Examples">💡</a> <a href="#ideas-lucascolley" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-lucascolley" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="#maintenance-lucascolley" title="Maintenance">🚧</a> <a href="#tool-lucascolley" title="Tools">🔧</a> <a href="/data-apis/array-api-extra/commits?author=lucascolley" title="Tests">⚠️</a> <a href="/data-apis/array-api-extra/issues?q=author%3Alucascolley" title="Bug reports">🐛</a> <a href="#platform-lucascolley" title="Packaging/porting to new platform">📦</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Alucascolley" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/mdhaber"><img src="https://avatars.githubusercontent.com/u/6570539?v=4?s=100" width="100px;" alt="Matt Haberland"/><br /><sub><b>Matt Haberland</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=mdhaber" title="Code">💻</a> <a href="#ideas-mdhaber" title="Ideas, Planning, & Feedback">🤔</a> <a href="/data-apis/array-api-extra/commits?author=mdhaber" title="Tests">⚠️</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/j-bowhay"><img src="https://avatars.githubusercontent.com/u/60778417?v=4?s=100" width="100px;" alt="Jake Bowhay"/><br /><sub><b>Jake Bowhay</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=j-bowhay" title="Code">💻</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Aj-bowhay" title="Reviewed Pull Requests">👀</a> <a href="#tool-j-bowhay" title="Tools">🔧</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/asmeurer"><img src="https://avatars.githubusercontent.com/u/71486?v=4?s=100" width="100px;" alt="Aaron Meurer"/><br /><sub><b>Aaron Meurer</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Aasmeurer" title="Reviewed Pull Requests">👀</a> <a href="#ideas-asmeurer" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-asmeurer" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/betatim"><img src="https://avatars.githubusercontent.com/u/1448859?v=4?s=100" width="100px;" alt="Tim Head"/><br /><sub><b>Tim Head</b></sub></a><br /><a href="#ideas-betatim" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/stdlib-js/stdlib"><img src="https://avatars.githubusercontent.com/u/2643044?v=4?s=100" width="100px;" alt="Athan"/><br /><sub><b>Athan</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Akgryte" title="Reviewed Pull Requests">👀</a> <a href="#ideas-kgryte" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/vnmabus"><img src="https://avatars.githubusercontent.com/u/2364173?v=4?s=100" width="100px;" alt="Carlos Ramos Carreño"/><br /><sub><b>Carlos Ramos Carreño</b></sub></a><br /><a href="#ideas-vnmabus" title="Ideas, Planning, & Feedback">🤔</a></td>
     </tr>
     <tr>
-      <td align="center" valign="top" width="14.28%"><a href="/rgommers/"><img src="https://avatars.githubusercontent.com/u/98330?v=4?s=100" width="100px;" alt="Ralf Gommers"/><br /><sub><b>Ralf Gommers</b></sub></a><br /><a href="#ideas-rgommers" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-rgommers" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Argommers" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/crusaderky"><img src="https://avatars.githubusercontent.com/u/6213168?v=4?s=100" width="100px;" alt="Guido Imperiale"/><br /><sub><b>Guido Imperiale</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=crusaderky" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=crusaderky" title="Documentation">📖</a> <a href="#tool-crusaderky" title="Tools">🔧</a> <a href="/data-apis/array-api-extra/commits?author=crusaderky" title="Tests">⚠️</a> <a href="#example-crusaderky" title="Examples">💡</a> <a href="/data-apis/array-api-extra/issues?q=author%3Acrusaderky" title="Bug reports">🐛</a> <a href="#ideas-crusaderky" title="Ideas, Planning, & Feedback">🤔</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Acrusaderky" title="Reviewed Pull Requests">👀</a> <a href="#maintenance-crusaderky" title="Maintenance">🚧</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/jorenham"><img src="https://avatars.githubusercontent.com/u/6208662?v=4?s=100" width="100px;" alt="Joren Hammudoglu"/><br /><sub><b>Joren Hammudoglu</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Ajorenham" title="Reviewed Pull Requests">👀</a></td>
       <td align="center" valign="top" width="14.28%"><a href="https://www.thomasjpfan.com/"><img src="https://avatars.githubusercontent.com/u/5402633?v=4?s=100" width="100px;" alt="Thomas J. Fan"/><br /><sub><b>Thomas J. Fan</b></sub></a><br /><a href="#ideas-thomasjpfan" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/izaid"><img src="https://avatars.githubusercontent.com/u/482179?v=4?s=100" width="100px;" alt="Irwin Zaid"/><br /><sub><b>Irwin Zaid</b></sub></a><br /><a href="#ideas-izaid" title="Ideas, Planning, & Feedback">🤔</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/jakirkham"><img src="https://avatars.githubusercontent.com/u/3019665?v=4?s=100" width="100px;" alt="jakirkham"/><br /><sub><b>jakirkham</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=jakirkham" title="Code">💻</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Ajakirkham" title="Reviewed Pull Requests">👀</a></td>
       <td align="center" valign="top" width="14.28%"><a href="/tupui"><img src="https://avatars.githubusercontent.com/u/23188539?v=4?s=100" width="100px;" alt="Pamphile Roy"/><br /><sub><b>Pamphile Roy</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=tupui" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/OmarManzoor"><img src="https://avatars.githubusercontent.com/u/17495884?v=4?s=100" width="100px;" alt="Omar Salman"/><br /><sub><b>Omar Salman</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=OmarManzoor" title="Code">💻</a></td>
+    </tr>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="/rgommers/"><img src="https://avatars.githubusercontent.com/u/98330?v=4?s=100" width="100px;" alt="Ralf Gommers"/><br /><sub><b>Ralf Gommers</b></sub></a><br /><a href="#ideas-rgommers" title="Ideas, Planning, & Feedback">🤔</a> <a href="#infra-rgommers" title="Infrastructure (Hosting, Build-Tools, etc)">🚇</a> <a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Argommers" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="https://ogrisel.com"><img src="https://avatars.githubusercontent.com/u/89061?v=4?s=100" width="100px;" alt="Olivier Grisel"/><br /><sub><b>Olivier Grisel</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=ogrisel" title="Code">💻</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/ev-br"><img src="https://avatars.githubusercontent.com/u/2133832?v=4?s=100" width="100px;" alt="Evgeni Burovski"/><br /><sub><b>Evgeni Burovski</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=ev-br" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=ev-br" title="Documentation">📖</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="http://www.vanderplas.com/"><img src="https://avatars.githubusercontent.com/u/781659?v=4?s=100" width="100px;" alt="Jake Vanderplas"/><br /><sub><b>Jake Vanderplas</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Ajakevdp" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/KotlinIsland"><img src="https://avatars.githubusercontent.com/u/65446343?v=4?s=100" width="100px;" alt="kotlinisland"/><br /><sub><b>kotlinisland</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Akotlinisland" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/DetachHead"><img src="https://avatars.githubusercontent.com/u/57028336?v=4?s=100" width="100px;" alt="detachhead"/><br /><sub><b>detachhead</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Adetachhead" title="Reviewed Pull Requests">👀</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/NeilGirdhar"><img src="https://avatars.githubusercontent.com/u/730137?v=4?s=100" width="100px;" alt="Neil Girdhar"/><br /><sub><b>Neil Girdhar</b></sub></a><br /><a href="/data-apis/array-api-extra/commits?author=NeilGirdhar" title="Code">💻</a> <a href="/data-apis/array-api-extra/commits?author=NeilGirdhar" title="Tests">⚠️</a></td>
+    </tr>
+    <tr>
+      <td align="center" valign="top" width="14.28%"><a href="/lithomas1"><img src="https://avatars.githubusercontent.com/u/47963215?v=4?s=100" width="100px;" alt="Thomas Li"/><br /><sub><b>Thomas Li</b></sub></a><br /><a href="/data-apis/array-api-extra/issues?q=author%3Alithomas1" title="Bug reports">🐛</a> <a href="#tool-lithomas1" title="Tools">🔧</a></td>
+      <td align="center" valign="top" width="14.28%"><a href="/pearu"><img src="https://avatars.githubusercontent.com/u/402156?v=4?s=100" width="100px;" alt="Pearu Peterson"/><br /><sub><b>Pearu Peterson</b></sub></a><br /><a href="/data-apis/array-api-extra/pulls?q=is%3Apr+reviewed-by%3Apearu" title="Reviewed Pull Requests">👀</a></td>
     </tr>
   </tbody>
 </table>
@@ -59,3 +101,7 @@ Extra array functions built on top of the array API standard.
 <!-- prettier-ignore-end -->
 
 <!-- ALL-CONTRIBUTORS-LIST:END -->
+
+We follow the
+[all-contributors](https://github.com/all-contributors/all-contributors)
+specification. Contributions of any kind welcome!
diff --git a/RELEASING.md b/RELEASING.md
new file mode 100644
index 00000000..564fc682
--- /dev/null
+++ b/RELEASING.md
@@ -0,0 +1,8 @@
+1. Update the version in `src/array_api_extra/__init__.py`
+2. Update the lockfile with `pixi update && pixi install`
+3. Push your changes
+4. Cut a release via the GitHub GUI
+5. Update the version to `{next micro version}.dev0`
+6. `pixi clean cache --pypi && pixi update && pixi install`
+7. Push your changes
+8. Merge the automated PR to conda-forge/array-api-extra-feedstock
diff --git a/codecov.yml b/codecov.yml
new file mode 100644
index 00000000..dc9b47cd
--- /dev/null
+++ b/codecov.yml
@@ -0,0 +1,9 @@
+comment: false
+github_checks:
+  annotations: false
+ignore:
+  - "src/array_api_extra/_lib/_compat"
+  - "src/array_api_extra/_lib/_typing"
+coverage:
+  status:
+    project: off
diff --git a/docs/api-lazy.md b/docs/api-lazy.md
new file mode 100644
index 00000000..abea5cbb
--- /dev/null
+++ b/docs/api-lazy.md
@@ -0,0 +1,15 @@
+# Tools for lazy backends
+
+These additional functions are meant to be used to support compatibility with
+lazy backends, e.g. Dask or JAX:
+
+```{eval-rst}
+.. currentmodule:: array_api_extra
+.. autosummary::
+    :nosignatures:
+    :toctree: generated
+
+    lazy_apply
+    testing.lazy_xp_function
+    testing.patch_lazy_xp_functions
+```
diff --git a/docs/api-reference.md b/docs/api-reference.md
index 1307b6fc..38d0d26e 100644
--- a/docs/api-reference.md
+++ b/docs/api-reference.md
@@ -6,10 +6,19 @@
     :nosignatures:
     :toctree: generated
 
+    apply_where
+    at
     atleast_nd
+    broadcast_shapes
     cov
     create_diagonal
+    default_dtype
     expand_dims
+    isclose
     kron
+    nunique
+    one_hot
+    pad
+    setdiff1d
     sinc
 ```
diff --git a/docs/conf.py b/docs/conf.py
index 5b2fdf05..e2cab35b 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -1,9 +1,11 @@
-from __future__ import annotations
+"""Sphinx config."""
 
 import importlib.metadata
 from typing import Any
 
 project = "array-api-extra"
+copyright = "Consortium for Python Data API Standards"
+author = "Consortium for Python Data API Standards"
 version = release = importlib.metadata.version("array_api_extra")
 
 extensions = [
@@ -38,7 +40,7 @@
                 <svg stroke="currentColor" fill="currentColor" stroke-width="0" viewBox="0 0 16 16">
                     <path fill-rule="evenodd" d="M8 0C3.58 0 0 3.58 0 8c0 3.54 2.29 6.53 5.47 7.59.4.07.55-.17.55-.38 0-.19-.01-.82-.01-1.49-2.01.37-2.53-.49-2.69-.94-.09-.23-.48-.94-.82-1.13-.28-.15-.68-.52-.01-.53.63-.01 1.08.58 1.23.82.72 1.21 1.87.87 2.33.66.07-.52.28-.87.51-1.07-1.78-.2-3.64-.89-3.64-3.95 0-.87.31-1.59.82-2.15-.08-.2-.36-1.02.08-2.12 0 0 .67-.21 2.2.82.64-.18 1.32-.27 2-.27.68 0 1.36.09 2 .27 1.53-1.04 2.2-.82 2.2-.82.44 1.1.16 1.92.08 2.12.51.56.82 1.27.82 2.15 0 3.07-1.87 3.75-3.65 3.95.29.25.54.73.54 1.48 0 1.07-.01 1.93-.01 2.2 0 .21.15.46.55.38A8.013 8.013 0 0 0 16 8c0-4.42-3.58-8-8-8z"></path>
                 </svg>
-            """,
+            """,  # noqa: E501
             "class": "",
         },
     ],
@@ -53,6 +55,10 @@
 
 intersphinx_mapping = {
     "python": ("https://docs.python.org/3", None),
+    "array-api": ("https://data-apis.org/array-api/draft", None),
+    "dask": ("https://docs.dask.org/en/stable", None),
+    "numpy": ("https://numpy.org/doc/stable", None),
+    "jax": ("https://jax.readthedocs.io/en/latest", None),
 }
 
 nitpick_ignore = [
diff --git a/docs/contributing.md b/docs/contributing.md
index 4ac7be1d..bfcfd0d0 100644
--- a/docs/contributing.md
+++ b/docs/contributing.md
@@ -2,11 +2,18 @@
 
 Contributions are welcome from any "array-consuming" library contributors who
 have found themselves writing private array-agnostic functions in the process of
-converting code to consume the standard!
+converting code to consume the standard.
 
-## How to contribute a function
+Thanks to [all contributors](contributors.md) so far!
 
-- Add the implementation of your function to `src/array_api_extra/_funcs.py`.
+## How to contribute a new function
+
+- [Open an issue](https://github.com/data-apis/array-api-extra/issues/new) to
+  propose the new function. You may want to wait for initial feedback on the
+  issue before diving into an implementation. Feel free to skip this step if
+  there is already an open issue for the function.
+- Add the implementation of your function to
+  `src/array_api_extra/_lib/_funcs.py`.
   - Ensure that your function includes type annotations and a
     [numpydoc-style docstring](https://numpydoc.readthedocs.io/en/latest/format.html).
   - Add your function to `__all__` at the top of the file.
@@ -16,6 +23,33 @@ converting code to consume the standard!
 - Add your function to `docs/api-reference.md`.
 - [Make a PR!](https://github.com/data-apis/array-api-extra/pulls)
 
+## How to add delegation to a function
+
+See [the tracker for adding delegation][delegation-tracker].
+
+[delegation-tracker]: https://github.com/data-apis/array-api-extra/issues/100
+
+- If you would like to discuss the task before diving into the implementation,
+  click on the three dots next to the function on the tracker issue, and choose
+  "Convert to sub-issue".
+- Create a function in `src/array_api_extra/_delegation.py` with a signature
+  matching the function in `src/array_api_extra/_lib/_funcs.py`, and move the
+  docstring to the new function. Leave a one-line docstring in `_funcs.py`,
+  pointing to `_delegation.py` to see the full docstring.
+- Also move the initial `array_namespace` call and any input validation over to
+  the new function.
+- Add delegation to backends using the `if _delegate` pattern. See
+  `src/array_api_extra/_lib/_backends.py` for the full list of backends we have
+  worked with so far.
+- After all delegation layers, return the result from the implementation in
+  `_funcs`.
+- Simplify the signature in `_funcs.py` to remove impossible arguments now that
+  it is only called internally via `_delegation`. For example, the `xp`
+  parameter can be changed from type `ModuleType | None` to `ModuleType`.
+- Don't worry if you are not sure how to do some of the above steps or think you
+  might have done something wrong -
+  [make a PR!](https://github.com/data-apis/array-api-extra/pulls)
+
 ## Development workflow
 
 If you are an experienced contributor to Python packages, feel free to develop
@@ -27,7 +61,7 @@ development of array-api-extra is made easy with
   at <https://github.com/data-apis/array-api-extra>.
 - `cd array-api-extra`.
 - [Install Pixi](https://pixi.sh/latest/#installation).
-- To enter a development environment:
+- To enter a development environment (if you prefer this to the `pixi run` interface):
 
 ```
 pixi shell -e dev
@@ -45,22 +79,28 @@ pixi run tests
 pixi run docs
 ```
 
-- To open and preview the locally-built docs:
+- To build and preview the docs locally:
 
 ```
 pixi run open-docs
 ```
 
-- To install a [pre-commit](https://pre-commit.com) hook:
+- To install pre-commit hooks:
+
+```
+pixi run hooks
+```
+
+- To run pre-commit checks on staged files:
 
 ```
-pixi run pre-commit-install
+pixi run pre-commit
 ```
 
-- To run the lint suite:
+- To run the full lint suite:
 
 ```
-pixi run lint
+pixi run --environment=lint lint
 ```
 
 - To enter an interactive Python prompt:
@@ -69,19 +109,39 @@ pixi run lint
 pixi run ipython
 ```
 
-- To run individual parts of the lint suite separately:
+- To run individual parts of the lint suite separately (for example):
 
 ```
-pixi run pre-commit
-pixi run pylint
-pixi run mypy
+pixi run --environment=lint pyright
+pixi run --environment=lint dprint
+```
+
+- To generate the coverage report:
+
+```
+pixi run coverage
+```
+
+- To generate and display the coverage report:
+
+```
+pixi run open-coverage
 ```
 
 Alternative environments are available with a subset of the dependencies and
 tasks available in the `dev` environment:
 
 ```
-pixi shell -e docs
-pixi shell -e tests
-pixi shell -e lint
+pixi shell --environment=docs
+pixi shell --environment=tests
+pixi shell --environment=tests-backends
+pixi shell --environment=lint
+```
+
+If you run on a host with CUDA hardware, you can enable extra tests:
+
+```
+pixi shell --environment=dev-cuda
+pixi shell --environment=tests-cuda
+pixi run --environment=tests-cuda tests
 ```
diff --git a/docs/contributors.md b/docs/contributors.md
index 724cdb77..c8e001d3 100644
--- a/docs/contributors.md
+++ b/docs/contributors.md
@@ -1,3 +1,2 @@
 ```{include} ../CONTRIBUTORS.md
-
 ```
diff --git a/docs/index.md b/docs/index.md
index 5a1ca6a2..5168e973 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -3,22 +3,32 @@
 ```{toctree}
 :maxdepth: 2
 :hidden:
-index.md
+self
 api-reference.md
+api-lazy.md
 contributing.md
 contributors.md
 ```
 
 This is a library housing "array-agnostic" implementations of functions built on
-top of [the Python array API standard](https://data-apis.org/array-api/).
+top of [the Python array API standard](https://data-apis.org/array-api/), as
+well as delegation to existing implementations for known array library backends.
 
 The intended users of this library are "array-consuming" libraries which are
 using [array-api-compat](https://data-apis.org/array-api-compat/) to make their
 own library's functions array-agnostic. In this library, they will find a set of
-tools which provide _extra_ functionality on top of the array API standard,
+tools which provide *extra* functionality on top of the array API standard,
 which other array-consuming libraries in a similar position have found useful
 themselves.
 
+It is currently used by:
+
+- [SciPy](https://github.com/scipy/scipy) — Fundamental algorithms for
+  scientific computing.
+- [scikit-learn](https://github.com/scikit-learn/scikit-learn) — Machine
+  Learning in Python.
+- *your library? Let us know!*
+
 (installation)=
 
 ## Installation
@@ -27,6 +37,8 @@ themselves.
 [on PyPI](https://pypi.org/project/array-api-extra/):
 
 ```shell
+uv add array-api-extra
+# or
 python -m pip install array-api-extra
 ```
 
@@ -34,9 +46,9 @@ And
 [on conda-forge](https://prefix.dev/channels/conda-forge/packages/array-api-extra):
 
 ```shell
-micromamba install -c https://repo.prefix.dev/conda-forge array-api-extra
-# or
 pixi add array-api-extra
+# or
+mamba install array-api-extra
 ```
 
 ```{warning}
@@ -45,18 +57,74 @@ If you require stability, it is recommended to pin `array-api-extra` to
 a specific version, or vendor the library inside your own.
 ```
 
+```{note}
+This library depends on `array-api-compat`. We aim for compatibility with
+the latest released version of array-api-compat, and your mileage may vary
+with older or dev versions.
+```
+
 (vendoring)=
 
 ## Vendoring
 
 To vendor the library, clone
-[the repository](https://github.com/data-apis/array-api-extra) and copy it into
-the appropriate place in your library, like:
+[the array-api-extra repository](https://github.com/data-apis/array-api-extra)
+and copy it into the appropriate place in your library, like:
+
+```
+cp -a array-api-extra/src/array_api_extra mylib/vendored/
+```
+
+You may either add a dependency to array-api-compat in your own project, or
+vendor it too:
+
+1. Clone
+   [the array-api-compat repository](https://github.com/data-apis/array-api-compat)
+   and copy it next to your vendored array-api-extra:
+
+   ```
+   cp -a array-api-compat/array_api_compat mylib/vendored/
+   ```
+
+2. Create a new hook file which array-api-extra will use instead of the
+   top-level array-api-compat if present:
 
+   ```
+   echo 'from mylib.vendored.array_api_compat import *' > mylib/vendored/_array_api_compat_vendor.py
+   ```
+
+This also allows overriding array-api-compat functions if you so wish. E.g. your
+`mylib/vendored/_array_api_compat_vendor.py` could look like this:
+
+```python
+from mylib.vendored.array_api_compat import *
+from mylib.vendored.array_api_compat import array_namespace as _array_namespace_orig
+
+
+def array_namespace(*xs, **kwargs):
+    import mylib
+
+    if any(isinstance(x, mylib.MyArray) for x in xs):
+        return mylib
+    else:
+        return _array_namespace_orig(*xs, **kwargs)
 ```
-cp -R array-api-extra/ mylib/vendored/array_api_extra
+
+```{tip}
+See [an example of this in SciPy][scipy-vendor-example].
 ```
 
+[scipy-vendor-example]: https://github.com/scipy/scipy/blob/main/scipy/_lib/_array_api_compat_vendor.py
+
+## Versioning
+
+This project uses [EffVer](https://jacobtomlinson.dev/effver/). TL;DR:
+
+- To bump from version `x.y.z` to `x.(y+1).0` of array-api-extra, expect that
+  you may need to put in some work.
+- To bump from version `x.y.z` to `x.y.(z+1)`, any work needed on your side
+  should be minimal. Please open an issue if this is not the case!
+
 (usage)=
 
 ## Usage
@@ -68,23 +136,29 @@ import array_api_extra as xpx
 
 ...
 xp = array_namespace(x)
-y = xp.sum(x)
+y = xp.sum(x)  # use functions from `xp` as normal
 ...
-return xpx.atleast_nd(y, ndim=2, xp=xp)
+return xpx.atleast_nd(y, ndim=2, xp=xp)  # use functions from `xpx`, passing `xp=xp`
 ```
 
 ```{note}
 Functions in this library assume input arrays *are arrays* (not "array-likes") and that
-the namespace passed as `xp` is compatible with the standard. This means that
-the namespace you pass as `xp` should come from array-api-compat's ``array_namespace``,
+the namespace passed as `xp` (if given) is compatible with the standard -
+this means that it should come from array-api-compat's `array_namespace`,
 or otherwise be compatible with the standard.
+
+Calling functions without providing an `xp` argument means that `array_namespace`
+is called internally to determine the namespace.
 ```
 
 In the examples shown in the docstrings of functions from this library,
-[`array-api-strict`](https://data-apis.org/array-api-strict/) is used as the
-array namespace `xp`. In reality, code using this library will be written to
-work with any compatible array namespace as `xp`, not any particular
-implementation.
+[array-api-strict](https://data-apis.org/array-api-strict/) is used as the array
+namespace `xp`. In reality, code using this library will be written to work with
+any compatible array namespace as `xp`, not any particular implementation.
+
+Some functions may only work with specific array libraries supported by
+array-api-compat. This should be clearly indicated in the docs - please open an
+issue if this is not the case!
 
 (scope)=
 
@@ -96,35 +170,35 @@ Functions that are in-scope for this library will:
   standard.
 - Implement functionality which may be generally useful across various
   libraries.
-- Be implemented purely in terms of the array API standard.
 - Be implemented with type annotations and
   [numpydoc-style docstrings](https://numpydoc.readthedocs.io/en/latest/format.html).
-- Be tested against `array-api-strict`.
+- Be tested against array-api-strict and various existing backends.
+
+Functions are implemented purely in terms of the array API standard where
+possible. Where functions must use library-specific helpers for libraries
+supported by array-api-compat, this will be clearly marked in their API
+reference page.
+
+Delegation is added for some functions to use native implementations for the
+given array type, instead of the array-agnostic implementations, as this may
+increase performance.
 
 In particular, the following kinds of function are also in-scope:
 
 - Functions which implement
-  [array API standard extension](https://data-apis.org/array-api/2023.12/extensions/index.html)
+  [array API standard extension](https://data-apis.org/array-api/latest/extensions/index.html)
   functions in terms of functions from the base standard.
 - Functions which add functionality (e.g. extra parameters) to functions from
   the standard.
 
 The following features are currently out-of-scope for this library:
 
-- Delegation to known, existing array libraries.
-  - It is quite simple to wrap functions in this library to also use existing
-    implementations where possible. Such delegation will not live in this
-    library for now, but the array-agnostic functions in this library could form
-    an array-agnostic backend for such delegating functions in the future, here
-    or elsewhere.
 - Functions which accept "array-like" input, or standard-incompatible
   namespaces.
   - It is possible to prepare input arrays and a standard-compatible namespace
-    via `array-api-compat` downstream in consumer libraries. Avoiding use of
-    `array-api-compat` in this library makes it easier to vendor and reduces
-    potential redundant calls to `xp.asarray` and `array_namespace`.
-  - For proposed alternatives to the `xp=xp` interface, see
-    [this issue](https://github.com/data-apis/array-api-extra/issues/6).
+    via array-api-compat downstream in consumer libraries. The `xp` argument can
+    also be omitted to infer the standard-compatible namespace using
+    `array_namespace` internally.
 - Functions which are specific to a particular domain.
   - These functions may belong better in an array-consuming library which is
     specific to that domain.
diff --git a/docs/requirements.txt b/docs/requirements.txt
deleted file mode 100644
index 77237968..00000000
--- a/docs/requirements.txt
+++ /dev/null
@@ -1,5 +0,0 @@
-furo>=2023.08.17
-myst_parser>=0.13
-sphinx>=7.0
-sphinx_autodoc_typehints
-sphinx_copybutton
diff --git a/lefthook.yml b/lefthook.yml
new file mode 100644
index 00000000..3ae3197d
--- /dev/null
+++ b/lefthook.yml
@@ -0,0 +1,56 @@
+lefthook: pixi run --no-progress --environment=lint lefthook
+
+templates:
+  run: run --quiet --no-progress --environment=lint
+
+colors: true
+
+output:
+  - meta # Print lefthook version
+  - summary # Print summary block (successful and failed steps)
+  - empty_summary # Print summary heading when there are no steps to run
+  # - success # Print successful steps
+  # - failure # Print failed steps printing
+  # - execution # Print any execution logs
+  # - execution_out # Print execution output
+  # - execution_info # Print `EXECUTE > ...` logging
+  - skips # Print "skip" (i.e. no files matched)
+
+pre-commit:
+  parallel: true
+  jobs:
+    - name: dprint
+      glob: "*.{json,jsonc,md,toml,yaml,yml}"
+      stage_fixed: true
+      run: pixi {run} dprint
+    - name: ruff
+      glob: "*.{py,pyi}"
+      stage_fixed: true
+      group:
+        piped: true
+        jobs:
+          - name: ruff check
+            run: pixi {run} ruff-check {staged_files}
+          - name: ruff format
+            run: pixi {run} ruff-format {staged_files}
+    - name: pyright
+      glob: "*.{py,pyi}"
+      run: pixi {run} pyright
+    - name: mypy
+      glob: "*.{py,pyi}"
+      run: pixi {run} mypy
+    - name: typos
+      stage_fixed: true
+      run: pixi {run} typos
+    - name: actionlint
+      run: pixi {run} actionlint
+    - name: blacken-docs
+      glob: "*.md"
+      stage_fixed: true
+      run: pixi {run} blacken-docs {staged_files}
+    - name: validate-pyproject
+      glob: "pyproject.toml"
+      run: pixi {run} validate-pyproject
+    - name: numpydoc
+      glob: "*.py"
+      run: pixi {run} numpydoc {staged_files}
diff --git a/pixi.lock b/pixi.lock
index 42bf41b9..5d4db067 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -1,6 +1,6 @@
-version: 5
+version: 6
 environments:
-  ci-py310:
+  default:
     channels:
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     indexes:
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+      - conda: https://prefix.dev/conda-forge/noarch/array-api-compat-1.12.0-pyhe01879c_0.conda
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diff --git a/pyproject.toml b/pyproject.toml
index 27ad7361..6feb40ff 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -5,113 +5,136 @@ build-backend = "hatchling.build"
 [project]
 name = "array-api-extra"
 authors = [
-    { name = "Lucas Colley", email = "lucas.colley8@gmail.com" },
-    { name = "Open Source Contributors" },
+  { name = "Lucas Colley", email = "lucas.colley8@gmail.com" },
+  # { name = "Open Source Contributors" },  # https://github.com/pypi/warehouse/issues/14813
 ]
 description = "Extra array functions built on top of the array API standard."
 readme = "README.md"
 license.file = "LICENSE"
 requires-python = ">=3.10"
 classifiers = [
-    "Intended Audience :: Developers",
-    "License :: OSI Approved :: MIT License",
-    "Operating System :: OS Independent",
-    "Programming Language :: Python",
-    "Programming Language :: Python :: 3",
-    "Programming Language :: Python :: 3 :: Only",
-    "Programming Language :: Python :: 3.10",
-    "Programming Language :: Python :: 3.11",
-    "Programming Language :: Python :: 3.12",
-    "Programming Language :: Python :: 3.13",
-    "Typing :: Typed",
+  "Intended Audience :: Developers",
+  "License :: OSI Approved :: MIT License",
+  "Operating System :: OS Independent",
+  "Programming Language :: Python",
+  "Programming Language :: Python :: 3",
+  "Programming Language :: Python :: 3 :: Only",
+  "Programming Language :: Python :: 3.10",
+  "Programming Language :: Python :: 3.11",
+  "Programming Language :: Python :: 3.12",
+  "Programming Language :: Python :: 3.13",
+  "Programming Language :: Python :: Free Threading :: 3 - Stable",
+  "Typing :: Typed",
 ]
 dynamic = ["version"]
-dependencies = []
-
-[project.optional-dependencies]
-tests = [
-    "pytest >=6",
-    "pytest-cov >=3",
-    "array-api-strict",
-    "numpy",
-]
-docs = [
-    "sphinx>=7.0",
-    "myst_parser>=0.13",
-    "sphinx_copybutton",
-    "sphinx_autodoc_typehints",
-    "furo>=2023.08.17",
-]
+dependencies = ["array-api-compat>=1.12.0,<2"]
 
 [project.urls]
 Homepage = "https://github.com/data-apis/array-api-extra"
 "Bug Tracker" = "https://github.com/data-apis/array-api-extra/issues"
-Discussions = "https://github.com/data-apis/array-api-extra/discussions"
 Changelog = "https://github.com/data-apis/array-api-extra/releases"
 
-
 # Hatch
 
 [tool.hatch]
 version.path = "src/array_api_extra/__init__.py"
 
+[tool.hatch.build.targets.sdist]
+exclude = ["codecov.yml", "pixi.lock", "RELEASING.md", "renovate.json"]
 
-# Pixi
+#  Pixi
 
 [tool.pixi.project]
 channels = ["https://prefix.dev/conda-forge"]
-platforms = ["linux-64", "osx-arm64", "win-64"]
+platforms = ["linux-64", "osx-64", "osx-arm64", "win-64"]
 
 [tool.pixi.dependencies]
-python = ">=3.10.15,<3.14"
+array-api-compat = ">=1.12.0,<2"
 
 [tool.pixi.pypi-dependencies]
 array-api-extra = { path = ".", editable = true }
 
 [tool.pixi.feature.lint.dependencies]
-pre-commit = "*"
-mypy = "*"
-pylint = "*"
+typing-extensions = ">=4.14.1"
+pylint = ">=3.3.7"
+mypy = ">=1.17.0"
+basedpyright = ">=1.31.0"
+numpydoc = ">=1.9.0,<2"
 # import dependencies for mypy:
-array-api-strict = "*"
-numpy = "*"
-pytest = "*"
+array-api-strict = ">=2.4.1,<2.5"
+numpy = ">=2.1.3"
+hypothesis = ">=6.135.16"
+dask-core = ">=2025.7.0" # No distributed, tornado, etc.
+dprint = ">=0.50.0,<0.51"
+lefthook = ">=1.12.2,<2"
+ruff = ">=0.12.5,<0.13"
+typos = ">=1.34.0,<2"
+actionlint = ">=1.7.7,<2"
+blacken-docs = ">=1.19.1,<2"
+pytest = ">=8.4.1,<9"
+validate-pyproject = ">=0.24.1,<0.25"
+# NOTE: don't add cupy, jax, pytorch, or sparse here,
+# as they slow down mypy and are not portable across target OSs
 
 [tool.pixi.feature.lint.tasks]
-pre-commit-install = { cmd = "pre-commit install" }
-pre-commit = { cmd = "pre-commit run -v --all-files --show-diff-on-failure" }
-mypy = { cmd = "mypy", cwd = "." }
-pylint = { cmd = ["pylint", "array_api_extra"], cwd = "src" }
-lint = { depends-on = ["pre-commit", "pylint", "mypy"] }
+lefthook = { cmd = "lefthook", description = "Run lefthook" }
+hooks = { cmd = "lefthook install", description = "Install pre-commit hooks" }
+pre-commit = { cmd = "lefthook run pre-commit", description = "Run pre-commit checks" }
+pylint = { cmd = "pylint array_api_extra", cwd = "src", description = "Lint with pylint" }
+mypy = { cmd = "mypy", description = "Type check with mypy" }
+pyright = { cmd = "basedpyright", description = "Type check with basedpyright" }
+ruff-check = { cmd = "ruff check --fix", description = "Lint with ruff" }
+ruff-format = { cmd = "ruff format", description = "Format with ruff" }
+dprint = { cmd = "dprint fmt", description = "Format with dprint" }
+typos = { cmd = "typos --write-changes --force-exclude", description = "Fix typos" }
+actionlint = { cmd = "actionlint", description = "Lint actions with actionlint" }
+blacken-docs = { cmd = "blacken-docs", description = "Format Python markdown blocks with Black" }
+validate-pyproject = { cmd = "validate-pyproject pyproject.toml", description = "Validate pyproject.toml" }
+numpydoc = { cmd = "numpydoc lint", description = "Validate docstrings with numpydoc" }
+lint = { cmd = "lefthook run pre-commit --all-files --force", description = "Run all linters" }
 
 [tool.pixi.feature.tests.dependencies]
-pytest = ">=6"
-pytest-cov = ">=3"
-array-api-strict = "*"
-numpy = "*"
+pytest = ">=8.4.1"
+pytest-cov = ">=6.2.1"
+hypothesis = ">=6.135.16"
+array-api-strict = ">=2.4.1,<2.5"
+numpy = ">=1.22.0"
 
 [tool.pixi.feature.tests.tasks]
-tests = { cmd = "pytest" }
-tests-ci = { cmd = "pytest -ra --cov --cov-report=xml --cov-report=term --durations=20" }
+tests = { cmd = "pytest -v", description = "Run tests" }
+tests-cov = { cmd = "pytest -v -ra --cov --cov-report=xml --cov-report=term --durations=20", description = "Run tests with coverage" }
 
-[tool.pixi.feature.docs.dependencies]
-sphinx = ">=7.0"
-furo = ">=2023.08.17"
+clean-vendor-compat = { cmd = "rm -rf vendor_tests/array_api_compat", description = "Delete the existing vendored version of array-api-compat" }
+clean-vendor-extra = { cmd = "rm -rf vendor_tests/array_api_extra", description = "Delete the existing vendored version of array-api-extra" }
+copy-vendor-compat = { cmd = "cp -r $(python -c 'import site; print(site.getsitepackages()[0])')/array_api_compat vendor_tests/", depends-on = ["clean-vendor-compat"], description = "Vendor a clean copy of array-api-compat" }
+copy-vendor-extra = { cmd = "cp -r src/array_api_extra vendor_tests/", depends-on = ["clean-vendor-extra"], description = "Vendor a clean copy of array-api-extra" }
+tests-vendor = { cmd = "pytest -v vendor_tests", depends-on = ["copy-vendor-compat", "copy-vendor-extra"], description = "Check that array-api-extra and array-api-compat can be vendored together" }
+
+tests-ci = { depends-on = ["tests-cov", "tests-vendor"], description = "Run tests with coverage and vendor tests" }
+coverage = { cmd = "coverage html", depends-on = ["tests-cov"], description = "Generate test coverage html report" }
+open-coverage = { cmd = "open htmlcov/index.html", depends-on = ["coverage"], description = "Open test coverage report" }
 
-[tool.pixi.feature.docs.pypi-dependencies]
-myst_parser = ">=0.13"
-sphinx_copybutton = "*"
-sphinx_autodoc_typehints = "*"
+[tool.pixi.feature.docs.dependencies]
+sphinx = ">=7.4.7"
+furo = ">=2024.8.6"
+myst-parser = ">=4.0.1"
+sphinx-copybutton = ">=0.5.2"
+sphinx-autodoc-typehints = ">=1.25.3"
+# Needed to import parsed modules with autodoc
+dask-core = ">=2025.7.0" # No distributed, tornado, etc.
+pytest = ">=8.4.1"
+typing-extensions = ">=4.14.1"
+numpy = ">=2.1.3"
 
 [tool.pixi.feature.docs.tasks]
-docs = { cmd = ["sphinx-build", ".", "build/"], cwd = "docs" }
-open-docs = { cmd = ["open", "build/index.html"], cwd = "docs" }
+docs = { cmd = "sphinx-build -E -W . build/", cwd = "docs", description = "Build docs" }
+open-docs = { cmd = "open build/index.html", cwd = "docs", depends-on = ["docs"], description = "Open the generated docs" }
 
 [tool.pixi.feature.dev.dependencies]
-ipython = "*"
+ipython = ">=7.33.0"
 
 [tool.pixi.feature.dev.tasks]
-ipython = { cmd = "ipython" }
+ipython = { cmd = "ipython", description = "Launch ipython" }
 
 [tool.pixi.feature.py310.dependencies]
 python = "~=3.10.0"
@@ -119,15 +142,87 @@ python = "~=3.10.0"
 [tool.pixi.feature.py313.dependencies]
 python = "~=3.13.0"
 
+[tool.pixi.feature.numpy1.dependencies]
+# Oldest NumPy version supported by scikit-learn.
+# Note that this is older than what SPEC0 recommends.
+numpy = "=1.22.0"
+
+# Backends that can run on CPU-only hosts
+# Note: JAX and PyTorch will install CPU variants.
+[tool.pixi.feature.backends.dependencies]
+pytorch = ">=2.7.1"
+dask-core = ">=2025.7.0" # No distributed, tornado, etc.
+sparse = ">=0.17.0"
+
+[tool.pixi.feature.backends.target.linux-64.dependencies]
+jax = ">=0.6.0,!=0.6.2" # 0.6.2 segfaults on Linux CUDA
+
+[tool.pixi.feature.backends.target.osx-64.dependencies]
+jax = ">=0.6.0,!=0.6.2"
+
+[tool.pixi.feature.backends.target.osx-arm64.dependencies]
+jax = ">=0.6.0,!=0.6.2"
+
+[tool.pixi.feature.backends.target.win-64.dependencies]
+# jax = "*"  # unavailable
+
+# Backends that require a GPU host and a CUDA driver.
+# Note that JAX and PyTorch automatically prefer CUDA variants
+# thanks to the `system-requirements` below, *if available*.
+# We request them explicitly below to ensure that we don't
+# quietly revert to CPU-only in the future, e.g. when CUDA 13
+# is released and CUDA 12 builds are dropped upstream.
+[tool.pixi.feature.cuda-backends]
+system-requirements = { cuda = "12" }
+
+[tool.pixi.feature.cuda-backends.target.linux-64.dependencies]
+cupy = ">=13.5.1"
+jaxlib = { version = ">=0.6.0", build = "cuda12*" }
+pytorch = { version = ">=2.7.1", build = "cuda12*" }
+
+[tool.pixi.feature.cuda-backends.target.osx-64.dependencies]
+# cupy = "*"  # unavailable
+# jaxlib = { version = "*", build = "cuda12*" }  # unavailable
+# pytorch = { version = "*", build = "cuda12*" }  # unavailable
+
+[tool.pixi.feature.cuda-backends.target.osx-arm64.dependencies]
+# cupy = "*"  # unavailable
+# jaxlib = { version = "*", build = "cuda12*" }  # unavailable
+# pytorch = { version = "*", build = "cuda12*" }  # unavailable
+
+[tool.pixi.feature.cuda-backends.target.win-64.dependencies]
+cupy = ">=13.5.1"
+# jaxlib = { version = "*", build = "cuda12*" }  # unavailable
+pytorch = { version = ">=2.7.1", build = "cuda12*" }
+
+[tool.pixi.feature.nogil.dependencies]
+python-freethreading = "~=3.13.0"
+pytest-run-parallel = ">=0.5.0"
+numpy = ">=2.3.2"
+# pytorch = "*"  # Not available on Python 3.13t yet
+dask-core = ">=2025.7.0" # No distributed, tornado, etc.
+# sparse = "*"  # numba not available on Python 3.13t yet
+# jax = "*"  # ml_dtypes not available on Python 3.13t yet
+
 [tool.pixi.environments]
-default = { solve-group = "default" }
-lint = { features = ["lint"], solve-group = "default" }
-tests = { features = ["tests"], solve-group = "default" }
-docs = { features = ["docs"], solve-group = "default" }
-dev = { features = ["lint", "tests", "docs", "dev"], solve-group = "default" }
-ci-py310 = ["py310", "tests"]
-ci-py313 = ["py313", "tests"]
+default = { features = ["py313"], solve-group = "py313" }
+lint = { features = ["py313", "lint"], solve-group = "py313" }
+docs = { features = ["py313", "docs"], solve-group = "py313" }
+tests = { features = ["py313", "tests"], solve-group = "py313" }
+tests-py313 = { features = ["py313", "tests"], solve-group = "py313" } # alias of tests
+
+# Some backends may pin numpy; use separate solve-group
+dev = { features = ["py310", "lint", "tests", "docs", "dev", "backends"], solve-group = "backends" }
+tests-backends = { features = ["py310", "tests", "backends"], solve-group = "backends" }
+
+# CUDA not available on free github actions and on some developers' PCs
+dev-cuda = { features = ["py310", "lint", "tests", "docs", "dev", "backends", "cuda-backends"], solve-group = "cuda" }
+tests-cuda = { features = ["py310", "tests", "backends", "cuda-backends"], solve-group = "cuda" }
 
+# Ungrouped environments
+tests-numpy1 = ["py310", "tests", "numpy1"]
+tests-py310 = ["py310", "tests"]
+tests-nogil = ["nogil", "tests"]
 
 # pytest
 
@@ -135,24 +230,18 @@ ci-py313 = ["py313", "tests"]
 minversion = "6.0"
 addopts = ["-ra", "--showlocals", "--strict-markers", "--strict-config"]
 xfail_strict = true
-filterwarnings = [
-    "error",
-]
+filterwarnings = ["error"]
 log_cli_level = "INFO"
-testpaths = [
-    "tests",
+testpaths = ["tests"]
+markers = [
+  "skip_xp_backend(library, /, *, reason=None): Skip test for a specific backend",
+  "xfail_xp_backend(library, /, *, reason=None, strict=None): Xfail test for a specific backend",
 ]
 
-
 # Coverage
 
 [tool.coverage]
 run.source = ["array_api_extra"]
-report.exclude_also = [
-    '\.\.\.',
-    'if typing.TYPE_CHECKING:',
-]
-
 
 # mypy
 
@@ -161,69 +250,119 @@ files = ["src", "tests"]
 python_version = "3.10"
 warn_unused_configs = true
 strict = true
-enable_error_code = ["ignore-without-code", "redundant-expr", "truthy-bool"]
-warn_unreachable = true
-disallow_untyped_defs = false
-disallow_incomplete_defs = false
+enable_error_code = ["ignore-without-code", "truthy-bool"]
+disable_error_code = ["no-any-return"]
 
 [[tool.mypy.overrides]]
-module = "array_api_extra.*"
-disallow_untyped_defs = true
-disallow_incomplete_defs = true
+# slow or unavailable on Windows; do not add to the lint env
+module = ["cupy.*", "jax.*", "sparse.*", "torch.*"]
+ignore_missing_imports = true
 
+[[tool.mypy.overrides]]
+module = ["tests/*"]
+disable_error_code = ["no-untyped-def"] # test(...) without -> None
+
+# pyright
+
+[tool.basedpyright]
+include = ["src", "tests"]
+pythonVersion = "3.10"
+pythonPlatform = "All"
+typeCheckingMode = "all"
+
+# https://github.com/data-apis/array-api-typing
+reportAny = false
+reportExplicitAny = false
+# no array-api-strict type stubs; pytest fixtures
+reportUnknownMemberType = false
+# no array-api-compat type stubs; pytest fixtures
+reportUnknownVariableType = false
+# Redundant with mypy checks
+reportMissingImports = false
+reportMissingTypeStubs = false
+# false positives for input validation
+reportUnreachable = false
+# ruff handles this
+reportUnusedParameter = false
+# cyclic imports inside function bodies
+reportImportCycles = false
+# PyRight can't trace types in lambdas
+reportUnknownLambdaType = false
+
+executionEnvironments = [
+  { root = "tests", reportPrivateUsage = false, reportUnknownArgumentType = false },
+  { root = "src" },
+]
 
 # Ruff
 
 [tool.ruff]
-target-version = "py39"
+target-version = "py310"
 
 [tool.ruff.lint]
 extend-select = [
-    "B",   # flake8-bugbear
-    "I",   # isort
-    "ARG", # flake8-unused-arguments
-    "C4",  # flake8-comprehensions
-    "EM",  # flake8-errmsg
-    "ICN", # flake8-import-conventions
-    "G",   # flake8-logging-format
-    "PGH", # pygrep-hooks
-    "PIE", # flake8-pie
-    "PL",  # pylint
-    "PT",  # flake8-pytest-style
-    "PTH", # flake8-use-pathlib
-    "RET", # flake8-return
-    "RUF", # Ruff-specific
-    "SIM", # flake8-simplify
-    "T20", # flake8-print
-    "UP",  # pyupgrade
-    "YTT", # flake8-2020
-    "EXE", # flake8-executable
-    "NPY", # NumPy specific rules
-    "PD",  # pandas-vet
+  "B", # flake8-bugbear
+  "F", # Pyflakes
+  "I", # isort
+  "E", # Pycodestyle
+  "W", # Pycodestyle
+  "N", # pep8-naming
+  "ARG", # flake8-unused-arguments
+  "C4", # flake8-comprehensions
+  "EM", # flake8-errmsg
+  "ICN", # flake8-import-conventions
+  "ISC", # flake8-implicit-str-concat
+  "G", # flake8-logging-format
+  "PGH", # pygrep-hooks
+  "PIE", # flake8-pie
+  "PL", # pylint
+  "PT", # flake8-pytest-style
+  "PTH", # flake8-use-pathlib
+  "RET", # flake8-return
+  "RUF", # Ruff-specific
+  "SIM", # flake8-simplify
+  "T20", # flake8-print
+  "UP", # pyupgrade
+  "YTT", # flake8-2020
+  "EXE", # flake8-executable
+  "NPY", # NumPy specific rules
+  "PD", # pandas-vet
+  "UP", # Pyupgrade
 ]
 ignore = [
-    "PLR09",   # Too many <...>
-    "PLR2004", # Magic value used in comparison
-    "ISC001",  # Conflicts with formatter
+  "PLR09", # Too many <...>
+  "PLR2004", # Magic value used in comparison
+  "ISC001", # Conflicts with formatter
+  "N801", # Class name should use CapWords convention
+  "N802", # Function name should be lowercase
+  "N806", # Variable in function should be lowercase
+  "PLC0415", # `import` should be at the top-level of a file
 ]
-isort.required-imports = ["from __future__ import annotations"]
-
-[tool.ruff.lint.per-file-ignores]
-"tests/**" = ["T20"]
-
 
 # Pylint
 
 [tool.pylint]
 py-version = "3.10"
-ignore-paths = [".*/_version.py"]
 reports.output-format = "colorized"
-similarities.ignore-imports = "yes"
 messages_control.disable = [
-    "design",
-    "fixme",
-    "line-too-long",
-    "missing-module-docstring",
-    "missing-function-docstring",
-    "wrong-import-position",
+  "design", # ignore heavily opinionated design checks
+  "fixme", #  allow FIXME comments
+  "line-too-long", # ruff handles this
+  "unused-argument", # ruff handles this
+  "missing-function-docstring", # numpydoc handles this
+  "import-error", # mypy handles this
+  "import-outside-toplevel", # optional dependencies
+]
+
+# numpydoc
+
+[tool.numpydoc_validation]
+checks = [
+  "all", # report on all checks, except the below
+  "EX01", # most docstrings do not need an example
+  "SA01", # data-apis/array-api-extra#87
+  "ES01", # most docstrings do not need an extended summary
+]
+exclude = [ # don't report on objects that match any of these regex
+  '.*test_*',
 ]
diff --git a/renovate.json b/renovate.json
new file mode 100644
index 00000000..d81ec2b4
--- /dev/null
+++ b/renovate.json
@@ -0,0 +1,48 @@
+{
+  "$schema": "https://docs.renovatebot.com/renovate-schema.json",
+  "extends": ["config:recommended", "helpers:pinGitHubActionDigests", ":automergeMinor"],
+  "dependencyDashboardTitle": "META: Dependency Dashboard",
+  "commitMessagePrefix": "deps:",
+  "labels": ["dependencies"],
+  "rangeStrategy": "bump",
+  "constraints": {
+    "pixi": ">=v0.45.0"
+  },
+  "minimumReleaseAge": "14 days",
+  "packageRules": [{
+    "description": "Do not bump deps pinned with '~=' or '='.",
+    "matchManagers": ["pixi"],
+    "matchCurrentValue": "/^~?=/",
+    "enabled": false
+  }, {
+    "description": "Do not bump requires-python.",
+    "matchManagers": ["pep621"],
+    "matchPackageNames": ["python"],
+    "enabled": false
+  }, {
+    "description": "Schedule automerged GHA updates for the 15th of each month.",
+    "matchManagers": ["github-actions"],
+    "groupName": "gha",
+    "schedule": ["* * 15 * *"],
+    "automerge": true
+  }, {
+    "description": "Block PRs for updates blocked on dropping Python 3.10.",
+    "matchManagers": ["pixi"],
+    "matchUpdateTypes": ["major", "minor"],
+    "matchPackageNames": ["numpy", "sphinx", "ipython", "sphinx-autodoc-typehints"],
+    "enabled": false
+  }, {
+    "description": "Group Dask packages.",
+    "matchPackageNames": ["dask", "dask-core"],
+    "groupName": "dask"
+  }, {
+    "description": "Group JAX packages.",
+    "matchPackageNames": ["jax", "jaxlib"],
+    "groupName": "jax"
+  }, {
+    "description": "Schedule hypothesis monthly as releases are frequent.",
+    "matchManagers": ["pixi"],
+    "matchPackageNames": ["hypothesis"],
+    "schedule": ["* * 10 * *"]
+  }]
+}
diff --git a/src/array_api_extra/__init__.py b/src/array_api_extra/__init__.py
index 2062f7d5..ddfc715e 100644
--- a/src/array_api_extra/__init__.py
+++ b/src/array_api_extra/__init__.py
@@ -1,15 +1,41 @@
-from __future__ import annotations
+"""Extra array functions built on top of the array API standard."""
 
-from ._funcs import atleast_nd, cov, create_diagonal, expand_dims, kron, sinc
+from ._delegation import isclose, one_hot, pad
+from ._lib._at import at
+from ._lib._funcs import (
+    apply_where,
+    atleast_nd,
+    broadcast_shapes,
+    cov,
+    create_diagonal,
+    default_dtype,
+    expand_dims,
+    kron,
+    nunique,
+    setdiff1d,
+    sinc,
+)
+from ._lib._lazy import lazy_apply
 
-__version__ = "0.2.0"
+__version__ = "0.8.1.dev0"
 
+# pylint: disable=duplicate-code
 __all__ = [
     "__version__",
+    "apply_where",
+    "at",
     "atleast_nd",
+    "broadcast_shapes",
     "cov",
     "create_diagonal",
+    "default_dtype",
     "expand_dims",
+    "isclose",
     "kron",
+    "lazy_apply",
+    "nunique",
+    "one_hot",
+    "pad",
+    "setdiff1d",
     "sinc",
 ]
diff --git a/src/array_api_extra/_delegation.py b/src/array_api_extra/_delegation.py
new file mode 100644
index 00000000..756841c8
--- /dev/null
+++ b/src/array_api_extra/_delegation.py
@@ -0,0 +1,249 @@
+"""Delegation to existing implementations for Public API Functions."""
+
+from collections.abc import Sequence
+from types import ModuleType
+from typing import Literal
+
+from ._lib import _funcs
+from ._lib._utils._compat import (
+    array_namespace,
+    is_cupy_namespace,
+    is_dask_namespace,
+    is_jax_namespace,
+    is_numpy_namespace,
+    is_pydata_sparse_namespace,
+    is_torch_namespace,
+)
+from ._lib._utils._compat import device as get_device
+from ._lib._utils._helpers import asarrays
+from ._lib._utils._typing import Array, DType
+
+__all__ = ["isclose", "one_hot", "pad"]
+
+
+def isclose(
+    a: Array | complex,
+    b: Array | complex,
+    *,
+    rtol: float = 1e-05,
+    atol: float = 1e-08,
+    equal_nan: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Return a boolean array where two arrays are element-wise equal within a tolerance.
+
+    The tolerance values are positive, typically very small numbers. The relative
+    difference ``(rtol * abs(b))`` and the absolute difference `atol` are added together
+    to compare against the absolute difference between `a` and `b`.
+
+    NaNs are treated as equal if they are in the same place and if ``equal_nan=True``.
+    Infs are treated as equal if they are in the same place and of the same sign in both
+    arrays.
+
+    Parameters
+    ----------
+    a, b : Array | int | float | complex | bool
+        Input objects to compare. At least one must be an array.
+    rtol : array_like, optional
+        The relative tolerance parameter (see Notes).
+    atol : array_like, optional
+        The absolute tolerance parameter (see Notes).
+    equal_nan : bool, optional
+        Whether to compare NaN's as equal. If True, NaN's in `a` will be considered
+        equal to NaN's in `b` in the output array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `a` and `b`. Default: infer.
+
+    Returns
+    -------
+    Array
+        A boolean array of shape broadcasted from `a` and `b`, containing ``True`` where
+        `a` is close to `b`, and ``False`` otherwise.
+
+    Warnings
+    --------
+    The default `atol` is not appropriate for comparing numbers with magnitudes much
+    smaller than one (see notes).
+
+    See Also
+    --------
+    math.isclose : Similar function in stdlib for Python scalars.
+
+    Notes
+    -----
+    For finite values, `isclose` uses the following equation to test whether two
+    floating point values are equivalent::
+
+        absolute(a - b) <= (atol + rtol * absolute(b))
+
+    Unlike the built-in `math.isclose`,
+    the above equation is not symmetric in `a` and `b`,
+    so that ``isclose(a, b)`` might be different from ``isclose(b, a)`` in some rare
+    cases.
+
+    The default value of `atol` is not appropriate when the reference value `b` has
+    magnitude smaller than one. For example, it is unlikely that ``a = 1e-9`` and
+    ``b = 2e-9`` should be considered "close", yet ``isclose(1e-9, 2e-9)`` is ``True``
+    with default settings. Be sure to select `atol` for the use case at hand, especially
+    for defining the threshold below which a non-zero value in `a` will be considered
+    "close" to a very small or zero value in `b`.
+
+    The comparison of `a` and `b` uses standard broadcasting, which means that `a` and
+    `b` need not have the same shape in order for ``isclose(a, b)`` to evaluate to
+    ``True``.
+
+    `isclose` is not defined for non-numeric data types.
+    ``bool`` is considered a numeric data-type for this purpose.
+    """
+    xp = array_namespace(a, b) if xp is None else xp
+
+    if (
+        is_numpy_namespace(xp)
+        or is_cupy_namespace(xp)
+        or is_dask_namespace(xp)
+        or is_jax_namespace(xp)
+    ):
+        return xp.isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
+    if is_torch_namespace(xp):
+        a, b = asarrays(a, b, xp=xp)  # Array API 2024.12 support
+        return xp.isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan)
+
+    return _funcs.isclose(a, b, rtol=rtol, atol=atol, equal_nan=equal_nan, xp=xp)
+
+
+def one_hot(
+    x: Array,
+    /,
+    num_classes: int,
+    *,
+    dtype: DType | None = None,
+    axis: int = -1,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    One-hot encode the given indices.
+
+    Each index in the input `x` is encoded as a vector of zeros of length `num_classes`
+    with the element at the given index set to one.
+
+    Parameters
+    ----------
+    x : array
+        An array with integral dtype whose values are between `0` and `num_classes - 1`.
+    num_classes : int
+        Number of classes in the one-hot dimension.
+    dtype : DType, optional
+        The dtype of the return value.  Defaults to the default float dtype (usually
+        float64).
+    axis : int, optional
+        Position in the expanded axes where the new axis is placed. Default: -1.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array having the same shape as `x` except for a new axis at the position
+        given by `axis` having size `num_classes`.  If `axis` is unspecified, it
+        defaults to -1, which appends a new axis.
+
+        If ``x < 0`` or ``x >= num_classes``, then the result is undefined, may raise
+        an exception, or may even cause a bad state.  `x` is not checked.
+
+    Examples
+    --------
+    >>> import array_api_extra as xpx
+    >>> import array_api_strict as xp
+    >>> xpx.one_hot(xp.asarray([1, 2, 0]), 3)
+    Array([[0., 1., 0.],
+          [0., 0., 1.],
+          [1., 0., 0.]], dtype=array_api_strict.float64)
+    """
+    # Validate inputs.
+    if xp is None:
+        xp = array_namespace(x)
+    if not xp.isdtype(x.dtype, "integral"):
+        msg = "x must have an integral dtype."
+        raise TypeError(msg)
+    if dtype is None:
+        dtype = _funcs.default_dtype(xp, device=get_device(x))
+    # Delegate where possible.
+    if is_jax_namespace(xp):
+        from jax.nn import one_hot as jax_one_hot
+
+        return jax_one_hot(x, num_classes, dtype=dtype, axis=axis)
+    if is_torch_namespace(xp):
+        from torch.nn.functional import one_hot as torch_one_hot
+
+        x = xp.astype(x, xp.int64)  # PyTorch only supports int64 here.
+        try:
+            out = torch_one_hot(x, num_classes)
+        except RuntimeError as e:
+            raise IndexError from e
+    else:
+        out = _funcs.one_hot(x, num_classes, xp=xp)
+    out = xp.astype(out, dtype, copy=False)
+    if axis != -1:
+        out = xp.moveaxis(out, -1, axis)
+    return out
+
+
+def pad(
+    x: Array,
+    pad_width: int | tuple[int, int] | Sequence[tuple[int, int]],
+    mode: Literal["constant"] = "constant",
+    *,
+    constant_values: complex = 0,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Pad the input array.
+
+    Parameters
+    ----------
+    x : array
+        Input array.
+    pad_width : int or tuple of ints or sequence of pairs of ints
+        Pad the input array with this many elements from each side.
+        If a sequence of tuples, ``[(before_0, after_0), ... (before_N, after_N)]``,
+        each pair applies to the corresponding axis of ``x``.
+        A single tuple, ``(before, after)``, is equivalent to a list of ``x.ndim``
+        copies of this tuple.
+    mode : str, optional
+        Only "constant" mode is currently supported, which pads with
+        the value passed to `constant_values`.
+    constant_values : python scalar, optional
+        Use this value to pad the input. Default is zero.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        The input array,
+        padded with ``pad_width`` elements equal to ``constant_values``.
+    """
+    xp = array_namespace(x) if xp is None else xp
+
+    if mode != "constant":
+        msg = "Only `'constant'` mode is currently supported"
+        raise NotImplementedError(msg)
+
+    if (
+        is_numpy_namespace(xp)
+        or is_cupy_namespace(xp)
+        or is_jax_namespace(xp)
+        or is_pydata_sparse_namespace(xp)
+    ):
+        return xp.pad(x, pad_width, mode, constant_values=constant_values)
+
+    # https://github.com/pytorch/pytorch/blob/cf76c05b4dc629ac989d1fb8e789d4fac04a095a/torch/_numpy/_funcs_impl.py#L2045-L2056
+    if is_torch_namespace(xp):
+        pad_width = xp.asarray(pad_width)
+        pad_width = xp.broadcast_to(pad_width, (x.ndim, 2))
+        pad_width = xp.flip(pad_width, axis=(0,)).flatten()
+        return xp.nn.functional.pad(x, tuple(pad_width), value=constant_values)  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+    return _funcs.pad(x, pad_width, constant_values=constant_values, xp=xp)
diff --git a/src/array_api_extra/_funcs.py b/src/array_api_extra/_funcs.py
deleted file mode 100644
index ce800189..00000000
--- a/src/array_api_extra/_funcs.py
+++ /dev/null
@@ -1,484 +0,0 @@
-from __future__ import annotations
-
-import warnings
-from typing import TYPE_CHECKING
-
-if TYPE_CHECKING:
-    from ._typing import Array, ModuleType
-
-__all__ = ["atleast_nd", "cov", "create_diagonal", "expand_dims", "kron", "sinc"]
-
-
-def atleast_nd(x: Array, /, *, ndim: int, xp: ModuleType) -> Array:
-    """
-    Recursively expand the dimension of an array to at least `ndim`.
-
-    Parameters
-    ----------
-    x : array
-    ndim : int
-        The minimum number of dimensions for the result.
-    xp : array_namespace
-        The standard-compatible namespace for `x`.
-
-    Returns
-    -------
-    res : array
-        An array with ``res.ndim`` >= `ndim`.
-        If ``x.ndim`` >= `ndim`, `x` is returned.
-        If ``x.ndim`` < `ndim`, `x` is expanded by prepending new axes
-        until ``res.ndim`` equals `ndim`.
-
-    Examples
-    --------
-    >>> import array_api_strict as xp
-    >>> import array_api_extra as xpx
-    >>> x = xp.asarray([1])
-    >>> xpx.atleast_nd(x, ndim=3, xp=xp)
-    Array([[[1]]], dtype=array_api_strict.int64)
-
-    >>> x = xp.asarray([[[1, 2],
-    ...                  [3, 4]]])
-    >>> xpx.atleast_nd(x, ndim=1, xp=xp) is x
-    True
-
-    """
-    if x.ndim < ndim:
-        x = xp.expand_dims(x, axis=0)
-        x = atleast_nd(x, ndim=ndim, xp=xp)
-    return x
-
-
-def cov(m: Array, /, *, xp: ModuleType) -> Array:
-    """
-    Estimate a covariance matrix.
-
-    Covariance indicates the level to which two variables vary together.
-    If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,
-    then the covariance matrix element :math:`C_{ij}` is the covariance of
-    :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
-    of :math:`x_i`.
-
-    This provides a subset of the functionality of ``numpy.cov``.
-
-    Parameters
-    ----------
-    m : array
-        A 1-D or 2-D array containing multiple variables and observations.
-        Each row of `m` represents a variable, and each column a single
-        observation of all those variables.
-    xp : array_namespace
-        The standard-compatible namespace for `m`.
-
-    Returns
-    -------
-    res : array
-        The covariance matrix of the variables.
-
-    Examples
-    --------
-    >>> import array_api_strict as xp
-    >>> import array_api_extra as xpx
-
-    Consider two variables, :math:`x_0` and :math:`x_1`, which
-    correlate perfectly, but in opposite directions:
-
-    >>> x = xp.asarray([[0, 2], [1, 1], [2, 0]]).T
-    >>> x
-    Array([[0, 1, 2],
-           [2, 1, 0]], dtype=array_api_strict.int64)
-
-    Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance
-    matrix shows this clearly:
-
-    >>> xpx.cov(x, xp=xp)
-    Array([[ 1., -1.],
-           [-1.,  1.]], dtype=array_api_strict.float64)
-
-
-    Note that element :math:`C_{0,1}`, which shows the correlation between
-    :math:`x_0` and :math:`x_1`, is negative.
-
-    Further, note how `x` and `y` are combined:
-
-    >>> x = xp.asarray([-2.1, -1,  4.3])
-    >>> y = xp.asarray([3,  1.1,  0.12])
-    >>> X = xp.stack((x, y), axis=0)
-    >>> xpx.cov(X, xp=xp)
-    Array([[11.71      , -4.286     ],
-           [-4.286     ,  2.14413333]], dtype=array_api_strict.float64)
-
-    >>> xpx.cov(x, xp=xp)
-    Array(11.71, dtype=array_api_strict.float64)
-
-    >>> xpx.cov(y, xp=xp)
-    Array(2.14413333, dtype=array_api_strict.float64)
-
-    """
-    m = xp.asarray(m, copy=True)
-    dtype = (
-        xp.float64 if xp.isdtype(m.dtype, "integral") else xp.result_type(m, xp.float64)
-    )
-
-    m = atleast_nd(m, ndim=2, xp=xp)
-    m = xp.astype(m, dtype)
-
-    avg = _mean(m, axis=1, xp=xp)
-    fact = m.shape[1] - 1
-
-    if fact <= 0:
-        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=2)
-        fact = 0.0
-
-    m -= avg[:, None]
-    m_transpose = m.T
-    if xp.isdtype(m_transpose.dtype, "complex floating"):
-        m_transpose = xp.conj(m_transpose)
-    c = m @ m_transpose
-    c /= fact
-    axes = tuple(axis for axis, length in enumerate(c.shape) if length == 1)
-    return xp.squeeze(c, axis=axes)
-
-
-def create_diagonal(x: Array, /, *, offset: int = 0, xp: ModuleType) -> Array:
-    """
-    Construct a diagonal array.
-
-    Parameters
-    ----------
-    x : array
-        A 1-D array
-    offset : int, optional
-        Offset from the leading diagonal (default is ``0``).
-        Use positive ints for diagonals above the leading diagonal,
-        and negative ints for diagonals below the leading diagonal.
-    xp : array_namespace
-        The standard-compatible namespace for `x`.
-
-    Returns
-    -------
-    res : array
-        A 2-D array with `x` on the diagonal (offset by `offset`).
-
-    Examples
-    --------
-    >>> import array_api_strict as xp
-    >>> import array_api_extra as xpx
-    >>> x = xp.asarray([2, 4, 8])
-
-    >>> xpx.create_diagonal(x, xp=xp)
-    Array([[2, 0, 0],
-           [0, 4, 0],
-           [0, 0, 8]], dtype=array_api_strict.int64)
-
-    >>> xpx.create_diagonal(x, offset=-2, xp=xp)
-    Array([[0, 0, 0, 0, 0],
-           [0, 0, 0, 0, 0],
-           [2, 0, 0, 0, 0],
-           [0, 4, 0, 0, 0],
-           [0, 0, 8, 0, 0]], dtype=array_api_strict.int64)
-
-    """
-    if x.ndim != 1:
-        err_msg = "`x` must be 1-dimensional."
-        raise ValueError(err_msg)
-    n = x.shape[0] + abs(offset)
-    diag = xp.zeros(n**2, dtype=x.dtype)
-    i = offset if offset >= 0 else abs(offset) * n
-    diag[i : min(n * (n - offset), diag.shape[0]) : n + 1] = x
-    return xp.reshape(diag, (n, n))
-
-
-def _mean(
-    x: Array,
-    /,
-    *,
-    axis: int | tuple[int, ...] | None = None,
-    keepdims: bool = False,
-    xp: ModuleType,
-) -> Array:
-    """
-    Complex mean, https://github.com/data-apis/array-api/issues/846.
-    """
-    if xp.isdtype(x.dtype, "complex floating"):
-        x_real = xp.real(x)
-        x_imag = xp.imag(x)
-        mean_real = xp.mean(x_real, axis=axis, keepdims=keepdims)
-        mean_imag = xp.mean(x_imag, axis=axis, keepdims=keepdims)
-        return mean_real + (mean_imag * xp.asarray(1j))
-    return xp.mean(x, axis=axis, keepdims=keepdims)
-
-
-def expand_dims(
-    a: Array, /, *, axis: int | tuple[int, ...] = (0,), xp: ModuleType
-) -> Array:
-    """
-    Expand the shape of an array.
-
-    Insert (a) new axis/axes that will appear at the position(s) specified by
-    `axis` in the expanded array shape.
-
-    This is ``xp.expand_dims`` for `axis` an int *or a tuple of ints*.
-    Roughly equivalent to ``numpy.expand_dims`` for NumPy arrays.
-
-    Parameters
-    ----------
-    a : array
-    axis : int or tuple of ints, optional
-        Position(s) in the expanded axes where the new axis (or axes) is/are placed.
-        If multiple positions are provided, they should be unique (note that a position
-        given by a positive index could also be referred to by a negative index -
-        that will also result in an error).
-        Default: ``(0,)``.
-    xp : array_namespace
-        The standard-compatible namespace for `a`.
-
-    Returns
-    -------
-    res : array
-        `a` with an expanded shape.
-
-    Examples
-    --------
-    >>> import array_api_strict as xp
-    >>> import array_api_extra as xpx
-    >>> x = xp.asarray([1, 2])
-    >>> x.shape
-    (2,)
-
-    The following is equivalent to ``x[xp.newaxis, :]`` or ``x[xp.newaxis]``:
-
-    >>> y = xpx.expand_dims(x, axis=0, xp=xp)
-    >>> y
-    Array([[1, 2]], dtype=array_api_strict.int64)
-    >>> y.shape
-    (1, 2)
-
-    The following is equivalent to ``x[:, xp.newaxis]``:
-
-    >>> y = xpx.expand_dims(x, axis=1, xp=xp)
-    >>> y
-    Array([[1],
-           [2]], dtype=array_api_strict.int64)
-    >>> y.shape
-    (2, 1)
-
-    ``axis`` may also be a tuple:
-
-    >>> y = xpx.expand_dims(x, axis=(0, 1), xp=xp)
-    >>> y
-    Array([[[1, 2]]], dtype=array_api_strict.int64)
-
-    >>> y = xpx.expand_dims(x, axis=(2, 0), xp=xp)
-    >>> y
-    Array([[[1],
-            [2]]], dtype=array_api_strict.int64)
-
-    """
-    if not isinstance(axis, tuple):
-        axis = (axis,)
-    ndim = a.ndim + len(axis)
-    if axis != () and (min(axis) < -ndim or max(axis) >= ndim):
-        err_msg = (
-            f"a provided axis position is out of bounds for array of dimension {a.ndim}"
-        )
-        raise IndexError(err_msg)
-    axis = tuple(dim % ndim for dim in axis)
-    if len(set(axis)) != len(axis):
-        err_msg = "Duplicate dimensions specified in `axis`."
-        raise ValueError(err_msg)
-    for i in sorted(axis):
-        a = xp.expand_dims(a, axis=i)
-    return a
-
-
-def kron(a: Array, b: Array, /, *, xp: ModuleType) -> Array:
-    """
-    Kronecker product of two arrays.
-
-    Computes the Kronecker product, a composite array made of blocks of the
-    second array scaled by the first.
-
-    Equivalent to ``numpy.kron`` for NumPy arrays.
-
-    Parameters
-    ----------
-    a, b : array
-    xp : array_namespace
-        The standard-compatible namespace for `a` and `b`.
-
-    Returns
-    -------
-    res : array
-        The Kronecker product of `a` and `b`.
-
-    Notes
-    -----
-    The function assumes that the number of dimensions of `a` and `b`
-    are the same, if necessary prepending the smallest with ones.
-    If ``a.shape = (r0,r1,..,rN)`` and ``b.shape = (s0,s1,...,sN)``,
-    the Kronecker product has shape ``(r0*s0, r1*s1, ..., rN*SN)``.
-    The elements are products of elements from `a` and `b`, organized
-    explicitly by::
-
-        kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
-
-    where::
-
-        kt = it * st + jt,  t = 0,...,N
-
-    In the common 2-D case (N=1), the block structure can be visualized::
-
-        [[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
-         [  ...                              ...   ],
-         [ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]
-
-
-    Examples
-    --------
-    >>> import array_api_strict as xp
-    >>> import array_api_extra as xpx
-    >>> xpx.kron(xp.asarray([1, 10, 100]), xp.asarray([5, 6, 7]), xp=xp)
-    Array([  5,   6,   7,  50,  60,  70, 500,
-           600, 700], dtype=array_api_strict.int64)
-
-    >>> xpx.kron(xp.asarray([5, 6, 7]), xp.asarray([1, 10, 100]), xp=xp)
-    Array([  5,  50, 500,   6,  60, 600,   7,
-            70, 700], dtype=array_api_strict.int64)
-
-    >>> xpx.kron(xp.eye(2), xp.ones((2, 2)), xp=xp)
-    Array([[1., 1., 0., 0.],
-           [1., 1., 0., 0.],
-           [0., 0., 1., 1.],
-           [0., 0., 1., 1.]], dtype=array_api_strict.float64)
-
-
-    >>> a = xp.reshape(xp.arange(100), (2, 5, 2, 5))
-    >>> b = xp.reshape(xp.arange(24), (2, 3, 4))
-    >>> c = xpx.kron(a, b, xp=xp)
-    >>> c.shape
-    (2, 10, 6, 20)
-    >>> I = (1, 3, 0, 2)
-    >>> J = (0, 2, 1)
-    >>> J1 = (0,) + J             # extend to ndim=4
-    >>> S1 = (1,) + b.shape
-    >>> K = tuple(xp.asarray(I) * xp.asarray(S1) + xp.asarray(J1))
-    >>> c[K] == a[I]*b[J]
-    Array(True, dtype=array_api_strict.bool)
-
-    """
-
-    b = xp.asarray(b)
-    singletons = (1,) * (b.ndim - a.ndim)
-    a = xp.broadcast_to(xp.asarray(a), singletons + a.shape)
-
-    nd_b, nd_a = b.ndim, a.ndim
-    nd_max = max(nd_b, nd_a)
-    if nd_a == 0 or nd_b == 0:
-        return xp.multiply(a, b)
-
-    a_shape = a.shape
-    b_shape = b.shape
-
-    # Equalise the shapes by prepending smaller one with 1s
-    a_shape = (1,) * max(0, nd_b - nd_a) + a_shape
-    b_shape = (1,) * max(0, nd_a - nd_b) + b_shape
-
-    # Insert empty dimensions
-    a_arr = expand_dims(a, axis=tuple(range(nd_b - nd_a)), xp=xp)
-    b_arr = expand_dims(b, axis=tuple(range(nd_a - nd_b)), xp=xp)
-
-    # Compute the product
-    a_arr = expand_dims(a_arr, axis=tuple(range(1, nd_max * 2, 2)), xp=xp)
-    b_arr = expand_dims(b_arr, axis=tuple(range(0, nd_max * 2, 2)), xp=xp)
-    result = xp.multiply(a_arr, b_arr)
-
-    # Reshape back and return
-    a_shape = xp.asarray(a_shape)
-    b_shape = xp.asarray(b_shape)
-    return xp.reshape(result, tuple(xp.multiply(a_shape, b_shape)))
-
-
-def sinc(x: Array, /, *, xp: ModuleType) -> Array:
-    r"""
-    Return the normalized sinc function.
-
-    The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument
-    :math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not
-    only everywhere continuous but also infinitely differentiable.
-
-    .. note::
-
-        Note the normalization factor of ``pi`` used in the definition.
-        This is the most commonly used definition in signal processing.
-        Use ``sinc(x / xp.pi)`` to obtain the unnormalized sinc function
-        :math:`\sin(x)/x` that is more common in mathematics.
-
-    Parameters
-    ----------
-    x : array
-        Array (possibly multi-dimensional) of values for which to calculate
-        ``sinc(x)``. Must have a real floating point dtype.
-    xp : array_namespace
-        The standard-compatible namespace for `x`.
-
-    Returns
-    -------
-    res : array
-        ``sinc(x)`` calculated elementwise, which has the same shape as the input.
-
-    Notes
-    -----
-    The name sinc is short for "sine cardinal" or "sinus cardinalis".
-
-    The sinc function is used in various signal processing applications,
-    including in anti-aliasing, in the construction of a Lanczos resampling
-    filter, and in interpolation.
-
-    For bandlimited interpolation of discrete-time signals, the ideal
-    interpolation kernel is proportional to the sinc function.
-
-    References
-    ----------
-    .. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
-           Resource. https://mathworld.wolfram.com/SincFunction.html
-    .. [2] Wikipedia, "Sinc function",
-           https://en.wikipedia.org/wiki/Sinc_function
-
-    Examples
-    --------
-    >>> import array_api_strict as xp
-    >>> import array_api_extra as xpx
-    >>> x = xp.linspace(-4, 4, 41)
-    >>> xpx.sinc(x, xp=xp)
-    Array([-3.89817183e-17, -4.92362781e-02,
-           -8.40918587e-02, -8.90384387e-02,
-           -5.84680802e-02,  3.89817183e-17,
-            6.68206631e-02,  1.16434881e-01,
-            1.26137788e-01,  8.50444803e-02,
-           -3.89817183e-17, -1.03943254e-01,
-           -1.89206682e-01, -2.16236208e-01,
-           -1.55914881e-01,  3.89817183e-17,
-            2.33872321e-01,  5.04551152e-01,
-            7.56826729e-01,  9.35489284e-01,
-            1.00000000e+00,  9.35489284e-01,
-            7.56826729e-01,  5.04551152e-01,
-            2.33872321e-01,  3.89817183e-17,
-           -1.55914881e-01, -2.16236208e-01,
-           -1.89206682e-01, -1.03943254e-01,
-           -3.89817183e-17,  8.50444803e-02,
-            1.26137788e-01,  1.16434881e-01,
-            6.68206631e-02,  3.89817183e-17,
-           -5.84680802e-02, -8.90384387e-02,
-           -8.40918587e-02, -4.92362781e-02,
-           -3.89817183e-17], dtype=array_api_strict.float64)
-
-    """
-    if not xp.isdtype(x.dtype, "real floating"):
-        err_msg = "`x` must have a real floating data type."
-        raise ValueError(err_msg)
-    # no scalars in `where` - array-api#807
-    y = xp.pi * xp.where(
-        x, x, xp.asarray(xp.finfo(x.dtype).smallest_normal, dtype=x.dtype)
-    )
-    return xp.sin(y) / y
diff --git a/src/array_api_extra/_lib/__init__.py b/src/array_api_extra/_lib/__init__.py
new file mode 100644
index 00000000..d7b32033
--- /dev/null
+++ b/src/array_api_extra/_lib/__init__.py
@@ -0,0 +1 @@
+"""Internals of array-api-extra."""
diff --git a/src/array_api_extra/_lib/_at.py b/src/array_api_extra/_lib/_at.py
new file mode 100644
index 00000000..fb2d6ab7
--- /dev/null
+++ b/src/array_api_extra/_lib/_at.py
@@ -0,0 +1,463 @@
+"""Update operations for read-only arrays."""
+
+from __future__ import annotations
+
+import operator
+from collections.abc import Callable
+from enum import Enum
+from types import ModuleType
+from typing import TYPE_CHECKING, ClassVar, cast
+
+from ._utils import _compat
+from ._utils._compat import (
+    array_namespace,
+    is_dask_array,
+    is_jax_array,
+    is_torch_array,
+    is_writeable_array,
+)
+from ._utils._helpers import meta_namespace
+from ._utils._typing import Array, SetIndex
+
+if TYPE_CHECKING:  # pragma: no cover
+    # TODO import from typing (requires Python >=3.11)
+    from typing_extensions import Self
+
+
+class _AtOp(Enum):
+    """Operations for use in `xpx.at`."""
+
+    SET = "set"
+    ADD = "add"
+    SUBTRACT = "subtract"
+    MULTIPLY = "multiply"
+    DIVIDE = "divide"
+    POWER = "power"
+    MIN = "min"
+    MAX = "max"
+
+    # @override from Python 3.12
+    def __str__(self) -> str:  # pyright: ignore[reportImplicitOverride]
+        """
+        Return string representation (useful for pytest logs).
+
+        Returns
+        -------
+        str
+            The operation's name.
+        """
+        return self.value
+
+
+class Undef(Enum):
+    """Sentinel for undefined values."""
+
+    UNDEF = 0
+
+
+_undef = Undef.UNDEF
+
+
+class at:  # pylint: disable=invalid-name  # numpydoc ignore=PR02
+    """
+    Update operations for read-only arrays.
+
+    This implements ``jax.numpy.ndarray.at`` for all writeable
+    backends (those that support ``__setitem__``) and routes
+    to the ``.at[]`` method for JAX arrays.
+
+    Parameters
+    ----------
+    x : array
+        Input array.
+    idx : index, optional
+        Only `array API standard compliant indices
+        <https://data-apis.org/array-api/latest/API_specification/indexing.html>`_
+        are supported.
+
+        You may use two alternate syntaxes::
+
+          >>> import array_api_extra as xpx
+          >>> xpx.at(x, idx).set(value)  # or add(value), etc.
+          >>> xpx.at(x)[idx].set(value)
+
+    copy : bool, optional
+        None (default)
+            The array parameter *may* be modified in place if it is
+            possible and beneficial for performance.
+            You should not reuse it after calling this function.
+        True
+            Ensure that the inputs are not modified.
+        False
+            Ensure that the update operation writes back to the input.
+            Raise ``ValueError`` if a copy cannot be avoided.
+
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    Updated input array.
+
+    Warnings
+    --------
+    (a) When you omit the ``copy`` parameter, you should never reuse the parameter
+    array later on; ideally, you should reassign it immediately::
+
+        >>> import array_api_extra as xpx
+        >>> x = xpx.at(x, 0).set(2)
+
+    The above best practice pattern ensures that the behaviour won't change depending
+    on whether ``x`` is writeable or not, as the original ``x`` object is dereferenced
+    as soon as ``xpx.at`` returns; this way there is no risk to accidentally update it
+    twice.
+
+    On the reverse, the anti-pattern below must be avoided, as it will result in
+    different behaviour on read-only versus writeable arrays::
+
+        >>> x = xp.asarray([0, 0, 0])
+        >>> y = xpx.at(x, 0).set(2)
+        >>> z = xpx.at(x, 1).set(3)
+
+    In the above example, both calls to ``xpx.at`` update ``x`` in place *if possible*.
+    This causes the behaviour to diverge depending on whether ``x`` is writeable or not:
+
+    - If ``x`` is writeable, then after the snippet above you'll have
+      ``x == y == z == [2, 3, 0]``
+    - If ``x`` is read-only, then you'll end up with
+      ``x == [0, 0, 0]``, ``y == [2, 0, 0]`` and ``z == [0, 3, 0]``.
+
+    The correct pattern to use if you want diverging outputs from the same input is
+    to enforce copies::
+
+        >>> x = xp.asarray([0, 0, 0])
+        >>> y = xpx.at(x, 0).set(2, copy=True)  # Never updates x
+        >>> z = xpx.at(x, 1).set(3)  # May or may not update x in place
+        >>> del x  # avoid accidental reuse of x as we don't know its state anymore
+
+    (b) The array API standard does not support integer array indices.
+    The behaviour of update methods when the index is an array of integers is
+    undefined and will vary between backends; this is particularly true when the
+    index contains multiple occurrences of the same index, e.g.::
+
+        >>> import numpy as np
+        >>> import jax.numpy as jnp
+        >>> import array_api_extra as xpx
+        >>> xpx.at(np.asarray([123]), np.asarray([0, 0])).add(1)
+        array([124])
+        >>> xpx.at(jnp.asarray([123]), jnp.asarray([0, 0])).add(1)
+        Array([125], dtype=int32)
+
+    See Also
+    --------
+    jax.numpy.ndarray.at : Equivalent array method in JAX.
+
+    Notes
+    -----
+    `sparse <https://sparse.pydata.org/>`_, as well as read-only arrays from libraries
+    not explicitly covered by ``array-api-compat``, are not supported by update
+    methods.
+
+    Boolean masks are supported on Dask and jitted JAX arrays exclusively
+    when `idx` has the same shape as `x` and `y` is 0-dimensional.
+    Note that this support is not available in JAX's native
+    ``x.at[mask].set(y)``.
+
+    This pattern::
+
+        >>> mask = m(x)
+        >>> x[mask] = f(x[mask])
+
+    Can't be replaced by `at`, as it won't work on Dask and JAX inside jax.jit::
+
+        >>> mask = m(x)
+        >>> x = xpx.at(x, mask).set(f(x[mask])  # Crash on Dask and jax.jit
+
+    You should instead use::
+
+        >>> x = xp.where(m(x), f(x), x)
+
+    Examples
+    --------
+    Given either of these equivalent expressions::
+
+      >>> import array_api_extra as xpx
+      >>> x = xpx.at(x)[1].add(2)
+      >>> x = xpx.at(x, 1).add(2)
+
+    If x is a JAX array, they are the same as::
+
+      >>> x = x.at[1].add(2)
+
+    If x is a read-only NumPy array, they are the same as::
+
+      >>> x = x.copy()
+      >>> x[1] += 2
+
+    For other known backends, they are the same as::
+
+      >>> x[1] += 2
+    """
+
+    _x: Array
+    _idx: SetIndex | Undef
+    __slots__: ClassVar[tuple[str, ...]] = ("_idx", "_x")
+
+    def __init__(
+        self, x: Array, idx: SetIndex | Undef = _undef, /
+    ) -> None:  # numpydoc ignore=GL08
+        self._x = x
+        self._idx = idx
+
+    def __getitem__(self, idx: SetIndex, /) -> Self:  # numpydoc ignore=PR01,RT01
+        """
+        Allow for the alternate syntax ``at(x)[start:stop:step]``.
+
+        It looks prettier than ``at(x, slice(start, stop, step))``
+        and feels more intuitive coming from the JAX documentation.
+        """
+        if self._idx is not _undef:
+            msg = "Index has already been set"
+            raise ValueError(msg)
+        return type(self)(self._x, idx)
+
+    def _op(
+        self,
+        at_op: _AtOp,
+        in_place_op: Callable[[Array, Array | complex], Array] | None,
+        out_of_place_op: Callable[[Array, Array], Array] | None,
+        y: Array | complex,
+        /,
+        copy: bool | None,
+        xp: ModuleType | None,
+    ) -> Array:
+        """
+        Implement all update operations.
+
+        Parameters
+        ----------
+        at_op : _AtOp
+            Method of JAX's Array.at[].
+        in_place_op : Callable[[Array, Array | complex], Array] | None
+            In-place operation to apply on mutable backends::
+
+                x[idx] = in_place_op(x[idx], y)
+
+            If None::
+
+                x[idx] = y
+
+        out_of_place_op : Callable[[Array, Array], Array] | None
+            Out-of-place operation to apply when idx is a boolean mask and the backend
+            doesn't support in-place updates::
+
+                x = xp.where(idx, out_of_place_op(x, y), x)
+
+            If None::
+
+                x = xp.where(idx, y, x)
+
+        y : array or complex
+            Right-hand side of the operation.
+        copy : bool or None
+            Whether to copy the input array. See the class docstring for details.
+        xp : array_namespace, optional
+            The array namespace for the input array. Default: infer.
+
+        Returns
+        -------
+        Array
+            Updated `x`.
+        """
+        from ._funcs import apply_where  # pylint: disable=cyclic-import
+
+        x, idx = self._x, self._idx
+        xp = array_namespace(x, y) if xp is None else xp
+
+        if isinstance(idx, Undef):
+            msg = (
+                "Index has not been set.\n"
+                "Usage: either\n"
+                "    at(x, idx).set(value)\n"
+                "or\n"
+                "    at(x)[idx].set(value)\n"
+                "(same for all other methods)."
+            )
+            raise ValueError(msg)
+
+        if copy not in (True, False, None):
+            msg = f"copy must be True, False, or None; got {copy!r}"
+            raise ValueError(msg)
+
+        writeable = None if copy else is_writeable_array(x)
+
+        # JAX inside jax.jit doesn't support in-place updates with boolean
+        # masks; Dask exclusively supports __setitem__ but not iops.
+        # We can handle the common special case of 0-dimensional y
+        # with where(idx, y, x) instead.
+        if (
+            (is_dask_array(idx) or is_jax_array(idx))
+            and idx.dtype == xp.bool
+            and idx.shape == x.shape
+        ):
+            y_xp = xp.asarray(y, dtype=x.dtype, device=_compat.device(x))
+            if y_xp.ndim == 0:
+                if out_of_place_op:  # add(), subtract(), ...
+                    # suppress inf warnings on Dask
+                    out = apply_where(
+                        idx, (x, y_xp), out_of_place_op, fill_value=x, xp=xp
+                    )
+                    # Undo int->float promotion on JAX after _AtOp.DIVIDE
+                    out = xp.astype(out, x.dtype, copy=False)
+                else:  # set()
+                    out = xp.where(idx, y_xp, x)
+
+                if copy is False:
+                    x[()] = out
+                    return x
+                return out
+
+            # else: this will work on eager JAX and crash on jax.jit and Dask
+
+        if copy or (copy is None and not writeable):
+            if is_jax_array(x):
+                # Use JAX's at[]
+                func = cast(
+                    Callable[[Array | complex], Array],
+                    getattr(x.at[idx], at_op.value),  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue,reportUnknownArgumentType]
+                )
+                out = func(y)
+                # Undo int->float promotion on JAX after _AtOp.DIVIDE
+                return xp.astype(out, x.dtype, copy=False)
+
+            # Emulate at[] behaviour for non-JAX arrays
+            # with a copy followed by an update
+
+            x = xp.asarray(x, copy=True)
+            # A copy of a read-only numpy array is writeable
+            # Note: this assumes that a copy of a writeable array is writeable
+            assert not writeable
+            writeable = None
+
+        if writeable is None:
+            writeable = is_writeable_array(x)
+        if not writeable:
+            # sparse crashes here
+            msg = f"Can't update read-only array {x}"
+            raise ValueError(msg)
+
+        # Work around bug in PyTorch where __setitem__ doesn't
+        # always support mismatched dtypes
+        # https://github.com/pytorch/pytorch/issues/150017
+        if is_torch_array(y):
+            y = xp.astype(y, x.dtype, copy=False)
+
+        # Backends without boolean indexing (other than JAX) crash here
+        if in_place_op:  # add(), subtract(), ...
+            x[idx] = in_place_op(x[idx], y)
+        else:  # set()
+            x[idx] = y
+        return x
+
+    def set(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] = y`` and return the update array."""
+        return self._op(_AtOp.SET, None, None, y, copy=copy, xp=xp)
+
+    def add(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] += y`` and return the updated array."""
+
+        # Note for this and all other methods based on _iop:
+        # operator.iadd and operator.add subtly differ in behaviour, as
+        # only iadd will trigger exceptions when y has an incompatible dtype.
+        return self._op(_AtOp.ADD, operator.iadd, operator.add, y, copy=copy, xp=xp)
+
+    def subtract(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] -= y`` and return the updated array."""
+        return self._op(
+            _AtOp.SUBTRACT, operator.isub, operator.sub, y, copy=copy, xp=xp
+        )
+
+    def multiply(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] *= y`` and return the updated array."""
+        return self._op(
+            _AtOp.MULTIPLY, operator.imul, operator.mul, y, copy=copy, xp=xp
+        )
+
+    def divide(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] /= y`` and return the updated array."""
+        return self._op(
+            _AtOp.DIVIDE, operator.itruediv, operator.truediv, y, copy=copy, xp=xp
+        )
+
+    def power(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] **= y`` and return the updated array."""
+        return self._op(_AtOp.POWER, operator.ipow, operator.pow, y, copy=copy, xp=xp)
+
+    def min(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] = minimum(x[idx], y)`` and return the updated array."""
+        # On Dask, this function runs on the chunks, so we need to determine the
+        # namespace that Dask is wrapping.
+        # Note that da.minimum _incidentally_ works on NumPy, CuPy, and sparse
+        # thanks to all these meta-namespaces implementing the __array_ufunc__
+        # interface, but there's no guarantee that it will work for other
+        # wrapped libraries in the future.
+        xp = array_namespace(self._x) if xp is None else xp
+        mxp = meta_namespace(self._x, xp=xp)
+        y = xp.asarray(y)
+        return self._op(_AtOp.MIN, mxp.minimum, mxp.minimum, y, copy=copy, xp=xp)
+
+    def max(
+        self,
+        y: Array | complex,
+        /,
+        copy: bool | None = None,
+        xp: ModuleType | None = None,
+    ) -> Array:  # numpydoc ignore=PR01,RT01
+        """Apply ``x[idx] = maximum(x[idx], y)`` and return the updated array."""
+        # See note on min()
+        xp = array_namespace(self._x) if xp is None else xp
+        mxp = meta_namespace(self._x, xp=xp)
+        y = xp.asarray(y)
+        return self._op(_AtOp.MAX, mxp.maximum, mxp.maximum, y, copy=copy, xp=xp)
diff --git a/src/array_api_extra/_lib/_backends.py b/src/array_api_extra/_lib/_backends.py
new file mode 100644
index 00000000..936f5dd0
--- /dev/null
+++ b/src/array_api_extra/_lib/_backends.py
@@ -0,0 +1,72 @@
+"""Backends against which array-api-extra runs its tests."""
+
+from __future__ import annotations
+
+from enum import Enum
+from typing import Any
+
+import numpy as np
+import pytest
+
+__all__ = ["NUMPY_VERSION", "Backend"]
+
+NUMPY_VERSION = tuple(int(v) for v in np.__version__.split(".")[:3])  # pyright: ignore[reportUnknownArgumentType]
+
+
+class Backend(Enum):  # numpydoc ignore=PR02
+    """
+    All array library backends explicitly tested by array-api-extra.
+
+    Parameters
+    ----------
+    value : str
+        Tag of the backend's module, in the format ``<namespace>[:<extra tag>]``.
+    """
+
+    # Use :<tag> to prevent Enum from deduplicating items with the same value
+    ARRAY_API_STRICT = "array_api_strict"
+    ARRAY_API_STRICTEST = "array_api_strict:strictest"
+    NUMPY = "numpy"
+    NUMPY_READONLY = "numpy:readonly"
+    CUPY = "cupy"
+    TORCH = "torch"
+    TORCH_GPU = "torch:gpu"
+    DASK = "dask.array"
+    SPARSE = "sparse"
+    JAX = "jax.numpy"
+    JAX_GPU = "jax.numpy:gpu"
+
+    @property
+    def modname(self) -> str:  # numpydoc ignore=RT01
+        """Module name to be imported."""
+        return self.value.split(":")[0]
+
+    def like(self, *others: Backend) -> bool:  # numpydoc ignore=PR01,RT01
+        """Check if this backend uses the same module as others."""
+        return any(self.modname == other.modname for other in others)
+
+    def pytest_param(self) -> Any:
+        """
+        Backend as a pytest parameter
+
+        Returns
+        -------
+        pytest.mark.ParameterSet
+        """
+        id_ = (
+            self.name.lower().replace("_gpu", ":gpu").replace("_readonly", ":readonly")
+        )
+
+        marks = []
+        if self.like(Backend.ARRAY_API_STRICT):
+            marks.append(
+                pytest.mark.skipif(
+                    NUMPY_VERSION < (1, 26),
+                    reason="array_api_strict is untested on NumPy <1.26",
+                )
+            )
+        if self.like(Backend.DASK, Backend.JAX):
+            # Monkey-patched by lazy_xp_function
+            marks.append(pytest.mark.thread_unsafe)
+
+        return pytest.param(self, id=id_, marks=marks)  # pyright: ignore[reportUnknownArgumentType]
diff --git a/src/array_api_extra/_lib/_funcs.py b/src/array_api_extra/_lib/_funcs.py
new file mode 100644
index 00000000..05db6251
--- /dev/null
+++ b/src/array_api_extra/_lib/_funcs.py
@@ -0,0 +1,990 @@
+"""Array-agnostic implementations for the public API."""
+
+import math
+import warnings
+from collections.abc import Callable, Sequence
+from types import ModuleType, NoneType
+from typing import Literal, cast, overload
+
+from ._at import at
+from ._utils import _compat, _helpers
+from ._utils._compat import array_namespace, is_dask_namespace, is_jax_array
+from ._utils._helpers import (
+    asarrays,
+    capabilities,
+    eager_shape,
+    meta_namespace,
+    ndindex,
+)
+from ._utils._typing import Array, Device, DType
+
+__all__ = [
+    "apply_where",
+    "atleast_nd",
+    "broadcast_shapes",
+    "cov",
+    "create_diagonal",
+    "expand_dims",
+    "kron",
+    "nunique",
+    "pad",
+    "setdiff1d",
+    "sinc",
+]
+
+
+@overload
+def apply_where(  # numpydoc ignore=GL08
+    cond: Array,
+    args: Array | tuple[Array, ...],
+    f1: Callable[..., Array],
+    f2: Callable[..., Array],
+    /,
+    *,
+    xp: ModuleType | None = None,
+) -> Array: ...
+
+
+@overload
+def apply_where(  # numpydoc ignore=GL08
+    cond: Array,
+    args: Array | tuple[Array, ...],
+    f1: Callable[..., Array],
+    /,
+    *,
+    fill_value: Array | complex,
+    xp: ModuleType | None = None,
+) -> Array: ...
+
+
+def apply_where(  # numpydoc ignore=PR01,PR02
+    cond: Array,
+    args: Array | tuple[Array, ...],
+    f1: Callable[..., Array],
+    f2: Callable[..., Array] | None = None,
+    /,
+    *,
+    fill_value: Array | complex | None = None,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Run one of two elementwise functions depending on a condition.
+
+    Equivalent to ``f1(*args) if cond else fill_value`` performed elementwise
+    when `fill_value` is defined, otherwise to ``f1(*args) if cond else f2(*args)``.
+
+    Parameters
+    ----------
+    cond : array
+        The condition, expressed as a boolean array.
+    args : Array or tuple of Arrays
+        Argument(s) to `f1` (and `f2`). Must be broadcastable with `cond`.
+    f1 : callable
+        Elementwise function of `args`, returning a single array.
+        Where `cond` is True, output will be ``f1(arg0[cond], arg1[cond], ...)``.
+    f2 : callable, optional
+        Elementwise function of `args`, returning a single array.
+        Where `cond` is False, output will be ``f2(arg0[cond], arg1[cond], ...)``.
+        Mutually exclusive with `fill_value`.
+    fill_value : Array or scalar, optional
+        If provided, value with which to fill output array where `cond` is False.
+        It does not need to be scalar; it needs however to be broadcastable with
+        `cond` and `args`.
+        Mutually exclusive with `f2`. You must provide one or the other.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `cond` and `args`. Default: infer.
+
+    Returns
+    -------
+    Array
+        An array with elements from the output of `f1` where `cond` is True and either
+        the output of `f2` or `fill_value` where `cond` is False. The returned array has
+        data type determined by type promotion rules between the output of `f1` and
+        either `fill_value` or the output of `f2`.
+
+    Notes
+    -----
+    ``xp.where(cond, f1(*args), f2(*args))`` requires explicitly evaluating `f1` even
+    when `cond` is False, and `f2` when cond is True. This function evaluates each
+    function only for their matching condition, if the backend allows for it.
+
+    On Dask, `f1` and `f2` are applied to the individual chunks and should use functions
+    from the namespace of the chunks.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> a = xp.asarray([5, 4, 3])
+    >>> b = xp.asarray([0, 2, 2])
+    >>> def f(a, b):
+    ...     return a // b
+    >>> xpx.apply_where(b != 0, (a, b), f, fill_value=xp.nan)
+    array([ nan,  2., 1.])
+    """
+    # Parse and normalize arguments
+    if (f2 is None) == (fill_value is None):
+        msg = "Exactly one of `fill_value` or `f2` must be given."
+        raise TypeError(msg)
+    args_ = list(args) if isinstance(args, tuple) else [args]
+    del args
+
+    xp = array_namespace(cond, fill_value, *args_) if xp is None else xp
+
+    if isinstance(fill_value, int | float | complex | NoneType):
+        cond, *args_ = xp.broadcast_arrays(cond, *args_)
+    else:
+        cond, fill_value, *args_ = xp.broadcast_arrays(cond, fill_value, *args_)
+
+    if is_dask_namespace(xp):
+        meta_xp = meta_namespace(cond, fill_value, *args_, xp=xp)
+        # map_blocks doesn't descend into tuples of Arrays
+        return xp.map_blocks(_apply_where, cond, f1, f2, fill_value, *args_, xp=meta_xp)
+    return _apply_where(cond, f1, f2, fill_value, *args_, xp=xp)
+
+
+def _apply_where(  # numpydoc ignore=PR01,RT01
+    cond: Array,
+    f1: Callable[..., Array],
+    f2: Callable[..., Array] | None,
+    fill_value: Array | int | float | complex | bool | None,
+    *args: Array,
+    xp: ModuleType,
+) -> Array:
+    """Helper of `apply_where`. On Dask, this runs on a single chunk."""
+
+    if not capabilities(xp, device=_compat.device(cond))["boolean indexing"]:
+        # jax.jit does not support assignment by boolean mask
+        return xp.where(cond, f1(*args), f2(*args) if f2 is not None else fill_value)
+
+    temp1 = f1(*(arr[cond] for arr in args))
+
+    if f2 is None:
+        dtype = xp.result_type(temp1, fill_value)
+        if isinstance(fill_value, int | float | complex):
+            out = xp.full_like(cond, dtype=dtype, fill_value=fill_value)
+        else:
+            out = xp.astype(fill_value, dtype, copy=True)
+    else:
+        ncond = ~cond
+        temp2 = f2(*(arr[ncond] for arr in args))
+        dtype = xp.result_type(temp1, temp2)
+        out = xp.empty_like(cond, dtype=dtype)
+        out = at(out, ncond).set(temp2)
+
+    return at(out, cond).set(temp1)
+
+
+def atleast_nd(x: Array, /, *, ndim: int, xp: ModuleType | None = None) -> Array:
+    """
+    Recursively expand the dimension of an array to at least `ndim`.
+
+    Parameters
+    ----------
+    x : array
+        Input array.
+    ndim : int
+        The minimum number of dimensions for the result.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array with ``res.ndim`` >= `ndim`.
+        If ``x.ndim`` >= `ndim`, `x` is returned.
+        If ``x.ndim`` < `ndim`, `x` is expanded by prepending new axes
+        until ``res.ndim`` equals `ndim`.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.asarray([1])
+    >>> xpx.atleast_nd(x, ndim=3, xp=xp)
+    Array([[[1]]], dtype=array_api_strict.int64)
+
+    >>> x = xp.asarray([[[1, 2],
+    ...                  [3, 4]]])
+    >>> xpx.atleast_nd(x, ndim=1, xp=xp) is x
+    True
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if x.ndim < ndim:
+        x = xp.expand_dims(x, axis=0)
+        x = atleast_nd(x, ndim=ndim, xp=xp)
+    return x
+
+
+# `float` in signature to accept `math.nan` for Dask.
+# `int`s are still accepted as `float` is a superclass of `int` in typing
+def broadcast_shapes(*shapes: tuple[float | None, ...]) -> tuple[int | None, ...]:
+    """
+    Compute the shape of the broadcasted arrays.
+
+    Duplicates :func:`numpy.broadcast_shapes`, with additional support for
+    None and NaN sizes.
+
+    This is equivalent to ``xp.broadcast_arrays(arr1, arr2, ...)[0].shape``
+    without needing to worry about the backend potentially deep copying
+    the arrays.
+
+    Parameters
+    ----------
+    *shapes : tuple[int | None, ...]
+        Shapes of the arrays to broadcast.
+
+    Returns
+    -------
+    tuple[int | None, ...]
+        The shape of the broadcasted arrays.
+
+    See Also
+    --------
+    numpy.broadcast_shapes : Equivalent NumPy function.
+    array_api.broadcast_arrays : Function to broadcast actual arrays.
+
+    Notes
+    -----
+    This function accepts the Array API's ``None`` for unknown sizes,
+    as well as Dask's non-standard ``math.nan``.
+    Regardless of input, the output always contains ``None`` for unknown sizes.
+
+    Examples
+    --------
+    >>> import array_api_extra as xpx
+    >>> xpx.broadcast_shapes((2, 3), (2, 1))
+    (2, 3)
+    >>> xpx.broadcast_shapes((4, 2, 3), (2, 1), (1, 3))
+    (4, 2, 3)
+    """
+    if not shapes:
+        return ()  # Match NumPy output
+
+    ndim = max(len(shape) for shape in shapes)
+    out: list[int | None] = []
+    for axis in range(-ndim, 0):
+        sizes = {shape[axis] for shape in shapes if axis >= -len(shape)}
+        # Dask uses NaN for unknown shape, which predates the Array API spec for None
+        none_size = None in sizes or math.nan in sizes  # noqa: PLW0177
+        sizes -= {1, None, math.nan}
+        if len(sizes) > 1:
+            msg = (
+                "shape mismatch: objects cannot be broadcast to a single shape: "
+                f"{shapes}."
+            )
+            raise ValueError(msg)
+        out.append(None if none_size else cast(int, sizes.pop()) if sizes else 1)
+
+    return tuple(out)
+
+
+def cov(m: Array, /, *, xp: ModuleType | None = None) -> Array:
+    """
+    Estimate a covariance matrix.
+
+    Covariance indicates the level to which two variables vary together.
+    If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,
+    then the covariance matrix element :math:`C_{ij}` is the covariance of
+    :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance
+    of :math:`x_i`.
+
+    This provides a subset of the functionality of ``numpy.cov``.
+
+    Parameters
+    ----------
+    m : array
+        A 1-D or 2-D array containing multiple variables and observations.
+        Each row of `m` represents a variable, and each column a single
+        observation of all those variables.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `m`. Default: infer.
+
+    Returns
+    -------
+    array
+        The covariance matrix of the variables.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+
+    Consider two variables, :math:`x_0` and :math:`x_1`, which
+    correlate perfectly, but in opposite directions:
+
+    >>> x = xp.asarray([[0, 2], [1, 1], [2, 0]]).T
+    >>> x
+    Array([[0, 1, 2],
+           [2, 1, 0]], dtype=array_api_strict.int64)
+
+    Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance
+    matrix shows this clearly:
+
+    >>> xpx.cov(x, xp=xp)
+    Array([[ 1., -1.],
+           [-1.,  1.]], dtype=array_api_strict.float64)
+
+    Note that element :math:`C_{0,1}`, which shows the correlation between
+    :math:`x_0` and :math:`x_1`, is negative.
+
+    Further, note how `x` and `y` are combined:
+
+    >>> x = xp.asarray([-2.1, -1,  4.3])
+    >>> y = xp.asarray([3,  1.1,  0.12])
+    >>> X = xp.stack((x, y), axis=0)
+    >>> xpx.cov(X, xp=xp)
+    Array([[11.71      , -4.286     ],
+           [-4.286     ,  2.14413333]], dtype=array_api_strict.float64)
+
+    >>> xpx.cov(x, xp=xp)
+    Array(11.71, dtype=array_api_strict.float64)
+
+    >>> xpx.cov(y, xp=xp)
+    Array(2.14413333, dtype=array_api_strict.float64)
+    """
+    if xp is None:
+        xp = array_namespace(m)
+
+    m = xp.asarray(m, copy=True)
+    dtype = (
+        xp.float64 if xp.isdtype(m.dtype, "integral") else xp.result_type(m, xp.float64)
+    )
+
+    m = atleast_nd(m, ndim=2, xp=xp)
+    m = xp.astype(m, dtype)
+
+    avg = _helpers.mean(m, axis=1, xp=xp)
+
+    m_shape = eager_shape(m)
+    fact = m_shape[1] - 1
+
+    if fact <= 0:
+        warnings.warn("Degrees of freedom <= 0 for slice", RuntimeWarning, stacklevel=2)
+        fact = 0
+
+    m -= avg[:, None]
+    m_transpose = m.T
+    if xp.isdtype(m_transpose.dtype, "complex floating"):
+        m_transpose = xp.conj(m_transpose)
+    c = m @ m_transpose
+    c /= fact
+    axes = tuple(axis for axis, length in enumerate(c.shape) if length == 1)
+    return xp.squeeze(c, axis=axes)
+
+
+def one_hot(
+    x: Array,
+    /,
+    num_classes: int,
+    *,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in `array_api_extra._delegation.py`."""
+    # TODO: Benchmark whether this is faster on the NumPy backend:
+    # if is_numpy_array(x):
+    #     out = xp.zeros((x.size, num_classes), dtype=dtype)
+    #     out[xp.arange(x.size), xp.reshape(x, (-1,))] = 1
+    #     return xp.reshape(out, (*x.shape, num_classes))
+    range_num_classes = xp.arange(num_classes, dtype=x.dtype, device=_compat.device(x))
+    return x[..., xp.newaxis] == range_num_classes
+
+
+def create_diagonal(
+    x: Array, /, *, offset: int = 0, xp: ModuleType | None = None
+) -> Array:
+    """
+    Construct a diagonal array.
+
+    Parameters
+    ----------
+    x : array
+        An array having shape ``(*batch_dims, k)``.
+    offset : int, optional
+        Offset from the leading diagonal (default is ``0``).
+        Use positive ints for diagonals above the leading diagonal,
+        and negative ints for diagonals below the leading diagonal.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        An array having shape ``(*batch_dims, k+abs(offset), k+abs(offset))`` with `x`
+        on the diagonal (offset by `offset`).
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.asarray([2, 4, 8])
+
+    >>> xpx.create_diagonal(x, xp=xp)
+    Array([[2, 0, 0],
+           [0, 4, 0],
+           [0, 0, 8]], dtype=array_api_strict.int64)
+
+    >>> xpx.create_diagonal(x, offset=-2, xp=xp)
+    Array([[0, 0, 0, 0, 0],
+           [0, 0, 0, 0, 0],
+           [2, 0, 0, 0, 0],
+           [0, 4, 0, 0, 0],
+           [0, 0, 8, 0, 0]], dtype=array_api_strict.int64)
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if x.ndim == 0:
+        err_msg = "`x` must be at least 1-dimensional."
+        raise ValueError(err_msg)
+
+    x_shape = eager_shape(x)
+    batch_dims = x_shape[:-1]
+    n = x_shape[-1] + abs(offset)
+    diag = xp.zeros((*batch_dims, n**2), dtype=x.dtype, device=_compat.device(x))
+
+    target_slice = slice(
+        offset if offset >= 0 else abs(offset) * n,
+        min(n * (n - offset), diag.shape[-1]),
+        n + 1,
+    )
+    for index in ndindex(*batch_dims):
+        diag = at(diag)[(*index, target_slice)].set(x[(*index, slice(None))])
+    return xp.reshape(diag, (*batch_dims, n, n))
+
+
+def default_dtype(
+    xp: ModuleType,
+    kind: Literal[
+        "real floating", "complex floating", "integral", "indexing"
+    ] = "real floating",
+    *,
+    device: Device | None = None,
+) -> DType:
+    """
+    Return the default dtype for the given namespace and device.
+
+    This is a convenience shorthand for
+    ``xp.__array_namespace_info__().default_dtypes(device=device)[kind]``.
+
+    Parameters
+    ----------
+    xp : array_namespace
+        The standard-compatible namespace for which to get the default dtype.
+    kind : {'real floating', 'complex floating', 'integral', 'indexing'}, optional
+        The kind of dtype to return. Default is 'real floating'.
+    device : Device, optional
+        The device for which to get the default dtype. Default: current device.
+
+    Returns
+    -------
+    dtype
+        The default dtype for the given namespace, kind, and device.
+    """
+    dtypes = xp.__array_namespace_info__().default_dtypes(device=device)
+    try:
+        return dtypes[kind]
+    except KeyError as e:
+        domain = ("real floating", "complex floating", "integral", "indexing")
+        assert set(dtypes) == set(domain), f"Non-compliant namespace: {dtypes}"
+        msg = f"Unknown kind '{kind}'. Expected one of {domain}."
+        raise ValueError(msg) from e
+
+
+def expand_dims(
+    a: Array, /, *, axis: int | tuple[int, ...] = (0,), xp: ModuleType | None = None
+) -> Array:
+    """
+    Expand the shape of an array.
+
+    Insert (a) new axis/axes that will appear at the position(s) specified by
+    `axis` in the expanded array shape.
+
+    This is ``xp.expand_dims`` for `axis` an int *or a tuple of ints*.
+    Roughly equivalent to ``numpy.expand_dims`` for NumPy arrays.
+
+    Parameters
+    ----------
+    a : array
+        Array to have its shape expanded.
+    axis : int or tuple of ints, optional
+        Position(s) in the expanded axes where the new axis (or axes) is/are placed.
+        If multiple positions are provided, they should be unique (note that a position
+        given by a positive index could also be referred to by a negative index -
+        that will also result in an error).
+        Default: ``(0,)``.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `a`. Default: infer.
+
+    Returns
+    -------
+    array
+        `a` with an expanded shape.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.asarray([1, 2])
+    >>> x.shape
+    (2,)
+
+    The following is equivalent to ``x[xp.newaxis, :]`` or ``x[xp.newaxis]``:
+
+    >>> y = xpx.expand_dims(x, axis=0, xp=xp)
+    >>> y
+    Array([[1, 2]], dtype=array_api_strict.int64)
+    >>> y.shape
+    (1, 2)
+
+    The following is equivalent to ``x[:, xp.newaxis]``:
+
+    >>> y = xpx.expand_dims(x, axis=1, xp=xp)
+    >>> y
+    Array([[1],
+           [2]], dtype=array_api_strict.int64)
+    >>> y.shape
+    (2, 1)
+
+    ``axis`` may also be a tuple:
+
+    >>> y = xpx.expand_dims(x, axis=(0, 1), xp=xp)
+    >>> y
+    Array([[[1, 2]]], dtype=array_api_strict.int64)
+
+    >>> y = xpx.expand_dims(x, axis=(2, 0), xp=xp)
+    >>> y
+    Array([[[1],
+            [2]]], dtype=array_api_strict.int64)
+    """
+    if xp is None:
+        xp = array_namespace(a)
+
+    if not isinstance(axis, tuple):
+        axis = (axis,)
+    ndim = a.ndim + len(axis)
+    if axis != () and (min(axis) < -ndim or max(axis) >= ndim):
+        err_msg = (
+            f"a provided axis position is out of bounds for array of dimension {a.ndim}"
+        )
+        raise IndexError(err_msg)
+    axis = tuple(dim % ndim for dim in axis)
+    if len(set(axis)) != len(axis):
+        err_msg = "Duplicate dimensions specified in `axis`."
+        raise ValueError(err_msg)
+    for i in sorted(axis):
+        a = xp.expand_dims(a, axis=i)
+    return a
+
+
+def isclose(
+    a: Array | complex,
+    b: Array | complex,
+    *,
+    rtol: float = 1e-05,
+    atol: float = 1e-08,
+    equal_nan: bool = False,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in array_api_extra._delegation."""
+    a, b = asarrays(a, b, xp=xp)
+
+    a_inexact = xp.isdtype(a.dtype, ("real floating", "complex floating"))
+    b_inexact = xp.isdtype(b.dtype, ("real floating", "complex floating"))
+    if a_inexact or b_inexact:
+        # prevent warnings on NumPy and Dask on inf - inf
+        mxp = meta_namespace(a, b, xp=xp)
+        out = apply_where(
+            xp.isinf(a) | xp.isinf(b),
+            (a, b),
+            lambda a, b: mxp.isinf(a) & mxp.isinf(b) & (mxp.sign(a) == mxp.sign(b)),  # pyright: ignore[reportUnknownArgumentType]
+            # Note: inf <= inf is True!
+            lambda a, b: mxp.abs(a - b) <= (atol + rtol * mxp.abs(b)),  # pyright: ignore[reportUnknownArgumentType]
+            xp=xp,
+        )
+        if equal_nan:
+            out = xp.where(xp.isnan(a) & xp.isnan(b), True, out)
+        return out
+
+    if xp.isdtype(a.dtype, "bool") or xp.isdtype(b.dtype, "bool"):
+        if atol >= 1 or rtol >= 1:
+            return xp.ones_like(a == b)
+        return a == b
+
+    # integer types
+    atol = int(atol)
+    if rtol == 0:
+        return xp.abs(a - b) <= atol
+
+    # Don't rely on OverflowError, as it is not guaranteed by the Array API.
+    nrtol = int(1.0 / rtol)
+    if nrtol > xp.iinfo(b.dtype).max:
+        # rtol * max_int < 1, so it's inconsequential
+        return xp.abs(a - b) <= atol
+    return xp.abs(a - b) <= (atol + xp.abs(b) // nrtol)
+
+
+def kron(
+    a: Array | complex,
+    b: Array | complex,
+    /,
+    *,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Kronecker product of two arrays.
+
+    Computes the Kronecker product, a composite array made of blocks of the
+    second array scaled by the first.
+
+    Equivalent to ``numpy.kron`` for NumPy arrays.
+
+    Parameters
+    ----------
+    a, b : Array | int | float | complex
+        Input arrays or scalars. At least one must be an array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `a` and `b`. Default: infer.
+
+    Returns
+    -------
+    array
+        The Kronecker product of `a` and `b`.
+
+    Notes
+    -----
+    The function assumes that the number of dimensions of `a` and `b`
+    are the same, if necessary prepending the smallest with ones.
+    If ``a.shape = (r0,r1,..,rN)`` and ``b.shape = (s0,s1,...,sN)``,
+    the Kronecker product has shape ``(r0*s0, r1*s1, ..., rN*SN)``.
+    The elements are products of elements from `a` and `b`, organized
+    explicitly by::
+
+        kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]
+
+    where::
+
+        kt = it * st + jt,  t = 0,...,N
+
+    In the common 2-D case (N=1), the block structure can be visualized::
+
+        [[ a[0,0]*b,   a[0,1]*b,  ... , a[0,-1]*b  ],
+         [  ...                              ...   ],
+         [ a[-1,0]*b,  a[-1,1]*b, ... , a[-1,-1]*b ]]
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> xpx.kron(xp.asarray([1, 10, 100]), xp.asarray([5, 6, 7]), xp=xp)
+    Array([  5,   6,   7,  50,  60,  70, 500,
+           600, 700], dtype=array_api_strict.int64)
+
+    >>> xpx.kron(xp.asarray([5, 6, 7]), xp.asarray([1, 10, 100]), xp=xp)
+    Array([  5,  50, 500,   6,  60, 600,   7,
+            70, 700], dtype=array_api_strict.int64)
+
+    >>> xpx.kron(xp.eye(2), xp.ones((2, 2)), xp=xp)
+    Array([[1., 1., 0., 0.],
+           [1., 1., 0., 0.],
+           [0., 0., 1., 1.],
+           [0., 0., 1., 1.]], dtype=array_api_strict.float64)
+
+    >>> a = xp.reshape(xp.arange(100), (2, 5, 2, 5))
+    >>> b = xp.reshape(xp.arange(24), (2, 3, 4))
+    >>> c = xpx.kron(a, b, xp=xp)
+    >>> c.shape
+    (2, 10, 6, 20)
+    >>> I = (1, 3, 0, 2)
+    >>> J = (0, 2, 1)
+    >>> J1 = (0,) + J             # extend to ndim=4
+    >>> S1 = (1,) + b.shape
+    >>> K = tuple(xp.asarray(I) * xp.asarray(S1) + xp.asarray(J1))
+    >>> c[K] == a[I]*b[J]
+    Array(True, dtype=array_api_strict.bool)
+    """
+    if xp is None:
+        xp = array_namespace(a, b)
+    a, b = asarrays(a, b, xp=xp)
+
+    singletons = (1,) * (b.ndim - a.ndim)
+    a = cast(Array, xp.broadcast_to(a, singletons + a.shape))
+
+    nd_b, nd_a = b.ndim, a.ndim
+    nd_max = max(nd_b, nd_a)
+    if nd_a == 0 or nd_b == 0:
+        return xp.multiply(a, b)
+
+    a_shape = eager_shape(a)
+    b_shape = eager_shape(b)
+
+    # Equalise the shapes by prepending smaller one with 1s
+    a_shape = (1,) * max(0, nd_b - nd_a) + a_shape
+    b_shape = (1,) * max(0, nd_a - nd_b) + b_shape
+
+    # Insert empty dimensions
+    a_arr = expand_dims(a, axis=tuple(range(nd_b - nd_a)), xp=xp)
+    b_arr = expand_dims(b, axis=tuple(range(nd_a - nd_b)), xp=xp)
+
+    # Compute the product
+    a_arr = expand_dims(a_arr, axis=tuple(range(1, nd_max * 2, 2)), xp=xp)
+    b_arr = expand_dims(b_arr, axis=tuple(range(0, nd_max * 2, 2)), xp=xp)
+    result = xp.multiply(a_arr, b_arr)
+
+    # Reshape back and return
+    res_shape = tuple(a_s * b_s for a_s, b_s in zip(a_shape, b_shape, strict=True))
+    return xp.reshape(result, res_shape)
+
+
+def nunique(x: Array, /, *, xp: ModuleType | None = None) -> Array:
+    """
+    Count the number of unique elements in an array.
+
+    Compatible with JAX and Dask, whose laziness would be otherwise
+    problematic.
+
+    Parameters
+    ----------
+    x : Array
+        Input array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array: 0-dimensional integer array
+        The number of unique elements in `x`. It can be lazy.
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if is_jax_array(x):
+        # size= is JAX-specific
+        # https://github.com/data-apis/array-api/issues/883
+        _, counts = xp.unique_counts(x, size=_compat.size(x))
+        return (counts > 0).sum()
+
+    # There are 3 general use cases:
+    # 1. backend has unique_counts and it returns an array with known shape
+    # 2. backend has unique_counts and it returns a None-sized array;
+    #    e.g. Dask, ndonnx
+    # 3. backend does not have unique_counts; e.g. wrapped JAX
+    if capabilities(xp, device=_compat.device(x))["data-dependent shapes"]:
+        # xp has unique_counts; O(n) complexity
+        _, counts = xp.unique_counts(x)
+        n = _compat.size(counts)
+        if n is None:
+            return xp.sum(xp.ones_like(counts))
+        return xp.asarray(n, device=_compat.device(x))
+
+    # xp does not have unique_counts; O(n*logn) complexity
+    x = xp.reshape(x, (-1,))
+    x = xp.sort(x)
+    mask = x != xp.roll(x, -1)
+    default_int = default_dtype(xp, "integral", device=_compat.device(x))
+    return xp.maximum(
+        # Special cases:
+        # - array is size 0
+        # - array has all elements equal to each other
+        xp.astype(xp.any(~mask), default_int),
+        xp.sum(xp.astype(mask, default_int)),
+    )
+
+
+def pad(
+    x: Array,
+    pad_width: int | tuple[int, int] | Sequence[tuple[int, int]],
+    *,
+    constant_values: complex = 0,
+    xp: ModuleType,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """See docstring in `array_api_extra._delegation.py`."""
+    # make pad_width a list of length-2 tuples of ints
+    if isinstance(pad_width, int):
+        pad_width_seq = [(pad_width, pad_width)] * x.ndim
+    elif (
+        isinstance(pad_width, tuple)
+        and len(pad_width) == 2
+        and all(isinstance(i, int) for i in pad_width)
+    ):
+        pad_width_seq = [cast(tuple[int, int], pad_width)] * x.ndim
+    else:
+        pad_width_seq = cast(list[tuple[int, int]], list(pad_width))
+
+    slices: list[slice] = []
+    newshape: list[int] = []
+    for ax, w_tpl in enumerate(pad_width_seq):
+        if len(w_tpl) != 2:
+            msg = f"expect a 2-tuple (before, after), got {w_tpl}."
+            raise ValueError(msg)
+
+        sh = eager_shape(x)[ax]
+
+        if w_tpl[0] == 0 and w_tpl[1] == 0:
+            sl = slice(None, None, None)
+        else:
+            stop: int | None
+            start, stop = w_tpl
+            stop = None if stop == 0 else -stop
+
+            sl = slice(start, stop, None)
+            sh += w_tpl[0] + w_tpl[1]
+
+        newshape.append(sh)
+        slices.append(sl)
+
+    padded = xp.full(
+        tuple(newshape),
+        fill_value=constant_values,
+        dtype=x.dtype,
+        device=_compat.device(x),
+    )
+    return at(padded, tuple(slices)).set(x)
+
+
+def setdiff1d(
+    x1: Array | complex,
+    x2: Array | complex,
+    /,
+    *,
+    assume_unique: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Find the set difference of two arrays.
+
+    Return the unique values in `x1` that are not in `x2`.
+
+    Parameters
+    ----------
+    x1 : array | int | float | complex | bool
+        Input array.
+    x2 : array
+        Input comparison array.
+    assume_unique : bool
+        If ``True``, the input arrays are both assumed to be unique, which
+        can speed up the calculation. Default is ``False``.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x1` and `x2`. Default: infer.
+
+    Returns
+    -------
+    array
+        1D array of values in `x1` that are not in `x2`. The result
+        is sorted when `assume_unique` is ``False``, but otherwise only sorted
+        if the input is sorted.
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+
+    >>> x1 = xp.asarray([1, 2, 3, 2, 4, 1])
+    >>> x2 = xp.asarray([3, 4, 5, 6])
+    >>> xpx.setdiff1d(x1, x2, xp=xp)
+    Array([1, 2], dtype=array_api_strict.int64)
+    """
+    if xp is None:
+        xp = array_namespace(x1, x2)
+    # https://github.com/microsoft/pyright/issues/10103
+    x1_, x2_ = asarrays(x1, x2, xp=xp)
+
+    if assume_unique:
+        x1_ = xp.reshape(x1_, (-1,))
+        x2_ = xp.reshape(x2_, (-1,))
+    else:
+        x1_ = xp.unique_values(x1_)
+        x2_ = xp.unique_values(x2_)
+
+    return x1_[_helpers.in1d(x1_, x2_, assume_unique=True, invert=True, xp=xp)]
+
+
+def sinc(x: Array, /, *, xp: ModuleType | None = None) -> Array:
+    r"""
+    Return the normalized sinc function.
+
+    The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument
+    :math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not
+    only everywhere continuous but also infinitely differentiable.
+
+    .. note::
+
+        Note the normalization factor of ``pi`` used in the definition.
+        This is the most commonly used definition in signal processing.
+        Use ``sinc(x / xp.pi)`` to obtain the unnormalized sinc function
+        :math:`\sin(x)/x` that is more common in mathematics.
+
+    Parameters
+    ----------
+    x : array
+        Array (possibly multi-dimensional) of values for which to calculate
+        ``sinc(x)``. Must have a real floating point dtype.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    array
+        ``sinc(x)`` calculated elementwise, which has the same shape as the input.
+
+    Notes
+    -----
+    The name sinc is short for "sine cardinal" or "sinus cardinalis".
+
+    The sinc function is used in various signal processing applications,
+    including in anti-aliasing, in the construction of a Lanczos resampling
+    filter, and in interpolation.
+
+    For bandlimited interpolation of discrete-time signals, the ideal
+    interpolation kernel is proportional to the sinc function.
+
+    References
+    ----------
+    #. Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web
+       Resource. https://mathworld.wolfram.com/SincFunction.html
+    #. Wikipedia, "Sinc function",
+       https://en.wikipedia.org/wiki/Sinc_function
+
+    Examples
+    --------
+    >>> import array_api_strict as xp
+    >>> import array_api_extra as xpx
+    >>> x = xp.linspace(-4, 4, 41)
+    >>> xpx.sinc(x, xp=xp)
+    Array([-3.89817183e-17, -4.92362781e-02,
+           -8.40918587e-02, -8.90384387e-02,
+           -5.84680802e-02,  3.89817183e-17,
+            6.68206631e-02,  1.16434881e-01,
+            1.26137788e-01,  8.50444803e-02,
+           -3.89817183e-17, -1.03943254e-01,
+           -1.89206682e-01, -2.16236208e-01,
+           -1.55914881e-01,  3.89817183e-17,
+            2.33872321e-01,  5.04551152e-01,
+            7.56826729e-01,  9.35489284e-01,
+            1.00000000e+00,  9.35489284e-01,
+            7.56826729e-01,  5.04551152e-01,
+            2.33872321e-01,  3.89817183e-17,
+           -1.55914881e-01, -2.16236208e-01,
+           -1.89206682e-01, -1.03943254e-01,
+           -3.89817183e-17,  8.50444803e-02,
+            1.26137788e-01,  1.16434881e-01,
+            6.68206631e-02,  3.89817183e-17,
+           -5.84680802e-02, -8.90384387e-02,
+           -8.40918587e-02, -4.92362781e-02,
+           -3.89817183e-17], dtype=array_api_strict.float64)
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if not xp.isdtype(x.dtype, "real floating"):
+        err_msg = "`x` must have a real floating data type."
+        raise ValueError(err_msg)
+    # no scalars in `where` - array-api#807
+    y = xp.pi * xp.where(
+        xp.astype(x, xp.bool),
+        x,
+        xp.asarray(xp.finfo(x.dtype).eps, dtype=x.dtype, device=_compat.device(x)),
+    )
+    return xp.sin(y) / y
diff --git a/src/array_api_extra/_lib/_lazy.py b/src/array_api_extra/_lib/_lazy.py
new file mode 100644
index 00000000..d5095001
--- /dev/null
+++ b/src/array_api_extra/_lib/_lazy.py
@@ -0,0 +1,357 @@
+"""Public API Functions."""
+
+from __future__ import annotations
+
+import math
+from collections.abc import Callable, Sequence
+from functools import partial, wraps
+from types import ModuleType
+from typing import TYPE_CHECKING, Any, ParamSpec, TypeAlias, cast, overload
+
+from ._funcs import broadcast_shapes
+from ._utils import _compat
+from ._utils._compat import (
+    array_namespace,
+    is_dask_namespace,
+    is_jax_namespace,
+)
+from ._utils._helpers import is_python_scalar
+from ._utils._typing import Array, DType
+
+if TYPE_CHECKING:  # pragma: no cover
+    import numpy as np
+    from numpy.typing import ArrayLike
+
+    NumPyObject: TypeAlias = np.ndarray[Any, Any] | np.generic
+else:
+    # Sphinx hack
+    NumPyObject = Any
+
+P = ParamSpec("P")
+
+
+@overload
+def lazy_apply(  # type: ignore[valid-type]
+    func: Callable[P, Array | ArrayLike],
+    *args: Array | complex | None,
+    shape: tuple[int | None, ...] | None = None,
+    dtype: DType | None = None,
+    as_numpy: bool = False,
+    xp: ModuleType | None = None,
+    **kwargs: P.kwargs,  # pyright: ignore[reportGeneralTypeIssues]
+) -> Array: ...  # numpydoc ignore=GL08
+
+
+@overload
+def lazy_apply(  # type: ignore[valid-type]
+    func: Callable[P, Sequence[Array | ArrayLike]],
+    *args: Array | complex | None,
+    shape: Sequence[tuple[int | None, ...]],
+    dtype: Sequence[DType] | None = None,
+    as_numpy: bool = False,
+    xp: ModuleType | None = None,
+    **kwargs: P.kwargs,  # pyright: ignore[reportGeneralTypeIssues]
+) -> tuple[Array, ...]: ...  # numpydoc ignore=GL08
+
+
+def lazy_apply(  # type: ignore[valid-type]  # numpydoc ignore=GL07,SA04
+    func: Callable[P, Array | ArrayLike | Sequence[Array | ArrayLike]],
+    *args: Array | complex | None,
+    shape: tuple[int | None, ...] | Sequence[tuple[int | None, ...]] | None = None,
+    dtype: DType | Sequence[DType] | None = None,
+    as_numpy: bool = False,
+    xp: ModuleType | None = None,
+    **kwargs: P.kwargs,  # pyright: ignore[reportGeneralTypeIssues]
+) -> Array | tuple[Array, ...]:
+    """
+    Lazily apply an eager function.
+
+    If the backend of the input arrays is lazy, e.g. Dask or jitted JAX, the execution
+    of the function is delayed until the graph is materialized; if it's eager, the
+    function is executed immediately.
+
+    Parameters
+    ----------
+    func : callable
+        The function to apply.
+
+        It must accept one or more array API compliant arrays as positional arguments.
+        If `as_numpy=True`, inputs are converted to NumPy before they are passed to
+        `func`.
+        It must return either a single array-like or a sequence of array-likes.
+
+        `func` must be a pure function, i.e. without side effects, as depending on the
+        backend it may be executed more than once or never.
+    *args : Array | int | float | complex | bool | None
+        One or more Array API compliant arrays, Python scalars, or None's.
+
+        If `as_numpy=True`, you need to be able to apply :func:`numpy.asarray` to
+        non-None args to convert them to NumPy; read notes below about specific
+        backends.
+    shape : tuple[int | None, ...] | Sequence[tuple[int | None, ...]], optional
+        Output shape or sequence of output shapes, one for each output of `func`.
+        Default: assume single output and broadcast shapes of the input arrays.
+    dtype : DType | Sequence[DType], optional
+        Output dtype or sequence of output dtypes, one for each output of `func`.
+        dtype(s) must belong to the same array namespace as the input arrays.
+        Default: infer the result type(s) from the input arrays.
+    as_numpy : bool, optional
+        If True, convert the input arrays to NumPy before passing them to `func`.
+        This is particularly useful to make NumPy-only functions, e.g. written in Cython
+       or Numba, work transparently with array API-compliant arrays.
+        Default: False.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `args`. Default: infer.
+    **kwargs : Any, optional
+        Additional keyword arguments to pass verbatim to `func`.
+        They cannot contain Array objects.
+
+    Returns
+    -------
+    Array | tuple[Array, ...]
+        The result(s) of `func` applied to the input arrays, wrapped in the same
+        array namespace as the inputs.
+        If shape is omitted or a single `tuple[int | None, ...]`, return a single array.
+        Otherwise, return a tuple of arrays.
+
+    Notes
+    -----
+    JAX
+        This allows applying eager functions to jitted JAX arrays, which are lazy.
+        The function won't be applied until the JAX array is materialized.
+        When running inside ``jax.jit``, `shape` must be fully known, i.e. it cannot
+        contain any `None` elements.
+
+        .. warning::
+
+            `func` must never raise inside ``jax.jit``, as the resulting behavior is
+            undefined.
+
+        Using this with `as_numpy=False` is particularly useful to apply non-jittable
+        JAX functions to arrays on GPU devices.
+        If ``as_numpy=True``, the :doc:`jax:transfer_guard` may prevent arrays on a GPU
+        device from being transferred back to CPU. This is treated as an implicit
+        transfer.
+
+    PyTorch, CuPy
+        If ``as_numpy=True``, these backends raise by default if you attempt to convert
+        arrays on a GPU device to NumPy.
+
+    Sparse
+        If ``as_numpy=True``, by default sparse prevents implicit densification through
+        :func:`numpy.asarray`. `This safety mechanism can be disabled
+        <https://sparse.pydata.org/en/stable/operations.html#package-configuration>`_.
+
+    Dask
+        This allows applying eager functions to Dask arrays.
+        The Dask graph won't be computed until the user calls ``compute()`` or
+        ``persist()`` down the line.
+
+        The function name will be prominently visible on the user-facing Dask
+        dashboard and on Prometheus metrics, so it is recommended for it to be
+        meaningful.
+
+        `lazy_apply` doesn't know if `func` reduces along any axes; also, shape
+        changes are non-trivial in chunked Dask arrays. For these reasons, all inputs
+        will be rechunked into a single chunk.
+
+        .. warning::
+
+           The whole operation needs to fit in memory all at once on a single worker.
+
+        The outputs will also be returned as a single chunk and you should consider
+        rechunking them into smaller chunks afterwards.
+
+        If you want to distribute the calculation across multiple workers, you
+        should use :func:`dask.array.map_blocks`, :func:`dask.array.map_overlap`,
+        :func:`dask.array.blockwise`, or a native Dask wrapper instead of
+        `lazy_apply`.
+
+    Dask wrapping around other backends
+        If ``as_numpy=False``, `func` will receive in input eager arrays of the meta
+        namespace, as defined by the ``._meta`` attribute of the input Dask arrays.
+        The outputs of `func` will be wrapped by the meta namespace, and then wrapped
+        again by Dask.
+
+    Raises
+    ------
+    ValueError
+        When ``xp=jax.numpy``, the output `shape` is unknown (it contains ``None`` on
+        one or more axes) and this function was called inside ``jax.jit``.
+    RuntimeError
+        When ``xp=sparse`` and auto-densification is disabled.
+    Exception (backend-specific)
+        When the backend disallows implicit device to host transfers and the input
+        arrays are on a non-CPU device, e.g. on GPU.
+
+    See Also
+    --------
+    jax.transfer_guard
+    jax.pure_callback
+    dask.array.map_blocks
+    dask.array.map_overlap
+    dask.array.blockwise
+    """
+    args_not_none = [arg for arg in args if arg is not None]
+    array_args = [arg for arg in args_not_none if not is_python_scalar(arg)]
+    if not array_args:
+        msg = "Must have at least one argument array"
+        raise ValueError(msg)
+    if xp is None:
+        xp = array_namespace(*args)
+
+    # Normalize and validate shape and dtype
+    shapes: list[tuple[int | None, ...]]
+    dtypes: list[DType]
+    multi_output = False
+
+    if shape is None:
+        shapes = [broadcast_shapes(*(arg.shape for arg in array_args))]
+    elif all(isinstance(s, int | None) for s in shape):
+        # Do not test for shape to be a tuple
+        # https://github.com/data-apis/array-api/issues/891#issuecomment-2637430522
+        shapes = [cast(tuple[int | None, ...], shape)]
+    else:
+        shapes = list(shape)  # type: ignore[arg-type]  # pyright: ignore[reportAssignmentType]
+        multi_output = True
+
+    if dtype is None:
+        dtypes = [xp.result_type(*args_not_none)] * len(shapes)
+    elif multi_output:
+        if not isinstance(dtype, Sequence):
+            msg = "Got multiple shapes but only one dtype"
+            raise ValueError(msg)
+        dtypes = list(dtype)  # pyright: ignore[reportUnknownArgumentType]
+    else:
+        if isinstance(dtype, Sequence):
+            msg = "Got single shape but multiple dtypes"
+            raise ValueError(msg)
+
+        dtypes = [dtype]
+
+    if len(shapes) != len(dtypes):
+        msg = f"Got {len(shapes)} shapes and {len(dtypes)} dtypes"
+        raise ValueError(msg)
+    del shape
+    del dtype
+    # End of shape and dtype parsing
+
+    # Backend-specific branches
+    if is_dask_namespace(xp):
+        import dask
+
+        metas: list[Array] = [arg._meta for arg in array_args]  # pylint: disable=protected-access    # pyright: ignore[reportAttributeAccessIssue]
+        meta_xp = array_namespace(*metas)
+
+        wrapped = dask.delayed(  # type: ignore[attr-defined]  # pyright: ignore[reportPrivateImportUsage]
+            _lazy_apply_wrapper(func, as_numpy, multi_output, meta_xp),
+            pure=True,
+        )
+        # This finalizes each arg, which is the same as arg.rechunk(-1).
+        # Please read docstring above for why we're not using
+        # dask.array.map_blocks or dask.array.blockwise!
+        delayed_out = wrapped(*args, **kwargs)
+
+        out = tuple(
+            xp.from_delayed(
+                delayed_out[i],  # pyright: ignore[reportIndexIssue]
+                # Dask's unknown shapes diverge from the Array API specification
+                shape=tuple(math.nan if s is None else s for s in shape),
+                dtype=dtype,
+                meta=metas[0],
+            )
+            for i, (shape, dtype) in enumerate(zip(shapes, dtypes, strict=True))
+        )
+
+    elif is_jax_namespace(xp) and _is_jax_jit_enabled(xp):
+        # Delay calling func with jax.pure_callback, which will forward to func eager
+        # JAX arrays. Do not use jax.pure_callback when running outside of the JIT,
+        # as it does not support raising exceptions:
+        # https://github.com/jax-ml/jax/issues/26102
+        import jax
+
+        if any(None in shape for shape in shapes):
+            msg = "Output shape must be fully known when running inside jax.jit"
+            raise ValueError(msg)
+
+        # Shield kwargs from being coerced into JAX arrays.
+        # jax.pure_callback calls jax.jit under the hood, but without the chance of
+        # passing static_argnames / static_argnums.
+        wrapped = _lazy_apply_wrapper(
+            partial(func, **kwargs), as_numpy, multi_output, xp
+        )
+
+        # suppress unused-ignore to run mypy in -e lint as well as -e dev
+        out = cast(  # type: ignore[bad-cast,unused-ignore]
+            tuple[Array, ...],
+            jax.pure_callback(
+                wrapped,
+                tuple(
+                    jax.ShapeDtypeStruct(shape, dtype)  # pyright: ignore[reportUnknownArgumentType]
+                    for shape, dtype in zip(shapes, dtypes, strict=True)
+                ),
+                *args,
+            ),
+        )
+
+    else:
+        # Eager backends, including non-jitted JAX
+        wrapped = _lazy_apply_wrapper(func, as_numpy, multi_output, xp)
+        out = wrapped(*args, **kwargs)
+
+    return out if multi_output else out[0]
+
+
+def _is_jax_jit_enabled(xp: ModuleType) -> bool:  # numpydoc ignore=PR01,RT01
+    """Return True if this function is being called inside ``jax.jit``."""
+    import jax  # pylint: disable=import-outside-toplevel
+
+    x = xp.asarray(False)
+    try:
+        return bool(x)
+    except jax.errors.TracerBoolConversionError:
+        return True
+
+
+def _lazy_apply_wrapper(  # numpydoc ignore=PR01,RT01
+    func: Callable[..., Array | ArrayLike | Sequence[Array | ArrayLike]],
+    as_numpy: bool,
+    multi_output: bool,
+    xp: ModuleType,
+) -> Callable[..., tuple[Array, ...]]:
+    """
+    Helper of `lazy_apply`.
+
+    Given a function that accepts one or more arrays as positional arguments and returns
+    a single array-like or a sequence of array-likes, return a function that accepts the
+    same number of Array API arrays and always returns a tuple of Array API array.
+
+    Any keyword arguments are passed through verbatim to the wrapped function.
+    """
+
+    # On Dask, @wraps causes the graph key to contain the wrapped function's name
+    @wraps(func)
+    def wrapper(
+        *args: Array | complex | None, **kwargs: Any
+    ) -> tuple[Array, ...]:  # numpydoc ignore=GL08
+        args_list = []
+        device = None
+        for arg in args:
+            if arg is not None and not is_python_scalar(arg):
+                if device is None:
+                    device = _compat.device(arg)
+                if as_numpy:
+                    import numpy as np
+
+                    arg = cast(Array, np.asarray(arg))  # pyright: ignore[reportInvalidCast] # noqa: PLW2901
+            args_list.append(arg)
+        assert device is not None
+
+        out = func(*args_list, **kwargs)
+
+        if multi_output:
+            assert isinstance(out, Sequence)
+            return tuple(xp.asarray(o, device=device) for o in out)
+        return (xp.asarray(out, device=device),)
+
+    return wrapper
diff --git a/src/array_api_extra/_lib/_testing.py b/src/array_api_extra/_lib/_testing.py
new file mode 100644
index 00000000..30e2f1ef
--- /dev/null
+++ b/src/array_api_extra/_lib/_testing.py
@@ -0,0 +1,304 @@
+"""
+Testing utilities.
+
+Note that this is private API; don't expect it to be stable.
+See also ..testing for public testing utilities.
+"""
+
+from __future__ import annotations
+
+import math
+from types import ModuleType
+from typing import Any, cast
+
+import numpy as np
+import pytest
+
+from ._utils._compat import (
+    array_namespace,
+    is_array_api_strict_namespace,
+    is_cupy_namespace,
+    is_dask_namespace,
+    is_jax_namespace,
+    is_numpy_namespace,
+    is_pydata_sparse_namespace,
+    is_torch_array,
+    is_torch_namespace,
+    to_device,
+)
+from ._utils._typing import Array, Device
+
+__all__ = ["as_numpy_array", "xp_assert_close", "xp_assert_equal", "xp_assert_less"]
+
+
+def _check_ns_shape_dtype(
+    actual: Array,
+    desired: Array,
+    check_dtype: bool,
+    check_shape: bool,
+    check_scalar: bool,
+) -> ModuleType:  # numpydoc ignore=RT03
+    """
+    Assert that namespace, shape and dtype of the two arrays match.
+
+    Parameters
+    ----------
+    actual : Array
+        The array produced by the tested function.
+    desired : Array
+        The expected array (typically hardcoded).
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    Returns
+    -------
+    Arrays namespace.
+    """
+    actual_xp = array_namespace(actual)  # Raises on scalars and lists
+    desired_xp = array_namespace(desired)
+
+    msg = f"namespaces do not match: {actual_xp} != f{desired_xp}"
+    assert actual_xp == desired_xp, msg
+
+    # Dask uses nan instead of None for unknown shapes
+    actual_shape = cast(tuple[float, ...], actual.shape)
+    desired_shape = cast(tuple[float, ...], desired.shape)
+    assert None not in actual_shape  # Requires explicit support
+    assert None not in desired_shape
+    if is_dask_namespace(desired_xp):
+        if any(math.isnan(i) for i in actual_shape):
+            actual_shape = actual.compute().shape  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+        if any(math.isnan(i) for i in desired_shape):
+            desired_shape = desired.compute().shape  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+    if check_shape:
+        msg = f"shapes do not match: {actual_shape} != f{desired_shape}"
+        assert actual_shape == desired_shape, msg
+    else:
+        # Ignore shape, but check flattened size. This is normally done by
+        # np.testing.assert_array_equal etc even when strict=False, but not for
+        # non-materializable arrays.
+        actual_size = math.prod(actual_shape)  # pyright: ignore[reportUnknownArgumentType]
+        desired_size = math.prod(desired_shape)  # pyright: ignore[reportUnknownArgumentType]
+        msg = f"sizes do not match: {actual_size} != f{desired_size}"
+        assert actual_size == desired_size, msg
+
+    if check_dtype:
+        msg = f"dtypes do not match: {actual.dtype} != {desired.dtype}"
+        assert actual.dtype == desired.dtype, msg
+
+    if is_numpy_namespace(actual_xp) and check_scalar:
+        # only NumPy distinguishes between scalars and arrays; we do if check_scalar.
+        _msg = (
+            "array-ness does not match:\n Actual: "
+            f"{type(actual)}\n Desired: {type(desired)}"
+        )
+        assert np.isscalar(actual) == np.isscalar(desired), _msg
+
+    return desired_xp
+
+
+def _is_materializable(x: Array) -> bool:
+    """
+    Return True if you can call `as_numpy_array(x)`; False otherwise.
+    """
+    # Important: here we assume that we're not tracing -
+    # e.g. we're not inside `jax.jit`` nor `cupy.cuda.Stream.begin_capture`.
+    return not is_torch_array(x) or x.device.type != "meta"  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+
+def as_numpy_array(array: Array, *, xp: ModuleType) -> np.typing.NDArray[Any]:
+    """
+    Convert array to NumPy, bypassing GPU-CPU transfer guards and densification guards.
+    """
+    if is_cupy_namespace(xp):
+        return xp.asnumpy(array)
+    if is_pydata_sparse_namespace(xp):
+        return array.todense()  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+    if is_torch_namespace(xp):
+        array = to_device(array, "cpu")
+    if is_array_api_strict_namespace(xp):
+        cpu: Device = xp.Device("CPU_DEVICE")
+        array = to_device(array, cpu)
+    if is_jax_namespace(xp):
+        import jax
+
+        # Note: only needed if the transfer guard is enabled
+        cpu = cast(Device, jax.devices("cpu")[0])
+        array = to_device(array, cpu)
+
+    return np.asarray(array)
+
+
+def xp_assert_equal(
+    actual: Array,
+    desired: Array,
+    *,
+    err_msg: str = "",
+    check_dtype: bool = True,
+    check_shape: bool = True,
+    check_scalar: bool = False,
+) -> None:
+    """
+    Array-API compatible version of `np.testing.assert_array_equal`.
+
+    Parameters
+    ----------
+    actual : Array
+        The array produced by the tested function.
+    desired : Array
+        The expected array (typically hardcoded).
+    err_msg : str, optional
+        Error message to display on failure.
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    See Also
+    --------
+    xp_assert_close : Similar function for inexact equality checks.
+    numpy.testing.assert_array_equal : Similar function for NumPy arrays.
+    """
+    xp = _check_ns_shape_dtype(actual, desired, check_dtype, check_shape, check_scalar)
+    if not _is_materializable(actual):
+        return
+    actual_np = as_numpy_array(actual, xp=xp)
+    desired_np = as_numpy_array(desired, xp=xp)
+    np.testing.assert_array_equal(actual_np, desired_np, err_msg=err_msg)
+
+
+def xp_assert_less(
+    x: Array,
+    y: Array,
+    *,
+    err_msg: str = "",
+    check_dtype: bool = True,
+    check_shape: bool = True,
+    check_scalar: bool = False,
+) -> None:
+    """
+    Array-API compatible version of `np.testing.assert_array_less`.
+
+    Parameters
+    ----------
+    x, y : Array
+        The arrays to compare according to ``x < y`` (elementwise).
+    err_msg : str, optional
+        Error message to display on failure.
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    See Also
+    --------
+    xp_assert_close : Similar function for inexact equality checks.
+    numpy.testing.assert_array_equal : Similar function for NumPy arrays.
+    """
+    xp = _check_ns_shape_dtype(x, y, check_dtype, check_shape, check_scalar)
+    if not _is_materializable(x):
+        return
+    x_np = as_numpy_array(x, xp=xp)
+    y_np = as_numpy_array(y, xp=xp)
+    np.testing.assert_array_less(x_np, y_np, err_msg=err_msg)
+
+
+def xp_assert_close(
+    actual: Array,
+    desired: Array,
+    *,
+    rtol: float | None = None,
+    atol: float = 0,
+    err_msg: str = "",
+    check_dtype: bool = True,
+    check_shape: bool = True,
+    check_scalar: bool = False,
+) -> None:
+    """
+    Array-API compatible version of `np.testing.assert_allclose`.
+
+    Parameters
+    ----------
+    actual : Array
+        The array produced by the tested function.
+    desired : Array
+        The expected array (typically hardcoded).
+    rtol : float, optional
+        Relative tolerance. Default: dtype-dependent.
+    atol : float, optional
+        Absolute tolerance. Default: 0.
+    err_msg : str, optional
+        Error message to display on failure.
+    check_dtype, check_shape : bool, default: True
+        Whether to check agreement between actual and desired dtypes and shapes
+    check_scalar : bool, default: False
+        NumPy only: whether to check agreement between actual and desired types -
+        0d array vs scalar.
+
+    See Also
+    --------
+    xp_assert_equal : Similar function for exact equality checks.
+    isclose : Public function for checking closeness.
+    numpy.testing.assert_allclose : Similar function for NumPy arrays.
+
+    Notes
+    -----
+    The default `atol` and `rtol` differ from `xp.all(xpx.isclose(a, b))`.
+    """
+    xp = _check_ns_shape_dtype(actual, desired, check_dtype, check_shape, check_scalar)
+    if not _is_materializable(actual):
+        return
+
+    if rtol is None:
+        if xp.isdtype(actual.dtype, ("real floating", "complex floating")):
+            # multiplier of 4 is used as for `np.float64` this puts the default `rtol`
+            # roughly half way between sqrt(eps) and the default for
+            # `numpy.testing.assert_allclose`, 1e-7
+            rtol = xp.finfo(actual.dtype).eps ** 0.5 * 4
+        else:
+            rtol = 1e-7
+
+    actual_np = as_numpy_array(actual, xp=xp)
+    desired_np = as_numpy_array(desired, xp=xp)
+    np.testing.assert_allclose(  # pyright: ignore[reportCallIssue]
+        actual_np,
+        desired_np,
+        rtol=rtol,  # pyright: ignore[reportArgumentType]
+        atol=atol,
+        err_msg=err_msg,
+    )
+
+
+def xfail(
+    request: pytest.FixtureRequest, *, reason: str, strict: bool | None = None
+) -> None:
+    """
+    XFAIL the currently running test.
+
+    Unlike ``pytest.xfail``, allow rest of test to execute instead of immediately
+    halting it, so that it may result in a XPASS.
+    xref https://github.com/pandas-dev/pandas/issues/38902
+
+    Parameters
+    ----------
+    request : pytest.FixtureRequest
+        ``request`` argument of the test function.
+    reason : str
+        Reason for the expected failure.
+    strict: bool, optional
+        If True, the test will be marked as failed if it passes.
+        If False, the test will be marked as passed if it fails.
+        Default: ``xfail_strict`` value in ``pyproject.toml``, or False if absent.
+    """
+    if strict is not None:
+        marker = pytest.mark.xfail(reason=reason, strict=strict)
+    else:
+        marker = pytest.mark.xfail(reason=reason)
+    request.node.add_marker(marker)
diff --git a/src/array_api_extra/_lib/_utils/__init__.py b/src/array_api_extra/_lib/_utils/__init__.py
new file mode 100644
index 00000000..3628c45f
--- /dev/null
+++ b/src/array_api_extra/_lib/_utils/__init__.py
@@ -0,0 +1 @@
+"""Modules housing private utility functions."""
diff --git a/src/array_api_extra/_lib/_utils/_compat.py b/src/array_api_extra/_lib/_utils/_compat.py
new file mode 100644
index 00000000..82ce76b8
--- /dev/null
+++ b/src/array_api_extra/_lib/_utils/_compat.py
@@ -0,0 +1,74 @@
+"""Acquire helpers from array-api-compat."""
+# Allow packages that vendor both `array-api-extra` and
+# `array-api-compat` to override the import location
+
+# pylint: disable=duplicate-code
+try:
+    from ...._array_api_compat_vendor import (
+        array_namespace,
+        device,
+        is_array_api_obj,
+        is_array_api_strict_namespace,
+        is_cupy_array,
+        is_cupy_namespace,
+        is_dask_array,
+        is_dask_namespace,
+        is_jax_array,
+        is_jax_namespace,
+        is_lazy_array,
+        is_numpy_array,
+        is_numpy_namespace,
+        is_pydata_sparse_array,
+        is_pydata_sparse_namespace,
+        is_torch_array,
+        is_torch_namespace,
+        is_writeable_array,
+        size,
+        to_device,
+    )
+except ImportError:
+    from array_api_compat import (
+        array_namespace,
+        device,
+        is_array_api_obj,
+        is_array_api_strict_namespace,
+        is_cupy_array,
+        is_cupy_namespace,
+        is_dask_array,
+        is_dask_namespace,
+        is_jax_array,
+        is_jax_namespace,
+        is_lazy_array,
+        is_numpy_array,
+        is_numpy_namespace,
+        is_pydata_sparse_array,
+        is_pydata_sparse_namespace,
+        is_torch_array,
+        is_torch_namespace,
+        is_writeable_array,
+        size,
+        to_device,
+    )
+
+__all__ = [
+    "array_namespace",
+    "device",
+    "is_array_api_obj",
+    "is_array_api_strict_namespace",
+    "is_cupy_array",
+    "is_cupy_namespace",
+    "is_dask_array",
+    "is_dask_namespace",
+    "is_jax_array",
+    "is_jax_namespace",
+    "is_lazy_array",
+    "is_numpy_array",
+    "is_numpy_namespace",
+    "is_pydata_sparse_array",
+    "is_pydata_sparse_namespace",
+    "is_torch_array",
+    "is_torch_namespace",
+    "is_writeable_array",
+    "size",
+    "to_device",
+]
diff --git a/src/array_api_extra/_lib/_utils/_compat.pyi b/src/array_api_extra/_lib/_utils/_compat.pyi
new file mode 100644
index 00000000..95c6bc8a
--- /dev/null
+++ b/src/array_api_extra/_lib/_utils/_compat.pyi
@@ -0,0 +1,45 @@
+"""Static type stubs for `_compat.py`."""
+
+# https://github.com/scikit-learn/scikit-learn/pull/27910#issuecomment-2568023972
+from __future__ import annotations
+
+from types import ModuleType
+from typing import Any, TypeGuard
+
+# TODO import from typing (requires Python >=3.13)
+from typing_extensions import TypeIs
+
+from ._typing import Array, Device
+
+# pylint: disable=missing-class-docstring,unused-argument
+
+def array_namespace(
+    *xs: Array | complex | None,
+    api_version: str | None = None,
+    use_compat: bool | None = None,
+) -> ModuleType: ...
+def device(x: Array, /) -> Device: ...
+def is_array_api_obj(x: object, /) -> TypeIs[Array]: ...
+def is_array_api_strict_namespace(xp: ModuleType, /) -> bool: ...
+def is_cupy_namespace(xp: ModuleType, /) -> bool: ...
+def is_dask_namespace(xp: ModuleType, /) -> bool: ...
+def is_jax_namespace(xp: ModuleType, /) -> bool: ...
+def is_numpy_namespace(xp: ModuleType, /) -> bool: ...
+def is_pydata_sparse_namespace(xp: ModuleType, /) -> bool: ...
+def is_torch_namespace(xp: ModuleType, /) -> bool: ...
+def is_cupy_array(x: object, /) -> TypeGuard[Array]: ...
+def is_dask_array(x: object, /) -> TypeGuard[Array]: ...
+def is_jax_array(x: object, /) -> TypeGuard[Array]: ...
+def is_numpy_array(x: object, /) -> TypeGuard[Array]: ...
+def is_pydata_sparse_array(x: object, /) -> TypeGuard[Array]: ...
+def is_torch_array(x: object, /) -> TypeGuard[Array]: ...
+def is_lazy_array(x: object, /) -> TypeGuard[Array]: ...
+def is_writeable_array(x: object, /) -> TypeGuard[Array]: ...
+def size(x: Array, /) -> int | None: ...
+def to_device(
+    x: Array,
+    device: Device,  # pylint: disable=redefined-outer-name
+    /,
+    *,
+    stream: int | Any | None = None,
+) -> Array: ...
diff --git a/src/array_api_extra/_lib/_utils/_helpers.py b/src/array_api_extra/_lib/_utils/_helpers.py
new file mode 100644
index 00000000..d177b376
--- /dev/null
+++ b/src/array_api_extra/_lib/_utils/_helpers.py
@@ -0,0 +1,598 @@
+"""Helper functions used by `array_api_extra/_funcs.py`."""
+
+from __future__ import annotations
+
+import io
+import math
+import pickle
+import types
+from collections.abc import Callable, Generator, Iterable
+from functools import wraps
+from types import ModuleType
+from typing import (
+    TYPE_CHECKING,
+    Any,
+    ClassVar,
+    Generic,
+    Literal,
+    ParamSpec,
+    TypeAlias,
+    TypeVar,
+    cast,
+)
+
+from . import _compat
+from ._compat import (
+    array_namespace,
+    is_array_api_obj,
+    is_dask_namespace,
+    is_jax_namespace,
+    is_numpy_array,
+    is_pydata_sparse_namespace,
+    is_torch_namespace,
+)
+from ._typing import Array, Device
+
+if TYPE_CHECKING:  # pragma: no cover
+    # TODO import from typing (requires Python >=3.12 and >=3.13)
+    from typing_extensions import TypeIs, override
+else:
+
+    def override(func):
+        return func
+
+
+P = ParamSpec("P")
+T = TypeVar("T")
+
+
+__all__ = [
+    "asarrays",
+    "capabilities",
+    "eager_shape",
+    "in1d",
+    "is_python_scalar",
+    "jax_autojit",
+    "mean",
+    "meta_namespace",
+    "pickle_flatten",
+    "pickle_unflatten",
+]
+
+
+def in1d(
+    x1: Array,
+    x2: Array,
+    /,
+    *,
+    assume_unique: bool = False,
+    invert: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """
+    Check whether each element of an array is also present in a second array.
+
+    Returns a boolean array the same length as `x1` that is True
+    where an element of `x1` is in `x2` and False otherwise.
+
+    This function has been adapted using the original implementation
+    present in numpy:
+    https://github.com/numpy/numpy/blob/v1.26.0/numpy/lib/arraysetops.py#L524-L758
+    """
+    if xp is None:
+        xp = array_namespace(x1, x2)
+
+    x1_shape = eager_shape(x1)
+    x2_shape = eager_shape(x2)
+
+    # This code is run to make the code significantly faster
+    if x2_shape[0] < 10 * x1_shape[0] ** 0.145 and isinstance(x2, Iterable):
+        if invert:
+            mask = xp.ones(x1_shape[0], dtype=xp.bool, device=_compat.device(x1))
+            for a in x2:
+                mask &= x1 != a
+        else:
+            mask = xp.zeros(x1_shape[0], dtype=xp.bool, device=_compat.device(x1))
+            for a in x2:
+                mask |= x1 == a
+        return mask
+
+    rev_idx = xp.empty(0)  # placeholder
+    if not assume_unique:
+        x1, rev_idx = xp.unique_inverse(x1)
+        x2 = xp.unique_values(x2)
+
+    ar = xp.concat((x1, x2))
+    device_ = _compat.device(ar)
+    # We need this to be a stable sort.
+    order = xp.argsort(ar, stable=True)
+    reverse_order = xp.argsort(order, stable=True)
+    sar = xp.take(ar, order, axis=0)
+    ar_size = _compat.size(sar)
+    assert ar_size is not None, "xp.unique*() on lazy backends raises"
+    if ar_size >= 1:
+        bool_ar = sar[1:] != sar[:-1] if invert else sar[1:] == sar[:-1]
+    else:
+        bool_ar = xp.asarray([False]) if invert else xp.asarray([True])
+    flag = xp.concat((bool_ar, xp.asarray([invert], device=device_)))
+    ret = xp.take(flag, reverse_order, axis=0)
+
+    if assume_unique:
+        return ret[: x1.shape[0]]
+    return xp.take(ret, rev_idx, axis=0)
+
+
+def mean(
+    x: Array,
+    /,
+    *,
+    axis: int | tuple[int, ...] | None = None,
+    keepdims: bool = False,
+    xp: ModuleType | None = None,
+) -> Array:  # numpydoc ignore=PR01,RT01
+    """
+    Complex mean, https://github.com/data-apis/array-api/issues/846.
+    """
+    if xp is None:
+        xp = array_namespace(x)
+
+    if xp.isdtype(x.dtype, "complex floating"):
+        x_real = xp.real(x)
+        x_imag = xp.imag(x)
+        mean_real = xp.mean(x_real, axis=axis, keepdims=keepdims)
+        mean_imag = xp.mean(x_imag, axis=axis, keepdims=keepdims)
+        return mean_real + (mean_imag * xp.asarray(1j))
+    return xp.mean(x, axis=axis, keepdims=keepdims)
+
+
+def is_python_scalar(x: object) -> TypeIs[complex]:  # numpydoc ignore=PR01,RT01
+    """Return True if `x` is a Python scalar, False otherwise."""
+    # isinstance(x, float) returns True for np.float64
+    # isinstance(x, complex) returns True for np.complex128
+    # bool is a subclass of int
+    return isinstance(x, int | float | complex) and not is_numpy_array(x)
+
+
+def asarrays(
+    a: Array | complex,
+    b: Array | complex,
+    xp: ModuleType,
+) -> tuple[Array, Array]:
+    """
+    Ensure both `a` and `b` are arrays.
+
+    If `b` is a python scalar, it is converted to the same dtype as `a`, and vice versa.
+
+    Behavior is not specified when mixing a Python ``float`` and an array with an
+    integer data type; this may give ``float32``, ``float64``, or raise an exception.
+    Behavior is implementation-specific.
+
+    Similarly, behavior is not specified when mixing a Python ``complex`` and an array
+    with a real-valued data type; this may give ``complex64``, ``complex128``, or raise
+    an exception. Behavior is implementation-specific.
+
+    Parameters
+    ----------
+    a, b : Array | int | float | complex | bool
+        Input arrays or scalars. At least one must be an array.
+    xp : array_namespace, optional
+        The standard-compatible namespace for `x`. Default: infer.
+
+    Returns
+    -------
+    Array, Array
+        The input arrays, possibly converted to arrays if they were scalars.
+
+    See Also
+    --------
+    mixing-arrays-with-python-scalars : Array API specification for the behavior.
+    """
+    a_scalar = is_python_scalar(a)
+    b_scalar = is_python_scalar(b)
+    if not a_scalar and not b_scalar:
+        # This includes misc. malformed input e.g. str
+        return a, b  # type: ignore[return-value]
+
+    swap = False
+    if a_scalar:
+        swap = True
+        b, a = a, b
+
+    if is_array_api_obj(a):
+        # a is an Array API object
+        # b is a int | float | complex | bool
+        xa = a
+
+        # https://data-apis.org/array-api/draft/API_specification/type_promotion.html#mixing-arrays-with-python-scalars
+        same_dtype = {
+            bool: "bool",
+            int: ("integral", "real floating", "complex floating"),
+            float: ("real floating", "complex floating"),
+            complex: "complex floating",
+        }
+        kind = same_dtype[type(cast(complex, b))]
+        if xp.isdtype(a.dtype, kind):
+            xb = xp.asarray(b, dtype=a.dtype)
+        else:
+            # Undefined behaviour. Let the function deal with it, if it can.
+            xb = xp.asarray(b)
+
+    else:
+        # Neither a nor b are Array API objects.
+        # Note: we can only reach this point when one explicitly passes
+        # xp=xp to the calling function; otherwise we fail earlier on
+        # array_namespace(a, b).
+        xa, xb = xp.asarray(a), xp.asarray(b)
+
+    return (xb, xa) if swap else (xa, xb)
+
+
+def ndindex(*x: int) -> Generator[tuple[int, ...]]:
+    """
+    Generate all N-dimensional indices for a given array shape.
+
+    Given the shape of an array, an ndindex instance iterates over the N-dimensional
+    index of the array. At each iteration a tuple of indices is returned, the last
+    dimension is iterated over first.
+
+    This has an identical API to numpy.ndindex.
+
+    Parameters
+    ----------
+    *x : int
+        The shape of the array.
+    """
+    if not x:
+        yield ()
+        return
+    for i in ndindex(*x[:-1]):
+        for j in range(x[-1]):
+            yield *i, j
+
+
+def eager_shape(x: Array, /) -> tuple[int, ...]:
+    """
+    Return shape of an array. Raise if shape is not fully defined.
+
+    Parameters
+    ----------
+    x : Array
+        Input array.
+
+    Returns
+    -------
+    tuple[int, ...]
+        Shape of the array.
+    """
+    shape = x.shape
+    # Dask arrays uses non-standard NaN instead of None
+    if any(s is None or math.isnan(s) for s in shape):
+        msg = "Unsupported lazy shape"
+        raise TypeError(msg)
+    return cast(tuple[int, ...], shape)
+
+
+def meta_namespace(
+    *arrays: Array | complex | None, xp: ModuleType | None = None
+) -> ModuleType:
+    """
+    Get the namespace of Dask chunks.
+
+    On all other backends, just return the namespace of the arrays.
+
+    Parameters
+    ----------
+    *arrays : Array | int | float | complex | bool | None
+        Input arrays.
+    xp : array_namespace, optional
+        The standard-compatible namespace for the input arrays. Default: infer.
+
+    Returns
+    -------
+    array_namespace
+        If xp is Dask, the namespace of the Dask chunks;
+        otherwise, the namespace of the arrays.
+    """
+    xp = array_namespace(*arrays) if xp is None else xp
+    if not is_dask_namespace(xp):
+        return xp
+    # Quietly skip scalars and None's
+    metas = [cast(Array | None, getattr(a, "_meta", None)) for a in arrays]
+    return array_namespace(*metas)
+
+
+def capabilities(
+    xp: ModuleType, *, device: Device | None = None
+) -> dict[str, int | None]:
+    """
+    Return patched ``xp.__array_namespace_info__().capabilities()``.
+
+    TODO this helper should be eventually removed once all the special cases
+    it handles are fixed in the respective backends.
+
+    Parameters
+    ----------
+    xp : array_namespace
+        The standard-compatible namespace.
+    device : Device, optional
+        The device to use.
+
+    Returns
+    -------
+    dict
+        Capabilities of the namespace.
+    """
+    out = xp.__array_namespace_info__().capabilities()
+    if is_pydata_sparse_namespace(xp):
+        if out["boolean indexing"]:
+            # FIXME https://github.com/pydata/sparse/issues/876
+            # boolean indexing is supported, but not when the index is a sparse array.
+            # boolean indexing by list or numpy array is not part of the Array API.
+            out = out.copy()
+            out["boolean indexing"] = False
+    elif is_jax_namespace(xp):
+        if out["boolean indexing"]:  # pragma: no cover
+            # Backwards compatibility with jax <0.6.0
+            # https://github.com/jax-ml/jax/issues/27418
+            out = out.copy()
+            out["boolean indexing"] = False
+    elif is_torch_namespace(xp):
+        # FIXME https://github.com/data-apis/array-api/issues/945
+        device = xp.get_default_device() if device is None else xp.device(device)
+        if device.type == "meta":  # type: ignore[union-attr]  # pyright: ignore[reportAttributeAccessIssue,reportOptionalMemberAccess]
+            out = out.copy()
+            out["boolean indexing"] = False
+            out["data-dependent shapes"] = False
+
+    return out
+
+
+_BASIC_PICKLED_TYPES = frozenset((
+    bool, int, float, complex, str, bytes, bytearray,
+    list, tuple, dict, set, frozenset, range, slice,
+    types.NoneType, types.EllipsisType,
+))  # fmt: skip
+_BASIC_REST_TYPES = frozenset((
+    type, types.BuiltinFunctionType, types.FunctionType, types.ModuleType
+))  # fmt: skip
+
+FlattenRest: TypeAlias = tuple[object, ...]
+
+
+def pickle_flatten(
+    obj: object, cls: type[T] | tuple[type[T], ...]
+) -> tuple[list[T], FlattenRest]:
+    """
+    Use the pickle machinery to extract objects out of an arbitrary container.
+
+    Unlike regular ``pickle.dumps``, this function always succeeds.
+
+    Parameters
+    ----------
+    obj : object
+        The object to pickle.
+    cls : type | tuple[type, ...]
+        One or multiple classes to extract from the object.
+        The instances of these classes inside ``obj`` will not be pickled.
+
+    Returns
+    -------
+    instances : list[cls]
+        All instances of ``cls`` found inside ``obj`` (not pickled).
+    rest
+        Opaque object containing the pickled bytes plus all other objects where
+        ``__reduce__`` / ``__reduce_ex__`` is either not implemented or raised.
+        These are unpickleable objects, types, modules, and functions.
+
+        This object is *typically* hashable save for fairly exotic objects
+        that are neither pickleable nor hashable.
+
+        This object is pickleable if everything except ``instances`` was pickleable
+        in the input object.
+
+    See Also
+    --------
+    pickle_unflatten : Reverse function.
+
+    Examples
+    --------
+    >>> class A:
+    ...     def __repr__(self):
+    ...         return "<A>"
+    >>> class NS:
+    ...     def __repr__(self):
+    ...         return "<NS>"
+    ...     def __reduce__(self):
+    ...         assert False, "not serializable"
+    >>> obj = {1: A(), 2: [A(), NS(), A()]}
+    >>> instances, rest = pickle_flatten(obj, A)
+    >>> instances
+    [<A>, <A>, <A>]
+    >>> pickle_unflatten(instances, rest)
+    {1: <A>, 2: [<A>, <NS>, <A>]}
+
+    This can be also used to swap inner objects; the only constraint is that
+    the number of objects in and out must be the same:
+
+    >>> pickle_unflatten(["foo", "bar", "baz"], rest)
+    {1: "foo", 2: ["bar", <NS>, "baz"]}
+    """
+    instances: list[T] = []
+    rest: list[object] = []
+
+    class Pickler(pickle.Pickler):  # numpydoc ignore=GL08
+        """
+        Use the `pickle.Pickler.persistent_id` hook to extract objects.
+        """
+
+        @override
+        def persistent_id(
+            self, obj: object
+        ) -> Literal[0, 1, None]:  # numpydoc ignore=GL08
+            if isinstance(obj, cls):
+                instances.append(obj)  # type: ignore[arg-type]
+                return 0
+
+            typ_ = type(obj)
+            if typ_ in _BASIC_PICKLED_TYPES:  # No subclasses!
+                # If obj is a collection, recursively descend inside it
+                return None
+            if typ_ in _BASIC_REST_TYPES:
+                rest.append(obj)
+                return 1
+
+            try:
+                # Note: a class that defines __slots__ without defining __getstate__
+                # cannot be pickled with __reduce__(), but can with __reduce_ex__(5)
+                _ = obj.__reduce_ex__(pickle.HIGHEST_PROTOCOL)
+            except Exception:  # pylint: disable=broad-exception-caught
+                rest.append(obj)
+                return 1
+
+            # Object can be pickled. Let the Pickler recursively descend inside it.
+            return None
+
+    f = io.BytesIO()
+    p = Pickler(f, protocol=pickle.HIGHEST_PROTOCOL)
+    p.dump(obj)
+    return instances, (f.getvalue(), *rest)
+
+
+def pickle_unflatten(instances: Iterable[object], rest: FlattenRest) -> Any:
+    """
+    Reverse of ``pickle_flatten``.
+
+    Parameters
+    ----------
+    instances : Iterable
+        Inner objects to be reinserted into the flattened container.
+    rest : FlattenRest
+        Extra bits, as returned by ``pickle_flatten``.
+
+    Returns
+    -------
+    object
+        The outer object originally passed to ``pickle_flatten`` after a
+        pickle->unpickle round-trip.
+
+    See Also
+    --------
+    pickle_flatten : Serializing function.
+    pickle.loads : Standard unpickle function.
+
+    Notes
+    -----
+    The `instances` iterable must yield at least the same number of elements as the ones
+    returned by ``pickle_flatten``, but the elements do not need to be the same objects
+    or even the same types of objects. Excess elements, if any, will be left untouched.
+    """
+    iters = iter(instances), iter(rest)
+    pik = cast(bytes, next(iters[1]))
+
+    class Unpickler(pickle.Unpickler):  # numpydoc ignore=GL08
+        """Mirror of the overridden Pickler in pickle_flatten."""
+
+        @override
+        def persistent_load(self, pid: Literal[0, 1]) -> object:  # numpydoc ignore=GL08
+            try:
+                return next(iters[pid])
+            except StopIteration as e:
+                msg = "Not enough objects to unpickle"
+                raise ValueError(msg) from e
+
+    f = io.BytesIO(pik)
+    return Unpickler(f).load()
+
+
+class _AutoJITWrapper(Generic[T]):  # numpydoc ignore=PR01
+    """
+    Helper of :func:`jax_autojit`.
+
+    Wrap arbitrary inputs and outputs of the jitted function and
+    convert them to/from PyTrees.
+    """
+
+    obj: T
+    _registered: ClassVar[bool] = False
+    __slots__: tuple[str, ...] = ("obj",)
+
+    def __init__(self, obj: T) -> None:  # numpydoc ignore=GL08
+        self._register()
+        self.obj = obj
+
+    @classmethod
+    def _register(cls) -> None:  # numpydoc ignore=SS06
+        """
+        Register upon first use instead of at import time, to avoid
+        globally importing JAX.
+        """
+        if not cls._registered:
+            import jax
+
+            jax.tree_util.register_pytree_node(
+                cls,
+                lambda obj: pickle_flatten(obj, jax.Array),  # pyright: ignore[reportUnknownArgumentType]
+                lambda aux_data, children: pickle_unflatten(children, aux_data),  # pyright: ignore[reportUnknownArgumentType]
+            )
+            cls._registered = True
+
+
+def jax_autojit(
+    func: Callable[P, T],
+) -> Callable[P, T]:  # numpydoc ignore=PR01,RT01,SS03
+    """
+    Wrap `func` with ``jax.jit``, with the following differences:
+
+    - Python scalar arguments and return values are not automatically converted to
+      ``jax.Array`` objects.
+    - All non-array arguments are automatically treated as static.
+      Unlike ``jax.jit``, static arguments must be either hashable or serializable with
+      ``pickle``.
+    - Unlike ``jax.jit``, non-array arguments and return values are not limited to
+      tuple/list/dict, but can be any object serializable with ``pickle``.
+    - Automatically descend into non-array arguments and find ``jax.Array`` objects
+      inside them, then rebuild the arguments when entering `func`, swapping the JAX
+      concrete arrays with tracer objects.
+    - Automatically descend into non-array return values and find ``jax.Array`` objects
+      inside them, then rebuild them downstream of exiting the JIT, swapping the JAX
+      tracer objects with concrete arrays.
+
+    See Also
+    --------
+    jax.jit : JAX JIT compilation function.
+
+    Notes
+    -----
+    These are useful choices *for testing purposes only*, which is how this function is
+    intended to be used. The output of ``jax.jit`` is a C++ level callable, that
+    directly dispatches to the compiled kernel after the initial call. In comparison,
+    ``jax_autojit`` incurs a much higher dispatch time.
+
+    Additionally, consider::
+
+        def f(x: Array, y: float, plus: bool) -> Array:
+            return x + y if plus else x - y
+
+        j1 = jax.jit(f, static_argnames="plus")
+        j2 = jax_autojit(f)
+
+    In the above example, ``j2`` requires a lot less setup to be tested effectively than
+    ``j1``, but on the flip side it means that it will be re-traced for every different
+    value of ``y``, which likely makes it not fit for purpose in production.
+    """
+    import jax
+
+    @jax.jit  # type: ignore[misc]  # pyright: ignore[reportUntypedFunctionDecorator]
+    def inner(  # numpydoc ignore=GL08
+        wargs: _AutoJITWrapper[Any],
+    ) -> _AutoJITWrapper[T]:
+        args, kwargs = wargs.obj
+        res = func(*args, **kwargs)  # pyright: ignore[reportCallIssue]
+        return _AutoJITWrapper(res)
+
+    @wraps(func)
+    def outer(*args: P.args, **kwargs: P.kwargs) -> T:  # numpydoc ignore=GL08
+        wargs = _AutoJITWrapper((args, kwargs))
+        return inner(wargs).obj
+
+    return outer
diff --git a/src/array_api_extra/_lib/_utils/_typing.py b/src/array_api_extra/_lib/_utils/_typing.py
new file mode 100644
index 00000000..8204be47
--- /dev/null
+++ b/src/array_api_extra/_lib/_utils/_typing.py
@@ -0,0 +1,10 @@
+# numpydoc ignore=GL08
+# pylint: disable=missing-module-docstring,duplicate-code
+
+Array = object
+DType = object
+Device = object
+GetIndex = object
+SetIndex = object
+
+__all__ = ["Array", "DType", "Device", "GetIndex", "SetIndex"]
diff --git a/src/array_api_extra/_lib/_utils/_typing.pyi b/src/array_api_extra/_lib/_utils/_typing.pyi
new file mode 100644
index 00000000..35c255fc
--- /dev/null
+++ b/src/array_api_extra/_lib/_utils/_typing.pyi
@@ -0,0 +1,105 @@
+"""Static typing helpers."""
+
+from __future__ import annotations
+
+from types import EllipsisType
+from typing import Protocol, TypeAlias
+
+# TODO import from typing (requires Python >=3.12)
+from typing_extensions import override
+
+# TODO: use array-api-typing once it is available
+
+class Array(Protocol):  # pylint: disable=missing-class-docstring
+    # Unary operations
+    def __abs__(self) -> Array: ...
+    def __pos__(self) -> Array: ...
+    def __neg__(self) -> Array: ...
+    def __invert__(self) -> Array: ...
+    # Binary operations
+    def __add__(self, other: Array | complex, /) -> Array: ...
+    def __sub__(self, other: Array | complex, /) -> Array: ...
+    def __mul__(self, other: Array | complex, /) -> Array: ...
+    def __truediv__(self, other: Array | complex, /) -> Array: ...
+    def __floordiv__(self, other: Array | complex, /) -> Array: ...
+    def __mod__(self, other: Array | complex, /) -> Array: ...
+    def __pow__(self, other: Array | complex, /) -> Array: ...
+    def __matmul__(self, other: Array, /) -> Array: ...
+    def __and__(self, other: Array | int, /) -> Array: ...
+    def __or__(self, other: Array | int, /) -> Array: ...
+    def __xor__(self, other: Array | int, /) -> Array: ...
+    def __lshift__(self, other: Array | int, /) -> Array: ...
+    def __rshift__(self, other: Array | int, /) -> Array: ...
+    def __lt__(self, other: Array | complex, /) -> Array: ...
+    def __le__(self, other: Array | complex, /) -> Array: ...
+    def __gt__(self, other: Array | complex, /) -> Array: ...
+    def __ge__(self, other: Array | complex, /) -> Array: ...
+    @override
+    def __eq__(self, other: Array | complex, /) -> Array: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    @override
+    def __ne__(self, other: Array | complex, /) -> Array: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+    # Reflected operations
+    def __radd__(self, other: Array | complex, /) -> Array: ...
+    def __rsub__(self, other: Array | complex, /) -> Array: ...
+    def __rmul__(self, other: Array | complex, /) -> Array: ...
+    def __rtruediv__(self, other: Array | complex, /) -> Array: ...
+    def __rfloordiv__(self, other: Array | complex, /) -> Array: ...
+    def __rmod__(self, other: Array | complex, /) -> Array: ...
+    def __rpow__(self, other: Array | complex, /) -> Array: ...
+    def __rmatmul__(self, other: Array, /) -> Array: ...
+    def __rand__(self, other: Array | int, /) -> Array: ...
+    def __ror__(self, other: Array | int, /) -> Array: ...
+    def __rxor__(self, other: Array | int, /) -> Array: ...
+    def __rlshift__(self, other: Array | int, /) -> Array: ...
+    def __rrshift__(self, other: Array | int, /) -> Array: ...
+    # Attributes
+    @property
+    def dtype(self) -> DType: ...
+    @property
+    def device(self) -> Device: ...
+    @property
+    def mT(self) -> Array: ...  # pylint: disable=invalid-name
+    @property
+    def ndim(self) -> int: ...
+    @property
+    def shape(self) -> tuple[int | None, ...]: ...
+    @property
+    def size(self) -> int | None: ...
+    @property
+    def T(self) -> Array: ...  # pylint: disable=invalid-name
+    # Collection operations (note: an Array does not have to be Sized or Iterable)
+    def __getitem__(self, key: GetIndex, /) -> Array: ...
+    def __setitem__(self, key: SetIndex, value: Array | complex, /) -> None: ...
+    # Materialization methods (may raise on lazy arrays)
+    def __bool__(self) -> bool: ...
+    def __complex__(self) -> complex: ...
+    def __float__(self) -> float: ...
+    def __index__(self) -> int: ...
+    def __int__(self) -> int: ...
+
+    # Misc methods (frequently not implemented in Arrays wrapped by array-api-compat)
+    # def __array_namespace__(*, api_version: str | None) -> ModuleType: ...
+    # def __dlpack__(
+    #     *,
+    #     stream: int | Any | None = None,
+    #     max_version: tuple[int, int] | None = None,
+    #     dl_device: tuple[int, int] | None = None,  # tuple[Enum, int]
+    #     copy: bool | None = None,
+    # ) -> Any: ...
+    # def __dlpack_device__() -> tuple[int, int]: ...  # tuple[Enum, int]
+    # def to_device(device: Device, /, *, stream: int | Any | None = None) -> Array: ...
+
+class DType(Protocol):  # pylint: disable=missing-class-docstring
+    pass
+
+class Device(Protocol):  # pylint: disable=missing-class-docstring
+    pass
+
+SetIndex: TypeAlias = (
+    int | slice | EllipsisType | Array | tuple[int | slice | EllipsisType | Array, ...]
+)
+GetIndex: TypeAlias = (
+    SetIndex | None | tuple[int | slice | EllipsisType | None | Array, ...]
+)
+
+__all__ = ["Array", "DType", "Device", "GetIndex", "SetIndex"]
diff --git a/src/array_api_extra/_typing.py b/src/array_api_extra/_typing.py
deleted file mode 100644
index 9ffa13f2..00000000
--- a/src/array_api_extra/_typing.py
+++ /dev/null
@@ -1,8 +0,0 @@
-from __future__ import annotations
-
-from types import ModuleType
-from typing import Any
-
-Array = Any  # To be changed to a Protocol later (see array-api#589)
-
-__all__ = ["Array", "ModuleType"]
diff --git a/src/array_api_extra/testing.py b/src/array_api_extra/testing.py
new file mode 100644
index 00000000..d40fea1a
--- /dev/null
+++ b/src/array_api_extra/testing.py
@@ -0,0 +1,415 @@
+"""
+Public testing utilities.
+
+See also _lib._testing for additional private testing utilities.
+"""
+
+from __future__ import annotations
+
+import contextlib
+import enum
+import warnings
+from collections.abc import Callable, Generator, Iterator, Sequence
+from functools import wraps
+from types import ModuleType
+from typing import TYPE_CHECKING, Any, ParamSpec, TypeVar, cast
+
+from ._lib._utils._compat import is_dask_namespace, is_jax_namespace
+from ._lib._utils._helpers import jax_autojit, pickle_flatten, pickle_unflatten
+
+__all__ = ["lazy_xp_function", "patch_lazy_xp_functions"]
+
+if TYPE_CHECKING:  # pragma: no cover
+    # TODO import override from typing (requires Python >=3.12)
+    import pytest
+    from dask.typing import Graph, Key, SchedulerGetCallable
+    from typing_extensions import override
+
+else:
+    # Sphinx hacks
+    SchedulerGetCallable = object
+
+    def override(func):
+        return func
+
+
+P = ParamSpec("P")
+T = TypeVar("T")
+
+_ufuncs_tags: dict[object, dict[str, Any]] = {}
+
+
+class Deprecated(enum.Enum):
+    """Unique type for deprecated parameters."""
+
+    DEPRECATED = 1
+
+
+DEPRECATED = Deprecated.DEPRECATED
+
+
+def lazy_xp_function(
+    func: Callable[..., Any],
+    *,
+    allow_dask_compute: bool | int = False,
+    jax_jit: bool = True,
+    static_argnums: Deprecated = DEPRECATED,
+    static_argnames: Deprecated = DEPRECATED,
+) -> None:  # numpydoc ignore=GL07
+    """
+    Tag a function to be tested on lazy backends.
+
+    Tag a function so that when any tests are executed with ``xp=jax.numpy`` the
+    function is replaced with a jitted version of itself, and when it is executed with
+    ``xp=dask.array`` the function will raise if it attempts to materialize the graph.
+    This will be later expanded to provide test coverage for other lazy backends.
+
+    In order for the tag to be effective, the test or a fixture must call
+    :func:`patch_lazy_xp_functions`.
+
+    Parameters
+    ----------
+    func : callable
+        Function to be tested.
+    allow_dask_compute : bool | int, optional
+        Whether `func` is allowed to internally materialize the Dask graph, or maximum
+        number of times it is allowed to do so. This is typically triggered by
+        ``bool()``, ``float()``, or ``np.asarray()``.
+
+        Set to 1 if you are aware that `func` converts the input parameters to NumPy and
+        want to let it do so at least for the time being, knowing that it is going to be
+        extremely detrimental for performance.
+
+        If a test needs values higher than 1 to pass, it is a canary that the conversion
+        to NumPy/bool/float is happening multiple times, which translates to multiple
+        computations of the whole graph. Short of making the function fully lazy, you
+        should at least add explicit calls to ``np.asarray()`` early in the function.
+        *Note:* the counter of `allow_dask_compute` resets after each call to `func`, so
+        a test function that invokes `func` multiple times should still work with this
+        parameter set to 1.
+
+        Set to True to allow `func` to materialize the graph an unlimited number
+        of times.
+
+        Default: False, meaning that `func` must be fully lazy and never materialize the
+        graph.
+    jax_jit : bool, optional
+        Set to True to replace `func` with a smart variant of ``jax.jit(func)`` after
+        calling the :func:`patch_lazy_xp_functions` test helper with ``xp=jax.numpy``.
+        This is the default behaviour.
+        Set to False if `func` is only compatible with eager (non-jitted) JAX.
+
+        Unlike with vanilla ``jax.jit``, all arguments and return types that are not JAX
+        arrays are treated as static; the function can accept and return arbitrary
+        wrappers around JAX arrays. This difference is because, in real life, most users
+        won't wrap the function directly with ``jax.jit`` but rather they will use it
+        within their own code, which is itself then wrapped by ``jax.jit``, and
+        internally consume the function's outputs.
+
+        In other words, the pattern that is being tested is::
+
+            >>> @jax.jit
+            ... def user_func(x):
+            ...     y = user_prepares_inputs(x)
+            ...     z = func(y, some_static_arg=True)
+            ...     return user_consumes(z)
+
+        Default: True.
+    static_argnums :
+        Deprecated; ignored
+    static_argnames :
+        Deprecated; ignored
+
+    See Also
+    --------
+    patch_lazy_xp_functions : Companion function to call from the test or fixture.
+    jax.jit : JAX function to compile a function for performance.
+
+    Examples
+    --------
+    In ``test_mymodule.py``::
+
+      from array_api_extra.testing import lazy_xp_function from mymodule import myfunc
+
+      lazy_xp_function(myfunc)
+
+      def test_myfunc(xp):
+          a = xp.asarray([1, 2])
+          # When xp=jax.numpy, this is similar to `b = jax.jit(myfunc)(a)`
+          # When xp=dask.array, crash on compute() or persist()
+          b = myfunc(a)
+
+    Notes
+    -----
+    In order for this tag to be effective, the test function must be imported into the
+    test module globals without its namespace; alternatively its namespace must be
+    declared in a ``lazy_xp_modules`` list in the test module globals.
+
+    Example 1::
+
+      from mymodule import myfunc
+
+      lazy_xp_function(myfunc)
+
+      def test_myfunc(xp):
+          x = myfunc(xp.asarray([1, 2]))
+
+    Example 2::
+
+      import mymodule
+
+      lazy_xp_modules = [mymodule]
+      lazy_xp_function(mymodule.myfunc)
+
+      def test_myfunc(xp):
+          x = mymodule.myfunc(xp.asarray([1, 2]))
+
+    A test function can circumvent this monkey-patching system by using a namespace
+    outside of the two above patterns. You need to sanitize your code to make sure this
+    only happens intentionally.
+
+    Example 1::
+
+      import mymodule
+      from mymodule import myfunc
+
+      lazy_xp_function(myfunc)
+
+      def test_myfunc(xp):
+          a = xp.asarray([1, 2])
+          b = myfunc(a)  # This is wrapped when xp=jax.numpy or xp=dask.array
+          c = mymodule.myfunc(a)  # This is not
+
+    Example 2::
+
+      import mymodule
+
+      class naked:
+          myfunc = mymodule.myfunc
+
+      lazy_xp_modules = [mymodule]
+      lazy_xp_function(mymodule.myfunc)
+
+      def test_myfunc(xp):
+          a = xp.asarray([1, 2])
+          b = mymodule.myfunc(a)  # This is wrapped when xp=jax.numpy or xp=dask.array
+          c = naked.myfunc(a)  # This is not
+    """
+    if static_argnums is not DEPRECATED or static_argnames is not DEPRECATED:
+        warnings.warn(
+            (
+                "The `static_argnums` and `static_argnames` parameters are deprecated "
+                "and ignored. They will be removed in a future version."
+            ),
+            DeprecationWarning,
+            stacklevel=2,
+        )
+    tags = {
+        "allow_dask_compute": allow_dask_compute,
+        "jax_jit": jax_jit,
+    }
+
+    try:
+        func._lazy_xp_function = tags  # type: ignore[attr-defined]  # pylint: disable=protected-access  # pyright: ignore[reportFunctionMemberAccess]
+    except AttributeError:  # @cython.vectorize
+        _ufuncs_tags[func] = tags
+
+
+def patch_lazy_xp_functions(
+    request: pytest.FixtureRequest,
+    monkeypatch: pytest.MonkeyPatch | None = None,
+    *,
+    xp: ModuleType,
+) -> contextlib.AbstractContextManager[None]:
+    """
+    Test lazy execution of functions tagged with :func:`lazy_xp_function`.
+
+    If ``xp==jax.numpy``, search for all functions which have been tagged with
+    :func:`lazy_xp_function` in the globals of the module that defines the current test,
+    as well as in the ``lazy_xp_modules`` list in the globals of the same module,
+    and wrap them with :func:`jax.jit`. Unwrap them at the end of the test.
+
+    If ``xp==dask.array``, wrap the functions with a decorator that disables
+    ``compute()`` and ``persist()`` and ensures that exceptions and warnings are raised
+    eagerly.
+
+    This function should be typically called by your library's `xp` fixture that runs
+    tests on multiple backends::
+
+        @pytest.fixture(params=[
+            numpy,
+            array_api_strict,
+            pytest.param(jax.numpy, marks=pytest.mark.thread_unsafe),
+            pytest.param(dask.array, marks=pytest.mark.thread_unsafe),
+        ])
+        def xp(request):
+            with patch_lazy_xp_functions(request, xp=request.param):
+                yield request.param
+
+    but it can be otherwise be called by the test itself too.
+
+    Parameters
+    ----------
+    request : pytest.FixtureRequest
+        Pytest fixture, as acquired by the test itself or by one of its fixtures.
+    monkeypatch : pytest.MonkeyPatch
+        Deprecated
+    xp : array_namespace
+        Array namespace to be tested.
+
+    See Also
+    --------
+    lazy_xp_function : Tag a function to be tested on lazy backends.
+    pytest.FixtureRequest : `request` test function parameter.
+
+    Notes
+    -----
+    This context manager monkey-patches modules and as such is thread unsafe
+    on Dask and JAX. If you run your test suite with
+    `pytest-run-parallel <https://github.com/Quansight-Labs/pytest-run-parallel/>`_,
+    you should mark these backends with ``@pytest.mark.thread_unsafe``, as shown in
+    the example above.
+    """
+    mod = cast(ModuleType, request.module)
+    mods = [mod, *cast(list[ModuleType], getattr(mod, "lazy_xp_modules", []))]
+
+    to_revert: list[tuple[ModuleType, str, object]] = []
+
+    def temp_setattr(mod: ModuleType, name: str, func: object) -> None:
+        """
+        Variant of monkeypatch.setattr, which allows monkey-patching only selected
+        parameters of a test so that pytest-run-parallel can run on the remainder.
+        """
+        assert hasattr(mod, name)
+        to_revert.append((mod, name, getattr(mod, name)))
+        setattr(mod, name, func)
+
+    if monkeypatch is not None:
+        warnings.warn(
+            (
+                "The `monkeypatch` parameter is deprecated and will be removed in a "
+                "future version. "
+                "Use `patch_lazy_xp_function` as a context manager instead."
+            ),
+            DeprecationWarning,
+            stacklevel=2,
+        )
+        # Enable using patch_lazy_xp_function not as a context manager
+        temp_setattr = monkeypatch.setattr  # type: ignore[assignment]  # pyright: ignore[reportAssignmentType]
+
+    def iter_tagged() -> Iterator[
+        tuple[ModuleType, str, Callable[..., Any], dict[str, Any]]
+    ]:
+        for mod in mods:
+            for name, func in mod.__dict__.items():
+                tags: dict[str, Any] | None = None
+                with contextlib.suppress(AttributeError):
+                    tags = func._lazy_xp_function  # pylint: disable=protected-access
+                if tags is None:
+                    with contextlib.suppress(KeyError, TypeError):
+                        tags = _ufuncs_tags[func]
+                if tags is not None:
+                    yield mod, name, func, tags
+
+    if is_dask_namespace(xp):
+        for mod, name, func, tags in iter_tagged():
+            n = tags["allow_dask_compute"]
+            if n is True:
+                n = 1_000_000
+            elif n is False:
+                n = 0
+            wrapped = _dask_wrap(func, n)
+            temp_setattr(mod, name, wrapped)
+
+    elif is_jax_namespace(xp):
+        for mod, name, func, tags in iter_tagged():
+            if tags["jax_jit"]:
+                wrapped = jax_autojit(func)
+                temp_setattr(mod, name, wrapped)
+
+    # We can't just decorate patch_lazy_xp_functions with
+    # @contextlib.contextmanager because it would not work with the
+    # deprecated monkeypatch when not used as a context manager.
+    @contextlib.contextmanager
+    def revert_on_exit() -> Generator[None]:
+        try:
+            yield
+        finally:
+            for mod, name, orig_func in to_revert:
+                setattr(mod, name, orig_func)
+
+    return revert_on_exit()
+
+
+class CountingDaskScheduler(SchedulerGetCallable):
+    """
+    Dask scheduler that counts how many times `dask.compute` is called.
+
+    If the number of times exceeds 'max_count', it raises an error.
+    This is a wrapper around Dask's own 'synchronous' scheduler.
+
+    Parameters
+    ----------
+    max_count : int
+        Maximum number of allowed calls to `dask.compute`.
+    msg : str
+        Assertion to raise when the count exceeds `max_count`.
+    """
+
+    count: int
+    max_count: int
+    msg: str
+
+    def __init__(self, max_count: int, msg: str):  # numpydoc ignore=GL08
+        self.count = 0
+        self.max_count = max_count
+        self.msg = msg
+
+    @override
+    def __call__(
+        self, dsk: Graph, keys: Sequence[Key] | Key, **kwargs: Any
+    ) -> Any:  # numpydoc ignore=GL08
+        import dask
+
+        self.count += 1
+        # This should yield a nice traceback to the
+        # offending line in the user's code
+        assert self.count <= self.max_count, self.msg
+
+        return dask.get(dsk, keys, **kwargs)  # type: ignore[attr-defined]  # pyright: ignore[reportPrivateImportUsage]
+
+
+def _dask_wrap(
+    func: Callable[P, T], n: int
+) -> Callable[P, T]:  # numpydoc ignore=PR01,RT01
+    """
+    Wrap `func` to raise if it attempts to call `dask.compute` more than `n` times.
+
+    After the function returns, materialize the graph in order to re-raise exceptions.
+    """
+    import dask
+    import dask.array as da
+
+    func_name = getattr(func, "__name__", str(func))
+    n_str = f"only up to {n}" if n else "no"
+    msg = (
+        f"Called `dask.compute()` or `dask.persist()` {n + 1} times, "
+        f"but {n_str} calls are allowed. Set "
+        f"`lazy_xp_function({func_name}, allow_dask_compute={n + 1})` "
+        "to allow for more (but note that this will harm performance). "
+    )
+
+    @wraps(func)
+    def wrapper(*args: P.args, **kwargs: P.kwargs) -> T:  # numpydoc ignore=GL08
+        scheduler = CountingDaskScheduler(n, msg)
+        with dask.config.set({"scheduler": scheduler}):  # pyright: ignore[reportPrivateImportUsage]
+            out = func(*args, **kwargs)
+
+        # Block until the graph materializes and reraise exceptions. This allows
+        # `pytest.raises` and `pytest.warns` to work as expected. Note that this would
+        # not work on scheduler='distributed', as it would not block.
+        arrays, rest = pickle_flatten(out, da.Array)
+        arrays = dask.persist(arrays, scheduler="threads")[0]  # type: ignore[attr-defined,no-untyped-call]  # pyright: ignore[reportPrivateImportUsage]
+        return pickle_unflatten(arrays, rest)  # pyright: ignore[reportUnknownArgumentType]
+
+    return wrapper
diff --git a/tests/__init__.py b/tests/__init__.py
new file mode 100644
index 00000000..3ccaf52b
--- /dev/null
+++ b/tests/__init__.py
@@ -0,0 +1 @@
+"""Needed to import .conftest from the test modules."""
diff --git a/tests/conftest.py b/tests/conftest.py
new file mode 100644
index 00000000..76fb7650
--- /dev/null
+++ b/tests/conftest.py
@@ -0,0 +1,234 @@
+"""Pytest fixtures."""
+
+from collections.abc import Callable, Generator
+from functools import partial, wraps
+from types import ModuleType
+from typing import ParamSpec, TypeVar, cast
+
+import numpy as np
+import pytest
+
+from array_api_extra._lib._backends import Backend
+from array_api_extra._lib._testing import xfail
+from array_api_extra._lib._utils._compat import array_namespace
+from array_api_extra._lib._utils._compat import device as get_device
+from array_api_extra._lib._utils._typing import Device
+from array_api_extra.testing import patch_lazy_xp_functions
+
+T = TypeVar("T")
+P = ParamSpec("P")
+
+np_compat = array_namespace(np.empty(0))  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+
+@pytest.fixture(params=[b.pytest_param() for b in Backend])
+def library(request: pytest.FixtureRequest) -> Backend:  # numpydoc ignore=PR01,RT03
+    """
+    Parameterized fixture that iterates on all libraries.
+
+    Returns
+    -------
+    The current Backend enum.
+    """
+    elem = cast(Backend, request.param)
+
+    for marker_name, skip_or_xfail, allow_kwargs in (
+        ("skip_xp_backend", pytest.skip, {"reason"}),
+        ("xfail_xp_backend", partial(xfail, request), {"reason", "strict"}),
+    ):
+        for marker in request.node.iter_markers(marker_name):
+            if len(marker.args) != 1:
+                msg = f"Expected exactly one positional argument; got {marker.args}"
+                raise TypeError(msg)
+            if not isinstance(marker.args[0], Backend):
+                msg = f"Argument of {marker_name} must be a Backend enum"
+                raise TypeError(msg)
+            if invalid_kwargs := set(marker.kwargs) - allow_kwargs:
+                msg = f"Unexpected kwarg(s): {invalid_kwargs}"
+                raise TypeError(msg)
+
+            library: Backend = marker.args[0]
+            reason: str | None = marker.kwargs.get("reason", None)
+            strict: bool | None = marker.kwargs.get("strict", None)
+
+            if library == elem:
+                reason = f"{library}: {reason}" if reason else str(library)
+                kwargs = {"strict": strict} if strict is not None else {}
+                skip_or_xfail(reason=reason, **kwargs)
+
+    return elem
+
+
+class NumPyReadOnly:
+    """
+    Variant of array_api_compat.numpy producing read-only arrays.
+
+    Read-only NumPy arrays fail on `__iadd__` etc., whereas read-only libraries such as
+    JAX and Sparse simply don't define those methods, which makes calls to `+=` fall
+    back to `__add__`.
+
+    Note that this is not a full read-only Array API library. Notably,
+    `array_namespace(x)` returns array_api_compat.numpy. This is actually the desired
+    behaviour, so that when a tested function internally calls `xp =
+    array_namespace(*args) or xp`, it will internally create writeable arrays.
+    For this reason, tests that explicitly pass xp=xp to the tested functions may
+    misbehave and should be skipped for NUMPY_READONLY.
+    """
+
+    def __getattr__(self, name: str) -> object:  # numpydoc ignore=PR01,RT01
+        """Wrap all functions that return arrays to make their output read-only."""
+        func = getattr(np_compat, name)
+        if not callable(func) or isinstance(func, type):
+            return func
+        return self._wrap(func)
+
+    @staticmethod
+    def _wrap(func: Callable[P, T]) -> Callable[P, T]:  # numpydoc ignore=PR01,RT01
+        """Wrap func to make all np.ndarrays it returns read-only."""
+
+        def as_readonly(o: T) -> T:  # numpydoc ignore=PR01,RT01
+            """Unset the writeable flag in o."""
+            try:
+                # Don't use is_numpy_array(o), as it includes np.generic
+                if isinstance(o, np.ndarray):
+                    o.flags.writeable = False
+            except TypeError:
+                # Cannot interpret as a data type
+                return o
+
+            # This works with namedtuples too
+            if isinstance(o, tuple | list):
+                return type(o)(*(as_readonly(i) for i in o))  # type: ignore[arg-type,return-value] # pyright: ignore[reportArgumentType]
+
+            return o
+
+        @wraps(func)
+        def wrapper(*args: P.args, **kwargs: P.kwargs) -> T:  # numpydoc ignore=GL08
+            return as_readonly(func(*args, **kwargs))
+
+        return wrapper
+
+
+@pytest.fixture
+def xp(
+    library: Backend, request: pytest.FixtureRequest
+) -> Generator[ModuleType]:  # numpydoc ignore=PR01,RT03
+    """
+    Parameterized fixture that iterates on all libraries.
+
+    Returns
+    -------
+    The current array namespace.
+    """
+    if library == Backend.NUMPY_READONLY:
+        yield NumPyReadOnly()  # type: ignore[misc]  # pyright: ignore[reportReturnType]
+        return
+
+    xp = pytest.importorskip(library.modname)
+    # Possibly wrap module with array_api_compat
+    xp = array_namespace(xp.empty(0))
+
+    if library == Backend.ARRAY_API_STRICTEST:
+        with xp.ArrayAPIStrictFlags(
+            boolean_indexing=False,
+            data_dependent_shapes=False,
+            # writeable=False,  # TODO implement in array-api-strict
+            # lazy=True,  # TODO implement in array-api-strict
+            enabled_extensions=(),
+        ):
+            yield xp
+        return
+
+    if library.like(Backend.JAX):
+        _setup_jax(library)
+    elif library.like(Backend.TORCH):
+        _setup_torch(library)
+
+    # On Dask and JAX, monkey-patch all functions tagged by `lazy_xp_function`
+    # in the global scope of the module containing the test function.
+    with patch_lazy_xp_functions(request, xp=xp):
+        yield xp
+
+
+def _setup_jax(library: Backend) -> None:
+    import jax
+
+    # suppress unused-ignore to run mypy in -e lint as well as -e dev
+    jax.config.update("jax_enable_x64", True)  # type: ignore[no-untyped-call,unused-ignore]
+
+    if library == Backend.JAX_GPU:
+        try:
+            device = jax.devices("cuda")[0]
+        except RuntimeError:
+            pytest.skip("no CUDA device available")
+    else:
+        device = jax.devices("cpu")[0]
+    jax.config.update("jax_default_device", device)
+
+
+def _setup_torch(library: Backend) -> None:
+    import torch
+
+    # This is already the default, but some tests or env variables may change it.
+    # TODO test both float32 and float64, like in scipy.
+    torch.set_default_dtype(torch.float32)
+
+    if library == Backend.TORCH_GPU:
+        import torch.cuda
+
+        if not torch.cuda.is_available():
+            pytest.skip("no CUDA device available")
+        torch.set_default_device("cuda")
+    else:
+        assert library == Backend.TORCH
+        torch.set_default_device("cpu")
+
+
+# Can select the test with `pytest -k dask`
+@pytest.fixture(params=[Backend.DASK.pytest_param()])
+def da(
+    request: pytest.FixtureRequest,
+) -> Generator[ModuleType]:  # numpydoc ignore=PR01,RT01
+    """Variant of the `xp` fixture that only yields dask.array."""
+    xp = pytest.importorskip("dask.array")
+    xp = array_namespace(xp.empty(0))
+    with patch_lazy_xp_functions(request, xp=xp):
+        yield xp
+
+
+@pytest.fixture(params=[Backend.JAX.pytest_param(), Backend.JAX_GPU.pytest_param()])
+def jnp(
+    request: pytest.FixtureRequest,
+) -> Generator[ModuleType]:  # numpydoc ignore=PR01,RT01
+    """Variant of the `xp` fixture that only yields jax.numpy."""
+    xp = pytest.importorskip("jax.numpy")
+    _setup_jax(request.param)
+    with patch_lazy_xp_functions(request, xp=xp):
+        yield xp
+
+
+@pytest.fixture(params=[Backend.TORCH, Backend.TORCH_GPU])
+def torch(request: pytest.FixtureRequest) -> ModuleType:  # numpydoc ignore=PR01,RT01
+    """Variant of the `xp` fixture that only yields torch."""
+    xp = pytest.importorskip("torch")
+    xp = array_namespace(xp.empty(0))
+    _setup_torch(request.param)
+    return xp
+
+
+@pytest.fixture
+def device(
+    library: Backend, xp: ModuleType
+) -> Device:  # numpydoc ignore=PR01,RT01,RT03
+    """
+    Return a valid device for the backend.
+
+    Where possible, return a device that is not the default one.
+    """
+    if library == Backend.ARRAY_API_STRICT:
+        return xp.Device("device1")
+    if library == Backend.TORCH:
+        return xp.device("meta")
+    if library == Backend.TORCH_GPU:
+        return xp.device("cpu")
+    return get_device(xp.empty(0))
diff --git a/tests/test_at.py b/tests/test_at.py
new file mode 100644
index 00000000..9558f7b8
--- /dev/null
+++ b/tests/test_at.py
@@ -0,0 +1,339 @@
+import math
+from collections.abc import Callable, Generator
+from contextlib import contextmanager
+from types import ModuleType
+from typing import cast
+
+import numpy as np
+import pytest
+
+from array_api_extra import at
+from array_api_extra._lib._at import _AtOp
+from array_api_extra._lib._backends import Backend
+from array_api_extra._lib._testing import xp_assert_equal
+from array_api_extra._lib._utils._compat import array_namespace, is_writeable_array
+from array_api_extra._lib._utils._compat import device as get_device
+from array_api_extra._lib._utils._typing import Array, Device, SetIndex
+from array_api_extra.testing import lazy_xp_function
+
+pytestmark = [
+    pytest.mark.skip_xp_backend(
+        Backend.SPARSE, reason="read-only backend without .at support"
+    ),
+    pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="boolean indexing"),
+]
+
+
+def at_op(
+    x: Array,
+    idx: SetIndex,
+    op: _AtOp,
+    y: Array | object,
+    copy: bool | None = None,
+    xp: ModuleType | None = None,
+) -> Array:
+    """
+    Wrapper around at(x, idx).op(y, copy=copy, xp=xp).
+
+    This is a hack to allow wrapping `at()` with `lazy_xp_function`.
+    For clarity, at() itself works inside jax.jit without hacks; this is
+    just a workaround for when one wants to apply jax.jit to `at()` directly,
+    which is not a common use case.
+    """
+    meth = cast(Callable[..., Array], getattr(at(x, idx), op.value))
+    return meth(y, copy=copy, xp=xp)
+
+
+lazy_xp_function(at_op)
+
+
+@contextmanager
+def assert_copy(
+    array: Array, copy: bool | None, expect_copy: bool | None = None
+) -> Generator[None, None, None]:
+    if copy is False and not is_writeable_array(array):
+        with pytest.raises((TypeError, ValueError)):
+            yield
+        return
+
+    xp = array_namespace(array)
+    array_orig = xp.asarray(array, copy=True)
+    yield
+
+    if expect_copy is None:
+        expect_copy = copy
+
+    if expect_copy:
+        # Original has not been modified
+        xp_assert_equal(array, array_orig)
+    elif expect_copy is False:
+        # Original has been modified
+        with pytest.raises(AssertionError):
+            xp_assert_equal(array, array_orig)
+    # Test nothing for copy=None. Dask changes behaviour depending on
+    # whether it's a special case of a bool mask with scalar RHS or not.
+
+
+@pytest.mark.parametrize("copy", [False, True, None])
+@pytest.mark.parametrize(
+    ("op", "y", "expect_list"),
+    [
+        (_AtOp.SET, 40.0, [10.0, 40.0, 40.0]),
+        (_AtOp.ADD, 40.0, [10.0, 60.0, 70.0]),
+        (_AtOp.SUBTRACT, 100.0, [10.0, -80.0, -70.0]),
+        (_AtOp.MULTIPLY, 2.0, [10.0, 40.0, 60.0]),
+        (_AtOp.DIVIDE, 2.0, [10.0, 10.0, 15.0]),
+        (_AtOp.POWER, 2.0, [10.0, 400.0, 900.0]),
+        (_AtOp.MIN, 25.0, [10.0, 20.0, 25.0]),
+        (_AtOp.MAX, 25.0, [10.0, 25.0, 30.0]),
+    ],
+)
+@pytest.mark.parametrize(
+    ("bool_mask", "x_ndim", "y_ndim"),
+    [
+        (False, 1, 0),
+        (False, 1, 1),
+        (True, 1, 0),  # Uses xp.where(idx, y, x) on JAX and Dask
+        pytest.param(
+            *(True, 1, 1),
+            marks=(
+                pytest.mark.xfail_xp_backend(
+                    Backend.JAX,
+                    reason="bool mask update with shaped rhs",
+                    strict=False,  # test passes when copy=False
+                ),
+                pytest.mark.xfail_xp_backend(
+                    Backend.JAX_GPU,
+                    reason="bool mask update with shaped rhs",
+                    strict=False,  # test passes when copy=False
+                ),
+                pytest.mark.xfail_xp_backend(
+                    Backend.DASK, reason="bool mask update with shaped rhs"
+                ),
+            ),
+        ),
+        (False, 0, 0),
+        (True, 0, 0),
+    ],
+)
+def test_update_ops(
+    xp: ModuleType,
+    copy: bool | None,
+    op: _AtOp,
+    y: float,
+    expect_list: list[float],
+    bool_mask: bool,
+    x_ndim: int,
+    y_ndim: int,
+):
+    if x_ndim == 1:
+        x = xp.asarray([10.0, 20.0, 30.0])
+        idx = xp.asarray([False, True, True]) if bool_mask else slice(1, None)
+        expect: list[float] | float = expect_list
+    else:
+        idx = xp.asarray(True) if bool_mask else ()
+        # Pick an element that does change with the operation
+        if op is _AtOp.MIN:
+            x = xp.asarray(30.0)
+            expect = expect_list[2]
+        else:
+            x = xp.asarray(20.0)
+            expect = expect_list[1]
+
+    if y_ndim == 1:
+        y = xp.asarray([y, y])
+
+    with assert_copy(x, copy):
+        z = at_op(x, idx, op, y, copy=copy)
+        assert isinstance(z, type(x))
+        xp_assert_equal(z, xp.asarray(expect))
+
+
+@pytest.mark.parametrize("op", list(_AtOp))
+def test_copy_default(xp: ModuleType, library: Backend, op: _AtOp):
+    """
+    Test that the default copy behaviour is False for writeable arrays
+    and True for read-only ones.
+    """
+    x = xp.asarray([1.0, 10.0, 20.0])
+    expect_copy = not is_writeable_array(x)
+    meth = cast(Callable[..., Array], getattr(at(x)[:2], op.value))
+    with assert_copy(x, None, expect_copy):
+        _ = meth(2.0)
+
+    x = xp.asarray([1.0, 10.0, 20.0])
+    # Dask's default copy value is True for bool masks,
+    # even if the arrays are writeable.
+    expect_copy = not is_writeable_array(x) or library is Backend.DASK
+    idx = xp.asarray([True, True, False])
+    meth = cast(Callable[..., Array], getattr(at(x, idx), op.value))
+    with assert_copy(x, None, expect_copy):
+        _ = meth(2.0)
+
+
+def test_copy_invalid():
+    a = np.asarray([1, 2, 3])
+    with pytest.raises(ValueError, match="copy"):
+        _ = at(a, 0).set(4, copy="invalid")  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+
+def test_xp():
+    a = cast(Array, np.asarray([1, 2, 3]))  # pyright: ignore[reportInvalidCast]
+    _ = at(a, 0).set(4, xp=np)
+    _ = at(a, 0).add(4, xp=np)
+    _ = at(a, 0).subtract(4, xp=np)
+    _ = at(a, 0).multiply(4, xp=np)
+    _ = at(a, 0).divide(4, xp=np)
+    _ = at(a, 0).power(4, xp=np)
+    _ = at(a, 0).min(4, xp=np)
+    _ = at(a, 0).max(4, xp=np)
+
+
+def test_alternate_index_syntax():
+    xp = cast(ModuleType, np)  # type: ignore[redundant-cast]  # pyright: ignore[reportInvalidCast]
+    a = cast(Array, xp.asarray([1, 2, 3]))
+    xp_assert_equal(at(a, 0).set(4, copy=True), xp.asarray([4, 2, 3]))
+    xp_assert_equal(at(a)[0].set(4, copy=True), xp.asarray([4, 2, 3]))
+
+    a_at = at(a)
+    xp_assert_equal(a_at[0].add(1, copy=True), xp.asarray([2, 2, 3]))
+    xp_assert_equal(a_at[1].add(2, copy=True), xp.asarray([1, 4, 3]))
+
+    with pytest.raises(ValueError, match="Index"):
+        _ = at(a).set(4)
+    with pytest.raises(ValueError, match="Index"):
+        _ = at(a, 0)[0].set(4)
+
+
+@pytest.mark.parametrize("copy", [True, None])
+@pytest.mark.parametrize("bool_mask", [False, True])
+@pytest.mark.parametrize("op", list(_AtOp))
+def test_incompatible_dtype(
+    xp: ModuleType,
+    library: Backend,
+    op: _AtOp,
+    copy: bool | None,
+    bool_mask: bool,
+):
+    """Test that at() replicates the backend's behaviour for
+    in-place operations with incompatible dtypes.
+
+    Behavior is backend-specific, but only two behaviors are allowed:
+    1. raise an exception, or
+    2. return the same dtype as x, disregarding y.dtype (no broadcasting).
+
+    Note that __i<op>__ and __<op>__ behave differently, and we want to
+    replicate the behavior of __i<op>__:
+
+    >>> a = np.asarray([1, 2, 3])
+    >>> a / 1.5
+    array([0.        , 0.66666667, 1.33333333])
+    >>> a /= 1.5
+    UFuncTypeError: Cannot cast ufunc 'divide' output from dtype('float64')
+    to dtype('int64') with casting rule 'same_kind'
+    """
+    x = xp.asarray([2, 4])
+    idx = xp.asarray([True, False]) if bool_mask else slice(None)
+    z = None
+
+    if library.like(Backend.JAX):
+        if bool_mask:
+            z = at_op(x, idx, op, 1.1, copy=copy)
+        else:
+            with pytest.warns(FutureWarning, match="cannot safely cast"):
+                z = at_op(x, idx, op, 1.1, copy=copy)
+
+    elif library.like(Backend.DASK):
+        z = at_op(x, idx, op, 1.1, copy=copy)
+
+    elif library.like(Backend.ARRAY_API_STRICT):
+        with pytest.raises(Exception, match=r"cast|promote|dtype"):
+            _ = at_op(x, idx, op, 1.1, copy=copy)
+
+    elif op in (_AtOp.SET, _AtOp.MIN, _AtOp.MAX):
+        # There is no __i<op>__ version of min/max.
+        # libraries other than array-api-strict are happy with
+        # int[:] = float
+        # int[:] = min(int[:], float)
+        # int[:] = max(int[:], float)
+        z = at_op(x, idx, op, 1.1, copy=copy)
+
+    else:
+        with pytest.raises(Exception, match=r"cast|promote|dtype"):
+            _ = at_op(x, idx, op, 1.1, copy=copy)
+
+    assert z is None or z.dtype == x.dtype
+
+
+def test_bool_mask_nd(xp: ModuleType):
+    x = xp.asarray([[1, 2, 3], [4, 5, 6]])
+    idx = xp.asarray([[True, False, False], [False, True, True]])
+    z = at_op(x, idx, _AtOp.SET, 0)
+    xp_assert_equal(z, xp.asarray([[0, 2, 3], [4, 0, 0]]))
+
+
+@pytest.mark.parametrize("bool_mask", [False, True])
+def test_no_inf_warnings(xp: ModuleType, bool_mask: bool):
+    x = xp.asarray([math.inf, 1.0, 2.0])
+    idx = ~xp.isinf(x) if bool_mask else slice(1, None)
+    # inf - inf -> nan with a warning
+    z = at_op(x, idx, _AtOp.SUBTRACT, math.inf)
+    xp_assert_equal(z, xp.asarray([math.inf, -math.inf, -math.inf]))
+
+
+@pytest.mark.parametrize(
+    "copy",
+    [
+        None,
+        pytest.param(
+            False,
+            marks=[
+                pytest.mark.skip_xp_backend(
+                    Backend.NUMPY, reason="np.generic is read-only"
+                ),
+                pytest.mark.skip_xp_backend(
+                    Backend.NUMPY_READONLY, reason="read-only backend"
+                ),
+                pytest.mark.skip_xp_backend(Backend.JAX, reason="read-only backend"),
+                pytest.mark.skip_xp_backend(
+                    Backend.JAX_GPU, reason="read-only backend"
+                ),
+                pytest.mark.skip_xp_backend(Backend.SPARSE, reason="read-only backend"),
+            ],
+        ),
+    ],
+)
+@pytest.mark.parametrize("bool_mask", [False, True])
+def test_gh134(xp: ModuleType, bool_mask: bool, copy: bool | None):
+    """
+    Test that xpx.at doesn't encroach in a bug of dask.array.Array.__setitem__, which
+    blindly assumes that chunk contents are writeable np.ndarray objects:
+
+    https://github.com/dask/dask/issues/11722
+
+    In other words: when special-casing bool masks for Dask, unless the user explicitly
+    asks for copy=False, do not needlessly write back to the input.
+    """
+    x = xp.zeros(1)
+
+    # In NumPy, we have a writeable np.ndarray in input and a read-only np.generic in
+    # output. As both are Arrays, this behaviour is Array API compliant.
+    # In Dask, we have a writeable da.Array on both sides, and if you call __setitem__
+    # on it all seems fine, but when you compute() your graph is corrupted.
+    y = x[0]
+
+    idx = xp.asarray(True) if bool_mask else ()
+    z = at_op(y, idx, _AtOp.SET, 1, copy=copy)
+    xp_assert_equal(z, xp.asarray(1, dtype=x.dtype))
+
+
+def test_device(xp: ModuleType, device: Device):
+    x = xp.asarray([1, 2, 3], device=device)
+
+    y = xp.asarray([4, 5], device=device)
+    z = at(x)[:2].set(y)
+    assert get_device(z) == get_device(x)
+
+    idx = xp.asarray([True, False, True], device=device)
+    z = at(x)[idx].set(4)
+    assert get_device(z) == get_device(x)
diff --git a/tests/test_funcs.py b/tests/test_funcs.py
index a8db9872..769b4119 100644
--- a/tests/test_funcs.py
+++ b/tests/test_funcs.py
@@ -1,190 +1,892 @@
-from __future__ import annotations
-
-import contextlib
+import math
 import warnings
-from typing import TYPE_CHECKING, Any
+from types import ModuleType
+from typing import Any, cast
 
-# array-api-strict#6
-import array_api_strict as xp  # type: ignore[import-untyped]
+import hypothesis
+import hypothesis.extra.numpy as npst
 import numpy as np
 import pytest
-from numpy.testing import assert_allclose, assert_array_equal, assert_equal
+from hypothesis import given
+from hypothesis import strategies as st
+
+from array_api_extra import (
+    apply_where,
+    at,
+    atleast_nd,
+    broadcast_shapes,
+    cov,
+    create_diagonal,
+    default_dtype,
+    expand_dims,
+    isclose,
+    kron,
+    nunique,
+    one_hot,
+    pad,
+    setdiff1d,
+    sinc,
+)
+from array_api_extra._lib._backends import NUMPY_VERSION, Backend
+from array_api_extra._lib._testing import xp_assert_close, xp_assert_equal
+from array_api_extra._lib._utils._compat import device as get_device
+from array_api_extra._lib._utils._helpers import eager_shape, ndindex
+from array_api_extra._lib._utils._typing import Array, Device
+from array_api_extra.testing import lazy_xp_function
+
+lazy_xp_function(apply_where)
+lazy_xp_function(atleast_nd)
+lazy_xp_function(cov)
+lazy_xp_function(create_diagonal)
+lazy_xp_function(expand_dims)
+lazy_xp_function(kron)
+lazy_xp_function(nunique)
+lazy_xp_function(one_hot)
+lazy_xp_function(pad)
+# FIXME calls in1d which calls xp.unique_values without size
+lazy_xp_function(setdiff1d, jax_jit=False)
+lazy_xp_function(sinc)
+
+
+class TestApplyWhere:
+    @staticmethod
+    def f1(x: Array, y: Array | int = 10) -> Array:
+        return x + y
+
+    @staticmethod
+    def f2(x: Array, y: Array | int = 10) -> Array:
+        return x - y
+
+    def test_f1_f2(self, xp: ModuleType):
+        x = xp.asarray([1, 2, 3, 4])
+        cond = x % 2 == 0
+        actual = apply_where(cond, x, self.f1, self.f2)
+        expect = xp.where(cond, self.f1(x), self.f2(x))
+        xp_assert_equal(actual, expect)
+
+    def test_fill_value(self, xp: ModuleType):
+        x = xp.asarray([1, 2, 3, 4])
+        cond = x % 2 == 0
+        actual = apply_where(x % 2 == 0, x, self.f1, fill_value=0)
+        expect = xp.where(cond, self.f1(x), xp.asarray(0))
+        xp_assert_equal(actual, expect)
+
+        actual = apply_where(x % 2 == 0, x, self.f1, fill_value=xp.asarray(0))
+        xp_assert_equal(actual, expect)
+
+    def test_args_tuple(self, xp: ModuleType):
+        x = xp.asarray([1, 2, 3, 4])
+        y = xp.asarray([10, 20, 30, 40])
+        cond = x % 2 == 0
+        actual = apply_where(cond, (x, y), self.f1, self.f2)
+        expect = xp.where(cond, self.f1(x, y), self.f2(x, y))
+        xp_assert_equal(actual, expect)
+
+    def test_broadcast(self, xp: ModuleType):
+        x = xp.asarray([1, 2])
+        y = xp.asarray([[10], [20], [30]])
+        cond = xp.broadcast_to(xp.asarray(True), (4, 1, 1))
+
+        actual = apply_where(cond, (x, y), self.f1, self.f2)
+        expect = xp.where(cond, self.f1(x, y), self.f2(x, y))
+        xp_assert_equal(actual, expect)
+
+        actual = apply_where(
+            cond,
+            (x, y),
+            lambda x, _: x,
+            lambda _, y: y,
+        )
+        expect = xp.where(cond, x, y)
+        xp_assert_equal(actual, expect)
+
+        # Shaped fill_value
+        actual = apply_where(cond, x, self.f1, fill_value=y)
+        expect = xp.where(cond, self.f1(x), y)
+        xp_assert_equal(actual, expect)
+
+    def test_dtype_propagation(self, xp: ModuleType, library: Backend):
+        x = xp.asarray([1, 2], dtype=xp.int8)
+        y = xp.asarray([3, 4], dtype=xp.int16)
+        cond = x % 2 == 0
+
+        mxp = np if library is Backend.DASK else xp
+        actual = apply_where(
+            cond,
+            (x, y),
+            self.f1,
+            lambda x, y: mxp.astype(x - y, xp.int64),  # pyright: ignore[reportArgumentType]
+        )
+        assert actual.dtype == xp.int64
+
+        actual = apply_where(cond, y, self.f1, fill_value=5)
+        assert actual.dtype == xp.int16
+
+    @pytest.mark.parametrize("fill_value_raw", [3, [3, 4]])
+    @pytest.mark.parametrize(
+        ("fill_value_dtype", "expect_dtype"), [("int32", "int32"), ("int8", "int16")]
+    )
+    def test_dtype_propagation_fill_value(
+        self,
+        xp: ModuleType,
+        fill_value_raw: int | list[int],
+        fill_value_dtype: str,
+        expect_dtype: str,
+    ):
+        x = xp.asarray([1, 2], dtype=xp.int16)
+        cond = x % 2 == 0
+        fill_value = xp.asarray(fill_value_raw, dtype=getattr(xp, fill_value_dtype))
+
+        actual = apply_where(cond, x, self.f1, fill_value=fill_value)
+        assert actual.dtype == getattr(xp, expect_dtype)
+
+    def test_dont_overwrite_fill_value(self, xp: ModuleType):
+        x = xp.asarray([1, 2])
+        fill_value = xp.asarray([100, 200])
+        actual = apply_where(x % 2 == 0, x, self.f1, fill_value=fill_value)
+        xp_assert_equal(actual, xp.asarray([100, 12]))
+        xp_assert_equal(fill_value, xp.asarray([100, 200]))
+
+    @pytest.mark.skip_xp_backend(
+        Backend.ARRAY_API_STRICTEST,
+        reason="no boolean indexing -> run everywhere",
+    )
+    @pytest.mark.skip_xp_backend(
+        Backend.SPARSE,
+        reason="no indexing by sparse array -> run everywhere",
+    )
+    def test_dont_run_on_false(self, xp: ModuleType):
+        x = xp.asarray([1.0, 2.0, 0.0])
+        y = xp.asarray([0.0, 3.0, 4.0])
+        # On NumPy, division by zero will trigger warnings
+        actual = apply_where(
+            x == 0,
+            (x, y),
+            lambda x, y: x / y,
+            lambda x, y: y / x,
+        )
+        xp_assert_equal(actual, xp.asarray([0.0, 1.5, 0.0]))
+
+    def test_bad_args(self, xp: ModuleType):
+        x = xp.asarray([1, 2, 3, 4])
+        cond = x % 2 == 0
+        # Neither f2 nor fill_value
+        with pytest.raises(TypeError, match="Exactly one of"):
+            apply_where(cond, x, self.f1)  # type: ignore[call-overload]  # pyright: ignore[reportCallIssue]
+        # Both f2 and fill_value
+        with pytest.raises(TypeError, match="Exactly one of"):
+            apply_where(cond, x, self.f1, self.f2, fill_value=0)  # type: ignore[call-overload]  # pyright: ignore[reportCallIssue]
+
+    @pytest.mark.skip_xp_backend(Backend.NUMPY_READONLY, reason="xp=xp")
+    def test_xp(self, xp: ModuleType):
+        x = xp.asarray([1, 2, 3, 4])
+        cond = x % 2 == 0
+        actual = apply_where(cond, x, self.f1, self.f2, xp=xp)
+        expect = xp.where(cond, self.f1(x), self.f2(x))
+        xp_assert_equal(actual, expect)
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray([1, 2, 3, 4], device=device)
+        y = apply_where(x % 2 == 0, x, self.f1, self.f2)
+        assert get_device(y) == device
+        y = apply_where(x % 2 == 0, x, self.f1, fill_value=0)
+        assert get_device(y) == device
+        y = apply_where(x % 2 == 0, x, self.f1, fill_value=x)
+        assert get_device(y) == device
+
+    @pytest.mark.filterwarnings("ignore::RuntimeWarning")  # overflows, etc.
+    @hypothesis.settings(
+        # The xp and library fixtures are not regenerated between hypothesis iterations
+        suppress_health_check=[hypothesis.HealthCheck.function_scoped_fixture],
+        # JAX can take a long time to initialize on the first call
+        deadline=None,
+    )
+    @given(
+        n_arrays=st.integers(min_value=1, max_value=3),
+        rng_seed=st.integers(min_value=1000000000, max_value=9999999999),
+        dtype=st.sampled_from((np.float32, np.float64)),
+        p=st.floats(min_value=0, max_value=1),
+        data=st.data(),
+    )
+    def test_hypothesis(
+        self,
+        n_arrays: int,
+        rng_seed: int,
+        dtype: np.dtype[Any],
+        p: float,
+        data: st.DataObject,
+        xp: ModuleType,
+        library: Backend,
+    ):
+        if (
+            library.like(Backend.NUMPY)
+            and NUMPY_VERSION < (2, 0)
+            and dtype is np.float32
+        ):
+            pytest.xfail(reason="NumPy 1.x dtype promotion for scalars")
+
+        mbs = npst.mutually_broadcastable_shapes(num_shapes=n_arrays + 1, min_side=0)
+        input_shapes, _ = data.draw(mbs)
+        cond_shape, *shapes = input_shapes
+
+        # cupy/cupy#8382
+        # https://github.com/jax-ml/jax/issues/26658
+        elements = {"allow_subnormal": not library.like(Backend.CUPY, Backend.JAX)}
+
+        fill_value = xp.asarray(
+            data.draw(npst.arrays(dtype=dtype, shape=(), elements=elements))
+        )
+        float_fill_value = float(fill_value)
+        if library is Backend.CUPY and dtype is np.float32:
+            # Avoid data-dependent dtype promotion when encountering subnormals
+            # close to the max float32 value
+            float_fill_value = float(np.clip(float_fill_value, -1e38, 1e38))
+
+        arrays = tuple(
+            xp.asarray(
+                data.draw(npst.arrays(dtype=dtype, shape=shape, elements=elements))
+            )
+            for shape in shapes
+        )
 
-from array_api_extra import atleast_nd, cov, create_diagonal, expand_dims, kron, sinc
+        def f1(*args: Array) -> Array:
+            return cast(Array, sum(args))
 
-if TYPE_CHECKING:
-    Array = Any  # To be changed to a Protocol later (see array-api#589)
+        def f2(*args: Array) -> Array:
+            return cast(Array, sum(args) / 2)
+
+        rng = np.random.default_rng(rng_seed)
+        cond = xp.asarray(rng.random(size=cond_shape) > p)
+
+        res1 = apply_where(cond, arrays, f1, fill_value=fill_value)
+        res2 = apply_where(cond, arrays, f1, f2)
+        res3 = apply_where(cond, arrays, f1, fill_value=float_fill_value)
+
+        ref1 = xp.where(cond, f1(*arrays), fill_value)
+        ref2 = xp.where(cond, f1(*arrays), f2(*arrays))
+        ref3 = xp.where(cond, f1(*arrays), float_fill_value)
+
+        xp_assert_close(res1, ref1, rtol=2e-16)
+        xp_assert_equal(res2, ref2)
+        xp_assert_equal(res3, ref3)
 
 
 class TestAtLeastND:
-    def test_0D(self):
-        x = xp.asarray(1)
+    def test_0D(self, xp: ModuleType):
+        x = xp.asarray(1.0)
 
-        y = atleast_nd(x, ndim=0, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=0)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=1, xp=xp)
-        assert_array_equal(y, xp.ones((1,)))
+        y = atleast_nd(x, ndim=1)
+        xp_assert_equal(y, xp.ones((1,)))
 
-        y = atleast_nd(x, ndim=5, xp=xp)
-        assert_array_equal(y, xp.ones((1, 1, 1, 1, 1)))
+        y = atleast_nd(x, ndim=5)
+        xp_assert_equal(y, xp.ones((1, 1, 1, 1, 1)))
 
-    def test_1D(self):
+    def test_1D(self, xp: ModuleType):
         x = xp.asarray([0, 1])
 
-        y = atleast_nd(x, ndim=0, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=0)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=1, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=1)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=2, xp=xp)
-        assert_array_equal(y, xp.asarray([[0, 1]]))
+        y = atleast_nd(x, ndim=2)
+        xp_assert_equal(y, xp.asarray([[0, 1]]))
 
-        y = atleast_nd(x, ndim=5, xp=xp)
-        assert_array_equal(y, xp.reshape(xp.arange(2), (1, 1, 1, 1, 2)))
+        y = atleast_nd(x, ndim=5)
+        xp_assert_equal(y, xp.asarray([[[[[0, 1]]]]]))
 
-    def test_2D(self):
-        x = xp.asarray([[3]])
+    def test_2D(self, xp: ModuleType):
+        x = xp.asarray([[3.0]])
 
-        y = atleast_nd(x, ndim=0, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=0)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=2, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=2)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=3, xp=xp)
-        assert_array_equal(y, 3 * xp.ones((1, 1, 1)))
+        y = atleast_nd(x, ndim=3)
+        xp_assert_equal(y, 3 * xp.ones((1, 1, 1)))
 
-        y = atleast_nd(x, ndim=5, xp=xp)
-        assert_array_equal(y, 3 * xp.ones((1, 1, 1, 1, 1)))
+        y = atleast_nd(x, ndim=5)
+        xp_assert_equal(y, 3 * xp.ones((1, 1, 1, 1, 1)))
 
-    def test_5D(self):
+    def test_5D(self, xp: ModuleType):
         x = xp.ones((1, 1, 1, 1, 1))
 
-        y = atleast_nd(x, ndim=0, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=0)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=4, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=4)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=5, xp=xp)
-        assert_array_equal(y, x)
+        y = atleast_nd(x, ndim=5)
+        xp_assert_equal(y, x)
 
-        y = atleast_nd(x, ndim=6, xp=xp)
-        assert_array_equal(y, xp.ones((1, 1, 1, 1, 1, 1)))
+        y = atleast_nd(x, ndim=6)
+        xp_assert_equal(y, xp.ones((1, 1, 1, 1, 1, 1)))
 
-        y = atleast_nd(x, ndim=9, xp=xp)
-        assert_array_equal(y, xp.ones((1, 1, 1, 1, 1, 1, 1, 1, 1)))
+        y = atleast_nd(x, ndim=9)
+        xp_assert_equal(y, xp.ones((1, 1, 1, 1, 1, 1, 1, 1, 1)))
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray([1, 2, 3], device=device)
+        assert get_device(atleast_nd(x, ndim=2)) == device
+
+    def test_xp(self, xp: ModuleType):
+        x = xp.asarray(1.0)
+        y = atleast_nd(x, ndim=1, xp=xp)
+        xp_assert_equal(y, xp.ones((1,)))
+
+
+class TestBroadcastShapes:
+    @pytest.mark.parametrize(
+        "args",
+        [
+            (),
+            ((),),
+            ((), ()),
+            ((1,),),
+            ((1,), (1,)),
+            ((2,), (1,)),
+            ((3, 1, 4), (2, 1)),
+            ((1, 1, 4), (2, 1)),
+            ((1,), ()),
+            ((), (2,), ()),
+            ((0,),),
+            ((0,), (1,)),
+            ((2, 0), (1, 1)),
+            ((2, 0, 3), (2, 1, 1)),
+        ],
+    )
+    def test_simple(self, args: tuple[tuple[int, ...], ...]):
+        expect = np.broadcast_shapes(*args)
+        actual = broadcast_shapes(*args)
+        assert actual == expect
+
+    @pytest.mark.parametrize(
+        "args",
+        [
+            ((2,), (3,)),
+            ((2, 3), (1, 2)),
+            ((2,), (0,)),
+            ((2, 0, 2), (1, 3, 1)),
+        ],
+    )
+    def test_fail(self, args: tuple[tuple[int, ...], ...]):
+        match = "cannot be broadcast to a single shape"
+        with pytest.raises(ValueError, match=match):
+            _ = np.broadcast_shapes(*args)
+        with pytest.raises(ValueError, match=match):
+            _ = broadcast_shapes(*args)
+
+    @pytest.mark.parametrize(
+        "args",
+        [
+            ((None,), (None,)),
+            ((math.nan,), (None,)),
+            ((1, None, 2, 4), (2, 3, None, 1), (2, None, None, 4)),
+            ((1, math.nan, 2), (4, 2, 3, math.nan), (4, 2, None, None)),
+            ((math.nan, 1), (None, 2), (None, 2)),
+        ],
+    )
+    def test_none(self, args: tuple[tuple[float | None, ...], ...]):
+        expect = args[-1]
+        actual = broadcast_shapes(*args[:-1])
+        assert actual == expect
 
 
 class TestCov:
-    def test_basic(self):
-        assert_allclose(
-            cov(xp.asarray([[0, 2], [1, 1], [2, 0]]).T, xp=xp),
-            xp.asarray([[1.0, -1.0], [-1.0, 1.0]]),
+    def test_basic(self, xp: ModuleType):
+        xp_assert_close(
+            cov(xp.asarray([[0, 2], [1, 1], [2, 0]]).T),
+            xp.asarray([[1.0, -1.0], [-1.0, 1.0]], dtype=xp.float64),
         )
 
-    def test_complex(self):
-        x = xp.asarray([[1, 2, 3], [1j, 2j, 3j]])
-        res = xp.asarray([[1.0, -1.0j], [1.0j, 1.0]])
-        assert_allclose(cov(x, xp=xp), res)
+    def test_complex(self, xp: ModuleType):
+        actual = cov(xp.asarray([[1, 2, 3], [1j, 2j, 3j]]))
+        expect = xp.asarray([[1.0, -1.0j], [1.0j, 1.0]], dtype=xp.complex128)
+        xp_assert_close(actual, expect)
 
-    def test_empty(self):
+    @pytest.mark.xfail_xp_backend(Backend.SPARSE, reason="sparse#877")
+    def test_empty(self, xp: ModuleType):
         with warnings.catch_warnings(record=True):
             warnings.simplefilter("always", RuntimeWarning)
-            assert_array_equal(cov(xp.asarray([]), xp=xp), xp.nan)
-            assert_array_equal(
-                cov(xp.reshape(xp.asarray([]), (0, 2)), xp=xp),
-                xp.reshape(xp.asarray([]), (0, 0)),
+            xp_assert_equal(cov(xp.asarray([])), xp.asarray(xp.nan, dtype=xp.float64))
+            xp_assert_equal(
+                cov(xp.reshape(xp.asarray([]), (0, 2))),
+                xp.reshape(xp.asarray([], dtype=xp.float64), (0, 0)),
             )
-            assert_array_equal(
-                cov(xp.reshape(xp.asarray([]), (2, 0)), xp=xp),
-                xp.asarray([[xp.nan, xp.nan], [xp.nan, xp.nan]]),
+            xp_assert_equal(
+                cov(xp.reshape(xp.asarray([]), (2, 0))),
+                xp.asarray([[xp.nan, xp.nan], [xp.nan, xp.nan]], dtype=xp.float64),
             )
 
-    def test_combination(self):
+    def test_combination(self, xp: ModuleType):
         x = xp.asarray([-2.1, -1, 4.3])
         y = xp.asarray([3, 1.1, 0.12])
         X = xp.stack((x, y), axis=0)
-        desired = xp.asarray([[11.71, -4.286], [-4.286, 2.144133]])
-        assert_allclose(cov(X, xp=xp), desired, rtol=1e-6)
-        assert_allclose(cov(x, xp=xp), xp.asarray(11.71))
-        assert_allclose(cov(y, xp=xp), xp.asarray(2.144133), rtol=1e-6)
+        desired = xp.asarray([[11.71, -4.286], [-4.286, 2.144133]], dtype=xp.float64)
+        xp_assert_close(cov(X), desired, rtol=1e-6)
+        xp_assert_close(cov(x), xp.asarray(11.71, dtype=xp.float64))
+        xp_assert_close(cov(y), xp.asarray(2.144133, dtype=xp.float64), rtol=1e-6)
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray([1, 2, 3], device=device)
+        assert get_device(cov(x)) == device
 
+    @pytest.mark.skip_xp_backend(Backend.NUMPY_READONLY, reason="xp=xp")
+    def test_xp(self, xp: ModuleType):
+        xp_assert_close(
+            cov(xp.asarray([[0.0, 2.0], [1.0, 1.0], [2.0, 0.0]]).T, xp=xp),
+            xp.asarray([[1.0, -1.0], [-1.0, 1.0]], dtype=xp.float64),
+        )
 
+
+@pytest.mark.xfail_xp_backend(Backend.SPARSE, reason="no arange", strict=False)
+class TestOneHot:
+    @pytest.mark.parametrize("n_dim", range(4))
+    @pytest.mark.parametrize("num_classes", [1, 3, 10])
+    def test_dims_and_classes(self, xp: ModuleType, n_dim: int, num_classes: int):
+        shape = tuple(range(2, 2 + n_dim))
+        rng = np.random.default_rng(2347823)
+        np_x = rng.integers(num_classes, size=shape)
+        x = xp.asarray(np_x)
+        y = one_hot(x, num_classes)
+        assert y.shape == (*x.shape, num_classes)
+        for *i_list, j in ndindex(*shape, num_classes):
+            i = tuple(i_list)
+            assert float(y[(*i, j)]) == (int(x[i]) == j)
+
+    def test_basic(self, xp: ModuleType):
+        actual = one_hot(xp.asarray([0, 1, 2]), 3)
+        expected = xp.asarray([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
+        xp_assert_equal(actual, expected)
+
+        actual = one_hot(xp.asarray([1, 2, 0]), 3)
+        expected = xp.asarray([[0.0, 1.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]])
+        xp_assert_equal(actual, expected)
+
+    def test_2d(self, xp: ModuleType):
+        actual = one_hot(xp.asarray([[2, 1, 0], [1, 0, 2]]), 3, axis=1)
+        expected = xp.asarray(
+            [
+                [[0.0, 0.0, 1.0], [0.0, 1.0, 0.0], [1.0, 0.0, 0.0]],
+                [[0.0, 1.0, 0.0], [1.0, 0.0, 0.0], [0.0, 0.0, 1.0]],
+            ]
+        )
+        xp_assert_equal(actual, expected)
+
+    @pytest.mark.skip_xp_backend(
+        Backend.ARRAY_API_STRICTEST, reason="backend doesn't support Boolean indexing"
+    )
+    def test_abstract_size(self, xp: ModuleType):
+        x = xp.arange(5)
+        x = x[x > 2]
+        actual = one_hot(x, 5)
+        expected = xp.asarray([[0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0]])
+        xp_assert_equal(actual, expected)
+
+    @pytest.mark.skip_xp_backend(
+        Backend.TORCH_GPU, reason="Puts Pytorch into a bad state."
+    )
+    def test_out_of_bound(self, xp: ModuleType):
+        # Undefined behavior.  Either return zero, or raise.
+        try:
+            actual = one_hot(xp.asarray([-1, 3]), 3)
+        except IndexError:
+            return
+        expected = xp.asarray([[0.0, 0.0, 0.0], [0.0, 0.0, 0.0]])
+        xp_assert_equal(actual, expected)
+
+    @pytest.mark.parametrize(
+        "int_dtype",
+        ["int8", "int16", "int32", "int64", "uint8", "uint16", "uint32", "uint64"],
+    )
+    def test_int_types(self, xp: ModuleType, int_dtype: str):
+        dtype = getattr(xp, int_dtype)
+        x = xp.asarray([0, 1, 2], dtype=dtype)
+        actual = one_hot(x, 3)
+        expected = xp.asarray([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])
+        xp_assert_equal(actual, expected)
+
+    def test_custom_dtype(self, xp: ModuleType):
+        actual = one_hot(xp.asarray([0, 1, 2], dtype=xp.int32), 3, dtype=xp.bool)
+        expected = xp.asarray(
+            [[True, False, False], [False, True, False], [False, False, True]]
+        )
+        xp_assert_equal(actual, expected)
+
+    def test_axis(self, xp: ModuleType):
+        expected = xp.asarray([[0.0, 1.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0]]).T
+        actual = one_hot(xp.asarray([1, 2, 0]), 3, axis=0)
+        xp_assert_equal(actual, expected)
+
+        actual = one_hot(xp.asarray([1, 2, 0]), 3, axis=-2)
+        xp_assert_equal(actual, expected)
+
+    def test_non_integer(self, xp: ModuleType):
+        with pytest.raises(TypeError):
+            _ = one_hot(xp.asarray([1.0]), 3)
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray([0, 1, 2], device=device)
+        y = one_hot(x, 3)
+        assert get_device(y) == device
+
+
+@pytest.mark.skip_xp_backend(
+    Backend.SPARSE, reason="read-only backend without .at support"
+)
 class TestCreateDiagonal:
-    def test_1d(self):
+    def test_1d_from_numpy(self, xp: ModuleType):
         # from np.diag tests
         vals = 100 * xp.arange(5, dtype=xp.float64)
-        b = xp.zeros((5, 5))
+        b = xp.zeros((5, 5), dtype=xp.float64)
         for k in range(5):
-            b[k, k] = vals[k]
-        assert_array_equal(create_diagonal(vals, xp=xp), b)
-        b = xp.zeros((7, 7))
+            b = at(b)[k, k].set(vals[k])
+        xp_assert_equal(create_diagonal(vals), b)
+        b = xp.zeros((7, 7), dtype=xp.float64)
         c = xp.asarray(b, copy=True)
         for k in range(5):
-            b[k, k + 2] = vals[k]
-            c[k + 2, k] = vals[k]
-        assert_array_equal(create_diagonal(vals, offset=2, xp=xp), b)
-        assert_array_equal(create_diagonal(vals, offset=-2, xp=xp), c)
+            b = at(b)[k, k + 2].set(vals[k])
+            c = at(c)[k + 2, k].set(vals[k])
+        xp_assert_equal(create_diagonal(vals, offset=2), b)
+        xp_assert_equal(create_diagonal(vals, offset=-2), c)
 
     @pytest.mark.parametrize("n", range(1, 10))
     @pytest.mark.parametrize("offset", range(1, 10))
-    def test_create_diagonal(self, n, offset):
+    def test_1d_from_scipy(self, xp: ModuleType, n: int, offset: int):
         # from scipy._lib tests
         rng = np.random.default_rng(2347823)
         one = xp.asarray(1.0)
         x = rng.random(n)
-        A = create_diagonal(xp.asarray(x, dtype=one.dtype), offset=offset, xp=xp)
+        A = create_diagonal(xp.asarray(x, dtype=one.dtype), offset=offset)
         B = xp.asarray(np.diag(x, offset), dtype=one.dtype)
-        assert_array_equal(A, B)
+        xp_assert_equal(A, B)
 
-    def test_0d(self):
+    def test_0d_raises(self, xp: ModuleType):
         with pytest.raises(ValueError, match="1-dimensional"):
-            create_diagonal(xp.asarray(1), xp=xp)
+            _ = create_diagonal(xp.asarray(1))
 
-    def test_2d(self):
-        with pytest.raises(ValueError, match="1-dimensional"):
-            create_diagonal(xp.asarray([[1]]), xp=xp)
+    @pytest.mark.parametrize(
+        "shape",
+        [
+            (0,),
+            (10,),
+            (0, 1),
+            (1, 0),
+            (0, 0),
+            (4, 2, 1),
+            (1, 1, 7),
+            (0, 0, 1),
+            (3, 2, 4, 5),
+        ],
+    )
+    def test_nd(self, xp: ModuleType, shape: tuple[int, ...]):
+        rng = np.random.default_rng(2347823)
+        b = xp.asarray(
+            rng.integers((1 << 64) - 1, size=shape, dtype=np.uint64), dtype=xp.uint64
+        )
+        c = create_diagonal(b)
+        zero = xp.zeros((), dtype=xp.uint64)
+        assert c.shape == (*b.shape, b.shape[-1])
+        for i in ndindex(*eager_shape(c)):
+            xp_assert_equal(c[i], b[i[:-1]] if i[-2] == i[-1] else zero)
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray([1, 2, 3], device=device)
+        assert get_device(create_diagonal(x)) == device
+
+    def test_xp(self, xp: ModuleType):
+        x = xp.asarray([1, 2])
+        y = create_diagonal(x, xp=xp)
+        xp_assert_equal(y, xp.asarray([[1, 0], [0, 2]]))
+
+
+class TestDefaultDType:
+    def test_basic(self, xp: ModuleType):
+        assert default_dtype(xp) == xp.empty(0).dtype
+
+    def test_kind(self, xp: ModuleType):
+        assert default_dtype(xp, "real floating") == xp.empty(0).dtype
+        assert default_dtype(xp, "complex floating") == (xp.empty(0) * 1j).dtype
+        assert default_dtype(xp, "integral") == xp.int64
+        assert default_dtype(xp, "indexing") == xp.int64
+
+        with pytest.raises(ValueError, match="Unknown kind"):
+            _ = default_dtype(xp, "foo")  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+    def test_device(self, xp: ModuleType, device: Device):
+        # Note: at the moment there are no known namespaces with
+        # device-specific default dtypes.
+        assert default_dtype(xp, device=None) == xp.empty(0).dtype
+        assert default_dtype(xp, device=device) == xp.empty(0).dtype
+
+    def test_torch(self, torch: ModuleType):
+        xp = torch
+        xp.set_default_dtype(xp.float64)
+        assert default_dtype(xp) == xp.float64
+        assert default_dtype(xp, "real floating") == xp.float64
+        assert default_dtype(xp, "complex floating") == xp.complex128
+
+        xp.set_default_dtype(xp.float32)
+        assert default_dtype(xp) == xp.float32
+        assert default_dtype(xp, "real floating") == xp.float32
+        assert default_dtype(xp, "complex floating") == xp.complex64
+
+
+class TestExpandDims:
+    def test_single_axis(self, xp: ModuleType):
+        """Trivial case where xpx.expand_dims doesn't add anything to xp.expand_dims"""
+        a = xp.asarray(np.reshape(np.arange(2 * 3 * 4 * 5), (2, 3, 4, 5)))
+        for axis in range(-5, 4):
+            b = expand_dims(a, axis=axis)
+            xp_assert_equal(b, xp.expand_dims(a, axis=axis))
+
+    def test_axis_tuple(self, xp: ModuleType):
+        a = xp.empty((3, 3, 3))
+        assert expand_dims(a, axis=(0, 1, 2)).shape == (1, 1, 1, 3, 3, 3)
+        assert expand_dims(a, axis=(0, -1, -2)).shape == (1, 3, 3, 3, 1, 1)
+        assert expand_dims(a, axis=(0, 3, 5)).shape == (1, 3, 3, 1, 3, 1)
+        assert expand_dims(a, axis=(0, -3, -5)).shape == (1, 1, 3, 1, 3, 3)
+
+    def test_axis_out_of_range(self, xp: ModuleType):
+        a = xp.empty((2, 3, 4, 5))
+        with pytest.raises(IndexError, match="out of bounds"):
+            _ = expand_dims(a, axis=-6)
+        with pytest.raises(IndexError, match="out of bounds"):
+            _ = expand_dims(a, axis=5)
+
+        a = xp.empty((3, 3, 3))
+        with pytest.raises(IndexError, match="out of bounds"):
+            _ = expand_dims(a, axis=(0, -6))
+        with pytest.raises(IndexError, match="out of bounds"):
+            _ = expand_dims(a, axis=(0, 5))
+
+    def test_repeated_axis(self, xp: ModuleType):
+        a = xp.empty((3, 3, 3))
+        with pytest.raises(ValueError, match="Duplicate dimensions"):
+            _ = expand_dims(a, axis=(1, 1))
+
+    def test_positive_negative_repeated(self, xp: ModuleType):
+        # https://github.com/data-apis/array-api/issues/760#issuecomment-1989449817
+        a = xp.empty((2, 3, 4, 5))
+        with pytest.raises(ValueError, match="Duplicate dimensions"):
+            _ = expand_dims(a, axis=(3, -3))
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray([1, 2, 3], device=device)
+        assert get_device(expand_dims(x, axis=0)) == device
+
+    def test_xp(self, xp: ModuleType):
+        x = xp.asarray([1, 2, 3])
+        y = expand_dims(x, axis=(0, 1, 2), xp=xp)
+        assert y.shape == (1, 1, 1, 3)
+
+
+@pytest.mark.filterwarnings(  # array_api_strictest
+    "ignore:invalid value encountered:RuntimeWarning:array_api_strict"
+)
+@pytest.mark.filterwarnings(  # sparse
+    "ignore:invalid value encountered:RuntimeWarning:sparse"
+)
+class TestIsClose:
+    @pytest.mark.parametrize("swap", [False, True])
+    @pytest.mark.parametrize(
+        ("a", "b"),
+        [
+            (0.0, 0.0),
+            (1.0, 1.0),
+            (1.0, 2.0),
+            (1.0, -1.0),
+            (100.0, 101.0),
+            (0, 0),
+            (1, 1),
+            (1, 2),
+            (1, -1),
+            (1.0 + 1j, 1.0 + 1j),
+            (1.0 + 1j, 1.0 - 1j),
+            (float("inf"), float("inf")),
+            (float("inf"), 100.0),
+            (float("inf"), float("-inf")),
+            (float("-inf"), float("-inf")),
+            (float("nan"), float("nan")),
+            (float("nan"), 100.0),
+            (1e6, 1e6 + 1),  # True - within rtol
+            (1e6, 1e6 + 100),  # False - outside rtol
+            (1e-6, 1.1e-6),  # False - outside atol
+            (1e-7, 1.1e-7),  # True - outside atol
+            (1e6 + 0j, 1e6 + 1j),  # True - within rtol
+            (1e6 + 0j, 1e6 + 100j),  # False - outside rtol
+        ],
+    )
+    def test_basic(self, a: float, b: float, swap: bool, xp: ModuleType):
+        if swap:
+            b, a = a, b
+        a_xp = xp.asarray(a)
+        b_xp = xp.asarray(b)
+
+        xp_assert_equal(isclose(a_xp, b_xp), xp.asarray(np.isclose(a, b)))
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            ar_np = a * np.arange(10)
+            br_np = b * np.arange(10)
+            ar_xp = xp.asarray(ar_np)
+            br_xp = xp.asarray(br_np)
+
+        xp_assert_equal(isclose(ar_xp, br_xp), xp.asarray(np.isclose(ar_np, br_np)))
+
+    @pytest.mark.parametrize("dtype", ["float32", "int32"])
+    def test_broadcast(self, dtype: str, xp: ModuleType):
+        dtype = getattr(xp, dtype)
+        a = xp.asarray([1, 2, 3], dtype=dtype)
+        b = xp.asarray([[1], [5]], dtype=dtype)
+        actual = isclose(a, b)
+        expect = xp.asarray(
+            [[True, False, False], [False, False, False]], dtype=xp.bool
+        )
+
+        xp_assert_equal(actual, expect)
+
+    def test_some_inf(self, xp: ModuleType):
+        a = xp.asarray([0.0, 1.0, xp.inf, xp.inf, xp.inf])
+        b = xp.asarray([1e-9, 1.0, xp.inf, -xp.inf, 2.0])
+        actual = isclose(a, b)
+        xp_assert_equal(actual, xp.asarray([True, True, True, False, False]))
+
+    def test_equal_nan(self, xp: ModuleType):
+        a = xp.asarray([xp.nan, xp.nan, 1.0])
+        b = xp.asarray([xp.nan, 1.0, xp.nan])
+        xp_assert_equal(isclose(a, b), xp.asarray([False, False, False]))
+        xp_assert_equal(isclose(a, b, equal_nan=True), xp.asarray([True, False, False]))
+
+    @pytest.mark.parametrize("dtype", ["float32", "complex64", "int32"])
+    def test_tolerance(self, dtype: str, xp: ModuleType):
+        dtype = getattr(xp, dtype)
+        a = xp.asarray([100, 100], dtype=dtype)
+        b = xp.asarray([101, 102], dtype=dtype)
+        xp_assert_equal(isclose(a, b), xp.asarray([False, False]))
+        xp_assert_equal(isclose(a, b, atol=1), xp.asarray([True, False]))
+        xp_assert_equal(isclose(a, b, rtol=0.01), xp.asarray([True, False]))
+
+        # Attempt to trigger division by 0 in rtol on int dtype
+        xp_assert_equal(isclose(a, b, rtol=0), xp.asarray([False, False]))
+        xp_assert_equal(isclose(a, b, atol=1, rtol=0), xp.asarray([True, False]))
+
+    @pytest.mark.parametrize("dtype", ["int8", "uint8"])
+    def test_tolerance_integer_overflow(self, dtype: str, xp: ModuleType):
+        """1/rtol is too large for dtype"""
+        a = xp.asarray([100, 100], dtype=getattr(xp, dtype))
+        b = xp.asarray([100, 101], dtype=getattr(xp, dtype))
+        xp_assert_equal(isclose(a, b), xp.asarray([True, False]))
+
+    def test_very_small_numbers(self, xp: ModuleType):
+        a = xp.asarray([1e-9, 1e-9])
+        b = xp.asarray([1.0001e-9, 1.00001e-9])
+        # Difference is below default atol
+        xp_assert_equal(isclose(a, b), xp.asarray([True, True]))
+        # Use only rtol
+        xp_assert_equal(isclose(a, b, atol=0), xp.asarray([False, True]))
+        xp_assert_equal(isclose(a, b, atol=0, rtol=0), xp.asarray([False, False]))
+
+    def test_bool_dtype(self, xp: ModuleType):
+        a = xp.asarray([False, True, False])
+        b = xp.asarray([True, True, False])
+        xp_assert_equal(isclose(a, b), xp.asarray([False, True, True]))
+        xp_assert_equal(isclose(a, b, atol=1), xp.asarray([True, True, True]))
+        xp_assert_equal(isclose(a, b, atol=2), xp.asarray([True, True, True]))
+        xp_assert_equal(isclose(a, b, rtol=1), xp.asarray([True, True, True]))
+        xp_assert_equal(isclose(a, b, rtol=2), xp.asarray([True, True, True]))
+
+        # Test broadcasting
+        xp_assert_equal(
+            isclose(a, xp.asarray(True), atol=1), xp.asarray([True, True, True])
+        )
+        xp_assert_equal(
+            isclose(xp.asarray(True), b, atol=1), xp.asarray([True, True, True])
+        )
+
+    @pytest.mark.skip_xp_backend(Backend.SPARSE, reason="index by sparse array")
+    @pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="unknown shape")
+    def test_none_shape(self, xp: ModuleType):
+        a = xp.asarray([1, 5, 0])
+        b = xp.asarray([1, 4, 2])
+        b = b[a < 5]
+        a = a[a < 5]
+        xp_assert_equal(isclose(a, b), xp.asarray([True, False]))
+
+    @pytest.mark.skip_xp_backend(Backend.SPARSE, reason="index by sparse array")
+    @pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="unknown shape")
+    def test_none_shape_bool(self, xp: ModuleType):
+        a = xp.asarray([True, True, False])
+        b = xp.asarray([True, False, True])
+        b = b[a]
+        a = a[a]
+        xp_assert_equal(isclose(a, b), xp.asarray([True, False]))
+
+    @pytest.mark.skip_xp_backend(Backend.NUMPY_READONLY, reason="xp=xp")
+    def test_python_scalar(self, xp: ModuleType):
+        a = xp.asarray([0.0, 0.1], dtype=xp.float32)
+        xp_assert_equal(isclose(a, 0.0), xp.asarray([True, False]))
+        xp_assert_equal(isclose(0.0, a), xp.asarray([True, False]))
+
+        a = xp.asarray([0, 1], dtype=xp.int16)
+        xp_assert_equal(isclose(a, 0), xp.asarray([True, False]))
+        xp_assert_equal(isclose(0, a), xp.asarray([True, False]))
+
+        xp_assert_equal(isclose(0, 0, xp=xp), xp.asarray(True))
+        xp_assert_equal(isclose(0, 1, xp=xp), xp.asarray(False))
+
+    def test_all_python_scalars(self):
+        with pytest.raises(TypeError, match="Unrecognized"):
+            _ = isclose(0, 0)
+
+    def test_xp(self, xp: ModuleType):
+        a = xp.asarray([0.0, 0.0])
+        b = xp.asarray([1e-9, 1e-4])
+        xp_assert_equal(isclose(a, b, xp=xp), xp.asarray([True, False]))
+
+    @pytest.mark.parametrize("equal_nan", [True, False])
+    def test_device(self, xp: ModuleType, device: Device, equal_nan: bool):
+        a = xp.asarray([0.0, 0.0, xp.nan], device=device)
+        b = xp.asarray([1e-9, 1e-4, xp.nan], device=device)
+        res = isclose(a, b, equal_nan=equal_nan)
+        assert get_device(res) == device
 
 
 class TestKron:
-    def test_basic(self):
+    def test_basic(self, xp: ModuleType):
         # Using 0-dimensional array
         a = xp.asarray(1)
         b = xp.asarray([[1, 2], [3, 4]])
-        k = xp.asarray([[1, 2], [3, 4]])
-        assert_array_equal(kron(a, b, xp=xp), k)
-        a = xp.asarray([[1, 2], [3, 4]])
-        b = xp.asarray(1)
-        assert_array_equal(kron(a, b, xp=xp), k)
+        xp_assert_equal(kron(a, b), b)
+        xp_assert_equal(kron(b, a), b)
 
         # Using 1-dimensional array
         a = xp.asarray([3])
         b = xp.asarray([[1, 2], [3, 4]])
         k = xp.asarray([[3, 6], [9, 12]])
-        assert_array_equal(kron(a, b, xp=xp), k)
-        a = xp.asarray([[1, 2], [3, 4]])
-        b = xp.asarray([3])
-        assert_array_equal(kron(a, b, xp=xp), k)
+        xp_assert_equal(kron(a, b), k)
+        xp_assert_equal(kron(b, a), k)
 
         # Using 3-dimensional array
         a = xp.asarray([[[1]], [[2]]])
         b = xp.asarray([[1, 2], [3, 4]])
         k = xp.asarray([[[1, 2], [3, 4]], [[2, 4], [6, 8]]])
-        assert_array_equal(kron(a, b, xp=xp), k)
-        a = xp.asarray([[1, 2], [3, 4]])
-        b = xp.asarray([[[1]], [[2]]])
-        k = xp.asarray([[[1, 2], [3, 4]], [[2, 4], [6, 8]]])
-        assert_array_equal(kron(a, b, xp=xp), k)
+        xp_assert_equal(kron(a, b), k)
+        xp_assert_equal(kron(b, a), k)
 
-    def test_kron_smoke(self):
-        a = xp.ones([3, 3])
-        b = xp.ones([3, 3])
-        k = xp.ones([9, 9])
+    def test_kron_smoke(self, xp: ModuleType):
+        a = xp.ones((3, 3))
+        b = xp.ones((3, 3))
+        k = xp.ones((9, 9))
 
-        assert_array_equal(kron(a, b, xp=xp), k)
+        xp_assert_equal(kron(a, b), k)
 
     @pytest.mark.parametrize(
         ("shape_a", "shape_b"),
@@ -197,7 +899,9 @@ def test_kron_smoke(self):
             ((2, 0, 0, 2), (2, 0, 2)),
         ],
     )
-    def test_kron_shape(self, shape_a, shape_b):
+    def test_kron_shape(
+        self, xp: ModuleType, shape_a: tuple[int, ...], shape_b: tuple[int, ...]
+    ):
         a = xp.ones(shape_a)
         b = xp.ones(shape_b)
         normalised_shape_a = xp.asarray(
@@ -210,73 +914,251 @@ def test_kron_shape(self, shape_a, shape_b):
             int(dim) for dim in xp.multiply(normalised_shape_a, normalised_shape_b)
         )
 
-        k = kron(a, b, xp=xp)
-        assert_equal(k.shape, expected_shape, err_msg="Unexpected shape from kron")
+        k = kron(a, b)
+        assert k.shape == expected_shape
 
+    def test_python_scalar(self, xp: ModuleType):
+        a = 1
+        # Test no dtype promotion to xp.asarray(a); use b.dtype
+        b = xp.asarray([[1, 2], [3, 4]], dtype=xp.int16)
+        xp_assert_equal(kron(a, b), b)
+        xp_assert_equal(kron(b, a), b)
+        xp_assert_equal(kron(1, 1, xp=xp), xp.asarray(1))
 
-class TestExpandDims:
-    def test_functionality(self):
-        def _squeeze_all(b: Array) -> Array:
-            """Mimics `np.squeeze(b)`. `xpx.squeeze`?"""
-            for axis in range(b.ndim):
-                with contextlib.suppress(ValueError):
-                    b = xp.squeeze(b, axis=axis)
-            return b
-
-        s = (2, 3, 4, 5)
-        a = xp.empty(s)
-        for axis in range(-5, 4):
-            b = expand_dims(a, axis=axis, xp=xp)
-            assert b.shape[axis] == 1
-            assert _squeeze_all(b).shape == s
+    def test_all_python_scalars(self):
+        with pytest.raises(TypeError, match="Unrecognized"):
+            _ = kron(1, 1)
 
-    def test_axis_tuple(self):
-        a = xp.empty((3, 3, 3))
-        assert expand_dims(a, axis=(0, 1, 2), xp=xp).shape == (1, 1, 1, 3, 3, 3)
-        assert expand_dims(a, axis=(0, -1, -2), xp=xp).shape == (1, 3, 3, 3, 1, 1)
-        assert expand_dims(a, axis=(0, 3, 5), xp=xp).shape == (1, 3, 3, 1, 3, 1)
-        assert expand_dims(a, axis=(0, -3, -5), xp=xp).shape == (1, 1, 3, 1, 3, 3)
-
-    def test_axis_out_of_range(self):
-        s = (2, 3, 4, 5)
-        a = xp.empty(s)
-        with pytest.raises(IndexError, match="out of bounds"):
-            expand_dims(a, axis=-6, xp=xp)
-        with pytest.raises(IndexError, match="out of bounds"):
-            expand_dims(a, axis=5, xp=xp)
+    def test_device(self, xp: ModuleType, device: Device):
+        x1 = xp.asarray([1, 2, 3], device=device)
+        x2 = xp.asarray([4, 5], device=device)
+        assert get_device(kron(x1, x2)) == device
 
-        a = xp.empty((3, 3, 3))
-        with pytest.raises(IndexError, match="out of bounds"):
-            expand_dims(a, axis=(0, -6), xp=xp)
-        with pytest.raises(IndexError, match="out of bounds"):
-            expand_dims(a, axis=(0, 5), xp=xp)
+    def test_xp(self, xp: ModuleType):
+        a = xp.ones((3, 3))
+        b = xp.ones((3, 3))
+        k = xp.ones((9, 9))
+        xp_assert_equal(kron(a, b, xp=xp), k)
 
-    def test_repeated_axis(self):
-        a = xp.empty((3, 3, 3))
-        with pytest.raises(ValueError, match="Duplicate dimensions"):
-            expand_dims(a, axis=(1, 1), xp=xp)
 
-    def test_positive_negative_repeated(self):
-        # https://github.com/data-apis/array-api/issues/760#issuecomment-1989449817
-        a = xp.empty((2, 3, 4, 5))
-        with pytest.raises(ValueError, match="Duplicate dimensions"):
-            expand_dims(a, axis=(3, -3), xp=xp)
+class TestNUnique:
+    def test_simple(self, xp: ModuleType):
+        a = xp.asarray([[1, 1], [0, 2], [2, 2]])
+        xp_assert_equal(nunique(a), xp.asarray(3))
+
+    def test_empty(self, xp: ModuleType):
+        a = xp.asarray([])
+        xp_assert_equal(nunique(a), xp.asarray(0))
+
+    def test_size1(self, xp: ModuleType):
+        a = xp.asarray([123])
+        xp_assert_equal(nunique(a), xp.asarray(1))
+
+    def test_all_equal(self, xp: ModuleType):
+        a = xp.asarray([123, 123, 123])
+        xp_assert_equal(nunique(a), xp.asarray(1))
+
+    @pytest.mark.xfail_xp_backend(Backend.DASK, reason="No equal_nan kwarg in unique")
+    @pytest.mark.xfail_xp_backend(Backend.SPARSE, reason="sparse#855")
+    def test_nan(self, xp: ModuleType, library: Backend):
+        if library.like(Backend.NUMPY) and NUMPY_VERSION < (1, 24):
+            pytest.xfail("NumPy <1.24 has no equal_nan kwarg in unique")
+
+        # Each NaN is counted separately
+        a = xp.asarray([xp.nan, 123.0, xp.nan])
+        xp_assert_equal(nunique(a), xp.asarray(3))
+
+    @pytest.mark.parametrize("size", [0, 1, 2])
+    def test_device(self, xp: ModuleType, device: Device, size: int):
+        a = xp.asarray([0.0] * size, device=device)
+        assert get_device(nunique(a)) == device
+
+    def test_xp(self, xp: ModuleType):
+        a = xp.asarray([[1, 1], [0, 2], [2, 2]])
+        xp_assert_equal(nunique(a, xp=xp), xp.asarray(3))
+
+
+class TestPad:
+    def test_simple(self, xp: ModuleType):
+        a = xp.asarray([1, 2, 3])
+        padded = pad(a, 2)
+        xp_assert_equal(padded, xp.asarray([0, 0, 1, 2, 3, 0, 0]))
+
+    @pytest.mark.xfail_xp_backend(
+        Backend.SPARSE, reason="constant_values can only be equal to fill value"
+    )
+    def test_fill_value(self, xp: ModuleType):
+        a = xp.asarray([1, 2, 3])
+        padded = pad(a, 2, constant_values=42)
+        xp_assert_equal(padded, xp.asarray([42, 42, 1, 2, 3, 42, 42]))
+
+    def test_ndim(self, xp: ModuleType):
+        a = xp.asarray(np.reshape(np.arange(2 * 3 * 4), (2, 3, 4)))
+        padded = pad(a, 2)
+        assert padded.shape == (6, 7, 8)
+
+    def test_mode_not_implemented(self, xp: ModuleType):
+        a = xp.asarray([1, 2, 3])
+        with pytest.raises(NotImplementedError, match="Only `'constant'`"):
+            _ = pad(a, 2, mode="edge")  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+    def test_device(self, xp: ModuleType, device: Device):
+        a = xp.asarray(0.0, device=device)
+        assert get_device(pad(a, 2)) == device
+
+    def test_xp(self, xp: ModuleType):
+        padded = pad(xp.asarray(0), 1, xp=xp)
+        xp_assert_equal(padded, xp.asarray(0))
+
+    def test_tuple_width(self, xp: ModuleType):
+        a = xp.asarray(np.reshape(np.arange(12), (3, 4)))
+        padded = pad(a, (1, 0))
+        assert padded.shape == (4, 5)
+
+        padded = pad(a, (1, 2))
+        assert padded.shape == (6, 7)
+
+        with pytest.raises((ValueError, RuntimeError)):
+            _ = pad(a, [(1, 2, 3)])  # type: ignore[list-item]  # pyright: ignore[reportArgumentType]
+
+    def test_sequence_of_tuples_width(self, xp: ModuleType):
+        a = xp.asarray(np.reshape(np.arange(12), (3, 4)))
+
+        padded = pad(a, ((1, 0), (0, 2)))
+        assert padded.shape == (4, 6)
+        padded = pad(a, ((1, 0), (0, 0)))
+        assert padded.shape == (4, 4)
+
+
+assume_unique = pytest.mark.parametrize(
+    "assume_unique",
+    [
+        True,
+        pytest.param(
+            False,
+            marks=pytest.mark.xfail_xp_backend(
+                Backend.DASK, reason="NaN-shaped arrays"
+            ),
+        ),
+    ],
+)
+
+
+@pytest.mark.xfail_xp_backend(Backend.SPARSE, reason="no argsort")
+@pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="no unique_values")
+class TestSetDiff1D:
+    @pytest.mark.xfail_xp_backend(Backend.DASK, reason="NaN-shaped arrays")
+    @pytest.mark.xfail_xp_backend(
+        Backend.TORCH, reason="index_select not implemented for uint32"
+    )
+    @pytest.mark.xfail_xp_backend(
+        Backend.TORCH_GPU, reason="index_select not implemented for uint32"
+    )
+    def test_setdiff1d(self, xp: ModuleType):
+        x1 = xp.asarray([6, 5, 4, 7, 1, 2, 7, 4])
+        x2 = xp.asarray([2, 4, 3, 3, 2, 1, 5])
+
+        expected = xp.asarray([6, 7])
+        actual = setdiff1d(x1, x2)
+        xp_assert_equal(actual, expected)
+
+        x1 = xp.arange(21)
+        x2 = xp.arange(19)
+        expected = xp.asarray([19, 20])
+        actual = setdiff1d(x1, x2)
+        xp_assert_equal(actual, expected)
+
+        xp_assert_equal(setdiff1d(xp.empty(0), xp.empty(0)), xp.empty(0))
+        x1 = xp.empty(0, dtype=xp.uint32)
+        x2 = x1
+        assert xp.isdtype(setdiff1d(x1, x2).dtype, xp.uint32)
+
+    def test_assume_unique(self, xp: ModuleType):
+        x1 = xp.asarray([3, 2, 1])
+        x2 = xp.asarray([7, 5, 2])
+        expected = xp.asarray([3, 1])
+        actual = setdiff1d(x1, x2, assume_unique=True)
+        xp_assert_equal(actual, expected)
+
+    @assume_unique
+    @pytest.mark.parametrize("shape1", [(), (1,), (1, 1)])
+    @pytest.mark.parametrize("shape2", [(), (1,), (1, 1)])
+    def test_shapes(
+        self,
+        assume_unique: bool,
+        shape1: tuple[int, ...],
+        shape2: tuple[int, ...],
+        xp: ModuleType,
+    ):
+        x1 = xp.zeros(shape1)
+        x2 = xp.zeros(shape2)
+        actual = setdiff1d(x1, x2, assume_unique=assume_unique)
+        xp_assert_equal(actual, xp.empty((0,)))
+
+    @assume_unique
+    @pytest.mark.skip_xp_backend(Backend.NUMPY_READONLY, reason="xp=xp")
+    def test_python_scalar(self, xp: ModuleType, assume_unique: bool):
+        # Test no dtype promotion to xp.asarray(x2); use x1.dtype
+        x1 = xp.asarray([3, 1, 2], dtype=xp.int16)
+        x2 = 3
+        actual = setdiff1d(x1, x2, assume_unique=assume_unique)
+        xp_assert_equal(actual, xp.asarray([1, 2], dtype=xp.int16))
+
+        actual = setdiff1d(x2, x1, assume_unique=assume_unique)
+        xp_assert_equal(actual, xp.asarray([], dtype=xp.int16))
+
+        xp_assert_equal(
+            setdiff1d(0, 0, assume_unique=assume_unique, xp=xp),
+            xp.asarray([0])[:0],  # Default int dtype for backend
+        )
+
+    @pytest.mark.parametrize("assume_unique", [True, False])
+    def test_all_python_scalars(self, assume_unique: bool):
+        with pytest.raises(TypeError, match="Unrecognized"):
+            _ = setdiff1d(0, 0, assume_unique=assume_unique)
+
+    @assume_unique
+    @pytest.mark.skip_xp_backend(
+        Backend.TORCH, reason="device='meta' does not support unknown shapes"
+    )
+    def test_device(self, xp: ModuleType, device: Device, assume_unique: bool):
+        x1 = xp.asarray([3, 8, 20], device=device)
+        x2 = xp.asarray([2, 3, 4], device=device)
+        assert get_device(setdiff1d(x1, x2, assume_unique=assume_unique)) == device
+
+    @pytest.mark.skip_xp_backend(Backend.NUMPY_READONLY, reason="xp=xp")
+    def test_xp(self, xp: ModuleType):
+        x1 = xp.asarray([3, 8, 20])
+        x2 = xp.asarray([2, 3, 4])
+        expected = xp.asarray([8, 20])
+        actual = setdiff1d(x1, x2, assume_unique=True, xp=xp)
+        xp_assert_equal(actual, expected)
 
 
 class TestSinc:
-    def test_simple(self):
-        assert_array_equal(sinc(xp.asarray(0.0), xp=xp), xp.asarray(1.0))
-        w = sinc(xp.linspace(-1, 1, 100), xp=xp)
+    def test_simple(self, xp: ModuleType):
+        xp_assert_equal(sinc(xp.asarray(0.0)), xp.asarray(1.0))
+        x = xp.asarray(np.linspace(-1, 1, 100))
+        w = sinc(x)
         # check symmetry
-        assert_allclose(w, xp.flip(w, axis=0))
+        xp_assert_close(w, xp.flip(w, axis=0))
 
     @pytest.mark.parametrize("x", [0, 1 + 3j])
-    def test_dtype(self, x):
+    def test_dtype(self, xp: ModuleType, x: int | complex):
         with pytest.raises(ValueError, match="real floating data type"):
-            sinc(xp.asarray(x), xp=xp)
+            _ = sinc(xp.asarray(x))
+
+    def test_3d(self, xp: ModuleType):
+        x = np.arange(18, dtype=np.float64).reshape((3, 3, 2))
+        expected = np.zeros_like(x)
+        expected[0, 0, 0] = 1
+        x = xp.asarray(x)
+        expected = xp.asarray(expected)
+        xp_assert_close(sinc(x), expected, atol=1e-15)
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray(0.0, device=device)
+        assert get_device(sinc(x)) == device
 
-    def test_3d(self):
-        x = xp.reshape(xp.arange(18, dtype=xp.float64), (3, 3, 2))
-        expected = xp.zeros((3, 3, 2))
-        expected[0, 0, 0] = 1.0
-        assert_allclose(sinc(x, xp=xp), expected, atol=1e-15)
+    def test_xp(self, xp: ModuleType):
+        xp_assert_equal(sinc(xp.asarray(0.0), xp=xp), xp.asarray(1.0))
diff --git a/tests/test_helpers.py b/tests/test_helpers.py
new file mode 100644
index 00000000..9f5c924d
--- /dev/null
+++ b/tests/test_helpers.py
@@ -0,0 +1,419 @@
+from types import ModuleType
+from typing import TYPE_CHECKING, Generic, TypeVar, cast
+
+import numpy as np
+import pytest
+
+from array_api_extra._lib._backends import Backend
+from array_api_extra._lib._testing import xp_assert_equal
+from array_api_extra._lib._utils._compat import array_namespace
+from array_api_extra._lib._utils._compat import device as get_device
+from array_api_extra._lib._utils._helpers import (
+    asarrays,
+    capabilities,
+    eager_shape,
+    in1d,
+    jax_autojit,
+    meta_namespace,
+    ndindex,
+    pickle_flatten,
+    pickle_unflatten,
+)
+from array_api_extra._lib._utils._typing import Array, Device, DType
+from array_api_extra.testing import lazy_xp_function
+
+from .conftest import np_compat
+
+if TYPE_CHECKING:  # pragma: no cover
+    # TODO import from typing (requires Python >=3.12)
+    from typing_extensions import override
+else:
+
+    def override(func):
+        return func
+
+
+T = TypeVar("T")
+
+# FIXME calls xp.unique_values without size
+lazy_xp_function(in1d, jax_jit=False)
+
+
+@pytest.mark.xfail_xp_backend(Backend.SPARSE, reason="no unique_inverse")
+@pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="no unique_inverse")
+class TestIn1D:
+    # cover both code paths
+    @pytest.mark.parametrize(
+        "n",
+        [
+            pytest.param(9, id="fast path"),
+            pytest.param(
+                15,
+                id="slow path",
+                marks=pytest.mark.xfail_xp_backend(
+                    Backend.DASK, reason="NaN-shaped array"
+                ),
+            ),
+        ],
+    )
+    def test_no_invert_assume_unique(self, xp: ModuleType, n: int):
+        x1 = xp.asarray([3, 8, 20])
+        x2 = xp.arange(n)
+        expected = xp.asarray([True, True, False])
+        actual = in1d(x1, x2)
+        xp_assert_equal(actual, expected)
+
+    def test_device(self, xp: ModuleType, device: Device):
+        x1 = xp.asarray([3, 8, 20], device=device)
+        x2 = xp.asarray([2, 3, 4], device=device)
+        assert get_device(in1d(x1, x2)) == device
+
+    @pytest.mark.skip_xp_backend(Backend.NUMPY_READONLY, reason="xp=xp")
+    def test_xp(self, xp: ModuleType):
+        x1 = xp.asarray([1, 6])
+        x2 = xp.asarray([0, 1, 2, 3, 4])
+        expected = xp.asarray([True, False])
+        actual = in1d(x1, x2, xp=xp)
+        xp_assert_equal(actual, expected)
+
+
+class TestAsArrays:
+    @pytest.mark.parametrize(
+        ("dtype", "b", "defined"),
+        [
+            # Well-defined cases of dtype promotion from Python scalar to Array
+            # bool vs. bool
+            ("bool", True, True),
+            # int vs. xp.*int*, xp.float*, xp.complex*
+            ("int16", 1, True),
+            ("uint8", 1, True),
+            ("float32", 1, True),
+            ("float64", 1, True),
+            ("complex64", 1, True),
+            ("complex128", 1, True),
+            # float vs. xp.float, xp.complex
+            ("float32", 1.0, True),
+            ("float64", 1.0, True),
+            ("complex64", 1.0, True),
+            ("complex128", 1.0, True),
+            # complex vs. xp.complex
+            ("complex64", 1.0j, True),
+            ("complex128", 1.0j, True),
+            # Undefined cases
+            ("bool", 1, False),
+            ("int64", 1.0, False),
+            ("float64", 1.0j, False),
+        ],
+    )
+    def test_array_vs_scalar(
+        self, dtype: str, b: complex, defined: bool, xp: ModuleType
+    ):
+        a = xp.asarray(1, dtype=getattr(xp, dtype))
+
+        xa, xb = asarrays(a, b, xp)
+        assert xa.dtype == a.dtype
+        if defined:
+            assert xb.dtype == a.dtype
+        else:
+            assert xb.dtype == xp.asarray(b).dtype
+
+        xbr, xar = asarrays(b, a, xp)
+        assert xar.dtype == xa.dtype
+        assert xbr.dtype == xb.dtype
+
+    def test_scalar_vs_scalar(self, xp: ModuleType):
+        a, b = asarrays(1, 2.2, xp=xp)
+        assert a.dtype == xp.asarray(1).dtype  # Default dtype
+        assert b.dtype == xp.asarray(2.2).dtype  # Default dtype; not broadcasted
+
+    ALL_TYPES: tuple[str, ...] = (
+        "int8",
+        "int16",
+        "int32",
+        "int64",
+        "uint8",
+        "uint16",
+        "uint32",
+        "uint64",
+        "float32",
+        "float64",
+        "complex64",
+        "complex128",
+        "bool",
+    )
+
+    @pytest.mark.parametrize("a_type", ALL_TYPES)
+    @pytest.mark.parametrize("b_type", ALL_TYPES)
+    def test_array_vs_array(self, a_type: str, b_type: str, xp: ModuleType):
+        """
+        Test that when both inputs of asarray are already Array API objects,
+        they are returned unchanged.
+        """
+        a = xp.asarray(1, dtype=getattr(xp, a_type))
+        b = xp.asarray(1, dtype=getattr(xp, b_type))
+        xa, xb = asarrays(a, b, xp)
+        assert xa.dtype == a.dtype
+        assert xb.dtype == b.dtype
+
+    @pytest.mark.parametrize("dtype", [np.float64, np.complex128])
+    def test_numpy_generics(self, dtype: DType):
+        """
+        Test special case of np.float64 and np.complex128,
+        which are subclasses of float and complex.
+        """
+        a = cast(Array, dtype(0))  # type: ignore[operator]  # pyright: ignore[reportCallIssue]
+        xa, xb = asarrays(a, 0, xp=np_compat)
+        assert xa.dtype == dtype
+        assert xb.dtype == dtype
+
+
+@pytest.mark.parametrize(
+    "shape", [(), (1,), (5,), (2, 3), (5, 3, 8), (0,), (3, 0), (0, 0, 1)]
+)
+def test_ndindex(shape: tuple[int, ...]):
+    assert tuple(ndindex(*shape)) == tuple(np.ndindex(*shape))
+
+
+@pytest.mark.skip_xp_backend(Backend.SPARSE, reason="index by sparse array")
+@pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="boolean indexing")
+def test_eager_shape(xp: ModuleType, library: Backend):
+    a = xp.asarray([1, 2, 3])
+    # Lazy arrays, like Dask, have an eager shape until you slice them with
+    # a lazy boolean mask
+    assert eager_shape(a) == a.shape == (3,)
+
+    b = a[a > 2]
+    if library is Backend.DASK:
+        with pytest.raises(TypeError, match="Unsupported lazy shape"):
+            _ = eager_shape(b)
+    # FIXME can't test use case for None in the shape until we add support for
+    # other lazy backends
+    else:
+        assert eager_shape(b) == b.shape == (1,)
+
+
+class TestMetaNamespace:
+    @pytest.mark.skip_xp_backend(Backend.NUMPY_READONLY, reason="namespace tests")
+    def test_basic(self, xp: ModuleType, library: Backend):
+        args = None, xp.asarray(0), 1
+        expect = np_compat if library is Backend.DASK else xp
+        assert meta_namespace(*args) is expect
+
+    def test_dask_metas(self, da: ModuleType):
+        cp = pytest.importorskip("cupy")
+        cp_compat = array_namespace(cp.empty(0))
+        args = None, da.from_array(cp.asarray(0)), 1
+        assert meta_namespace(*args) is cp_compat
+
+    def test_xp(self, xp: ModuleType):
+        args = None, xp.asarray(0), 1
+        assert meta_namespace(*args, xp=xp) in (xp, np_compat)
+
+
+class TestCapabilities:
+    def test_basic(self, xp: ModuleType):
+        expect = {"boolean indexing", "data-dependent shapes"}
+        if xp.__array_api_version__ >= "2024.12":
+            expect.add("max dimensions")
+        assert capabilities(xp).keys() == expect
+
+    def test_device(self, xp: ModuleType, library: Backend, device: Device):
+        expect_keys = {"boolean indexing", "data-dependent shapes"}
+        if xp.__array_api_version__ >= "2024.12":
+            expect_keys.add("max dimensions")
+        assert capabilities(xp, device=device).keys() == expect_keys
+
+        if library.like(Backend.TORCH):
+            # The output of capabilities is device-specific.
+
+            # Test that device=None gets the current default device.
+            expect = capabilities(xp, device=device)
+            with xp.device(device):
+                actual = capabilities(xp)
+            assert actual == expect
+
+            # Test that we're accepting anything that is accepted by the
+            # device= parameter in other functions
+            actual = capabilities(xp, device=device.type)  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+
+class Wrapper(Generic[T]):  # noqa: PLW1641
+    """Trivial opaque wrapper. Must be pickleable."""
+
+    x: T
+    # __slots__ make this object serializable with __reduce_ex__(5),
+    # but not with __reduce__
+    __slots__: tuple[str, ...] = ("x",)
+
+    def __init__(self, x: T):
+        self.x = x
+
+    # Note: this makes the object not hashable
+    @override
+    def __eq__(self, other: object) -> bool:
+        return isinstance(other, Wrapper) and self.x == other.x
+
+
+class TestPickleFlatten:
+    def test_roundtrip(self):
+        class NotSerializable:
+            @override
+            def __reduce__(self) -> tuple[object, ...]:
+                raise NotImplementedError()
+
+        # Note: NotHashable() instances can be reduced to an
+        # unserializable local class
+        class NotHashable:  # noqa: PLW1641
+            @override
+            def __eq__(self, other: object) -> bool:
+                return isinstance(other, type(self)) and other.__dict__ == self.__dict__
+
+        with pytest.raises(TypeError):
+            _ = hash(NotHashable())
+
+        # Extracted objects need be neither pickleable nor serializable
+        class C(NotSerializable, NotHashable):
+            x: int
+
+            def __init__(self, x: int):
+                self.x = x
+
+        class D(C):
+            pass
+
+        c1 = C(1)
+        c2 = C(2)
+        d3 = D(3)
+
+        # An assorted bunch of opaque containers, standard containers,
+        # non-serializable objects, and non-hashable objects (but not at the same time)
+        obj = Wrapper([1, c1, {2: (c2, {NotSerializable()})}, NotHashable(), d3])
+        instances, rest = pickle_flatten(obj, C)
+
+        assert instances == [c1, c2, d3]
+        obj2 = pickle_unflatten(instances, rest)
+        assert obj2 == obj
+
+    def test_swap_objects(self):
+        class C:
+            pass
+
+        obj = [1, C(), {2: (C(), {C()})}]
+        _, rest = pickle_flatten(obj, C)
+        obj2 = pickle_unflatten(["foo", "bar", "baz"], rest)
+        assert obj2 == [1, "foo", {2: ("bar", {"baz"})}]
+
+    def test_multi_class(self):
+        class C:
+            pass
+
+        class D:
+            pass
+
+        c, d = C(), D()
+        instances, _ = pickle_flatten([c, d], (C, D))
+        assert len(instances) == 2
+        assert instances[0] is c
+        assert instances[1] is d
+
+    def test_no_class(self):
+        obj = {1: "foo", 2: (3, 4)}
+        instances, rest = pickle_flatten(obj, ())  # type: ignore[var-annotated]
+        assert instances == []
+        obj2 = pickle_unflatten([], rest)
+        assert obj2 == obj
+
+    def test_flattened_stream(self):
+        """
+        Test that multiple calls to flatten() can feed into the same stream of instances
+        """
+        obj1 = Wrapper(1)
+        obj2 = [Wrapper(2), Wrapper(3)]
+        instances1, rest1 = pickle_flatten(obj1, Wrapper)
+        instances2, rest2 = pickle_flatten(obj2, Wrapper)
+        it = iter(instances1 + instances2 + [Wrapper(4)])
+        assert pickle_unflatten(it, rest1) == obj1
+        assert pickle_unflatten(it, rest2) == obj2
+        assert list(it) == [Wrapper(4)]
+
+    def test_too_short(self):
+        obj = [Wrapper(1), Wrapper(2)]
+        instances, rest = pickle_flatten(obj, Wrapper)
+        with pytest.raises(ValueError, match="Not enough"):
+            pickle_unflatten(instances[:1], rest)
+
+    def test_recursion(self):
+        obj: list[object] = [Wrapper(1)]
+        obj.append(obj)
+
+        instances, rest = pickle_flatten(obj, Wrapper)
+        assert instances == [Wrapper(1)]
+
+        obj2 = pickle_unflatten(instances, rest)
+        assert len(obj2) == 2
+        assert obj2[0] is obj[0]
+        assert obj2[1] is obj2
+
+
+class TestJAXAutoJIT:
+    def test_basic(self, jnp: ModuleType):
+        @jax_autojit
+        def f(x: Array, k: object = False) -> Array:
+            return x + 1 if k else x - 1
+
+        # Basic recognition of static_argnames
+        xp_assert_equal(f(jnp.asarray([1, 2])), jnp.asarray([0, 1]))
+        xp_assert_equal(f(jnp.asarray([1, 2]), False), jnp.asarray([0, 1]))
+        xp_assert_equal(f(jnp.asarray([1, 2]), True), jnp.asarray([2, 3]))
+        xp_assert_equal(f(jnp.asarray([1, 2]), 1), jnp.asarray([2, 3]))
+
+        # static argument is not an ArrayLike
+        xp_assert_equal(f(jnp.asarray([1, 2]), "foo"), jnp.asarray([2, 3]))
+
+        # static argument is not hashable, but serializable
+        xp_assert_equal(f(jnp.asarray([1, 2]), ["foo"]), jnp.asarray([2, 3]))
+
+    def test_wrapper(self, jnp: ModuleType):
+        @jax_autojit
+        def f(w: Wrapper[Array]) -> Wrapper[Array]:
+            return Wrapper(w.x + 1)
+
+        inp = Wrapper(jnp.asarray([1, 2]))
+        out = f(inp).x
+        xp_assert_equal(out, jnp.asarray([2, 3]))
+
+    def test_static_hashable(self, jnp: ModuleType):
+        """Static argument/return value is hashable, but not serializable"""
+
+        class C:
+            def __reduce__(self) -> object:  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride,reportImplicitOverride]
+                raise Exception()
+
+        @jax_autojit
+        def f(x: object) -> object:
+            return x
+
+        inp = C()
+        out = f(inp)
+        assert out is inp
+
+        # Serializable opaque input contains non-serializable object plus array
+        winp = Wrapper((C(), jnp.asarray([1, 2])))
+        out = f(winp)
+        assert isinstance(out, Wrapper)
+        assert out.x[0] is winp.x[0]
+        assert out.x[1] is not winp.x[1]
+        xp_assert_equal(out.x[1], winp.x[1])
+
+    def test_arraylikes_are_static(self):
+        pytest.importorskip("jax")
+
+        @jax_autojit
+        def f(x: list[int]) -> list[int]:
+            assert isinstance(x, list)
+            assert x == [1, 2]
+            return [3, 4]
+
+        out = f([1, 2])
+        assert isinstance(out, list)
+        assert out == [3, 4]
diff --git a/tests/test_lazy.py b/tests/test_lazy.py
new file mode 100644
index 00000000..07904a33
--- /dev/null
+++ b/tests/test_lazy.py
@@ -0,0 +1,454 @@
+import contextlib
+from types import ModuleType
+from typing import cast
+
+import numpy as np
+import pytest
+
+import array_api_extra as xpx  # Let some tests bypass lazy_xp_function
+from array_api_extra import lazy_apply
+from array_api_extra._lib._backends import Backend
+from array_api_extra._lib._testing import xp_assert_equal
+from array_api_extra._lib._utils import _compat
+from array_api_extra._lib._utils._compat import array_namespace, is_dask_array
+from array_api_extra._lib._utils._helpers import eager_shape
+from array_api_extra._lib._utils._typing import Array, Device
+from array_api_extra.testing import lazy_xp_function
+
+lazy_xp_function(lazy_apply)
+
+as_numpy = pytest.mark.parametrize(
+    "as_numpy",
+    [
+        False,
+        pytest.param(
+            True,
+            marks=[
+                pytest.mark.skip_xp_backend(Backend.CUPY, reason="device->host copy"),
+                pytest.mark.skip_xp_backend(
+                    Backend.TORCH_GPU, reason="device->host copy"
+                ),
+                pytest.mark.skip_xp_backend(Backend.SPARSE, reason="densification"),
+            ],
+        ),
+    ],
+)
+
+
+@as_numpy
+@pytest.mark.parametrize("shape", [(2,), (3, 2)])
+@pytest.mark.parametrize("dtype", ["int32", "float64"])
+def test_lazy_apply_simple(
+    xp: ModuleType, library: Backend, shape: tuple[int, ...], dtype: str, as_numpy: bool
+):
+    def f(x: Array) -> Array:
+        xp2 = array_namespace(x)
+        if as_numpy or library in (Backend.NUMPY_READONLY, Backend.DASK):
+            assert isinstance(x, np.ndarray)
+        else:
+            assert xp2 is xp
+
+        y = xp2.broadcast_to(xp2.astype(x + 1, getattr(xp2, dtype)), shape)
+        return xp2.asarray(y, copy=True)  # PyTorch: ensure writeable NumPy array
+
+    x = xp.asarray([1, 2], dtype=xp.int16)
+    expect = xp.broadcast_to(xp.astype(x + 1, getattr(xp, dtype)), shape)
+    actual = lazy_apply(f, x, shape=shape, dtype=getattr(xp, dtype), as_numpy=as_numpy)
+    xp_assert_equal(actual, expect)
+
+
+@as_numpy
+def test_lazy_apply_broadcast(xp: ModuleType, as_numpy: bool):
+    """Test that default shape and dtype are broadcasted from the inputs."""
+
+    def f(x: Array, y: Array) -> Array:
+        return x + y
+
+    x = xp.asarray([1, 2], dtype=xp.int16)
+    y = xp.asarray([[4], [5], [6]], dtype=xp.int32)
+    z = lazy_apply(f, x, y, as_numpy=as_numpy)
+    xp_assert_equal(z, x + y)
+
+
+@as_numpy
+def test_lazy_apply_multi_output(xp: ModuleType, as_numpy: bool):
+    def f(x: Array) -> tuple[Array, Array]:
+        xp2 = array_namespace(x)
+        y = x + xp2.asarray(2, dtype=xp2.int8)  # Sparse: bad dtype propagation
+        z = xp2.broadcast_to(xp2.astype(x + 1, xp2.int16), (3, 2))
+        z = xp2.asarray(z, copy=True)  # PyTorch: ensure writeable NumPy array
+        return y, z
+
+    x = xp.asarray([1, 2], dtype=xp.int8)
+    expect = (
+        xp.asarray([3, 4], dtype=xp.int8),
+        xp.asarray([[2, 3], [2, 3], [2, 3]], dtype=xp.int16),
+    )
+    actual = lazy_apply(
+        f, x, shape=((2,), (3, 2)), dtype=(xp.int8, xp.int16), as_numpy=as_numpy
+    )
+    assert isinstance(actual, tuple)
+    assert len(actual) == 2
+    xp_assert_equal(actual[0], expect[0])
+    xp_assert_equal(actual[1], expect[1])
+
+
+@pytest.mark.parametrize(
+    "as_numpy",
+    [
+        False,
+        pytest.param(
+            True,
+            marks=[
+                pytest.mark.skip_xp_backend(Backend.CUPY, reason="device->host copy"),
+                pytest.mark.skip_xp_backend(
+                    Backend.TORCH_GPU, reason="device->host copy"
+                ),
+                pytest.mark.skip_xp_backend(Backend.SPARSE, reason="densification"),
+            ],
+        ),
+    ],
+)
+def test_lazy_apply_multi_output_broadcast_dtype(xp: ModuleType, as_numpy: bool):
+    """
+    If dtype is omitted and there are multiple shapes, use the same
+    dtype for all output arrays, broadcasted from the inputs
+    """
+
+    def f(x: Array, y: Array) -> tuple[Array, Array]:
+        return x + y, x - y
+
+    x = xp.asarray([1, 2], dtype=xp.float32)
+    y = xp.asarray([3], dtype=xp.float64)
+    expect = (
+        xp.asarray([4, 5], dtype=xp.float64),
+        xp.asarray([-2, -1], dtype=xp.float64),
+    )
+    actual = lazy_apply(f, x, y, shape=((2,), (2,)), as_numpy=as_numpy)
+    assert isinstance(actual, tuple)
+    assert len(actual) == 2
+    xp_assert_equal(actual[0], expect[0])
+    xp_assert_equal(actual[1], expect[1])
+
+
+def test_lazy_apply_core_indices(da: ModuleType):
+    """
+    Test that a function that performs reductions along axes does so
+    globally and not locally to each Dask chunk.
+    """
+
+    def f(x: Array) -> Array:
+        xp = array_namespace(x)
+        return xp.sum(x, axis=0) + x
+
+    x_np = cast(Array, np.arange(15).reshape(5, 3))  # pyright: ignore[reportInvalidCast]
+    expect = da.asarray(f(x_np))
+    x_da = da.asarray(x_np).rechunk(3)
+
+    # A naive map_blocks fails because it applies f to each chunk separately,
+    # but f needs to reduce along axis 0 which is broken into multiple chunks.
+    # axis 0 is a "core axis" or "core index" (from xarray.apply_ufunc's
+    # "core dimension").
+    with pytest.raises(AssertionError):
+        xp_assert_equal(da.map_blocks(f, x_da), expect)
+
+    xp_assert_equal(lazy_apply(f, x_da), expect)
+
+
+def test_lazy_apply_dont_run_on_meta(da: ModuleType):
+    """Test that Dask won't try running func on the meta array,
+    as it may have minimum size requirements.
+    """
+
+    def f(x: Array) -> Array:
+        assert x.size
+        return x + 1
+
+    x = da.arange(10)
+    assert not x._meta.size
+    y = lazy_apply(f, x)
+    xp_assert_equal(y, x + 1)
+
+
+def test_lazy_apply_dask_non_numpy_meta(da: ModuleType):
+    """Test Dask wrapping around a meta-namespace other than numpy."""
+    # At the moment of writing, of all Array API namespaces CuPy is
+    # the only one that Dask supports.
+    # For this reason, we can only test as_numpy=False since
+    # np.asarray(cp.Array) is blocked by the transfer guard.
+
+    cp = pytest.importorskip("cupy")
+    cp = array_namespace(cp.empty(0))
+    x_cp = cp.asarray([1, 2, 3])
+    x_da = da.asarray([1, 2, 3]).map_blocks(cp.asarray)
+    assert array_namespace(x_da._meta) is cp
+
+    def f(x: Array) -> Array:
+        return x + 1
+
+    y = lazy_apply(f, x_da)
+    assert array_namespace(y._meta) is cp  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+    xp_assert_equal(y.compute(), x_cp + 1)  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+
+def test_dask_key(da: ModuleType):
+    """Test that the function name is visible on the Dask dashboard and in metrics."""
+
+    def helloworld(x: Array) -> Array:
+        return x + 1
+
+    x = da.asarray([1, 2])
+    # Use full namespace to bypass monkey-patching by lazy_xp_function,
+    # which calls persist() to materialize exceptions and warnings and in
+    # doing so squashes the graph.
+    y = xpx.lazy_apply(helloworld, x)
+
+    prefixes = set()
+    for key in y.__dask_graph__():  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+        name = key[0] if isinstance(key, tuple) else key
+        assert isinstance(name, str)
+        prefixes.add(name.split("-")[0])
+
+    assert "helloworld" in prefixes
+
+
+def test_lazy_apply_none_shape_in_args(xp: ModuleType, library: Backend):
+    x = xp.asarray([1, 1, 2, 2, 2])
+
+    # TODO mxp = meta_namespace(x, xp=xp)
+    mxp = np if library is Backend.DASK else xp
+    int_type = xp.asarray(0).dtype
+
+    ctx: contextlib.AbstractContextManager[object]
+    if library.like(Backend.JAX):
+        ctx = pytest.raises(ValueError, match="Output shape must be fully known")
+    elif library is Backend.ARRAY_API_STRICTEST:
+        ctx = pytest.raises(RuntimeError, match="data-dependent shapes")
+    else:
+        ctx = contextlib.nullcontext()
+
+    # Single output
+    with ctx:
+        values = lazy_apply(mxp.unique_values, x, shape=(None,))
+        xp_assert_equal(xp.sort(values), xp.asarray([1, 2]))
+
+    with ctx:
+        # Multi output
+        values, counts = lazy_apply(
+            mxp.unique_counts,
+            x,
+            shape=((None,), (None,)),
+            dtype=(x.dtype, int_type),
+        )
+        xp_assert_equal(values, xp.asarray([1, 2]))
+        xp_assert_equal(counts, xp.asarray([2, 3]))
+
+
+def check_lazy_apply_none_shape_broadcast(x: Array) -> Array:
+    def f(x: Array) -> Array:
+        return x
+
+    x = x[x > 1]
+    # Use explicit namespace to bypass monkey-patching by lazy_xp_function
+    return xpx.lazy_apply(f, x)
+
+
+lazy_xp_function(check_lazy_apply_none_shape_broadcast)
+
+
+@pytest.mark.skip_xp_backend(Backend.SPARSE, reason="index by sparse array")
+@pytest.mark.skip_xp_backend(Backend.JAX, reason="boolean indexing")
+@pytest.mark.skip_xp_backend(Backend.JAX_GPU, reason="boolean indexing")
+@pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="boolean indexing")
+def test_lazy_apply_none_shape_broadcast(xp: ModuleType):
+    """Broadcast from input array with unknown shape"""
+    x = xp.asarray([1, 2, 2])
+    actual = check_lazy_apply_none_shape_broadcast(x)
+    xp_assert_equal(actual, xp.asarray([2, 2]))
+
+
+@pytest.mark.parametrize(
+    "as_numpy",
+    [
+        False,
+        pytest.param(
+            True,
+            marks=[
+                pytest.mark.skip_xp_backend(
+                    Backend.ARRAY_API_STRICT, reason="device->host copy"
+                ),
+                pytest.mark.skip_xp_backend(Backend.CUPY, reason="device->host copy"),
+                pytest.mark.skip_xp_backend(
+                    Backend.TORCH, reason="materialize 'meta' device"
+                ),
+                pytest.mark.skip_xp_backend(
+                    Backend.TORCH_GPU, reason="device->host copy"
+                ),
+                pytest.mark.skip_xp_backend(Backend.SPARSE, reason="densification"),
+            ],
+        ),
+    ],
+)
+def test_lazy_apply_device(xp: ModuleType, as_numpy: bool, device: Device):
+    def f(x: Array) -> Array:
+        xp2 = array_namespace(x)
+        # Deliberately forgetting to add device here to test that the
+        # output is transferred to the right device. This is necessary when
+        # as_numpy=True anyway.
+        return xp2.zeros(x.shape, dtype=x.dtype)
+
+    x = xp.asarray([1, 2], device=device)
+    y = lazy_apply(f, x, as_numpy=as_numpy)
+    assert _compat.device(y) == device
+
+
+def test_lazy_apply_arraylike(xp: ModuleType):
+    """Wrapped func returns an array-like"""
+    x = xp.asarray([1, 2, 3])
+
+    # Single output
+    def f(x: Array) -> int:
+        shape = eager_shape(x)
+        return shape[0]
+
+    expect = xp.asarray(3)
+    actual = lazy_apply(f, x, shape=(), dtype=expect.dtype)
+    xp_assert_equal(actual, expect)
+
+    # Multi output
+    def g(x: Array) -> tuple[int, list[int]]:
+        shape = eager_shape(x)
+        return shape[0], list(shape)
+
+    actual2 = lazy_apply(g, x, shape=((), (1,)), dtype=(expect.dtype, expect.dtype))
+    xp_assert_equal(actual2[0], xp.asarray(3))
+    xp_assert_equal(actual2[1], xp.asarray([3]))
+
+
+def test_lazy_apply_scalars_and_nones(xp: ModuleType, library: Backend):
+    def f(x: Array, y: None, z: int | Array) -> Array:
+        mxp = array_namespace(x, y, z)
+        mtyp = type(mxp.asarray(0))
+        assert isinstance(x, mtyp)
+        assert y is None
+        # jax.pure_callback wraps scalar args
+        assert isinstance(z, mtyp if library.like(Backend.JAX) else int)
+        return x + z
+
+    x = xp.asarray([1, 2])
+    w = lazy_apply(f, x, None, 3)
+    xp_assert_equal(w, x + 3)
+
+
+def check_lazy_apply_kwargs(x: Array, expect_cls: type, as_numpy: bool) -> Array:
+    is_dask = is_dask_array(x)
+    recursive: list[object] = []
+    if not is_dask:  # dask.delayed crashes on recursion
+        recursive.append(recursive)
+
+    def eager(
+        x: Array,
+        z: dict[int, list[int]],
+        msg: str,
+        msgs: list[str],
+        scalar: int,
+        recursive: list[list[object]],
+    ) -> Array:
+        assert isinstance(x, expect_cls)
+        # JAX will crash if x isn't material
+        assert int(x) == 0
+        # Did we re-wrap the namedtuple correctly, or did it get
+        # accidentally changed to a basic tuple?
+        assert z == {0: [1, 2]}
+        assert msg == "Hello World"  # must be hidden from JAX
+        assert msgs[0] == "Hello World"  # must be hidden from JAX
+        assert isinstance(msg, str)
+        assert isinstance(msgs[0], str)
+        assert scalar == 1  # must be hidden from JAX
+        assert isinstance(scalar, int)
+        assert isinstance(recursive, list)
+        if not is_dask:
+            assert recursive[0][0] is recursive[0]
+        return x + 1
+
+    # Use explicit namespace to bypass monkey-patching by lazy_xp_function
+    return xpx.lazy_apply(  # pyright: ignore[reportCallIssue]
+        eager,
+        x,
+        z={0: [1, 2]},
+        msg="Hello World",
+        msgs=["Hello World"],
+        # This will be automatically cast to jax.Array if we don't wrap it
+        scalar=1,
+        recursive=recursive,
+        shape=x.shape,
+        dtype=x.dtype,
+        as_numpy=as_numpy,
+    )
+
+
+lazy_xp_function(check_lazy_apply_kwargs)
+
+
+@as_numpy
+def test_lazy_apply_kwargs(xp: ModuleType, library: Backend, as_numpy: bool):
+    """When as_numpy=True, search and replace arrays in the (nested) keywords arguments
+    with numpy arrays, and leave the rest untouched."""
+    x = xp.asarray(0)
+    expect_cls = np.ndarray if as_numpy or library is Backend.DASK else type(x)
+    actual = check_lazy_apply_kwargs(x, expect_cls, as_numpy)
+    xp_assert_equal(actual, x + 1)
+
+
+class CustomError(Exception):
+    pass
+
+
+def raises(x: Array) -> Array:
+    def eager(_: Array) -> Array:
+        msg = "Hello World"
+        raise CustomError(msg)
+
+    # Use explicit namespace to bypass monkey-patching by lazy_xp_function
+    return xpx.lazy_apply(eager, x, shape=x.shape, dtype=x.dtype)
+
+
+# jax.pure_callback does not support raising
+# https://github.com/jax-ml/jax/issues/26102
+lazy_xp_function(raises, jax_jit=False)
+
+
+def test_lazy_apply_raises(xp: ModuleType):
+    """
+    See Also
+    --------
+    test_testing.py::test_lazy_xp_function_eagerly_raises
+    """
+    x = xp.asarray(0)
+
+    with pytest.raises(CustomError, match="Hello World"):
+        # Here we are disregarding the return value, which would
+        # normally cause the graph not to materialize and the
+        # exception not to be raised.
+        # However, lazy_xp_function will do it for us on function exit.
+        _ = raises(x)
+
+
+def test_invalid_args():
+    def f(x: Array) -> Array:
+        return x
+
+    x = np.asarray(1)
+
+    with pytest.raises(ValueError, match="at least one argument array"):
+        _ = lazy_apply(f, shape=(1,), dtype=np.int32, xp=np)
+    with pytest.raises(ValueError, match="at least one argument array"):
+        _ = lazy_apply(f, 1, shape=(1,), dtype=np.int32, xp=np)
+    with pytest.raises(ValueError, match="at least one argument array"):
+        _ = lazy_apply(f, shape=(1,), dtype=np.int32)
+    with pytest.raises(ValueError, match="multiple shapes but only one dtype"):
+        _ = lazy_apply(f, x, shape=[(1,), (2,)], dtype=np.int32)  # type: ignore[call-overload]  # pyright: ignore[reportCallIssue,reportArgumentType]
+    with pytest.raises(ValueError, match="single shape but multiple dtypes"):
+        _ = lazy_apply(f, x, shape=(1,), dtype=[np.int32, np.int64])  # pyright: ignore[reportCallIssue,reportArgumentType]
+    with pytest.raises(ValueError, match="2 shapes and 1 dtypes"):
+        _ = lazy_apply(f, x, shape=[(1,), (2,)], dtype=[np.int32])  # type: ignore[arg-type]  # pyright: ignore[reportCallIssue,reportArgumentType]
diff --git a/tests/test_testing.py b/tests/test_testing.py
new file mode 100644
index 00000000..3a93e287
--- /dev/null
+++ b/tests/test_testing.py
@@ -0,0 +1,470 @@
+from collections.abc import Callable
+from types import ModuleType
+from typing import cast
+
+import numpy as np
+import pytest
+
+from array_api_extra._lib._backends import Backend
+from array_api_extra._lib._testing import (
+    as_numpy_array,
+    xp_assert_close,
+    xp_assert_equal,
+    xp_assert_less,
+)
+from array_api_extra._lib._utils._compat import (
+    array_namespace,
+    is_dask_namespace,
+    is_jax_namespace,
+)
+from array_api_extra._lib._utils._typing import Array, Device
+from array_api_extra.testing import lazy_xp_function, patch_lazy_xp_functions
+
+# pyright: reportUnknownParameterType=false,reportMissingParameterType=false
+
+
+class TestAsNumPyArray:
+    def test_basic(self, xp: ModuleType):
+        x = xp.asarray([1, 2, 3])
+        y = as_numpy_array(x, xp=xp)
+        xp_assert_equal(y, np.asarray([1, 2, 3]))  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+    @pytest.mark.skip_xp_backend(Backend.TORCH, reason="materialize 'meta' device")
+    def test_device(self, xp: ModuleType, device: Device):
+        x = xp.asarray([1, 2, 3], device=device)
+        y = as_numpy_array(x, xp=xp)
+        xp_assert_equal(y, np.asarray([1, 2, 3]))  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+
+class TestAssertEqualCloseLess:
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close])
+    def test_assert_equal_close_basic(self, xp: ModuleType, func: Callable[..., None]):
+        func(xp.asarray(0), xp.asarray(0))
+        func(xp.asarray([1, 2]), xp.asarray([1, 2]))
+
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            func(xp.asarray([1, 2]), xp.asarray([2, 1]))
+
+        with pytest.raises(AssertionError, match="hello"):
+            func(xp.asarray([1, 2]), xp.asarray([2, 1]), err_msg="hello")
+
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close, xp_assert_less])
+    def test_shape_dtype(self, xp: ModuleType, func: Callable[..., None]):
+        with pytest.raises(AssertionError, match="shapes do not match"):
+            func(xp.asarray([0]), xp.asarray([[0]]))
+
+        with pytest.raises(AssertionError, match="dtypes do not match"):
+            func(xp.asarray(0, dtype=xp.float32), xp.asarray(0, dtype=xp.float64))
+
+    @pytest.mark.skip_xp_backend(Backend.NUMPY, reason="test other ns vs. numpy")
+    @pytest.mark.skip_xp_backend(
+        Backend.NUMPY_READONLY, reason="test other ns vs. numpy"
+    )
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close, xp_assert_less])
+    def test_namespace(self, xp: ModuleType, func: Callable[..., None]):
+        with pytest.raises(AssertionError, match="namespaces do not match"):
+            func(xp.asarray(0), np.asarray(0))
+        with pytest.raises(TypeError, match="Unrecognized array input"):
+            func(xp.asarray(0), 0)
+        with pytest.raises(TypeError, match="list is not a supported array type"):
+            func(xp.asarray([0]), [0])
+
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close, xp_assert_less])
+    def test_check_shape(self, xp: ModuleType, func: Callable[..., None]):
+        a = xp.asarray([1] if func is xp_assert_less else [2])
+        b = xp.asarray(2)
+        c = xp.asarray(0)
+        d = xp.asarray([2, 2])
+
+        with pytest.raises(AssertionError, match="shapes do not match"):
+            func(a, b)
+        func(a, b, check_shape=False)
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            func(a, c, check_shape=False)
+        with pytest.raises(AssertionError, match="sizes do not match"):
+            func(a, d, check_shape=False)
+
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close, xp_assert_less])
+    def test_check_dtype(self, xp: ModuleType, func: Callable[..., None]):
+        a = xp.asarray(1 if func is xp_assert_less else 2)
+        b = xp.asarray(2, dtype=xp.int16)
+        c = xp.asarray(0, dtype=xp.int16)
+
+        with pytest.raises(AssertionError, match="dtypes do not match"):
+            func(a, b)
+        func(a, b, check_dtype=False)
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            func(a, c, check_dtype=False)
+
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close, xp_assert_less])
+    @pytest.mark.xfail_xp_backend(
+        Backend.SPARSE, reason="sparse [()] returns np.generic"
+    )
+    def test_check_scalar(
+        self, xp: ModuleType, library: Backend, func: Callable[..., None]
+    ):
+        a = xp.asarray(1 if func is xp_assert_less else 2)
+        b = xp.asarray(2)[()]  # Note: only makes a difference on NumPy
+        c = xp.asarray(0)
+
+        func(a, b)
+        if library.like(Backend.NUMPY):
+            with pytest.raises(AssertionError, match="array-ness does not match"):
+                func(a, b, check_scalar=True)
+        else:
+            func(a, b, check_scalar=True)
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            func(a, c, check_scalar=True)
+
+    @pytest.mark.parametrize("dtype", ["int64", "float64"])
+    def test_assert_close_tolerance(self, dtype: str, xp: ModuleType):
+        a = xp.asarray([100], dtype=getattr(xp, dtype))
+        b = xp.asarray([102], dtype=getattr(xp, dtype))
+
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            xp_assert_close(a, b)
+
+        xp_assert_close(a, b, rtol=0.03)
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            xp_assert_close(a, b, rtol=0.01)
+
+        xp_assert_close(a, b, atol=3)
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            xp_assert_close(a, b, atol=1)
+
+    def test_assert_less(self, xp: ModuleType):
+        xp_assert_less(xp.asarray(-1), xp.asarray(0))
+        xp_assert_less(xp.asarray([1, 2]), xp.asarray([2, 3]))
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            xp_assert_less(xp.asarray([1, 1]), xp.asarray([2, 1]))
+
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close, xp_assert_less])
+    @pytest.mark.skip_xp_backend(Backend.SPARSE, reason="index by sparse array")
+    @pytest.mark.skip_xp_backend(Backend.ARRAY_API_STRICTEST, reason="boolean indexing")
+    def test_none_shape(self, xp: ModuleType, func: Callable[..., None]):
+        """On Dask and other lazy backends, test that a shape with NaN's or None's
+        can be compared to a real shape.
+        """
+        # actual has shape=(None, )
+        a = xp.asarray([1] if func is xp_assert_less else [2])
+        a = a[a > 0]
+
+        func(a, xp.asarray([2]))
+        with pytest.raises(AssertionError, match="shapes do not match"):
+            func(a, xp.asarray(2))
+        with pytest.raises(AssertionError, match="shapes do not match"):
+            func(a, xp.asarray([2, 3]))
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            func(a, xp.asarray([0]))
+
+        # desired has shape=(None, )
+        a = xp.asarray([3] if func is xp_assert_less else [2])
+        a = a[a > 0]
+
+        func(xp.asarray([2]), a)
+        with pytest.raises(AssertionError, match="shapes do not match"):
+            func(xp.asarray(2), a)
+        with pytest.raises(AssertionError, match="shapes do not match"):
+            func(xp.asarray([2, 3]), a)
+        with pytest.raises(AssertionError, match="Mismatched elements"):
+            func(xp.asarray([4]), a)
+
+    @pytest.mark.parametrize("func", [xp_assert_equal, xp_assert_close, xp_assert_less])
+    def test_device(self, xp: ModuleType, device: Device, func: Callable[..., None]):
+        a = xp.asarray([1] if func is xp_assert_less else [2], device=device)
+        b = xp.asarray([2], device=device)
+        c = xp.asarray([2, 2], device=device)
+
+        func(a, b)
+        with pytest.raises(AssertionError, match="shapes do not match"):
+            func(a, c)
+        # This is normally performed by np.testing.assert_array_equal etc.
+        # but in case of torch device='meta' we have to do it manually
+        with pytest.raises(AssertionError, match="sizes do not match"):
+            func(a, c, check_shape=False)
+
+
+def good_lazy(x: Array) -> Array:
+    """A function that behaves well in Dask and jax.jit"""
+    return x * 2.0
+
+
+def non_materializable(x: Array) -> Array:
+    """
+    This function materializes the input array, so it will fail when wrapped in jax.jit
+    and it will trigger an expensive computation in Dask.
+    """
+    xp = array_namespace(x)
+    # Crashes inside jax.jit
+    # On Dask, this triggers two computations of the whole graph
+    if xp.any(x < 0.0) or xp.any(x > 10.0):
+        msg = "Values must be in the [0, 10] range"
+        raise ValueError(msg)
+    return x
+
+
+def non_materializable2(x: Array) -> Array:
+    return non_materializable(x)
+
+
+def non_materializable3(x: Array) -> Array:
+    return non_materializable(x)
+
+
+def non_materializable4(x: Array) -> Array:
+    return non_materializable(x)
+
+
+def non_materializable5(x: Array) -> Array:
+    return non_materializable(x)
+
+
+lazy_xp_function(good_lazy)
+# Works on JAX and Dask
+lazy_xp_function(non_materializable2, jax_jit=False, allow_dask_compute=2)
+lazy_xp_function(non_materializable3, jax_jit=False, allow_dask_compute=True)
+# Works on JAX, but not Dask
+lazy_xp_function(non_materializable4, jax_jit=False, allow_dask_compute=1)
+# Works neither on Dask nor JAX
+lazy_xp_function(non_materializable5)
+
+
+def test_lazy_xp_function(xp: ModuleType):
+    x = xp.asarray([1.0, 2.0])
+
+    xp_assert_equal(good_lazy(x), xp.asarray([2.0, 4.0]))
+    # Not wrapped
+    xp_assert_equal(non_materializable(x), xp.asarray([1.0, 2.0]))
+    # Wrapping explicitly disabled
+    xp_assert_equal(non_materializable2(x), xp.asarray([1.0, 2.0]))
+    xp_assert_equal(non_materializable3(x), xp.asarray([1.0, 2.0]))
+
+    if is_jax_namespace(xp):
+        xp_assert_equal(non_materializable4(x), xp.asarray([1.0, 2.0]))
+        with pytest.raises(
+            TypeError, match="Attempted boolean conversion of traced array"
+        ):
+            _ = non_materializable5(x)  # Wrapped
+
+    elif is_dask_namespace(xp):
+        with pytest.raises(
+            AssertionError,
+            match=r"dask\.compute.* 2 times, but only up to 1 calls are allowed",
+        ):
+            _ = non_materializable4(x)
+        with pytest.raises(
+            AssertionError,
+            match=r"dask\.compute.* 1 times, but no calls are allowed",
+        ):
+            _ = non_materializable5(x)
+
+    else:
+        xp_assert_equal(non_materializable4(x), xp.asarray([1.0, 2.0]))
+        xp_assert_equal(non_materializable5(x), xp.asarray([1.0, 2.0]))
+
+
+def static_params(x: Array, n: int, flag: bool = False) -> Array:
+    """Function with static parameters that must not be jitted"""
+    if flag and n > 0:  # This fails if n or flag are jitted arrays
+        return x * 2.0
+    return x * 3.0
+
+
+lazy_xp_function(static_params)
+
+
+def test_lazy_xp_function_static_params(xp: ModuleType):
+    x = xp.asarray([1.0, 2.0])
+    xp_assert_equal(static_params(x, 1), xp.asarray([3.0, 6.0]))
+    xp_assert_equal(static_params(x, 1, True), xp.asarray([2.0, 4.0]))
+    xp_assert_equal(static_params(x, 1, False), xp.asarray([3.0, 6.0]))
+    xp_assert_equal(static_params(x, 0, False), xp.asarray([3.0, 6.0]))
+    xp_assert_equal(static_params(x, 1, flag=True), xp.asarray([2.0, 4.0]))
+    xp_assert_equal(static_params(x, n=1, flag=True), xp.asarray([2.0, 4.0]))
+
+
+def test_lazy_xp_function_deprecated_static_argnames():
+    with pytest.warns(DeprecationWarning, match="static_argnames"):
+        lazy_xp_function(static_params, static_argnames=["flag"])  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+    with pytest.warns(DeprecationWarning, match="static_argnums"):
+        lazy_xp_function(static_params, static_argnums=[1])  # type: ignore[arg-type]  # pyright: ignore[reportArgumentType]
+
+
+try:
+    # Test an arbitrary Cython ufunc (@cython.vectorize).
+    # When SCIPY_ARRAY_API is not set, this is the same as
+    # scipy.special.erf.
+    from scipy.special._ufuncs import erf  # type: ignore[import-untyped]
+
+    lazy_xp_function(erf)
+except ImportError:
+    erf = None
+
+
+@pytest.mark.skip_xp_backend(Backend.TORCH_GPU, reason="device->host copy")
+@pytest.mark.filterwarnings("ignore:__array_wrap__:DeprecationWarning")  # PyTorch
+def test_lazy_xp_function_cython_ufuncs(xp: ModuleType, library: Backend):
+    pytest.importorskip("scipy")
+    assert erf is not None
+    x = xp.asarray([6.0, 7.0])
+    if library.like(Backend.ARRAY_API_STRICT, Backend.JAX):
+        # array-api-strict arrays are auto-converted to NumPy
+        # which results in an assertion error for mismatched namespaces
+        # eager JAX arrays are auto-converted to NumPy in eager JAX
+        # and fail in jax.jit (which lazy_xp_function tests here)
+        with pytest.raises((TypeError, AssertionError)):
+            xp_assert_equal(cast(Array, erf(x)), xp.asarray([1.0, 1.0]))
+    else:
+        # CuPy, Dask and sparse define __array_ufunc__ and dispatch accordingly
+        # note that when sparse reduces to scalar it returns a np.generic, which
+        # would make xp_assert_equal fail.
+        xp_assert_equal(cast(Array, erf(x)), xp.asarray([1.0, 1.0]))
+
+
+def dask_raises(x: Array) -> Array:
+    def _raises(x: Array) -> Array:
+        # Test that map_blocks doesn't eagerly call the function;
+        # dtype and meta should be sufficient to skip the trial run.
+        assert x.shape == (3,)
+        msg = "Hello world"
+        raise ValueError(msg)
+
+    return x.map_blocks(_raises, dtype=x.dtype, meta=x._meta)  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+
+
+lazy_xp_function(dask_raises)
+
+
+def test_lazy_xp_function_eagerly_raises(da: ModuleType):
+    """Test that the pattern::
+
+        with pytest.raises(Exception):
+            func(x)
+
+    works with Dask, even though it normally wouldn't as we're disregarding the func
+    output so the graph would not be ordinarily materialized.
+    lazy_xp_function contains ad-hoc code to materialize and reraise exceptions.
+    """
+    x = da.arange(3)
+    with pytest.raises(ValueError, match="Hello world"):
+        _ = dask_raises(x)
+
+
+class Wrapper:
+    """Trivial opaque wrapper. Must be pickleable."""
+
+    x: Array
+
+    def __init__(self, x: Array):
+        self.x = x
+
+
+def check_opaque_wrapper(w: Wrapper, xp: ModuleType) -> Wrapper:
+    assert isinstance(w, Wrapper)
+    assert array_namespace(w.x) == xp
+    return Wrapper(w.x + 1)
+
+
+lazy_xp_function(check_opaque_wrapper)
+
+
+def test_lazy_xp_function_opaque_wrappers(xp: ModuleType):
+    """
+    Test that function input and output can be wrapped into arbitrary
+    serializable Python objects, even if jax.jit does not support them.
+    """
+    x = xp.asarray([1, 2])
+    xp2 = array_namespace(x)  # Revert NUMPY_READONLY to array_api_compat.numpy
+    res = check_opaque_wrapper(Wrapper(x), xp2)
+    xp_assert_equal(res.x, xp.asarray([2, 3]))
+
+
+def test_lazy_xp_function_opaque_wrappers_eagerly_raise(da: ModuleType):
+    """
+    Like `test_lazy_xp_function_eagerly_raises`, but the returned object is
+    wrapped in an opaque wrapper.
+    """
+    x = da.arange(3)
+    with pytest.raises(ValueError, match="Hello world"):
+        _ = Wrapper(dask_raises(x))
+
+
+def check_recursive(x: list[object]) -> list[object]:
+    assert isinstance(x, list)
+    assert x[1] is x
+    y: list[object] = [cast(Array, x[0]) + 1]
+    y.append(y)
+    return y
+
+
+lazy_xp_function(check_recursive)
+
+
+def test_lazy_xp_function_recursive(xp: ModuleType):
+    """Test that inputs and outputs can be recursive data structures."""
+    x: list[object] = [xp.asarray([1, 2])]
+    x.append(x)
+    y = check_recursive(x)
+    assert isinstance(y, list)
+    xp_assert_equal(cast(Array, y[0]), xp.asarray([2, 3]))
+    assert y[1] is y
+
+
+wrapped = ModuleType("wrapped")
+naked = ModuleType("naked")
+
+
+def f(x: Array) -> Array:
+    xp = array_namespace(x)
+    # Crash in jax.jit and trigger compute() on Dask
+    if not xp.all(x):
+        msg = "Values must be non-zero"
+        raise ValueError(msg)
+    return x
+
+
+wrapped.f = f  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+naked.f = f  # type: ignore[attr-defined]  # pyright: ignore[reportAttributeAccessIssue]
+del f
+
+
+lazy_xp_function(wrapped.f)
+lazy_xp_modules = [wrapped]
+
+
+def test_lazy_xp_modules(xp: ModuleType, library: Backend):
+    x = xp.asarray([1.0, 2.0])
+    y = naked.f(x)
+    xp_assert_equal(y, x)
+
+    if library.like(Backend.JAX):
+        with pytest.raises(
+            TypeError, match="Attempted boolean conversion of traced array"
+        ):
+            wrapped.f(x)
+    elif library.like(Backend.DASK):
+        with pytest.raises(AssertionError, match=r"dask\.compute"):
+            wrapped.f(x)
+    else:
+        y = wrapped.f(x)
+        xp_assert_equal(y, x)
+
+
+def test_patch_lazy_xp_functions_deprecated_monkeypatch(
+    request: pytest.FixtureRequest, monkeypatch: pytest.MonkeyPatch
+):
+    xp = pytest.importorskip("dask.array")
+
+    x = xp.asarray([1.0, 2.0])
+    y = non_materializable5(x)
+    xp_assert_equal(y, x)
+
+    with pytest.warns(DeprecationWarning, match="`monkeypatch` parameter"):
+        _ = patch_lazy_xp_functions(request, monkeypatch, xp=xp)
+
+    with pytest.raises(AssertionError, match=r"dask\.compute.* 1 times"):
+        _ = non_materializable5(x)
+
+    monkeypatch.undo()
+    y = non_materializable5(x)
+    xp_assert_equal(y, x)
diff --git a/tests/test_version.py b/tests/test_version.py
index 21d43d17..b9717a50 100644
--- a/tests/test_version.py
+++ b/tests/test_version.py
@@ -1,5 +1,3 @@
-from __future__ import annotations
-
 import importlib.metadata
 
 import array_api_extra as xpx
diff --git a/typos.toml b/typos.toml
new file mode 100644
index 00000000..34233590
--- /dev/null
+++ b/typos.toml
@@ -0,0 +1,8 @@
+[files]
+extend-exclude = [".git/", ".pixi/"]
+ignore-hidden = false
+
+[default.extend-words]
+nd = "nd"
+typ = "typ"
+cardinalis = "cardinalis"
diff --git a/vendor_tests/__init__.py b/vendor_tests/__init__.py
new file mode 100644
index 00000000..9fd27fde
--- /dev/null
+++ b/vendor_tests/__init__.py
@@ -0,0 +1 @@
+"""Allow for relative imports in `test_vendor.py`."""
diff --git a/vendor_tests/_array_api_compat_vendor.py b/vendor_tests/_array_api_compat_vendor.py
new file mode 100644
index 00000000..9bc129b5
--- /dev/null
+++ b/vendor_tests/_array_api_compat_vendor.py
@@ -0,0 +1,11 @@
+"""This file is a hook imported by `src/array_api_extra/_lib/_compat.py`."""
+# pyright: reportUnknownParameterType=false, reportMissingParameterType=false
+
+from .array_api_compat import *  # noqa: F403
+from .array_api_compat import array_namespace as array_namespace_compat
+
+
+# Let unit tests check with `is` that we are picking up the function from this module
+# and not from the original array_api_compat module.
+def array_namespace(*xs, **kwargs):  # numpydoc ignore=GL08
+    return array_namespace_compat(*xs, **kwargs)
diff --git a/vendor_tests/test_vendor.py b/vendor_tests/test_vendor.py
new file mode 100644
index 00000000..e43c82fb
--- /dev/null
+++ b/vendor_tests/test_vendor.py
@@ -0,0 +1,76 @@
+# pyright: reportAttributeAccessIssue=false
+
+from typing import Any
+
+import array_api_strict as xp
+from numpy.testing import assert_array_equal
+
+
+def test_vendor_compat():
+    from ._array_api_compat_vendor import (  # type: ignore[attr-defined]
+        array_namespace,
+        device,
+        is_array_api_obj,
+        is_array_api_strict_namespace,
+        is_cupy_array,
+        is_cupy_namespace,
+        is_dask_array,
+        is_dask_namespace,
+        is_jax_array,
+        is_jax_namespace,
+        is_lazy_array,
+        is_numpy_array,
+        is_numpy_namespace,
+        is_pydata_sparse_array,
+        is_pydata_sparse_namespace,
+        is_torch_array,
+        is_torch_namespace,
+        is_writeable_array,
+        size,
+        to_device,
+    )
+
+    x = xp.asarray([1, 2, 3])
+    assert array_namespace(x) is xp
+    to_device(x, device(x))
+    assert is_array_api_obj(x)
+    assert is_array_api_strict_namespace(xp)
+    assert not is_cupy_array(x)
+    assert not is_cupy_namespace(xp)
+    assert not is_dask_array(x)
+    assert not is_dask_namespace(xp)
+    assert not is_jax_array(x)
+    assert not is_jax_namespace(xp)
+    assert not is_lazy_array(x)
+    assert not is_numpy_array(x)
+    assert not is_numpy_namespace(xp)
+    assert not is_pydata_sparse_array(x)
+    assert not is_pydata_sparse_namespace(xp)
+    assert not is_torch_array(x)
+    assert not is_torch_namespace(xp)
+    assert is_writeable_array(x)
+    assert size(x) == 3
+
+
+def test_vendor_extra():
+    from .array_api_extra import atleast_nd
+
+    x = xp.asarray(1)
+    y = atleast_nd(x, ndim=0)
+    assert_array_equal(y, x)  # pyright: ignore[reportUnknownArgumentType]
+
+
+def test_vendor_extra_testing():
+    from .array_api_extra.testing import lazy_xp_function
+
+    def f(x: Any) -> Any:
+        return x
+
+    lazy_xp_function(f)
+
+
+def test_vendor_extra_uses_vendor_compat():
+    from ._array_api_compat_vendor import array_namespace as n1
+    from .array_api_extra._lib._utils._compat import array_namespace as n2
+
+    assert n1 is n2