Merge branch 'master' into chiphogg/mod#509

2025-08-05 21:24:27 +02:00 · 2024-11-13 08:41:52 -05:00
parent 6c982d4202 9dd59e845c
commit b99faf051b
39 changed files with 3381 additions and 2069 deletions
--- a/.flake8
+++ b/.flake8
@@ -7,3 +7,6 @@ ignore =
    E712,
    # line break before binary operator
    W503
+per-file-ignores =
+    # flake8 is just plain wrong here, contradicting black
+    .github/generate-job-matrix.py:E225,E231
--- a/.github/generate-job-matrix.py
+++ b/.github/generate-job-matrix.py
@@ -0,0 +1,206 @@
+import argparse
+import json
+import os
+import random
+import typing
+from types import SimpleNamespace
+
+from job_matrix import CombinationCollector, Compiler, Configuration
+
+
+def make_gcc_config(version: int) -> Configuration:
+    return Configuration(
+        name=f"GCC-{version}",
+        os="ubuntu-24.04",
+        compiler=Compiler(
+            type="GCC",
+            version=version,
+            cc=f"gcc-{version}",
+            cxx=f"g++-{version}",
+        ),
+        cxx_modules=False,
+        std_format_support=version >= 13,
+    )
+
+
+def make_clang_config(
+    version: int, platform: typing.Literal["x86-64", "arm64"] = "x86-64"
+) -> Configuration:
+    cfg = SimpleNamespace(
+        name=f"Clang-{version} ({platform})",
+        compiler=SimpleNamespace(
+            type="CLANG",
+            version=version,
+        ),
+        lib="libc++",
+        cxx_modules=version >= 17,
+        std_format_support=version >= 17,
+    )
+    match platform:
+        case "x86-64":
+            cfg.os = "ubuntu-22.04" if version < 17 else "ubuntu-24.04"
+            cfg.compiler.cc = f"clang-{version}"
+            cfg.compiler.cxx = f"clang++-{version}"
+        case "arm64":
+            cfg.os = "macos-14"
+            pfx = f"/opt/homebrew/opt/llvm@{version}/bin"
+            cfg.compiler.cc = f"{pfx}/clang"
+            cfg.compiler.cxx = f"{pfx}/clang++"
+        case _:
+            raise KeyError(f"Unsupported platform {platform!r} for Clang")
+    ret = cfg
+    ret.compiler = Compiler(**vars(cfg.compiler))
+    return Configuration(**vars(ret))
+
+
+def make_apple_clang_config(version: int) -> Configuration:
+    ret = Configuration(
+        name=f"Apple Clang {version}",
+        os="macos-13",
+        compiler=Compiler(
+            type="APPLE_CLANG",
+            version=f"{version}.0",
+            cc="clang",
+            cxx="clang++",
+        ),
+        cxx_modules=False,
+        std_format_support=False,
+    )
+    return ret
+
+
+def make_msvc_config(release: str, version: int) -> Configuration:
+    ret = Configuration(
+        name=f"MSVC {release}",
+        os="windows-2022",
+        compiler=Compiler(
+            type="MSVC",
+            version=version,
+            cc="",
+            cxx="",
+        ),
+        cxx_modules=False,
+        std_format_support=True,
+    )
+    return ret
+
+
+configs = {
+    c.name: c
+    for c in [make_gcc_config(ver) for ver in [12, 13, 14]]
+    + [
+        make_clang_config(ver, platform)
+        for ver in [16, 17, 18]
+        for platform in ["x86-64", "arm64"]
+        # arm64 runners are expensive; only consider one version
+        if ver == 18 or platform != "arm64"
+    ]
+    + [make_apple_clang_config(ver) for ver in [15]]
+    + [make_msvc_config(release="14.4", version=194)]
+}
+
+full_matrix = dict(
+    config=list(configs.values()),
+    std=[20, 23],
+    formatting=["std::format", "fmtlib"],
+    contracts=["none", "gsl-lite", "ms-gsl"],
+    build_type=["Release", "Debug"],
+)
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    #    parser.add_argument("-I","--include",nargs="+",action="append")
+    #    parser.add_argument("-X","--exclude",nargs="+",action="append")
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--preset", default=None)
+    parser.add_argument("--debug", nargs="+", default=["combinations"])
+    parser.add_argument("--suppress-output", default=False, action="store_true")
+
+    args = parser.parse_args()
+
+    rgen = random.Random(args.seed)
+
+    collector = CombinationCollector(
+        full_matrix,
+        hard_excludes=lambda e: (
+            e.formatting == "std::format" and not e.config.std_format_support
+        ),
+    )
+    match args.preset:
+        case None:
+            pass
+        case "all":
+            collector.all_combinations()
+        case "conan" | "cmake":
+            collector.all_combinations(
+                formatting="std::format",
+                contracts="gsl-lite",
+                build_type="Debug",
+                std=20,
+            )
+            collector.all_combinations(
+                filter=lambda me: not me.config.std_format_support,
+                formatting="fmtlib",
+                contracts="gsl-lite",
+                build_type="Debug",
+                std=20,
+            )
+            collector.sample_combinations(rgen=rgen, min_samples_per_value=2)
+        case "clang-tidy":
+            collector.all_combinations(config=configs["Clang-18 (x86-64)"])
+        case "freestanding":
+            # TODO For some reason Clang-18 Debug with -ffreestanding does not pass CMakeTestCXXCompiler
+            collector.all_combinations(
+                filter=lambda e: not (
+                    e.config.name.startswith("Clang-18") and e.build_type == "Debug"
+                ),
+                config=[configs[c] for c in ["GCC-14", "Clang-18 (x86-64)"]],
+                contracts="none",
+                std=23,
+            )
+        case _:
+            raise KeyError(f"Unsupported preset {args.preset!r}")
+
+    if not collector.combinations:
+        raise ValueError("No combination has been produced")
+
+    data = sorted(collector.combinations)
+
+    json_data = [e.as_json() for e in data]
+
+    output_file = os.environ.get("GITHUB_OUTPUT")
+    if not args.suppress_output:
+        if output_file:
+            print(f"Writing outputs to {output_file}")
+            with open(output_file, "wt") as fh:
+                fh.write(f"matrix={json.dumps(json_data)}")
+        else:
+            print("No output file received!")
+
+    for dbg in args.debug:
+        match dbg:
+            case "yaml":
+                import yaml
+
+                json_data = json.loads(json.dumps(json_data))
+                print(yaml.safe_dump(json_data))
+            case "json":
+                print(json.dumps(json_data, indent=4))
+            case "combinations":
+                for e in data:
+                    print(
+                        f"{e.config!s:17s}  c++{e.std:2d}  {e.formatting:11s}  {e.contracts:8s}  {e.build_type:8s}"
+                    )
+            case "counts":
+                print(f"Total combinations {len(data)}")
+                for (k, v), n in sorted(collector.per_value_counts.items()):
+                    print(f"  {k}={v}: {n}")
+            case "none":
+                pass
+            case _:
+                raise KeyError(f"Unknown debug mode {dbg!r}")
+
+
+if __name__ == "__main__":
+    main()
--- a/.github/job_matrix.py
+++ b/.github/job_matrix.py
@@ -0,0 +1,139 @@
+import dataclasses
+import itertools
+import random
+import typing
+from dataclasses import dataclass
+
+
+@dataclass(frozen=True, order=True)
+class Compiler:
+    type: typing.Literal["GCC", "CLANG", "APPLE_CLANG", "MSVC"]
+    version: str | int
+    cc: str
+    cxx: str
+
+
+@dataclass(frozen=True, order=True)
+class Configuration:
+    name: str
+    os: str
+    compiler: Compiler
+    cxx_modules: bool
+    std_format_support: bool
+    conan_config: str = ""
+    lib: typing.Literal["libc++", "libstdc++"] | None = None
+
+    def __str__(self):
+        return self.name
+
+
+@dataclass(frozen=True, order=True)
+class MatrixElement:
+    config: Configuration
+    std: typing.Literal[20, 23]
+    formatting: typing.Literal["std::format", "fmtlib"]
+    contracts: typing.Literal["none", "gsl-lite", "ms-gsl"]
+    build_type: typing.Literal["Release", "Debug"]
+
+    def as_json(self):
+        def dataclass_to_json(obj):
+            """Convert dataclasses to something json-serialisable"""
+            if dataclasses.is_dataclass(obj):
+                return {
+                    k: dataclass_to_json(v) for k, v in dataclasses.asdict(obj).items()
+                }
+            return obj
+
+        ret = dataclass_to_json(self)
+        # patch boolean conan configuration options
+        config = ret["config"]
+        for k in ["cxx_modules"]:
+            config[k] = "True" if config[k] else "False"
+        return ret
+
+
+class CombinationCollector:
+    """Incremental builder of MatrixElements, allowing successive selection of entries."""
+
+    def __init__(
+        self,
+        full_matrix: dict[str, list[typing.Any]],
+        *,
+        hard_excludes: typing.Callable[[MatrixElement], bool] | None = None,
+    ):
+        self.full_matrix = full_matrix
+        self.hard_excludes = hard_excludes
+        self.combinations: set[MatrixElement] = set()
+        self.per_value_counts: dict[tuple[str, typing.Any], int] = {
+            (k, v): 0 for k, options in full_matrix.items() for v in options
+        }
+
+    def _make_submatrix(self, **overrides):
+        new_matrix = dict(self.full_matrix)
+        for k, v in overrides.items():
+            if not isinstance(v, list):
+                v = [v]
+            new_matrix[k] = v
+        return new_matrix
+
+    def _add_combination(self, e: MatrixElement):
+        if e in self.combinations or (
+            self.hard_excludes is not None and self.hard_excludes(e)
+        ):
+            return
+        self.combinations.add(e)
+        # update per_value_counts
+        for k, v in vars(e).items():
+            idx = (k, v)
+            self.per_value_counts[idx] = self.per_value_counts.get(idx, 0) + 1
+
+    def all_combinations(
+        self,
+        *,
+        filter: typing.Callable[[MatrixElement], bool] | None = None,
+        **overrides,
+    ):
+        """Adds all combinations in the submatrix defined by `overrides`."""
+        matrix = self._make_submatrix(**overrides)
+        keys = tuple(matrix.keys())
+        for combination in itertools.product(*matrix.values()):
+            cand = MatrixElement(**dict(zip(keys, combination)))
+            if filter and not filter(cand):
+                continue
+            self._add_combination(cand)
+
+    def sample_combinations(
+        self,
+        *,
+        rgen: random.Random,
+        min_samples_per_value: int = 1,
+        filter: typing.Callable[[MatrixElement], bool] | None = None,
+        **overrides,
+    ):
+        """Adds samples from the submatrix defined by `overrides`,
+        ensuring each individual value appears at least n times.
+        """
+        matrix = self._make_submatrix(**overrides)
+        missing: dict[tuple[str, typing.Any], int] = {}
+        for key, options in matrix.items():
+            for value in options:
+                idx = (key, value)
+                missing[idx] = min_samples_per_value - self.per_value_counts.get(idx, 0)
+        while missing:
+            (force_key, force_option), remaining = next(iter(missing.items()))
+            if remaining <= 0:
+                missing.pop((force_key, force_option))
+                continue
+            choice = {}
+            for key, options in matrix.items():
+                choice[key] = force_option if key == force_key else rgen.choice(options)
+            cand = MatrixElement(**choice)
+            if filter and not filter(cand):
+                continue
+            self._add_combination(cand)
+            for idx in choice.items():
+                if missing.pop(idx, 0) <= 0:
+                    continue
+                remaining = min_samples_per_value - self.per_value_counts.get(idx, 0)
+                if remaining > 0:
+                    missing[idx] = remaining
--- a/.github/workflows/ci-clang-tidy.yml
+++ b/.github/workflows/ci-clang-tidy.yml
@@ -34,33 +34,33 @@ on:
    paths-ignore:
      - "docs/**"

+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
+  generate-matrix:
+    name: "Generate build matrix for ${{ github.workflow }}"
+    outputs:
+      matrix: ${{ steps.set-matrix.outputs.matrix }}
+    runs-on: ubuntu-24.04
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: 3.x
+      - id: set-matrix
+        run: python .github/generate-job-matrix.py --preset clang-tidy --seed 42 --debug combinations counts
  build:
    name: "${{ matrix.formatting }} ${{ matrix.contracts }} C++${{ matrix.std }} ${{ matrix.config.name }} ${{ matrix.build_type }}"
    runs-on: ${{ matrix.config.os }}
+    needs: generate-matrix
    strategy:
      fail-fast: false
      matrix:
-        formatting: ["std::format", "fmtlib"]
-        contracts: ["none", "gsl-lite", "ms-gsl"]
-        std: [20, 23]
-        config:
-          - {
-              name: "Clang-18",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 18,
-                  cc: "clang-18",
-                  cxx: "clang++-18",
-                },
-              lib: "libc++",
-              cxx_modules: "False",
-              std_format_support: "True",
-              conan-config: "",
-            }
-        build_type: ["Release", "Debug"]
+        include: ${{fromJson(needs.generate-matrix.outputs.matrix)}}

    env:
      CC: ${{ matrix.config.compiler.cc }}
@@ -127,8 +127,11 @@ jobs:
          sed -i.backup '/^\[settings\]$/,/^\[/ s/^compiler.cppstd=.*/compiler.cppstd=${{ matrix.std }}/' ~/.conan2/profiles/default
          sed -i.backup '/^\[settings\]$/,/^\[/ s/^build_type=.*/build_type=${{ matrix.build_type }}/' ~/.conan2/profiles/default
          conan profile show -pr default
-      - run: echo "std_format=$([ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
-      - run: echo "import_std=$([ "${{ matrix.config.cxx_modules }}" == "True" ] && [ "${{ matrix.config.contracts }}" == "none" ] && [ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
+      - name: Set 'std_format' and 'import_std' environment variables
+        shell: bash
+        run: |
+          echo "std_format=$([ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
+          echo "import_std=$([ "${{ matrix.std }}" -ge "23" ] && [ "${{ matrix.config.cxx_modules }}" == "True" ] && [ "${{ matrix.config.contracts }}" == "none" ] && [ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
      - name: Run clang-tidy
        shell: bash
        run: |
--- a/.github/workflows/ci-conan.yml
+++ b/.github/workflows/ci-conan.yml
@@ -33,149 +33,35 @@ on:
 env:
  CHANNEL: ${{ fromJSON('["testing", "stable"]')[github.ref_type == 'tag' && startsWith(github.ref_name, 'v')] }}

+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
+  generate-matrix:
+    name: "Generate build matrix for ${{ github.workflow }}"
+    outputs:
+      matrix: ${{ steps.set-matrix.outputs.matrix }}
+    runs-on: ubuntu-24.04
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: 3.x
+      - id: set-matrix
+        run: python .github/generate-job-matrix.py --preset conan --seed 42 --debug combinations counts
  build:
    name: "${{ matrix.formatting }} ${{ matrix.contracts }} C++${{ matrix.std }} ${{ matrix.config.name }} ${{ matrix.build_type }}"
    runs-on: ${{ matrix.config.os }}
+    needs: generate-matrix
    strategy:
      fail-fast: false
      matrix:
-        formatting: ["std::format", "fmtlib"]
-        contracts: ["none", "gsl-lite", "ms-gsl"]
-        std: [20, 23]
-        config:
-          - {
-              name: "MSVC 14.4",
-              os: windows-2022,
-              compiler: { type: MSVC, version: 194, cc: "", cxx: "" },
-              cxx_modules: "False",
-              std_format_support: "True",
-              conan-config: "",
-            }
-          - {
-              name: "GCC-12",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: GCC,
-                  version: 12,
-                  cc: "gcc-12",
-                  cxx: "g++-12",
-                },
-              cxx_modules: "False",
-              std_format_support: "False",
-              conan-config: "",
-            }
-          - {
-              name: "GCC-13",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: GCC,
-                  version: 13,
-                  cc: "gcc-13",
-                  cxx: "g++-13",
-                },
-              cxx_modules: "False",
-              std_format_support: "True",
-              conan-config: "",
-            }
-          - {
-              name: "GCC-14",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: GCC,
-                  version: 14,
-                  cc: "gcc-14",
-                  cxx: "g++-14",
-                },
-              cxx_modules: "False",
-              std_format_support: "True",
-              conan-config: "",
-            }
-          - {
-              name: "Clang-16",
-              os: ubuntu-22.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 16,
-                  cc: "clang-16",
-                  cxx: "clang++-16",
-                },
-              lib: "libc++",
-              cxx_modules: "False",
-              std_format_support: "False",
-              conan-config: "",
-            }
-          - {
-              name: "Clang-17",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 17,
-                  cc: "clang-17",
-                  cxx: "clang++-17",
-                },
-              lib: "libc++",
-              cxx_modules: "True",
-              std_format_support: "True",
-              conan-config: "",
-            }
-          - {
-              name: "Clang-18",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 18,
-                  cc: "clang-18",
-                  cxx: "clang++-18",
-                },
-              lib: "libc++",
-              cxx_modules: "True",
-              std_format_support: "True",
-              conan-config: "",
-            }
-          - {
-              name: "Clang-18 on Apple M1 (arm64)",
-              os: macos-14,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 18,
-                  cc: "/opt/homebrew/opt/llvm@18/bin/clang-18",
-                  cxx: "/opt/homebrew/opt/llvm@18/bin/clang++",
-                },
-              lib: "libc++",
-              cxx_modules: "False",
-              std_format_support: "True"
-            }
-          - {
-              name: "Apple Clang 15",
-              os: macos-13,
-              compiler:
-                {
-                  type: APPLE_CLANG,
-                  version: "15.0",
-                  cc: "clang",
-                  cxx: "clang++",
-                },
-              cxx_modules: "False",
-              std_format_support: "False",
-              conan-config: "",
-            }
-        build_type: ["Release", "Debug"]
-        exclude:
-          - formatting: "std::format"
-            config: { std_format_support: "False" }
-
+        include: ${{fromJson(needs.generate-matrix.outputs.matrix)}}
    env:
      CC: ${{ matrix.config.compiler.cc }}
      CXX: ${{ matrix.config.compiler.cxx }}
-
    steps:
      - uses: actions/checkout@v4
      - name: Generate unique cache id
@@ -258,21 +144,21 @@ jobs:
        shell: bash
        run: |
          echo "std_format=$([ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
-          echo "import_std=$([ "${{ matrix.config.cxx_modules }}" == "True" ] && [ "${{ matrix.config.contracts }}" == "none" ] && [ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
+          echo "import_std=$([ "${{ matrix.std }}" -ge "23" ] && [ "${{ matrix.config.cxx_modules }}" == "True" ] && [ "${{ matrix.config.contracts }}" == "none" ] && [ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
      - name: Create Conan package
        if: matrix.config.compiler.type != 'MSVC'
        shell: bash
        run: |
          conan create . --user mpusz --channel ${CHANNEL} --lockfile-out=package.lock \
                         -b mp-units/* -b missing -c tools.cmake.cmaketoolchain:generator="Ninja Multi-Config" -c user.mp-units.build:all=True \
-                         -o '&:cxx_modules=${{ matrix.config.cxx_modules }}' -o '&:import_std=${{ env.import_std }}' -o '&:std_format=${{ env.std_format }}' -o '&:contracts=${{ matrix.contracts }}' ${{ matrix.config.conan-config }}
+                         -o '&:cxx_modules=${{ matrix.config.cxx_modules }}' -o '&:import_std=${{ env.import_std }}' -o '&:std_format=${{ env.std_format }}' -o '&:contracts=${{ matrix.contracts }}' ${{ matrix.config.conan_config }}
      - name: Create Conan package
        if: matrix.config.compiler.type == 'MSVC'
        shell: bash
        run: |
          conan create . --user mpusz --channel ${CHANNEL} --lockfile-out=package.lock \
                         -b mp-units/* -b missing -c tools.cmake.cmaketoolchain:generator="Ninja Multi-Config" -c user.mp-units.build:all=False \
-                         -o '&:cxx_modules=${{ matrix.config.cxx_modules }}' -o '&:import_std=${{ env.import_std }}' -o '&:std_format=${{ env.std_format }}' -o '&:contracts=${{ matrix.contracts }}' ${{ matrix.config.conan-config }}
+                         -o '&:cxx_modules=${{ matrix.config.cxx_modules }}' -o '&:import_std=${{ env.import_std }}' -o '&:std_format=${{ env.std_format }}' -o '&:contracts=${{ matrix.contracts }}' ${{ matrix.config.conan_config }}
      - name: Obtain package reference
        id: get-package-ref
        shell: bash
--- a/.github/workflows/ci-formatting.yml
+++ b/.github/workflows/ci-formatting.yml
@@ -24,6 +24,10 @@ name: Formatting CI

 on: [push, pull_request]

+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
  check:
    runs-on: ubuntu-24.04
--- a/.github/workflows/ci-freestanding.yml
+++ b/.github/workflows/ci-freestanding.yml
@@ -34,51 +34,32 @@ on:
    paths-ignore:
      - "docs/**"

+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
+  generate-matrix:
+    name: "Generate build matrix for ${{ github.workflow }}"
+    outputs:
+      matrix: ${{ steps.set-matrix.outputs.matrix }}
+    runs-on: ubuntu-24.04
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: 3.x
+      - id: set-matrix
+        run: python .github/generate-job-matrix.py --preset freestanding --seed 42 --debug combinations counts
  build:
    name: "${{ matrix.formatting }} ${{ matrix.contracts }} C++${{ matrix.std }} ${{ matrix.config.name }} ${{ matrix.build_type }}"
    runs-on: ${{ matrix.config.os }}
+    needs: generate-matrix
    strategy:
      fail-fast: false
      matrix:
-        formatting: ["std::format", "fmtlib"]
-        contracts: ["none"]
-        std: [23]
-        config:
-          - {
-              name: "GCC-14",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: GCC,
-                  version: 14,
-                  cc: "gcc-14",
-                  cxx: "g++-14",
-                },
-              cxx_modules: "False",
-              std_format_support: "True",
-              conan-config: "",
-            }
-          - {
-              name: "Clang-18",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 18,
-                  cc: "clang-18",
-                  cxx: "clang++-18",
-                },
-              lib: "libc++",
-              cxx_modules: "True",
-              std_format_support: "True",
-              conan-config: "",
-            }
-        build_type: ["Release", "Debug"]
-        # TODO For some reason Clang-18 Debug with -ffreestanding does not pass CMakeTestCXXCompiler
-        exclude:
-          - build_type: "Debug"
-            config: { name: "Clang-18" }
+        include: ${{fromJson(needs.generate-matrix.outputs.matrix)}}

    env:
      CC: ${{ matrix.config.compiler.cc }}
--- a/.github/workflows/ci-test-package-cmake.yml
+++ b/.github/workflows/ci-test-package-cmake.yml
@@ -38,136 +38,32 @@ on:
      - "example/**"
      - "test/**"

+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
+  generate-matrix:
+    name: "Generate build matrix for ${{ github.workflow }}"
+    outputs:
+      matrix: ${{ steps.set-matrix.outputs.matrix }}
+    runs-on: ubuntu-24.04
+    steps:
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: 3.x
+      - id: set-matrix
+        run: python .github/generate-job-matrix.py --preset conan --seed 42 --debug combinations counts
  test_package:
    name: "${{ matrix.formatting }} ${{ matrix.contracts }} C++${{ matrix.std }} ${{ matrix.config.name }} ${{ matrix.build_type }}"
    runs-on: ${{ matrix.config.os }}
+    needs: generate-matrix
    strategy:
      fail-fast: false
      matrix:
-        formatting: ["std::format", "fmtlib"]
-        contracts: ["none", "gsl-lite", "ms-gsl"]
-        std: [20, 23]
-        config:
-          - {
-              name: "MSVC 14.4",
-              os: windows-2022,
-              compiler: { type: MSVC, version: 194, cc: "", cxx: "" },
-              cxx_modules: "False",
-              std_format_support: "True",
-            }
-          - {
-              name: "GCC-12",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: GCC,
-                  version: 12,
-                  cc: "gcc-12",
-                  cxx: "g++-12",
-                },
-              cxx_modules: "False",
-              std_format_support: "False",
-            }
-          - {
-              name: "GCC-13",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: GCC,
-                  version: 13,
-                  cc: "gcc-13",
-                  cxx: "g++-13",
-                },
-              cxx_modules: "False",
-              std_format_support: "True",
-            }
-          - {
-              name: "GCC-14",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: GCC,
-                  version: 14,
-                  cc: "gcc-14",
-                  cxx: "g++-14",
-                },
-              cxx_modules: "False",
-              std_format_support: "True"
-            }
-          - {
-              name: "Clang-16",
-              os: ubuntu-22.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 16,
-                  cc: "clang-16",
-                  cxx: "clang++-16",
-                },
-              lib: "libc++",
-              cxx_modules: "False",
-              std_format_support: "False",
-            }
-          - {
-              name: "Clang-17",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 17,
-                  cc: "clang-17",
-                  cxx: "clang++-17",
-                },
-              lib: "libc++",
-              cxx_modules: "False",
-              std_format_support: "True",
-            }
-          - {
-              name: "Clang-18",
-              os: ubuntu-24.04,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 18,
-                  cc: "clang-18",
-                  cxx: "clang++-18",
-                },
-              lib: "libc++",
-              cxx_modules: "False",
-              std_format_support: "True"
-            }
-          - {
-              name: "Clang-18 on Apple M1 (arm64)",
-              os: macos-14,
-              compiler:
-                {
-                  type: CLANG,
-                  version: 18,
-                  cc: "/opt/homebrew/opt/llvm@18/bin/clang-18",
-                  cxx: "/opt/homebrew/opt/llvm@18/bin/clang++",
-                },
-              lib: "libc++",
-              cxx_modules: "False",
-              std_format_support: "True"
-            }
-          - {
-              name: "Apple Clang 15",
-              os: macos-14,
-              compiler:
-                {
-                  type: APPLE_CLANG,
-                  version: "15.0",
-                  cc: "clang",
-                  cxx: "clang++",
-                },
-              cxx_modules: "False",
-              std_format_support: "False",
-            }
-        build_type: ["Release", "Debug"]
-        exclude:
-          - formatting: "std::format"
-            config: { std_format_support: "False" }
+        include: ${{fromJson(needs.generate-matrix.outputs.matrix)}}

    env:
      CC: ${{ matrix.config.compiler.cc }}
@@ -255,8 +151,8 @@ jobs:
      - name: Set 'std_format' and 'import_std' environment variables
        shell: bash
        run: |
-            echo "std_format=$([ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
-            echo "import_std=$([ "${{ matrix.config.cxx_modules }}" == "True" ] && [ "${{ matrix.config.contracts }}" == "none" ] && [ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
+          echo "std_format=$([ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
+          echo "import_std=$([ "${{ matrix.std }}" -ge "23" ] && [ "${{ matrix.config.cxx_modules }}" == "True" ] && [ "${{ matrix.config.contracts }}" == "none" ] && [ "${{ matrix.formatting }}" == "std::format" ] && echo "True" || echo "False")" >> $GITHUB_ENV
      - name: Install Conan dependencies
        shell: bash
        run: |
--- a/.github/workflows/citation.yml
+++ b/.github/workflows/citation.yml
@@ -5,6 +5,10 @@ on:
    paths:
      - CITATION.cff

+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
  Validate-CITATION-cff:
    runs-on: ubuntu-latest
--- a/.github/workflows/codeql.yml
+++ b/.github/workflows/codeql.yml
@@ -22,6 +22,10 @@ on:
    paths-ignore:
      - "docs/**"

+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
  analyze:
    name: Analyze
--- a/.github/workflows/documentation.yml
+++ b/.github/workflows/documentation.yml
@@ -36,6 +36,11 @@ on:
      - "mkdocs.yml"
 permissions:
  contents: write
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
  deploy:
    runs-on: ubuntu-latest
--- a/docs/blog/posts/isq-part-1-introduction.md
+++ b/docs/blog/posts/isq-part-1-introduction.md
@@ -26,6 +26,7 @@ In this series, we will describe:
 - [Part 3 - Modeling ISQ](isq-part-3-modeling-isq.md)
 - [Part 4 - Implementing ISQ](isq-part-4-implemeting-isq.md)
 - [Part 5 - Benefits](isq-part-5-benefits.md)
+- [Part 6 - Challenges](isq-part-6-challenges.md)


 ## Terms and Definitions
--- a/docs/blog/posts/isq-part-2-problems-when-isq-is-not-used.md
+++ b/docs/blog/posts/isq-part-2-problems-when-isq-is-not-used.md
@@ -28,6 +28,7 @@ library on just units or dimensions.
 - [Part 3 - Modeling ISQ](isq-part-3-modeling-isq.md)
 - [Part 4 - Implementing ISQ](isq-part-4-implemeting-isq.md)
 - [Part 5 - Benefits](isq-part-5-benefits.md)
+- [Part 6 - Challenges](isq-part-6-challenges.md)


 ## Limitations of units-only solutions
--- a/docs/blog/posts/isq-part-3-modeling-isq.md
+++ b/docs/blog/posts/isq-part-3-modeling-isq.md
@@ -27,6 +27,7 @@ language.
 - Part 3 - Modeling ISQ
 - [Part 4 - Implementing ISQ](isq-part-4-implemeting-isq.md)
 - [Part 5 - Benefits](isq-part-5-benefits.md)
+- [Part 6 - Challenges](isq-part-6-challenges.md)


 ## Dimension is not enough to describe a quantity
--- a/docs/blog/posts/isq-part-4-implemeting-isq.md
+++ b/docs/blog/posts/isq-part-4-implemeting-isq.md
@@ -28,6 +28,7 @@ Now, it is time to see how we can implement hierarchies of quantities of the sam
 - [Part 3 - Modeling ISQ](isq-part-3-modeling-isq.md)
 - Part 4 - Implementing ISQ
 - [Part 5 - Benefits](isq-part-5-benefits.md)
+- [Part 6 - Challenges](isq-part-6-challenges.md)


 ## Modeling a hierarchy of kind _length_
--- a/docs/blog/posts/isq-part-5-benefits.md
+++ b/docs/blog/posts/isq-part-5-benefits.md
@@ -26,6 +26,7 @@ how our ISQ model elegantly addresses the remaining problems.
 - [Part 3 - Modeling ISQ](isq-part-3-modeling-isq.md)
 - [Part 4 - Implementing ISQ](isq-part-4-implemeting-isq.md)
 - Part 5 - Benefits
+- [Part 6 - Challenges](isq-part-6-challenges.md)


 ## Generic but safe interfaces
--- a/docs/blog/posts/isq-part-6-challenges.md
+++ b/docs/blog/posts/isq-part-6-challenges.md
@@ -0,0 +1,530 @@
+---
+date: 2024-11-11
+authors:
+ - mpusz
+categories:
+ - Metrology
+comments: true
+---
+
+# International System of Quantities (ISQ): Part 6 - Challenges
+
+This article might be the last one from our series. This time, we will discuss the challenges and
+issues with modeling of the ISQ in software.
+
+<!-- more -->
+
+## Articles from this series
+
+- [Part 1 - Introduction](isq-part-1-introduction.md)
+- [Part 2 - Problems when ISQ is not used](isq-part-2-problems-when-isq-is-not-used.md)
+- [Part 3 - Modeling ISQ](isq-part-3-modeling-isq.md)
+- [Part 4 - Implementing ISQ](isq-part-4-implemeting-isq.md)
+- [Part 5 - Benefits](isq-part-5-benefits.md)
+- Part 6 - Challenges
+
+
+## Ambiguity
+
+Some quantity names are ambiguous. It is not a problem of ISQ but of the English language and
+the way we communicate things. When I say: "Every _width_ is a _length_, but not every _length_
+is a _width_" most people understand this right away. However, the same people trying to model
+[our 3D box problem](isq-part-2-problems-when-isq-is-not-used.md#various-quantities-of-the-same-dimension-and-kinds)
+try to do it as follows:
+
+```cpp
+class Box {
+  quantity<isq::length[m]> length_;
+  quantity<isq::width[m]> width_;
+  quantity<isq::height[m]> height_;
+public:
+  // ...
+};
+```
+
+This looks correct at first sight. Only when we think about the sentence mentioned above will
+we realize that this implementation has a problem. We intended to specify three orthogonal
+dimensions of the box, each of which will be a strong quantity that is not convertible to others.
+But we've failed.
+
+When we look at the
+[tree of quantities of length](isq-part-4-implemeting-isq.md#modeling-a-hierarchy-of-kind-length)
+we immediately see that both _width_ and _height_ are special _lengths_ so they are convertible to
+it.
+
+To implement our task correctly, we had to define and use a new quantity of kind _length_:
+
+```cpp
+inline constexpr struct horizontal_length final : quantity_spec<isq::length> {} horizontal_length;
+```
+
+We do not propose adding _horizontal length_ to ISO 80000-3. There are probably other similar
+cases as well, but so far, this was the most common and obvious one we've encountered.
+
+
+## No common quantities
+
+ISO 80000-1:2009 explicitly states:
+
+!!! quote
+
+    Two or more quantities cannot be added or subtracted unless they belong to the same category
+    of mutually comparable quantities.
+
+This means that we should be able to add and subtract any quantities as long as they belong to
+the same kind. However, ISO/IEC documents do not provide any rules or even hints about what should
+be the result of such operations.
+
+If it is possible to add _radius_ and _distance_, then what quantity should be provided
+in return? Undoubtedly, the resulting quantity type can't be the same as any of the arguments.
+It is not a _radius_ or _distance_. It is some closer unspecified _length_, though.
+
+!!! info
+
+    Finding the correct solution took us many months of experimentation and implementation.
+    Based on the hierarchy tree of quantities, we can define
+    [conversion rules](isq-part-3-modeling-isq.md#converting-between-quantities-of-the-same-kind)
+    and what a [common quantity should be](isq-part-3-modeling-isq.md#comparing-adding-and-subtracting-quantities-of-the-same-kind).
+
+
+## Lack of consistency
+
+The documents of ISO/IEC 80000 are not 100% consistent, and programming languages do not like
+inconsistencies.
+
+For example:
+
+- _time_ is mentioned as a base quantity of ISQ in ISO 80000-1 chapter 4.5.
+- ISO 80000-3 "Space and time", does not define a quantity of _time_. It provides a _duration_
+  quantity (item 3-9) with symbol _t_, and states in the Remarks section:
+
+    !!! quote
+
+        Duration is often just called time.
+
+- Other parts (e.g., IEC 80000-6 "Electromagnetism") often say:
+
+    !!! quote
+
+        ... _t_ is time (ISO 80000-3)
+
+To be consistent, ISO/IEC should either:
+
+- change ISO 80000-1 chapter 4.5 and all references in other parts to use _duration_ (unlikely),
+- or add _time_ as an alias name to _duration_ in the definition 3-9 of ISO 80000-3.
+
+
+## Lack of definitions
+
+ISQ defines derived quantities in terms of other quantities provided in the series. However, some
+definitions mention quantities that are not defined in the ISQ at all.
+
+For example, _weight_ is defined as $F_\textsf{g} = m\;g$, where $m$ is the _mass_ of the body
+(item 4-1 of ISO 80000-4 "Mechanics"), and $g$ is the _local acceleration of free fall_ (ISO 80000-3).
+
+The problem here is that ISO 80000-3 never defines a quantity with a symbol $g$ or named as a
+_local acceleration of free fall_. The closest one we have is _acceleration_ (item 3-11) with
+a symbol $a$.
+
+!!! info
+
+    To have a proper definition of _weight_ in **mp-units** that is not defined in terms of just
+    any kind of _acceleration_, we have added `isq::acceleration_of_free_fall` in our definitions
+    as an extension to the original ISQ set of quantities.
+
+
+## Not engineering-friendly
+
+Many quantities have proper physical definitions, but they are sometimes not engineering-friendly.
+
+For example, _velocity_ is defined as a rate of change of _position vector_
+$v = \frac{\textsf{d}r}{\textsf{d}t}$, where $r$ denotes the _position vector_ (item 3‑1.10) and
+$t$ the _duration_ (item 3‑9).
+
+Next, a _speed_ quantity is defined as the magnitude of _velocity_. Despite being
+physically correct, requiring every _speed_ to be derived from the vector quantity of _velocity_
+in software would be inconvenient. If this was the only case, people would always need to use
+vector representations of _position vectors_ to talk about _speeds_, which differs from what we
+do in practice. In practice, we divide any kind of _length_ by _time_ to get some kind of _speed_.
+
+ISO 80000-3 provides _length_, _height_, _distance_ and other quantities of kind _length_ that when
+divided by _duration_ can serve really well to calculate _speed_.
+
+!!! info
+
+    This is why in **mp-units**, we decided to divert from the official definition of _speed_ and
+    define it as:
+
+    ```cpp
+    inline constexpr struct speed : quantity_spec<speed, length / time> {} speed;
+    ```
+
+    This allows us to create a quantity of kind _speed_ from any quantity of _length_ divided
+    by _time_.
+
+    Additionally, it is essential to note that for the needs of our library, defining _velocity_
+    as `position_vector / duration` would be wrong. We miss the delta part here. Even though it is
+    not mentioned in ISO 80000-3, the delta of _position vectors_ is actually a _displacement_.
+    This is why our _velocity_ is defined as:
+
+    ```cpp
+    inline constexpr struct velocity : quantity_spec<speed, displacement / duration> {} velocity;
+    ```
+
+    Please also note that _velocity_ is defined as a more specialized quantity of _speed_.
+
+
+## Affine space agnostic
+
+[The affine space](../../users_guide/framework_basics/the_affine_space.md) is a powerful
+abstraction, allowing us to model some problems safer or more accurately. It has two types of
+entities:
+
+- point - a position specified with coordinate values (e.g., location, address, etc.),
+- displacement vector - the difference between two points (e.g., shift, offset, displacement,
+  duration, etc.).
+
+Vectors support all the arithmetics operations, but points have some limitations. It is not
+possible to:
+
+- add two _points_,
+- subtract a _point_ from a _vector_,
+- multiply nor divide _points_ with anything else.
+
+ISO/IEC series does not acknowledge this abstraction even though it would be really useful in
+some cases. Let's discuss the following two examples.
+
+What does it mean to add two _altitudes_? It is not meaningful. On the other hand, subtracting
+those should not result in an _altitude_, but in a quantity of _height_. Adding or
+subtracting _height_ to/from _altitude_ results in _altitude_. Subtracting _altitude_ from
+_height_ is meaningless again. Those quantities clearly model affine space. Maybe this is why
+ISQ defines them as one quantity type _height_/_depth_/_altitude_?
+
+What does it mean to add two _position vectors_? It is not meaningful again. However, subtracting
+those results in a _displacement_ as we noted in the previous chapter. Adding or subtracting
+_displacement_ to/from _position vector_ results in another _position vector_, and subtracting
+_position vector_ from _displacement_ does not have physical sense. Again, those quantities
+perfectly model affine space. However, this time, those are defined as separate and independent
+quantities (i.e., displacement is not modeled as delta _position vector_ or _position vector_
+is not modeled as a _displacement_ from the origin of a coordinate system).
+
+!!! info
+
+    Currently, **mp-units** does not enforce the affine space behavior for such quantities.
+    Today, subtracting two _altitudes_ result in an _altitude_ and subtracting two
+    _position vectors_ result in a _position vector_. However, we plan to support automatic
+    conversion to a proper quantity type on subtraction and addition shortly.
+
+
+## Non-negative quantities
+
+Some quantities in the ISQ are defined as non-negative. This is a really interesting property that
+may be checked at runtime to increase safety. However, the number of such quantities is minimal.
+From a few hundred quantities provided by the ISO/IEC series, only the following have this property
+mentioned explicitly:
+
+- _width_/_breadth_,
+- _thickness_,
+- _diameter_,
+- _radius_.
+
+If _height_ was defined separately from _altitude_, it could probably also join this group.
+
+Let's think a bit more about this. What does it mean that a quantity is non-negative? Indeed,
+it is hard to imagine something of a negative _width_ or _radius_. However, if we subtract
+two _widths_, the second one may be larger. This will result in a negative
+quantity of _width_, violating our precondition. So, is it non-negative or not?
+
+Again, we have to talk about the affine space abstractions. Every empirical measurement can be
+expressed as a point. Such points for some quantities may be non-negative indeed.
+
+Non-negative quantities do not end on the ones provided above. For example, _speed_ is a good
+example here as well. In general, all magnitudes of vector quantities will also have this property.
+
+When subtracting two points, we end up with a delta/displacement type, which may be negative
+even for quantities listed as non-negative in the ISQ. As stated in the previous chapter,
+having affine space abstractions acknowledged in ISQ would greatly help here.
+
+
+## Lack of quantity recipes
+
+Definition of many derived quantities provides their recipes in the form of
+[quantity equations](../../appendix/glossary.md#quantity-equation) (e.g., _weight_ equation
+in the previous chapter). However, some of them do not. Instead, they often provide a very
+generic description.
+
+For example, _force_ is defined as:
+
+!!! quote
+
+    vector (ISO 80000-2) quantity describing interaction between bodies or particles.
+
+This is not helpful for programming languages that like explicit definitions. Different
+vendors may interpret the above differently, which will result in different implementations that
+will not be compatible with each other.
+
+As the derived quantity of _force_ has to be a vector quantity, it has to be defined in terms of
+at least one other vector quantity. We have a few to choose from:
+
+- _displacement_ ($\Delta{r}$),
+- _velocity_ ($v$),
+- _acceleration_ ($a$).
+
+It is not stated explicitly in ISQ which one of those should be used and how.
+
+!!! info
+
+    In **mp-units** we decided to define _force_ as $F = m\;a$.
+
+
+## Lack of generic quantities and name conflicts
+
+In the previous chapter, we complained about some definitions needing to be more complex or generic.
+On the other hand, we also lack some generic quantities in ISQ that could serve as a root for
+a quantity hierarchy tree.
+
+For example:
+
+- ISO 80000-4 "Mechanics" defines _power &lt;mechanics&gt;_ as $P = F\;v$ (scalar product of force $F$
+  (item 4-9.1) acting to a body and its velocity $v$ (ISO 80000-3)),
+- ISO 80000-6 "Electromagnetism" defines _power_ as $p = u\;i$ (scalar quantity given by the
+  product of _instantaneous voltage_ $u$ (item 6-11.3) and _instantaneous electric current_ $i$
+  (item 6-1)).
+
+First, the above definitions have somehow conflicting names which makes it hard for the programming
+languages to name them consistently by different vendors.
+
+!!! info
+
+    In **mp-units**, we chose `mechanical_power` and `electromagnetism_power` for those.
+
+Second, we do not have any other more generic definition of _power_ to put above those in the tree.
+Not having it makes it hard to answer what should be the result of:
+
+```cpp
+quantity q = isq::mechanical_power(42 * W) + isq::electromagnetism_power(60 * W);
+```
+
+!!! info
+
+    To solve the above problem, we have added `isq::power` in **mp-units**, that has a really
+    generic definition of:
+
+    ```cpp
+    inline constexpr struct power : quantity_spec<mass* pow<2>(length) / pow<3>(time)> {} power;
+    ```
+
+
+## Invalid definitions order
+
+_Energy_ is defined a bit better than _power_, but still not without issues.
+
+The first time ISQ mentions _energy_ is in the ISO 80000-4 "Mechanics". It defines
+_potential energy_, _kinetic energy_, and a _mechanical energy_ as the sum of the first two.
+Right after that a _mechanical work/work_ is defined.
+
+Then ISO 80000-5 "Thermodynamics" defines _energy &lt;thermodynamics&gt;_ as:
+
+!!! quote
+
+    ability of a system to do work (ISO 80000-4).
+
+Next, _internal energy/thermodynamic energy_ is defined in terms of the change of heat.
+
+From the above, it seems that what is called _energy &lt;thermodynamics&gt;_ should actually be
+the root of our tree and probably be provided in Part 4 before the _mechanical energy_ is defined.
+
+
+## Hierarchies of derived quantities
+
+Derived quantities of the same kind are often independently defined in the ISQ. The ISO/IEC 80000
+series often does not suggest any hierarchy between those. Even more, it states:
+
+!!! quote "ISO/IEC Guide 99"
+
+    The division of ‘quantity’ according to ‘kind of quantity’ is, to some extent, arbitrary.
+
+Because of this, it is unknown or ambiguous how to form a hierarchy tree for such quantities.
+
+To get some sense of the complexity here, let's look again at our tree of quantities of a kind
+_energy_:
+
+```mermaid
+flowchart TD
+    energy["<b>energy</b><br><i>(mass * length<sup>2</sup> / time<sup>2</sup>)</i><br>[J]"]
+    energy --- mechanical_energy["<b>mechanical_energy</b>"]
+    mechanical_energy --- potential_energy["<b>potential_energy</b>"]
+    mechanical_energy --- kinetic_energy["<b>kinetic_energy</b>"]
+    energy --- enthalpy["<b>enthalpy</b>"]
+    enthalpy --- internal_energy["<b>internal_energy</b> / <b>thermodynamic_energy</b>"]
+    internal_energy --- Helmholtz_energy["<b>Helmholtz_energy</b> / <b>Helmholtz_function</b>"]
+    enthalpy --- Gibbs_energy["<b>Gibbs_energy</b> / <b>Gibbs_function</b>"]
+    energy --- active_energy["<b>active_energy</b>"]
+```
+
+Not being exact means that every vendor may implement it differently. This will result in:
+
+- different convertibility rules among quantities:
+
+    ```cpp
+    static_assert(implicitly_convertible(isq::potential_energy, isq::mechanical_energy));
+    static_assert(explicitly_convertible(isq::mechanical_energy, isq::potential_energy));
+    ```
+
+- different common quantities resulting from the arithmetics on various quantities of the same
+  kind:
+
+    ```cpp
+    static_assert((isq::potential_energy(1 * J) + isq::kinetic_energy(1 * J)).quantity_spec == isq::mechanical_energy);
+    ```
+
+It would be great if ISQ could provide specific division of quantities into kinds and more
+information about the position of each quantity within the hierarchy of quantities of
+the same kind.
+
+!!! important
+
+    We can try to do this by ourselves, but it is tough. Probably no one, for sure we are
+    not, is an expert in all the fields of ISO/IEC 80000 applicability.
+
+    We need the help of subject matter experts who will help us build those trees for their domains
+    and then verify that everything works as expected.
+
+
+## The same or a different kind?
+
+Some quantities are more complicated than others. For example, _power_ has:
+
+- scalar quantities expressed in:
+    - W (watts) (e.g., _mechanical power_, _active power_),
+    - VA (volt-ampere) (e.g., _apparent power_),
+    - var (e.g., _reactive power_),
+- complex quantities expressed in VA (volt-ampere) (e.g., _complex power_).
+
+How should we model this? Maybe those should be two or three independent trees of quantities, each
+having its own unit?
+
+```mermaid
+flowchart TD
+    power["<b>power</b><br><i>(mass * length<sup>2</sup> / time<sup>3</sup>)</i><br>[W]"]
+    power --- mechanical_power["<b>mechanical_power</b><br><i>(scalar_product(force, velocity))</i>"]
+    power --- electromagnetism_power["<b>electromagnetism_power</b> | <b>instantaneous_power</b><br><i>(instantaneous_voltage * instantaneous_electric_current)</i>"]
+    power --- active_power["<b>active_power</b><br><i>(1 / period * instantaneous_power * time)<br>(re(complex_power))</i>"]
+
+    nonactive_power["<b>nonactive_power</b><br><i>(mass * length<sup>2</sup> / time<sup>3</sup>)</i><br>[VA]"]
+    nonactive_power --- reactive_power["<b>reactive_power</b><br><i>(im(complex_power))</i><br>[var]"]
+
+    complex_power["<b>complex_power</b><br>{complex}<br><i>(voltage_phasor * electric_current_phasor)<br>(active_power + j * reactive_power)</i><br>[VA]"]
+    complex_power --- apparent_power["<b>apparent_power</b><br><i>(voltage * electric_current)<br>(mod(complex_power))</i>"]
+```
+
+This will mean that we will not be able to add or compare _active power_, _reactive power_, and
+_apparent power_, which probably makes a lot of sense. However, it also means that the following
+will fail to compile:
+
+```cpp
+quantity apparent = isq::apparent_power(100 * VA);
+quantity active = isq::active_power(60 * W);
+quantity<isq::nonactive_power[VA]> q = sqrt(pow<2>(apparent) - pow<2>(active)); // Compile-time error
+```
+
+Also the following will not work:
+
+```cpp
+quantity active = isq::active_power(60 * W);
+quantity reactive = isq::reactive_power(40 * var);
+quantity<isq::apparent_power[VA]> q = sqrt(pow<2>(active) + pow<2>(reactive)); // Compile-time error
+```
+
+If we want the above to work maybe we need to implement the tree as follows?
+
+```mermaid
+flowchart TD
+    power["<b>power</b><br><i>(mass * length<sup>2</sup> / time<sup>3</sup>)</i><br>[W]"]
+    power --- mechanical_power["<b>mechanical_power</b><br><i>(scalar_product(force, velocity))</i>"]
+    power --- electromagnetism_power["<b>electromagnetism_power</b> | <b>instantaneous_power</b><br><i>(instantaneous_voltage * instantaneous_electric_current)</i>"]
+    power --- apparent_power["<b>apparent_power</b><br><i>(voltage * electric_current)<br>(mod(complex_power))</i><br>[VA]"]
+    apparent_power --- active_power["<b>active_power</b><br><i>(1 / period * instantaneous_power * time)<br>(re(complex_power))</i>"]
+    apparent_power --- nonactive_power["<b>nonactive_power</b><br><i>(sqrt(apparent_power<sup>2</sup> - active_power<sup>2</sup>))</i><br>"]
+    nonactive_power --- reactive_power["<b>reactive_power</b><br><i>(im(complex_power))</i><br>[var]"]
+    apparent_power --- complex_power["<b>complex_power</b><br>{complex}<br><i>(voltage_phasor * electric_current_phasor)<br>(active_power + j * reactive_power)</i>"]
+```
+
+However, the above allows direct addition and comparison of _active power_ and _nonactive power_,
+and also will not complain if someone will try to use watt (W) as a unit of _apparent power_ or
+_reactive power_.
+
+Again, ISQ does not provide a direct answer here.
+
+
+## More base quantities?
+
+Is ISQ really based on only seven base quantities? Let's look at the definition of
+_traffic intensity_ in IEC 80000-13 "Information science and technology":
+
+!!! quote
+
+    number of simultaneously busy resources in a particular pool of resources.
+
+It looks like a definition of a specialized dimensionless quantity or, more correctly, a quantity
+of dimension one. This would not be the only such case. Even in the same Part 13, we can find
+quantities like _storage capacity_ with a similar property.
+
+Only when we look closer do we start to see differences. All dimensionless quantities, even if they
+have their own dedicated units, can also be measured in a unit of one (1). This is true for
+_storage capacity_ (also measured in bits), _angular measure_ (also measured in radians),
+_solid angular measure (also measured in steradians), and more.
+
+However, _traffic intensity_ can only be measured in erlangs (E), not in a unit one (1).
+Does it mean that it is a "hidden" 8-th base quantity in ISQ? If so, should it have its own
+dimension as well?
+
+Angular quantities are another interesting case here. Scientists have written petitions and papers
+for years to make them an additional dimension in ISQ and SI. More about this can be found in
+our documentation's [Strong Angular System](../../users_guide/systems/strong_angular_system.md)
+chapter.
+
+
+## Summary
+
+ISQ is tremendous and solves many problems we had in modeling various subjects for years in
+software. As a result, we have more powerful tools in our hands that allow us to deliver safer
+products.
+
+Unfortunately, ISQ, contrarily to SI, is not widely recognized, and no libraries besides
+**mp-units** model it in any programming language. Keeping it behind a paywall does not help
+either. We hope that posts from this series will spread in the community, raise awareness
+of ISQ and its benefits, and encourage authors of other libraries to implement it in their
+products.
+
+Despite all the benefits, it is essential to realize that ISQ has many problems. International
+standards should be specified in such a way that there is no room for ambiguity in their
+interpretation by different parties trying to use them. As described above, this is not the case
+here.
+
+ISQ is not ready to be unambiguously modeled in software by various vendors. Here are the most
+important problems to solve to allow this:
+
+1. ISQ needs to define basic operations on quantities:
+
+    - what the result of addition and subtraction should be when arguments differ,
+    - convertibility rules.
+
+2. The exact quantity equation recipe needs to be included for many derived quantities.
+3. Many ISQ quantities do not provide their exact relation versus other quantities of the same
+   kind (no strict hierarchy).
+4. Some missing quantities need to be included. Others would benefit from corrected names.
+
+Additionally:
+
+- extending ISQ with affine space abstractions,
+- specifying more quantities as non-negative,
+- adding more base quantities (i.e., _angle_)
+
+could improve the safety of our programs and products that people depend on with their lives on
+a daily basis.
+
+I hope you enjoyed following this series and learned more about the International System
+of Quantities. Please try it out in your domain and share feedback with us. We always love to
+hear about the projects in which our library is being used and about use cases it helps
+address.
--- a/docs/users_guide/examples/si_constants.md
+++ b/docs/users_guide/examples/si_constants.md
@@ -16,19 +16,11 @@ work in practice.
 --8<-- "example/si_constants.cpp:28:40"
 ```

-As always, we start with the inclusion of all the needed header files. After that, for
-the simplicity of this example, we
-[hack the character of quantities](../framework_basics/character_of_a_quantity.md#hacking-the-character)
-to be able to express vector quantities with simple scalar types.
-
-```cpp title="si_constants.cpp" linenums="14"
--8<-- "example/si_constants.cpp:42:44"
-```
-
+As always, we start with the inclusion of all the needed header files.
 The main part of the example prints all of the SI-defining constants:

-```cpp title="si_constants.cpp" linenums="17"
--8<-- "example/si_constants.cpp:45:"
+```cpp title="si_constants.cpp" linenums="14"
+--8<-- "example/si_constants.cpp:42:"
 ```

 While analyzing the output of this program (provided below), we can easily notice that a direct
--- a/example/include/validated_type.h
+++ b/example/include/validated_type.h
@@ -129,8 +129,8 @@ std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>&
 template<typename T, typename Validator, typename Char>
 struct MP_UNITS_STD_FMT::formatter<validated_type<T, Validator>, Char> : formatter<T, Char> {
  template<typename FormatContext>
-  auto format(const validated_type<T, Validator>& v, FormatContext& ctx) const -> decltype(ctx.out())
+  auto format(const validated_type<T, Validator>& val, FormatContext& ctx) const -> decltype(ctx.out())
  {
-    return formatter<T, Char>::format(v.value(), ctx);
+    return formatter<T, Char>::format(val.value(), ctx);
  }
 };
--- a/example/si_constants.cpp
+++ b/example/si_constants.cpp
@@ -39,10 +39,6 @@ import mp_units;
 #include <mp-units/systems/si.h>
 #endif

-template<class T>
-  requires mp_units::is_scalar<T>
-constexpr bool mp_units::is_vector<T> = true;
-
 int main()
 {
  using namespace mp_units;
--- a/src/core/CMakeLists.txt
+++ b/src/core/CMakeLists.txt
@@ -91,6 +91,7 @@ if(NOT ${projectPrefix}API_FREESTANDING)
               include/mp-units/bits/fmt.h
               include/mp-units/bits/requires_hosted.h
               include/mp-units/ext/format.h
+               include/mp-units/cartesian_vector.h
               include/mp-units/complex.h
               include/mp-units/format.h
               include/mp-units/math.h
--- a/src/core/include/mp-units/cartesian_vector.h
+++ b/src/core/include/mp-units/cartesian_vector.h
@@ -0,0 +1,230 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#pragma once
+
+#include <mp-units/bits/requires_hosted.h>
+//
+#include <mp-units/bits/module_macros.h>
+#include <mp-units/framework/customization_points.h>
+
+#if MP_UNITS_HOSTED
+#include <mp-units/bits/fmt.h>
+#endif
+
+#ifndef MP_UNITS_IN_MODULE_INTERFACE
+#ifdef MP_UNITS_IMPORT_STD
+import std;
+#else
+#include <cmath>
+#include <cstddef>
+#include <type_traits>
+#if MP_UNITS_HOSTED
+#include <ostream>
+#endif
+#endif
+#endif
+
+namespace mp_units {
+
+MP_UNITS_EXPORT template<typename T = double>
+class cartesian_vector {
+public:
+  // public members required to satisfy structural type requirements :-(
+  T _coordinates_[3];
+  using value_type = T;
+
+  cartesian_vector() = default;
+  cartesian_vector(const cartesian_vector&) = default;
+  cartesian_vector(cartesian_vector&&) = default;
+  cartesian_vector& operator=(const cartesian_vector&) = default;
+  cartesian_vector& operator=(cartesian_vector&&) = default;
+
+  template<std::convertible_to<T> Arg1, std::convertible_to<T>... Args>
+  constexpr cartesian_vector(Arg1&& arg1, Args&&... args) :
+      _coordinates_(std::forward<Arg1>(arg1), std::forward<Args>(args)...)
+  {
+  }
+
+  template<std::convertible_to<T> U>
+  constexpr cartesian_vector(const cartesian_vector<U>& other) : _coordinates_{other[0], other[1], other[2]}
+  {
+  }
+
+  template<std::convertible_to<T> U>
+  constexpr cartesian_vector(cartesian_vector<U>&& other) :
+      _coordinates_{std::move(other[0]), std::move(other[1]), std::move(other[2])}
+  {
+  }
+
+  template<std::convertible_to<T> U>
+  constexpr cartesian_vector& operator=(const cartesian_vector<U>& other)
+  {
+    _coordinates_[0] = other[0];
+    _coordinates_[1] = other[1];
+    _coordinates_[2] = other[2];
+    return *this;
+  }
+
+  template<std::convertible_to<T> U>
+  constexpr cartesian_vector& operator=(cartesian_vector<U>&& other)
+  {
+    _coordinates_[0] = std::move(other[0]);
+    _coordinates_[1] = std::move(other[1]);
+    _coordinates_[2] = std::move(other[2]);
+    return *this;
+  }
+
+  [[nodiscard]] constexpr T magnitude() const
+    requires treat_as_floating_point<T>
+  {
+    return std::hypot(_coordinates_[0], _coordinates_[1], _coordinates_[2]);
+  }
+
+  [[nodiscard]] constexpr cartesian_vector unit() const
+    requires treat_as_floating_point<T>
+  {
+    return *this / magnitude();
+  }
+
+  [[nodiscard]] constexpr T& operator[](std::size_t i) { return _coordinates_[i]; }
+  [[nodiscard]] constexpr const T& operator[](std::size_t i) const { return _coordinates_[i]; }
+
+  [[nodiscard]] constexpr cartesian_vector operator+() const { return *this; }
+  [[nodiscard]] constexpr cartesian_vector operator-() const
+  {
+    return {-_coordinates_[0], -_coordinates_[1], -_coordinates_[2]};
+  }
+
+  template<std::same_as<T> U, typename V>
+    requires requires(U u, V v) { u + v; }
+  [[nodiscard]] friend constexpr auto operator+(const cartesian_vector<U>& lhs, const cartesian_vector<V>& rhs)
+  {
+    return ::mp_units::cartesian_vector{lhs._coordinates_[0] + rhs._coordinates_[0],
+                                        lhs._coordinates_[1] + rhs._coordinates_[1],
+                                        lhs._coordinates_[2] + rhs._coordinates_[2]};
+  }
+
+  template<std::same_as<T> U, typename V>
+    requires requires(U u, V v) { u - v; }
+  [[nodiscard]] friend constexpr auto operator-(const cartesian_vector<U>& lhs, const cartesian_vector<V>& rhs)
+  {
+    return ::mp_units::cartesian_vector{lhs._coordinates_[0] - rhs._coordinates_[0],
+                                        lhs._coordinates_[1] - rhs._coordinates_[1],
+                                        lhs._coordinates_[2] - rhs._coordinates_[2]};
+  }
+
+  template<std::same_as<T> U>
+    requires requires(U u, T t) { u* t; }
+  [[nodiscard]] friend constexpr auto operator*(const cartesian_vector<U>& lhs, const T& rhs)
+  {
+    return ::mp_units::cartesian_vector{lhs._coordinates_[0] * rhs, lhs._coordinates_[1] * rhs,
+                                        lhs._coordinates_[2] * rhs};
+  }
+
+  template<std::same_as<T> U>
+    requires requires(T t, U u) { t* u; }
+  [[nodiscard]] friend constexpr auto operator*(const T& lhs, const cartesian_vector<U>& rhs)
+  {
+    return rhs * lhs;
+  }
+
+  template<std::same_as<T> U>
+    requires requires(U u, T t) { u / t; }
+  [[nodiscard]] friend constexpr auto operator/(const cartesian_vector<U>& lhs, const T& rhs)
+  {
+    return ::mp_units::cartesian_vector{lhs._coordinates_[0] / rhs, lhs._coordinates_[1] / rhs,
+                                        lhs._coordinates_[2] / rhs};
+  }
+
+  template<std::same_as<T> U, std::equality_comparable_with<U> V>
+  [[nodiscard]] friend constexpr bool operator==(const cartesian_vector<U>& lhs, const cartesian_vector<V>& rhs)
+  {
+    return lhs._coordinates_[0] == rhs._coordinates_[0] && lhs._coordinates_[1] == rhs._coordinates_[1] &&
+           lhs._coordinates_[2] == rhs._coordinates_[2];
+  }
+
+  [[nodiscard]] friend constexpr T norm(const cartesian_vector& vec)
+    requires treat_as_floating_point<T>
+  {
+    return vec.magnitude();
+  }
+
+  [[nodiscard]] friend constexpr cartesian_vector unit_vector(const cartesian_vector& vec)
+    requires treat_as_floating_point<T>
+  {
+    return vec.unit();
+  }
+
+  template<std::same_as<T> U, typename V>
+    requires requires(U u, V v, decltype(u * v) t) {
+      u* v;
+      t + t;
+    }
+  [[nodiscard]] friend constexpr auto scalar_product(const cartesian_vector<U>& lhs, const cartesian_vector<V>& rhs)
+  {
+    return lhs._coordinates_[0] * rhs._coordinates_[0] + lhs._coordinates_[1] * rhs._coordinates_[1] +
+           lhs._coordinates_[2] * rhs._coordinates_[2];
+  }
+
+  template<std::same_as<T> U, typename V>
+    requires requires(U u, V v, decltype(u * v) t) {
+      u* v;
+      t - t;
+    }
+  [[nodiscard]] friend constexpr auto vector_product(const cartesian_vector<U>& lhs, const cartesian_vector<V>& rhs)
+  {
+    return ::mp_units::cartesian_vector{
+      lhs._coordinates_[1] * rhs._coordinates_[2] - lhs._coordinates_[2] * rhs._coordinates_[1],
+      lhs._coordinates_[2] * rhs._coordinates_[0] - lhs._coordinates_[0] * rhs._coordinates_[2],
+      lhs._coordinates_[0] * rhs._coordinates_[1] - lhs._coordinates_[1] * rhs._coordinates_[0]};
+  }
+
+#if MP_UNITS_HOSTED
+  friend constexpr std::ostream& operator<<(std::ostream& os, const cartesian_vector& vec)
+  {
+    return os << '[' << vec[0] << ", " << vec[1] << ", " << vec[2] << ']';
+  }
+#endif
+};
+
+template<typename Arg, typename... Args>
+  requires(sizeof...(Args) <= 2) && requires { typename std::common_type_t<Arg, Args...>; }
+cartesian_vector(Arg, Args...) -> cartesian_vector<std::common_type_t<Arg, Args...>>;
+
+template<class T>
+constexpr bool is_vector<cartesian_vector<T>> = true;
+
+}  // namespace mp_units
+
+#if MP_UNITS_HOSTED
+// TODO use parse and use formatter for the underlying type
+template<typename T, typename Char>
+struct MP_UNITS_STD_FMT::formatter<mp_units::cartesian_vector<T>, Char> :
+    formatter<std::basic_string_view<Char>, Char> {
+  template<typename FormatContext>
+  auto format(const mp_units::cartesian_vector<T>& vec, FormatContext& ctx) const
+  {
+    return format_to(ctx.out(), "[{}, {}, {}]", vec[0], vec[1], vec[2]);
+  }
+};
+#endif
--- a/src/core/include/mp-units/core.h
+++ b/src/core/include/mp-units/core.h
@@ -28,6 +28,7 @@
 #include <mp-units/framework.h>

 #if MP_UNITS_HOSTED
+#include <mp-units/cartesian_vector.h>
 #include <mp-units/complex.h>
 #include <mp-units/format.h>
 #include <mp-units/math.h>
--- a/src/core/include/mp-units/ext/inplace_vector.h
+++ b/src/core/include/mp-units/ext/inplace_vector.h
@@ -90,16 +90,16 @@ public:
  constexpr T* data() noexcept { return data_; }
  constexpr const T* data() const noexcept { return data_; }

-  constexpr reference push_back(const T& v)
+  constexpr reference push_back(const T& val)
    requires std::constructible_from<T, const T&>
  {
-    return emplace_back(v);
+    return emplace_back(val);
  }

-  constexpr reference push_back(T&& v)
+  constexpr reference push_back(T&& val)
    requires std::constructible_from<T, T&&>
  {
-    return emplace_back(std::forward<T&&>(v));
+    return emplace_back(std::forward<T&&>(val));
  }

  template<typename... Args>
--- a/src/core/include/mp-units/framework/quantity.h
+++ b/src/core/include/mp-units/framework/quantity.h
@@ -174,21 +174,21 @@ public:

  template<typename FwdValue, Reference R2>
    requires detail::SameValueAs<R2{}, R, std::remove_cvref_t<FwdValue>, Rep>
-  constexpr quantity(FwdValue&& v, R2) : numerical_value_is_an_implementation_detail_(std::forward<FwdValue>(v))
+  constexpr quantity(FwdValue&& val, R2) : numerical_value_is_an_implementation_detail_(std::forward<FwdValue>(val))
  {
  }

  template<typename FwdValue, Reference R2, typename Value = std::remove_cvref_t<FwdValue>>
    requires(!detail::SameValueAs<R2{}, R, Value, Rep>) &&
            detail::QuantityConvertibleTo<quantity<R2{}, Value>, quantity>
-  constexpr quantity(FwdValue&& v, R2) : quantity(quantity<R2{}, Value>{std::forward<FwdValue>(v), R2{}})
+  constexpr quantity(FwdValue&& val, R2) : quantity(quantity<R2{}, Value>{std::forward<FwdValue>(val), R2{}})
  {
  }

  template<detail::ValuePreservingTo<Rep> FwdValue>
    requires(unit == ::mp_units::one)
-  constexpr explicit(false) quantity(FwdValue&& v) :
-      numerical_value_is_an_implementation_detail_(std::forward<FwdValue>(v))
+  constexpr explicit(false) quantity(FwdValue&& val) :
+      numerical_value_is_an_implementation_detail_(std::forward<FwdValue>(val))
  {
  }

@@ -214,9 +214,9 @@ public:

  template<detail::ValuePreservingTo<Rep> FwdValue>
    requires(unit == ::mp_units::one)
-  constexpr quantity& operator=(FwdValue&& v)
+  constexpr quantity& operator=(FwdValue&& val)
  {
-    numerical_value_is_an_implementation_detail_ = std::forward<FwdValue>(v);
+    numerical_value_is_an_implementation_detail_ = std::forward<FwdValue>(val);
    return *this;
  }

@@ -422,11 +422,11 @@ public:
    requires(!Quantity<Value>) && requires(rep a, Value b) {
      { a *= b } -> std::same_as<rep&>;
    }
-  friend constexpr decltype(auto) operator*=(Q&& lhs, const Value& v)
+  friend constexpr decltype(auto) operator*=(Q&& lhs, const Value& val)
  {
    // TODO use *= when compiler bug is resolved:
    // https://developercommunity.visualstudio.com/t/Discrepancy-in-Behavior-of-operator-an/10732445
-    lhs.numerical_value_is_an_implementation_detail_ = lhs.numerical_value_is_an_implementation_detail_ * v;
+    lhs.numerical_value_is_an_implementation_detail_ = lhs.numerical_value_is_an_implementation_detail_ * val;
    return std::forward<Q>(lhs);
  }

@@ -444,12 +444,12 @@ public:
    requires(!Quantity<Value>) && requires(rep a, Value b) {
      { a /= b } -> std::same_as<rep&>;
    }
-  friend constexpr decltype(auto) operator/=(Q&& lhs, const Value& v)
+  friend constexpr decltype(auto) operator/=(Q&& lhs, const Value& val)
  {
-    MP_UNITS_EXPECTS_DEBUG(v != quantity_values<Value>::zero());
+    MP_UNITS_EXPECTS_DEBUG(val != quantity_values<Value>::zero());
    // TODO use /= when compiler bug is resolved:
    // https://developercommunity.visualstudio.com/t/Discrepancy-in-Behavior-of-operator-an/10732445
-    lhs.numerical_value_is_an_implementation_detail_ = lhs.numerical_value_is_an_implementation_detail_ / v;
+    lhs.numerical_value_is_an_implementation_detail_ = lhs.numerical_value_is_an_implementation_detail_ / val;
    return std::forward<Q>(lhs);
  }

@@ -551,17 +551,17 @@ public:
  template<std::derived_from<quantity> Q, typename Value>
    requires(!Quantity<Value>) &&
            (!Reference<Value>) && detail::InvokeResultOf<quantity_spec, std::multiplies<>, Rep, const Value&>
-  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const Q& q, const Value& v)
+  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const Q& q, const Value& val)
  {
-    return ::mp_units::quantity{q.numerical_value_ref_in(unit) * v, R};
+    return ::mp_units::quantity{q.numerical_value_ref_in(unit) * val, R};
  }

  template<typename Value, std::derived_from<quantity> Q>
    requires(!Quantity<Value>) &&
            (!Reference<Value>) && detail::InvokeResultOf<quantity_spec, std::multiplies<>, const Value&, Rep>
-  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const Value& v, const Q& q)
+  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const Value& val, const Q& q)
  {
-    return ::mp_units::quantity{v * q.numerical_value_ref_in(unit), R};
+    return ::mp_units::quantity{val * q.numerical_value_ref_in(unit), R};
  }

  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
@@ -575,18 +575,18 @@ public:
  template<std::derived_from<quantity> Q, typename Value>
    requires(!Quantity<Value>) &&
            (!Reference<Value>) && detail::InvokeResultOf<quantity_spec, std::divides<>, Rep, const Value&>
-  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator/(const Q& q, const Value& v)
+  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator/(const Q& q, const Value& val)
  {
-    MP_UNITS_EXPECTS_DEBUG(v != quantity_values<Value>::zero());
-    return ::mp_units::quantity{q.numerical_value_ref_in(unit) / v, R};
+    MP_UNITS_EXPECTS_DEBUG(val != quantity_values<Value>::zero());
+    return ::mp_units::quantity{q.numerical_value_ref_in(unit) / val, R};
  }

  template<typename Value, std::derived_from<quantity> Q>
    requires(!Quantity<Value>) &&
            (!Reference<Value>) && detail::InvokeResultOf<quantity_spec, std::divides<>, const Value&, Rep>
-  [[nodiscard]] friend constexpr QuantityOf<inverse(quantity_spec)> auto operator/(const Value& v, const Q& q)
+  [[nodiscard]] friend constexpr QuantityOf<inverse(quantity_spec)> auto operator/(const Value& val, const Q& q)
  {
-    return ::mp_units::quantity{v / q.numerical_value_ref_in(unit), ::mp_units::one / R};
+    return ::mp_units::quantity{val / q.numerical_value_ref_in(unit), ::mp_units::one / R};
  }

  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
--- a/src/core/include/mp-units/framework/quantity_spec.h
+++ b/src/core/include/mp-units/framework/quantity_spec.h
@@ -59,7 +59,7 @@ template<QuantitySpec QS, Unit U>
  requires(!AssociatedUnit<U>) || UnitOf<U, QS{}>
 [[nodiscard]] consteval Reference auto make_reference(QS, U u)
 {
-  if constexpr (QuantityKindSpec<QS>)
+  if constexpr (requires { requires(get_quantity_spec(U{}) == QS{}); })
    return u;
  else
    return reference<QS, U>{};
--- a/src/core/include/mp-units/framework/representation_concepts.h
+++ b/src/core/include/mp-units/framework/representation_concepts.h
@@ -118,12 +118,11 @@ concept ComplexRepresentation = Complex<T> && WeaklyRegular<T> && requires(T a,
  { a - b } -> Complex;
  { a* b } -> Complex;
  { a / b } -> Complex;
-  // TBD
-  // { re(a) } -> Scalar;
-  // { im(a) } -> Scalar;
-  // { mod(a) } -> Scalar;
-  // { arg(a) } -> Scalar;
-  // { conj(a) } -> Complex;
+  { real(a) } -> Scalar;
+  { imag(a) } -> Scalar;
+  { abs(a) } -> Scalar;
+  { arg(a) } -> Scalar;
+  { conj(a) } -> Complex;
 };

 // TODO how to check for a complex(Scalar, Scalar) -> Complex?
--- a/src/core/include/mp-units/ostream.h
+++ b/src/core/include/mp-units/ostream.h
@@ -68,8 +68,8 @@ void to_stream_impl(std::basic_ostream<CharT, Traits>& os, const quantity<R, Rep
 }

 template<typename CharT, class Traits, typename T>
-std::basic_ostream<CharT, Traits>& to_stream(std::basic_ostream<CharT, Traits>& os, const T& v)
-  requires requires { detail::to_stream_impl(os, v); }
+std::basic_ostream<CharT, Traits>& to_stream(std::basic_ostream<CharT, Traits>& os, const T& val)
+  requires requires { detail::to_stream_impl(os, val); }
 {
  if (os.width()) {
    // std::setw() applies to the whole output so it has to be first put into std::string
@@ -77,11 +77,11 @@ std::basic_ostream<CharT, Traits>& to_stream(std::basic_ostream<CharT, Traits>&
    oss.flags(os.flags());
    oss.imbue(os.getloc());
    oss.precision(os.precision());
-    detail::to_stream_impl(oss, v);
+    detail::to_stream_impl(oss, val);
    return os << std::move(oss).str();
  }

-  detail::to_stream_impl(os, v);
+  detail::to_stream_impl(os, val);
  return os;
 }

@@ -93,10 +93,10 @@ constexpr bool is_mp_units_stream = requires(OStream os, T v) { detail::to_strea
 MP_UNITS_EXPORT_BEGIN

 template<typename CharT, typename Traits, typename T>
-std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const T& v)
+std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const T& val)
  requires detail::is_mp_units_stream<std::basic_ostream<CharT, Traits>, T>
 {
-  return detail::to_stream(os, v);
+  return detail::to_stream(os, val);
 }

 MP_UNITS_EXPORT_END
--- a/src/systems/include/mp-units/systems/si/chrono.h
+++ b/src/systems/include/mp-units/systems/si/chrono.h
@@ -83,10 +83,10 @@ struct quantity_like_traits<std::chrono::duration<Rep, Period>> {
    return q.count();
  }

-  [[nodiscard]] static constexpr T from_numerical_value(const rep& v) noexcept(
+  [[nodiscard]] static constexpr T from_numerical_value(const rep& val) noexcept(
    std::is_nothrow_copy_constructible_v<rep>)
  {
-    return T(v);
+    return T(val);
  }
 };

@@ -113,10 +113,10 @@ struct quantity_point_like_traits<std::chrono::time_point<C, std::chrono::durati
    return tp.time_since_epoch().count();
  }

-  [[nodiscard]] static constexpr T from_numerical_value(const rep& v) noexcept(
+  [[nodiscard]] static constexpr T from_numerical_value(const rep& val) noexcept(
    std::is_nothrow_copy_constructible_v<rep>)
  {
-    return T(std::chrono::duration<Rep, Period>(v));
+    return T(std::chrono::duration<Rep, Period>(val));
  }
 };

--- a/test/runtime/CMakeLists.txt
+++ b/test/runtime/CMakeLists.txt
@@ -24,13 +24,14 @@ find_package(Catch2 3 REQUIRED)

 add_executable(
    unit_tests_runtime
+    atomic_test.cpp
+    cartesian_vector_test.cpp
    distribution_test.cpp
    fixed_string_test.cpp
    fmt_test.cpp
    math_test.cpp
-    atomic_test.cpp
-    truncation_test.cpp
    quantity_test.cpp
+    truncation_test.cpp
 )
 if(${projectPrefix}BUILD_CXX_MODULES)
    target_compile_definitions(unit_tests_runtime PUBLIC ${projectPrefix}MODULES)
--- a/test/runtime/cartesian_vector_test.cpp
+++ b/test/runtime/cartesian_vector_test.cpp
@@ -0,0 +1,381 @@
+// The MIT License (MIT)
+//
+// Copyright (c) 2018 Mateusz Pusz
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "almost_equals.h"
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers_floating_point.hpp>
+#include <mp-units/compat_macros.h>
+#include <mp-units/ext/format.h>
+#ifdef MP_UNITS_IMPORT_STD
+import std;
+#else
+#include <sstream>
+#endif
+#ifdef MP_UNITS_MODULES
+import mp_units;
+#else
+#include <mp-units/cartesian_vector.h>
+#endif
+
+using namespace mp_units;
+using namespace Catch::Matchers;
+
+TEST_CASE("cartesian_vector operations", "[vector]")
+{
+  SECTION("cartesian_vector initialization and access")
+  {
+    SECTION("one argument")
+    {
+      cartesian_vector v{1.0};
+      REQUIRE(v[0] == 1.0);
+      REQUIRE(v[1] == 0);
+      REQUIRE(v[2] == 0);
+    }
+
+    SECTION("two arguments")
+    {
+      cartesian_vector v{1.0, 2.0};
+      REQUIRE(v[0] == 1.0);
+      REQUIRE(v[1] == 2.0);
+      REQUIRE(v[2] == 0);
+    }
+
+    SECTION("all arguments")
+    {
+      cartesian_vector v{1.0, 2.0, 3.0};
+      REQUIRE(v[0] == 1.0);
+      REQUIRE(v[1] == 2.0);
+      REQUIRE(v[2] == 3.0);
+    }
+  }
+
+  SECTION("convertibility")
+  {
+    cartesian_vector v1{1, 2, 3};
+
+    SECTION("construction")
+    {
+      cartesian_vector v2 = v1;
+      REQUIRE(v2[0] == 1.0);
+      REQUIRE(v2[1] == 2.0);
+      REQUIRE(v2[2] == 3.0);
+    }
+
+    SECTION("assignment")
+    {
+      cartesian_vector v2{3.0, 2.0, 1.0};
+      v2 = v1;
+      REQUIRE(v2[0] == 1.0);
+      REQUIRE(v2[1] == 2.0);
+      REQUIRE(v2[2] == 3.0);
+    }
+  }
+
+  SECTION("cartesian_vector addition")
+  {
+    SECTION("double + double")
+    {
+      cartesian_vector v1{1.0, 2.0, 3.0};
+      cartesian_vector v2{4.0, 5.0, 6.0};
+      cartesian_vector result = v1 + v2;
+      REQUIRE(result[0] == 5.0);
+      REQUIRE(result[1] == 7.0);
+      REQUIRE(result[2] == 9.0);
+    }
+
+    SECTION("double + int")
+    {
+      cartesian_vector v1{1.0, 2.0, 3.0};
+      cartesian_vector v2{4, 5, 6};
+      cartesian_vector result = v1 + v2;
+      REQUIRE(result[0] == 5.0);
+      REQUIRE(result[1] == 7.0);
+      REQUIRE(result[2] == 9.0);
+    }
+
+    SECTION("int + double")
+    {
+      cartesian_vector v1{1, 2, 3};
+      cartesian_vector v2{4.0, 5.0, 6.0};
+      cartesian_vector result = v1 + v2;
+      REQUIRE(result[0] == 5.0);
+      REQUIRE(result[1] == 7.0);
+      REQUIRE(result[2] == 9.0);
+    }
+
+    SECTION("int + int")
+    {
+      cartesian_vector v1{1, 2, 3};
+      cartesian_vector v2{4, 5, 6};
+      cartesian_vector result = v1 + v2;
+      REQUIRE(result[0] == 5);
+      REQUIRE(result[1] == 7);
+      REQUIRE(result[2] == 9);
+    }
+  }
+
+  SECTION("cartesian_vector subtraction")
+  {
+    SECTION("double - double")
+    {
+      cartesian_vector v1{4.0, 5.0, 6.0};
+      cartesian_vector v2{1.0, 2.0, 3.0};
+      cartesian_vector result = v1 - v2;
+      REQUIRE(result[0] == 3.0);
+      REQUIRE(result[1] == 3.0);
+      REQUIRE(result[2] == 3.0);
+    }
+
+    SECTION("double - int")
+    {
+      cartesian_vector v1{4.0, 5.0, 6.0};
+      cartesian_vector v2{1, 2, 3};
+      cartesian_vector result = v1 - v2;
+      REQUIRE(result[0] == 3.0);
+      REQUIRE(result[1] == 3.0);
+      REQUIRE(result[2] == 3.0);
+    }
+
+    SECTION("int - double")
+    {
+      cartesian_vector v1{4, 5, 6};
+      cartesian_vector v2{1.0, 2.0, 3.0};
+      cartesian_vector result = v1 - v2;
+      REQUIRE(result[0] == 3.0);
+      REQUIRE(result[1] == 3.0);
+      REQUIRE(result[2] == 3.0);
+    }
+
+    SECTION("int - int")
+    {
+      cartesian_vector v1{4, 5, 6};
+      cartesian_vector v2{1, 2, 3};
+      cartesian_vector result = v1 - v2;
+      REQUIRE(result[0] == 3);
+      REQUIRE(result[1] == 3);
+      REQUIRE(result[2] == 3);
+    }
+  }
+
+  SECTION("cartesian_vector scalar multiplication")
+  {
+    SECTION("double * double")
+    {
+      cartesian_vector v{1.0, 2.0, 3.0};
+      cartesian_vector result = v * 2.0;
+      REQUIRE(result[0] == 2.0);
+      REQUIRE(result[1] == 4.0);
+      REQUIRE(result[2] == 6.0);
+    }
+
+    SECTION("double * int")
+    {
+      cartesian_vector v{1.0, 2.0, 3.0};
+      cartesian_vector result = v * 2;
+      REQUIRE(result[0] == 2.0);
+      REQUIRE(result[1] == 4.0);
+      REQUIRE(result[2] == 6.0);
+    }
+
+    SECTION("int * double")
+    {
+      cartesian_vector v{1, 2, 3};
+      cartesian_vector result = v * 2.0;
+      REQUIRE(result[0] == 2.0);
+      REQUIRE(result[1] == 4.0);
+      REQUIRE(result[2] == 6.0);
+    }
+
+    SECTION("int * int")
+    {
+      cartesian_vector v{1, 2, 3};
+      cartesian_vector result = v * 2;
+      REQUIRE(result[0] == 2);
+      REQUIRE(result[1] == 4);
+      REQUIRE(result[2] == 6);
+    }
+  }
+
+  SECTION("cartesian_vector scalar division")
+  {
+    SECTION("double / double")
+    {
+      cartesian_vector v{2.0, 4.0, 6.0};
+      cartesian_vector result = v / 2.0;
+      REQUIRE(result[0] == 1.0);
+      REQUIRE(result[1] == 2.0);
+      REQUIRE(result[2] == 3.0);
+    }
+
+    SECTION("double / int")
+    {
+      cartesian_vector v{2.0, 4.0, 6.0};
+      cartesian_vector result = v / 2;
+      REQUIRE(result[0] == 1.0);
+      REQUIRE(result[1] == 2.0);
+      REQUIRE(result[2] == 3.0);
+    }
+
+    SECTION("int / double")
+    {
+      cartesian_vector v{2, 4, 6};
+      cartesian_vector result = v / 2.0;
+      REQUIRE(result[0] == 1.0);
+      REQUIRE(result[1] == 2.0);
+      REQUIRE(result[2] == 3.0);
+    }
+
+    SECTION("int / int")
+    {
+      cartesian_vector v{2, 4, 6};
+      cartesian_vector result = v / 2;
+      REQUIRE(result[0] == 1);
+      REQUIRE(result[1] == 2);
+      REQUIRE(result[2] == 3);
+    }
+  }
+
+  SECTION("cartesian_vector magnitude")
+  {
+    cartesian_vector v1{3.0, 4.0, 0.0};
+    cartesian_vector v2{2.0, 3.0, 6.0};
+    REQUIRE(v1.magnitude() == 5.0);
+    REQUIRE(v2.magnitude() == 7.0);
+  }
+
+  SECTION("cartesian_vector unit vector")
+  {
+    cartesian_vector v{3.0, 4.0, 0.0};
+    cartesian_vector unit_v = v.unit();
+    REQUIRE_THAT(unit_v.magnitude(), WithinULP(1.0, 1));
+  }
+
+  SECTION("cartesian_vector equality")
+  {
+    cartesian_vector v1{1.0, 2.0, 3.0};
+    cartesian_vector v2{1, 2, 3};
+    cartesian_vector v3{1.1, 2.0, 3.0};
+    cartesian_vector v4{1.0, 2.1, 3.0};
+    cartesian_vector v5{1.0, 2.0, 3.1};
+    REQUIRE(v1 == v2);
+    REQUIRE(v1 != v3);
+    REQUIRE(v1 != v4);
+    REQUIRE(v1 != v5);
+  }
+
+  SECTION("cartesian_vector scalar product")
+  {
+    SECTION("double * double")
+    {
+      cartesian_vector v1{1.0, 2.0, 3.0};
+      cartesian_vector v2{4.0, 5.0, 6.0};
+      REQUIRE(scalar_product(v1, v2) == 32.0);
+    }
+
+    SECTION("double * int")
+    {
+      cartesian_vector v1{1.0, 2.0, 3.0};
+      cartesian_vector v2{4, 5, 6};
+      REQUIRE(scalar_product(v1, v2) == 32.0);
+    }
+
+    SECTION("int * double")
+    {
+      cartesian_vector v1{1, 2, 3};
+      cartesian_vector v2{4.0, 5.0, 6.0};
+      REQUIRE(scalar_product(v1, v2) == 32.0);
+    }
+
+    SECTION("int * int")
+    {
+      cartesian_vector v1{1, 2, 3};
+      cartesian_vector v2{4, 5, 6};
+      REQUIRE(scalar_product(v1, v2) == 32);
+    }
+  }
+
+  SECTION("cartesian_vector vector product")
+  {
+    SECTION("double * double")
+    {
+      cartesian_vector v1{1.0, 2.0, 3.0};
+      cartesian_vector v2{4.0, 5.0, 6.0};
+      cartesian_vector result = vector_product(v1, v2);
+      REQUIRE(result[0] == -3.0);
+      REQUIRE(result[1] == 6.0);
+      REQUIRE(result[2] == -3.0);
+    }
+
+    SECTION("double * int")
+    {
+      cartesian_vector v1{1.0, 2.0, 3.0};
+      cartesian_vector v2{4, 5, 6};
+      cartesian_vector result = vector_product(v1, v2);
+      REQUIRE(result[0] == -3.0);
+      REQUIRE(result[1] == 6.0);
+      REQUIRE(result[2] == -3.0);
+    }
+
+    SECTION("int * double")
+    {
+      cartesian_vector v1{1, 2, 3};
+      cartesian_vector v2{4.0, 5.0, 6.0};
+      cartesian_vector result = vector_product(v1, v2);
+      REQUIRE(result[0] == -3.0);
+      REQUIRE(result[1] == 6.0);
+      REQUIRE(result[2] == -3.0);
+    }
+
+    SECTION("int * int")
+    {
+      cartesian_vector v1{1, 2, 3};
+      cartesian_vector v2{4, 5, 6};
+      cartesian_vector result = vector_product(v1, v2);
+      REQUIRE(result[0] == -3);
+      REQUIRE(result[1] == 6);
+      REQUIRE(result[2] == -3);
+    }
+  }
+}
+
+TEST_CASE("cartesian_vector text output", "[vector][fmt][ostream]")
+{
+  std::ostringstream os;
+
+  SECTION("integral representation")
+  {
+    cartesian_vector v{1, 2, 3};
+    os << v;
+
+    SECTION("iostream") { CHECK(os.str() == "[1, 2, 3]"); }
+    SECTION("fmt with default format {}") { CHECK(MP_UNITS_STD_FMT::format("{}", v) == os.str()); }
+  }
+
+  SECTION("floating-point representation")
+  {
+    cartesian_vector v{1.2, 2.3, 3.4};
+    os << v;
+
+    SECTION("iostream") { CHECK(os.str() == "[1.2, 2.3, 3.4]"); }
+    SECTION("fmt with default format {}") { CHECK(MP_UNITS_STD_FMT::format("{}", v) == os.str()); }
+  }
+}
--- a/test/runtime/distribution_test.cpp
+++ b/test/runtime/distribution_test.cpp
--- a/test/runtime/fixed_string_test.cpp
+++ b/test/runtime/fixed_string_test.cpp
@@ -38,19 +38,22 @@ import mp_units;

 using namespace mp_units;

-TEST_CASE("fixed_string::at", "[fixed_string]")
+TEST_CASE("fixed_string operations", "[fixed_string]")
 {
-  basic_fixed_string txt = "abc";
-  SECTION("in range")
+  SECTION("fixed_string::at")
  {
-    CHECK(txt.at(0) == 'a');
-    CHECK(txt.at(1) == 'b');
-    CHECK(txt.at(2) == 'c');
-  }
-  SECTION("out of range")
-  {
-    REQUIRE_THROWS_MATCHES(txt.at(3), std::out_of_range, Catch::Matchers::Message("basic_fixed_string::at"));
-    REQUIRE_THROWS_MATCHES(txt.at(1024), std::out_of_range, Catch::Matchers::Message("basic_fixed_string::at"));
+    basic_fixed_string txt = "abc";
+    SECTION("in range")
+    {
+      CHECK(txt.at(0) == 'a');
+      CHECK(txt.at(1) == 'b');
+      CHECK(txt.at(2) == 'c');
+    }
+    SECTION("out of range")
+    {
+      REQUIRE_THROWS_MATCHES(txt.at(3), std::out_of_range, Catch::Matchers::Message("basic_fixed_string::at"));
+      REQUIRE_THROWS_MATCHES(txt.at(1024), std::out_of_range, Catch::Matchers::Message("basic_fixed_string::at"));
+    }
  }
 }

--- a/test/runtime/fmt_test.cpp
+++ b/test/runtime/fmt_test.cpp
--- a/test/runtime/math_test.cpp
+++ b/test/runtime/math_test.cpp
@@ -43,486 +43,488 @@ using namespace mp_units::si::unit_symbols;

 // classical

-TEST_CASE("'pow<N>()' on quantity changes the value and the dimension accordingly", "[math][pow]")
+TEST_CASE("math operations", "[math]")
 {
-  SECTION("'pow<0>(q)' returns '1'") { CHECK(pow<0>(2 * isq::length[m]) == 1 * one); }
-
-  SECTION("'pow<1>(q)' returns 'q'") { CHECK(pow<1>(2 * isq::length[m]) == 2 * isq::length[m]); }
-
-  SECTION("'pow<2>(q)' squares both the value and a dimension")
+  SECTION("'pow<N>()' on quantity changes the value and the dimension accordingly")
  {
-    CHECK(pow<2>(2 * isq::length[m]) == 4 * isq::area[m2]);
+    SECTION("'pow<0>(q)' returns '1'") { CHECK(pow<0>(2 * isq::length[m]) == 1 * one); }
+
+    SECTION("'pow<1>(q)' returns 'q'") { CHECK(pow<1>(2 * isq::length[m]) == 2 * isq::length[m]); }
+
+    SECTION("'pow<2>(q)' squares both the value and a dimension")
+    {
+      CHECK(pow<2>(2 * isq::length[m]) == 4 * isq::area[m2]);
+    }
+
+    SECTION("'pow<3>(q)' cubes both the value and a dimension")
+    {
+      CHECK(pow<3>(2 * isq::length[m]) == 8 * isq::volume[m3]);
+    }
  }

-  SECTION("'pow<3>(q)' cubes both the value and a dimension")
+  SECTION("'sqrt()' on quantity changes the value and the dimension accordingly")
  {
-    CHECK(pow<3>(2 * isq::length[m]) == 8 * isq::volume[m3]);
-  }
-}
-
-TEST_CASE("'sqrt()' on quantity changes the value and the dimension accordingly", "[math][sqrt]")
-{
-  REQUIRE(sqrt(4 * isq::area[m2]) == 2 * isq::length[m]);
-}
-
-TEST_CASE("'cbrt()' on quantity changes the value and the dimension accordingly", "[math][cbrt]")
-{
-  REQUIRE(cbrt(8 * isq::volume[m3]) == 2 * isq::length[m]);
-}
-
-TEST_CASE("'fma()' on quantity changes the value and the dimension accordingly", "[math][fma]")
-{
-  REQUIRE(fma(1.0 * isq::length[m], 2.0 * one, 2.0 * isq::length[m]) == 4.0 * isq::length[m]);
-  REQUIRE(fma(isq::speed(10.0 * m / s), isq::time(2.0 * s), isq::height(42.0 * m)) == isq::length(62.0 * m));
-}
-
-TEST_CASE("fmod functions", "[math][fmod]")
-{
-  SECTION("fmod should work on the same quantities")
-  {
-    REQUIRE(fmod(4. * isq::length[km], 3. * isq::length[km]) == 1. * isq::length[km]);
-    REQUIRE(fmod(-9. * isq::length[km], 3. * isq::length[km]) == -0. * isq::length[km]);
-    REQUIRE(fmod(3 * isq::length[km], 2 * isq::length[km]) == 1 * isq::length[km]);
-    REQUIRE(fmod(4 * isq::length[km], 2.5f * isq::length[km]) == 1.5 * isq::length[km]);
-  }
-  SECTION("fmod should work with different units of the same dimension")
-  {
-    REQUIRE(fmod(4. * isq::length[km], 3000. * isq::length[m]) == 1000. * isq::length[m]);
-    REQUIRE(fmod(-9. * isq::length[km], 3000. * isq::length[m]) == -0. * isq::length[m]);
-    REQUIRE(fmod(3. * isq::length[km], 2000. * isq::length[m]) == 1000 * isq::length[m]);
-    REQUIRE(fmod(4 * isq::length[km], 2500 * isq::length[m]) == 1500 * isq::length[m]);
-  }
-}
-
-TEST_CASE("remainder functions", "[math][remainder]")
-{
-  SECTION("remainder should work on the same quantities")
-  {
-    REQUIRE(remainder(4. * isq::length[km], 3. * isq::length[km]) == 1. * isq::length[km]);
-    REQUIRE(remainder(-9. * isq::length[km], 3. * isq::length[km]) == -0. * isq::length[km]);
-    REQUIRE(remainder(3 * isq::length[km], 2 * isq::length[km]) == -1 * isq::length[km]);
-    REQUIRE(remainder(4 * isq::length[km], 2.75f * isq::length[km]) == 1.25 * isq::length[km]);
-  }
-  SECTION("remainder should work with different units of the same dimension")
-  {
-    REQUIRE(remainder(4. * isq::length[km], 3000. * isq::length[m]) == 1000. * isq::length[m]);
-    REQUIRE(remainder(-9. * isq::length[km], 3000. * isq::length[m]) == -0. * isq::length[m]);
-    REQUIRE(remainder(3. * isq::length[km], 2000. * isq::length[m]) == -1000 * isq::length[m]);
-    REQUIRE(remainder(4 * isq::length[km], 2750 * isq::length[m]) == 1250 * isq::length[m]);
-  }
-}
-
-TEST_CASE("'isfinite()' accepts dimensioned arguments", "[math][isfinite]") { REQUIRE(isfinite(4.0 * isq::length[m])); }
-
-TEST_CASE("'isinf()' accepts dimensioned arguments", "[math][isinf]") { REQUIRE(!isinf(4.0 * isq::length[m])); }
-
-TEST_CASE("'isnan()' accepts dimensioned arguments", "[math][isnan]") { REQUIRE(!isnan(4.0 * isq::length[m])); }
-
-
-TEST_CASE("'pow<Num, Den>()' on quantity changes the value and the dimension accordingly", "[math][pow]")
-{
-  REQUIRE(pow<1, 4>(16 * isq::area[m2]) == sqrt(4 * isq::length[m]));
-}
-
-// TODO add tests for exp()
-
-TEST_CASE("absolute functions on quantity returns the absolute value", "[math][abs][fabs]")
-{
-  SECTION("'abs()' on a negative quantity returns the abs")
-  {
-    SECTION("integral representation") { REQUIRE(abs(-1 * isq::length[m]) == 1 * isq::length[m]); }
-
-    SECTION("floating-point representation") { REQUIRE(abs(-1. * isq::length[m]) == 1 * isq::length[m]); }
-  }
-
-  SECTION("'abs()' on a positive quantity returns the abs")
-  {
-    SECTION("integral representation") { REQUIRE(abs(1 * isq::length[m]) == 1 * isq::length[m]); }
-
-    SECTION("floating-point representation") { REQUIRE(abs(1. * isq::length[m]) == 1 * isq::length[m]); }
-  }
-}
-
-TEST_CASE("numeric_limits functions", "[limits]")
-{
-  SECTION("'epsilon' works as expected using default floating type")
-  {
-    REQUIRE(epsilon<double>(isq::length[m]).numerical_value_in(m) ==
-            std::numeric_limits<decltype(1. * isq::length[m])::rep>::epsilon());
-  }
-  SECTION("'epsilon' works as expected using integers")
-  {
-    REQUIRE(epsilon<int>(isq::length[m]).numerical_value_in(m) ==
-            std::numeric_limits<decltype(1 * isq::length[m])::rep>::epsilon());
-  }
-}
-
-TEST_CASE("floor functions", "[floor]")
-{
-  SECTION("floor 1 second with target unit second should be 1 second")
-  {
-    REQUIRE(floor<si::second>(1 * isq::time[s]) == 1 * isq::time[s]);
-  }
-  SECTION("floor 1000 milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(floor<si::second>(1000 * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("floor 1001 milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(floor<si::second>(1001 * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("floor 1999 milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(floor<si::second>(1999 * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("floor -1000 milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(floor<si::second>(-1000 * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("floor -999 milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(floor<si::second>(-999 * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("floor 1.3 seconds with target unit second should be 1 second")
-  {
-    REQUIRE(floor<si::second>(1.3 * isq::time[s]) == 1 * isq::time[s]);
-  }
-  SECTION("floor -1.3 seconds with target unit second should be -2 seconds")
-  {
-    REQUIRE(floor<si::second>(-1.3 * isq::time[s]) == -2 * isq::time[s]);
-  }
-  SECTION("floor 1001. milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(floor<si::second>(1001. * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("floor 1999. milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(floor<si::second>(1999. * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("floor -1000. milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(floor<si::second>(-1000. * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("floor -999. milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(floor<si::second>(-999. * isq::time[ms]) == -1 * isq::time[s]);
-  }
-
-  // TODO Add tests for `N`, `kN` and `kg * m / s2` i `kg * km / s2`
-}
-
-TEST_CASE("ceil functions", "[ceil]")
-{
-  SECTION("ceil 1 second with target unit second should be 1 second")
-  {
-    REQUIRE(ceil<si::second>(1 * isq::time[s]) == 1 * isq::time[s]);
-  }
-  SECTION("ceil 1000 milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(ceil<si::second>(1000 * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("ceil 1001 milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(ceil<si::second>(1001 * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("ceil 1999 milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(ceil<si::second>(1999 * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("ceil -1000 milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(ceil<si::second>(-1000 * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("ceil -999 milliseconds with target unit second should be 0 seconds")
-  {
-    REQUIRE(ceil<si::second>(-999 * isq::time[ms]) == 0 * isq::time[s]);
-  }
-  SECTION("ceil 1.3 seconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(ceil<si::second>(1.3 * isq::time[s]) == 2 * isq::time[s]);
-  }
-  SECTION("ceil -1.3 seconds with target unit second should be -1 second")
-  {
-    REQUIRE(ceil<si::second>(-1.3 * isq::time[s]) == -1 * isq::time[s]);
-  }
-  SECTION("ceil 1001. milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(ceil<si::second>(1001. * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("ceil 1999. milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(ceil<si::second>(1999. * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("ceil -1000. milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(ceil<si::second>(-1000. * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("ceil -999. milliseconds with target unit second should be 0 seconds")
-  {
-    REQUIRE(ceil<si::second>(-999. * isq::time[ms]) == 0 * isq::time[s]);
-  }
-}
-
-TEST_CASE("round functions", "[round]")
-{
-  SECTION("round 1 second with target unit second should be 1 second")
-  {
-    REQUIRE(round<si::second>(1 * isq::time[s]) == 1 * isq::time[s]);
-  }
-  SECTION("round 1000 milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(round<si::second>(1000 * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("round 1001 milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(round<si::second>(1001 * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("round 1499 milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(round<si::second>(1499 * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("round 1500 milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(round<si::second>(1500 * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("round 1999 milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(round<si::second>(1999 * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("round -1000 milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(round<si::second>(-1000 * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("round -1001 milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(round<si::second>(-1001 * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("round -1499 milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(round<si::second>(-1499 * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("round -1500 milliseconds with target unit second should be -2 seconds")
-  {
-    REQUIRE(round<si::second>(-1500 * isq::time[ms]) == -2 * isq::time[s]);
-  }
-  SECTION("round -1999 milliseconds with target unit second should be -2 seconds")
-  {
-    REQUIRE(round<si::second>(-1999 * isq::time[ms]) == -2 * isq::time[s]);
-  }
-  SECTION("round 1000. milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(round<si::second>(1000. * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("round 1001. milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(round<si::second>(1001. * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("round 1499. milliseconds with target unit second should be 1 second")
-  {
-    REQUIRE(round<si::second>(1499. * isq::time[ms]) == 1 * isq::time[s]);
-  }
-  SECTION("round 1500. milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(round<si::second>(1500. * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("round 1999. milliseconds with target unit second should be 2 seconds")
-  {
-    REQUIRE(round<si::second>(1999. * isq::time[ms]) == 2 * isq::time[s]);
-  }
-  SECTION("round -1000. milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(round<si::second>(-1000. * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("round -1001. milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(round<si::second>(-1001. * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("round -1499. milliseconds with target unit second should be -1 second")
-  {
-    REQUIRE(round<si::second>(-1499. * isq::time[ms]) == -1 * isq::time[s]);
-  }
-  SECTION("round -1500. milliseconds with target unit second should be -2 seconds")
-  {
-    REQUIRE(round<si::second>(-1500. * isq::time[ms]) == -2 * isq::time[s]);
-  }
-  SECTION("round -1999. milliseconds with target unit second should be -2 seconds")
-  {
-    REQUIRE(round<si::second>(-1999. * isq::time[ms]) == -2 * isq::time[s]);
-  }
-}
-
-TEST_CASE("hypot functions", "[hypot]")
-{
-  SECTION("hypot should work on the same quantities")
-  {
-    REQUIRE(hypot(3. * isq::length[km], 4. * isq::length[km]) == 5. * isq::length[km]);
-    REQUIRE(hypot(2. * isq::length[km], 3. * isq::length[km], 6. * isq::length[km]) == 7. * isq::length[km]);
-  }
-  SECTION("hypot should work with different units of the same dimension")
-  {
-    REQUIRE(hypot(3. * isq::length[km], 4000. * isq::length[m]) == 5. * isq::length[km]);
-    REQUIRE(hypot(2. * isq::length[km], 3000. * isq::length[m], 6. * isq::length[km]) == 7. * isq::length[km]);
-  }
-}
-
-TEST_CASE("SI trigonometric functions", "[trig][si]")
-{
-  SECTION("sin")
-  {
-    REQUIRE_THAT(si::sin(0 * deg), AlmostEquals(0. * one));
-    REQUIRE_THAT(si::sin(90 * deg), AlmostEquals(1. * one));
-    REQUIRE_THAT(si::sin(180 * deg), AlmostEquals(0. * one));
-    REQUIRE_THAT(si::sin(270 * deg), AlmostEquals(-1. * one));
-  }
-
-  SECTION("cos")
-  {
-    REQUIRE_THAT(si::cos(0 * deg), AlmostEquals(1. * one));
-    REQUIRE_THAT(si::cos(90 * deg), AlmostEquals(0. * one));
-    REQUIRE_THAT(si::cos(180 * deg), AlmostEquals(-1. * one));
-    REQUIRE_THAT(si::cos(270 * deg), AlmostEquals(0. * one));
-  }
-
-  SECTION("tan")
-  {
-    REQUIRE_THAT(si::tan(0 * deg), AlmostEquals(0. * one));
-    REQUIRE_THAT(si::tan(45. * deg), AlmostEquals(1. * one));
-    REQUIRE_THAT(si::tan(135. * deg), AlmostEquals(-1. * one));
-    REQUIRE_THAT(si::tan(180. * deg), AlmostEquals(0. * one));
-  }
-}
-
-TEST_CASE("SI inverse trigonometric functions", "[inv trig][si]")
-{
-  SECTION("asin")
-  {
-    REQUIRE_THAT(si::asin(-1 * one), AlmostEquals(-90. * deg));
-    REQUIRE_THAT(si::asin(0 * one), AlmostEquals(0. * deg));
-    REQUIRE_THAT(si::asin(1 * one), AlmostEquals(90. * deg));
-  }
-
-  SECTION("acos")
-  {
-    REQUIRE_THAT(si::asin(-1 * one), AlmostEquals(-90. * deg));
-    REQUIRE_THAT(si::asin(0 * one), AlmostEquals(0. * deg));
-    REQUIRE_THAT(si::asin(1 * one), AlmostEquals(90. * deg));
-  }
-
-  SECTION("atan")
-  {
-    REQUIRE_THAT(si::atan(-1 * one), AlmostEquals(-45. * deg));
-    REQUIRE_THAT(si::atan(0 * one), AlmostEquals(0. * deg));
-    REQUIRE_THAT(si::atan(1 * one), AlmostEquals(45. * deg));
-  }
-}
-
-TEST_CASE("SI atan2 functions", "[atan2][si]")
-{
-  SECTION("atan2 should work on the same quantities")
-  {
-    REQUIRE_THAT(si::atan2(-1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(-45. * deg));
-    REQUIRE_THAT(si::atan2(0. * isq::length[km], 1. * isq::length[km]), AlmostEquals(0. * deg));
-    REQUIRE_THAT(si::atan2(1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(45. * deg));
-  }
-  SECTION("atan2 should work with different units of the same dimension")
-  {
-    REQUIRE_THAT(si::atan2(-1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(-45. * deg));
-    REQUIRE_THAT(si::atan2(0. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(0. * deg));
-    REQUIRE_THAT(si::atan2(1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(45. * deg));
-  }
-}
-
-
-TEST_CASE("Angle trigonometric functions", "[trig][angle]")
-{
-  using namespace mp_units::angular;
-  using namespace mp_units::angular::unit_symbols;
-  using mp_units::angular::unit_symbols::deg;
-
-  SECTION("sin")
-  {
-    REQUIRE_THAT(sin(0 * angle[deg]), AlmostEquals(0. * one));
-    REQUIRE_THAT(sin(90 * angle[deg]), AlmostEquals(1. * one));
-    REQUIRE_THAT(sin(180 * angle[deg]), AlmostEquals(0. * one));
-    REQUIRE_THAT(sin(270 * angle[deg]), AlmostEquals(-1. * one));
-
-    REQUIRE_THAT(sin(0 * angle[grad]), AlmostEquals(0. * one));
-    REQUIRE_THAT(sin(100 * angle[grad]), AlmostEquals(1. * one));
-    REQUIRE_THAT(sin(200 * angle[grad]), AlmostEquals(0. * one, 2));
-    REQUIRE_THAT(sin(300 * angle[grad]), AlmostEquals(-1. * one));
-  }
-
-  SECTION("cos")
-  {
-    REQUIRE_THAT(cos(0 * angle[deg]), AlmostEquals(1. * one));
-    REQUIRE_THAT(cos(90 * angle[deg]), AlmostEquals(0. * one));
-    REQUIRE_THAT(cos(180 * angle[deg]), AlmostEquals(-1. * one));
-    REQUIRE_THAT(cos(270 * angle[deg]), AlmostEquals(0. * one));
-
-    REQUIRE_THAT(cos(0 * angle[grad]), AlmostEquals(1. * one));
-    REQUIRE_THAT(cos(100 * angle[grad]), AlmostEquals(0. * one));
-    REQUIRE_THAT(cos(200 * angle[grad]), AlmostEquals(-1. * one));
-    REQUIRE_THAT(cos(300 * angle[grad]), AlmostEquals(0. * one));
-  }
-
-  SECTION("tan")
-  {
-    REQUIRE_THAT(tan(0 * angle[deg]), AlmostEquals(0. * one));
-    REQUIRE_THAT(tan(45 * angle[deg]), AlmostEquals(1. * one));
-    REQUIRE_THAT(tan(135 * angle[deg]), AlmostEquals(-1. * one));
-    REQUIRE_THAT(tan(180 * angle[deg]), AlmostEquals(0. * one));
-
-    REQUIRE_THAT(tan(0 * angle[grad]), AlmostEquals(0. * one));
-    REQUIRE_THAT(tan(50 * angle[grad]), AlmostEquals(1. * one));
-    REQUIRE_THAT(tan(150 * angle[grad]), AlmostEquals(-1. * one));
-    REQUIRE_THAT(tan(200 * angle[grad]), AlmostEquals(0. * one, 2));
-  }
-}
-
-TEST_CASE("Angle inverse trigonometric functions", "[inv trig][angle]")
-{
-  using namespace mp_units::angular;
-  using namespace mp_units::angular::unit_symbols;
-  using mp_units::angular::unit_symbols::deg;
-
-  SECTION("asin")
-  {
-    REQUIRE_THAT(asin(-1 * one), AlmostEquals(-90. * angle[deg]));
-    REQUIRE_THAT(asin(0 * one), AlmostEquals(0. * angle[deg]));
-    REQUIRE_THAT(asin(1 * one), AlmostEquals(90. * angle[deg]));
-  }
-
-  SECTION("acos")
-  {
-    REQUIRE_THAT(asin(-1 * one), AlmostEquals(-90. * angle[deg]));
-    REQUIRE_THAT(asin(0 * one), AlmostEquals(0. * angle[deg]));
-    REQUIRE_THAT(asin(1 * one), AlmostEquals(90. * angle[deg]));
-  }
-
-  SECTION("atan")
-  {
-    REQUIRE_THAT(atan(-1 * one), AlmostEquals(-45. * angle[deg]));
-    REQUIRE_THAT(atan(0 * one), AlmostEquals(0. * angle[deg]));
-    REQUIRE_THAT(atan(1 * one), AlmostEquals(45. * angle[deg]));
-  }
-}
-
-TEST_CASE("Angle atan2 functions", "[atan2][angle]")
-{
-  using namespace mp_units::angular;
-  using namespace mp_units::angular::unit_symbols;
-  using mp_units::angular::unit_symbols::deg;
-
-  SECTION("atan2 should work on the same quantities")
-  {
-    REQUIRE_THAT(atan2(-1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(-45. * angle[deg]));
-    REQUIRE_THAT(atan2(0. * isq::length[km], 1. * isq::length[km]), AlmostEquals(0. * angle[deg]));
-    REQUIRE_THAT(atan2(1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(45. * angle[deg]));
-  }
-  SECTION("atan2 should work with different units of the same dimension")
-  {
-    REQUIRE_THAT(atan2(-1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(-45. * angle[deg]));
-    REQUIRE_THAT(atan2(0. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(0. * angle[deg]));
-    REQUIRE_THAT(atan2(1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(45. * angle[deg]));
+    REQUIRE(sqrt(4 * isq::area[m2]) == 2 * isq::length[m]);
+  }
+
+  SECTION("'cbrt()' on quantity changes the value and the dimension accordingly")
+  {
+    REQUIRE(cbrt(8 * isq::volume[m3]) == 2 * isq::length[m]);
+  }
+
+  SECTION("'fma()' on quantity changes the value and the dimension accordingly")
+  {
+    REQUIRE(fma(1.0 * isq::length[m], 2.0 * one, 2.0 * isq::length[m]) == 4.0 * isq::length[m]);
+    REQUIRE(fma(isq::speed(10.0 * m / s), isq::time(2.0 * s), isq::height(42.0 * m)) == isq::length(62.0 * m));
+  }
+
+  SECTION("fmod functions")
+  {
+    SECTION("fmod should work on the same quantities")
+    {
+      REQUIRE(fmod(4. * isq::length[km], 3. * isq::length[km]) == 1. * isq::length[km]);
+      REQUIRE(fmod(-9. * isq::length[km], 3. * isq::length[km]) == -0. * isq::length[km]);
+      REQUIRE(fmod(3 * isq::length[km], 2 * isq::length[km]) == 1 * isq::length[km]);
+      REQUIRE(fmod(4 * isq::length[km], 2.5f * isq::length[km]) == 1.5 * isq::length[km]);
+    }
+    SECTION("fmod should work with different units of the same dimension")
+    {
+      REQUIRE(fmod(4. * isq::length[km], 3000. * isq::length[m]) == 1000. * isq::length[m]);
+      REQUIRE(fmod(-9. * isq::length[km], 3000. * isq::length[m]) == -0. * isq::length[m]);
+      REQUIRE(fmod(3. * isq::length[km], 2000. * isq::length[m]) == 1000 * isq::length[m]);
+      REQUIRE(fmod(4 * isq::length[km], 2500 * isq::length[m]) == 1500 * isq::length[m]);
+    }
+  }
+
+  SECTION("remainder functions")
+  {
+    SECTION("remainder should work on the same quantities")
+    {
+      REQUIRE(remainder(4. * isq::length[km], 3. * isq::length[km]) == 1. * isq::length[km]);
+      REQUIRE(remainder(-9. * isq::length[km], 3. * isq::length[km]) == -0. * isq::length[km]);
+      REQUIRE(remainder(3 * isq::length[km], 2 * isq::length[km]) == -1 * isq::length[km]);
+      REQUIRE(remainder(4 * isq::length[km], 2.75f * isq::length[km]) == 1.25 * isq::length[km]);
+    }
+    SECTION("remainder should work with different units of the same dimension")
+    {
+      REQUIRE(remainder(4. * isq::length[km], 3000. * isq::length[m]) == 1000. * isq::length[m]);
+      REQUIRE(remainder(-9. * isq::length[km], 3000. * isq::length[m]) == -0. * isq::length[m]);
+      REQUIRE(remainder(3. * isq::length[km], 2000. * isq::length[m]) == -1000 * isq::length[m]);
+      REQUIRE(remainder(4 * isq::length[km], 2750 * isq::length[m]) == 1250 * isq::length[m]);
+    }
+  }
+
+  SECTION("'isfinite()' accepts dimensioned arguments") { REQUIRE(isfinite(4.0 * isq::length[m])); }
+
+  SECTION("'isinf()' accepts dimensioned arguments") { REQUIRE(!isinf(4.0 * isq::length[m])); }
+
+  SECTION("'isnan()' accepts dimensioned arguments") { REQUIRE(!isnan(4.0 * isq::length[m])); }
+
+
+  SECTION("'pow<Num, Den>()' on quantity changes the value and the dimension accordingly")
+  {
+    REQUIRE(pow<1, 4>(16 * isq::area[m2]) == sqrt(4 * isq::length[m]));
+  }
+
+  // TODO add tests for exp()
+
+  SECTION("absolute functions on quantity returns the absolute value")
+  {
+    SECTION("'abs()' on a negative quantity returns the abs")
+    {
+      SECTION("integral representation") { REQUIRE(abs(-1 * isq::length[m]) == 1 * isq::length[m]); }
+
+      SECTION("floating-point representation") { REQUIRE(abs(-1. * isq::length[m]) == 1 * isq::length[m]); }
+    }
+
+    SECTION("'abs()' on a positive quantity returns the abs")
+    {
+      SECTION("integral representation") { REQUIRE(abs(1 * isq::length[m]) == 1 * isq::length[m]); }
+
+      SECTION("floating-point representation") { REQUIRE(abs(1. * isq::length[m]) == 1 * isq::length[m]); }
+    }
+  }
+
+  SECTION("numeric_limits functions")
+  {
+    SECTION("'epsilon' works as expected using default floating type")
+    {
+      REQUIRE(epsilon<double>(isq::length[m]).numerical_value_in(m) ==
+              std::numeric_limits<decltype(1. * isq::length[m])::rep>::epsilon());
+    }
+    SECTION("'epsilon' works as expected using integers")
+    {
+      REQUIRE(epsilon<int>(isq::length[m]).numerical_value_in(m) ==
+              std::numeric_limits<decltype(1 * isq::length[m])::rep>::epsilon());
+    }
+  }
+
+  SECTION("floor functions")
+  {
+    SECTION("floor 1 second with target unit second should be 1 second")
+    {
+      REQUIRE(floor<si::second>(1 * isq::time[s]) == 1 * isq::time[s]);
+    }
+    SECTION("floor 1000 milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(floor<si::second>(1000 * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("floor 1001 milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(floor<si::second>(1001 * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("floor 1999 milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(floor<si::second>(1999 * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("floor -1000 milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(floor<si::second>(-1000 * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("floor -999 milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(floor<si::second>(-999 * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("floor 1.3 seconds with target unit second should be 1 second")
+    {
+      REQUIRE(floor<si::second>(1.3 * isq::time[s]) == 1 * isq::time[s]);
+    }
+    SECTION("floor -1.3 seconds with target unit second should be -2 seconds")
+    {
+      REQUIRE(floor<si::second>(-1.3 * isq::time[s]) == -2 * isq::time[s]);
+    }
+    SECTION("floor 1001. milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(floor<si::second>(1001. * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("floor 1999. milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(floor<si::second>(1999. * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("floor -1000. milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(floor<si::second>(-1000. * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("floor -999. milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(floor<si::second>(-999. * isq::time[ms]) == -1 * isq::time[s]);
+    }
+
+    // TODO Add tests for `N`, `kN` and `kg * m / s2` i `kg * km / s2`
+  }
+
+  SECTION("ceil functions")
+  {
+    SECTION("ceil 1 second with target unit second should be 1 second")
+    {
+      REQUIRE(ceil<si::second>(1 * isq::time[s]) == 1 * isq::time[s]);
+    }
+    SECTION("ceil 1000 milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(ceil<si::second>(1000 * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("ceil 1001 milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(ceil<si::second>(1001 * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("ceil 1999 milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(ceil<si::second>(1999 * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("ceil -1000 milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(ceil<si::second>(-1000 * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("ceil -999 milliseconds with target unit second should be 0 seconds")
+    {
+      REQUIRE(ceil<si::second>(-999 * isq::time[ms]) == 0 * isq::time[s]);
+    }
+    SECTION("ceil 1.3 seconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(ceil<si::second>(1.3 * isq::time[s]) == 2 * isq::time[s]);
+    }
+    SECTION("ceil -1.3 seconds with target unit second should be -1 second")
+    {
+      REQUIRE(ceil<si::second>(-1.3 * isq::time[s]) == -1 * isq::time[s]);
+    }
+    SECTION("ceil 1001. milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(ceil<si::second>(1001. * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("ceil 1999. milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(ceil<si::second>(1999. * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("ceil -1000. milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(ceil<si::second>(-1000. * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("ceil -999. milliseconds with target unit second should be 0 seconds")
+    {
+      REQUIRE(ceil<si::second>(-999. * isq::time[ms]) == 0 * isq::time[s]);
+    }
+  }
+
+  SECTION("round functions")
+  {
+    SECTION("round 1 second with target unit second should be 1 second")
+    {
+      REQUIRE(round<si::second>(1 * isq::time[s]) == 1 * isq::time[s]);
+    }
+    SECTION("round 1000 milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(round<si::second>(1000 * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("round 1001 milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(round<si::second>(1001 * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("round 1499 milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(round<si::second>(1499 * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("round 1500 milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(round<si::second>(1500 * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("round 1999 milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(round<si::second>(1999 * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("round -1000 milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(round<si::second>(-1000 * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("round -1001 milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(round<si::second>(-1001 * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("round -1499 milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(round<si::second>(-1499 * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("round -1500 milliseconds with target unit second should be -2 seconds")
+    {
+      REQUIRE(round<si::second>(-1500 * isq::time[ms]) == -2 * isq::time[s]);
+    }
+    SECTION("round -1999 milliseconds with target unit second should be -2 seconds")
+    {
+      REQUIRE(round<si::second>(-1999 * isq::time[ms]) == -2 * isq::time[s]);
+    }
+    SECTION("round 1000. milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(round<si::second>(1000. * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("round 1001. milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(round<si::second>(1001. * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("round 1499. milliseconds with target unit second should be 1 second")
+    {
+      REQUIRE(round<si::second>(1499. * isq::time[ms]) == 1 * isq::time[s]);
+    }
+    SECTION("round 1500. milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(round<si::second>(1500. * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("round 1999. milliseconds with target unit second should be 2 seconds")
+    {
+      REQUIRE(round<si::second>(1999. * isq::time[ms]) == 2 * isq::time[s]);
+    }
+    SECTION("round -1000. milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(round<si::second>(-1000. * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("round -1001. milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(round<si::second>(-1001. * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("round -1499. milliseconds with target unit second should be -1 second")
+    {
+      REQUIRE(round<si::second>(-1499. * isq::time[ms]) == -1 * isq::time[s]);
+    }
+    SECTION("round -1500. milliseconds with target unit second should be -2 seconds")
+    {
+      REQUIRE(round<si::second>(-1500. * isq::time[ms]) == -2 * isq::time[s]);
+    }
+    SECTION("round -1999. milliseconds with target unit second should be -2 seconds")
+    {
+      REQUIRE(round<si::second>(-1999. * isq::time[ms]) == -2 * isq::time[s]);
+    }
+  }
+
+  SECTION("hypot functions")
+  {
+    SECTION("hypot should work on the same quantities")
+    {
+      REQUIRE(hypot(3. * isq::length[km], 4. * isq::length[km]) == 5. * isq::length[km]);
+      REQUIRE(hypot(2. * isq::length[km], 3. * isq::length[km], 6. * isq::length[km]) == 7. * isq::length[km]);
+    }
+    SECTION("hypot should work with different units of the same dimension")
+    {
+      REQUIRE(hypot(3. * isq::length[km], 4000. * isq::length[m]) == 5. * isq::length[km]);
+      REQUIRE(hypot(2. * isq::length[km], 3000. * isq::length[m], 6. * isq::length[km]) == 7. * isq::length[km]);
+    }
+  }
+
+  SECTION("SI trigonometric functions")
+  {
+    SECTION("sin")
+    {
+      REQUIRE_THAT(si::sin(0 * deg), AlmostEquals(0. * one));
+      REQUIRE_THAT(si::sin(90 * deg), AlmostEquals(1. * one));
+      REQUIRE_THAT(si::sin(180 * deg), AlmostEquals(0. * one));
+      REQUIRE_THAT(si::sin(270 * deg), AlmostEquals(-1. * one));
+    }
+
+    SECTION("cos")
+    {
+      REQUIRE_THAT(si::cos(0 * deg), AlmostEquals(1. * one));
+      REQUIRE_THAT(si::cos(90 * deg), AlmostEquals(0. * one));
+      REQUIRE_THAT(si::cos(180 * deg), AlmostEquals(-1. * one));
+      REQUIRE_THAT(si::cos(270 * deg), AlmostEquals(0. * one));
+    }
+
+    SECTION("tan")
+    {
+      REQUIRE_THAT(si::tan(0 * deg), AlmostEquals(0. * one));
+      REQUIRE_THAT(si::tan(45. * deg), AlmostEquals(1. * one));
+      REQUIRE_THAT(si::tan(135. * deg), AlmostEquals(-1. * one));
+      REQUIRE_THAT(si::tan(180. * deg), AlmostEquals(0. * one));
+    }
+  }
+
+  SECTION("SI inverse trigonometric functions")
+  {
+    SECTION("asin")
+    {
+      REQUIRE_THAT(si::asin(-1 * one), AlmostEquals(-90. * deg));
+      REQUIRE_THAT(si::asin(0 * one), AlmostEquals(0. * deg));
+      REQUIRE_THAT(si::asin(1 * one), AlmostEquals(90. * deg));
+    }
+
+    SECTION("acos")
+    {
+      REQUIRE_THAT(si::asin(-1 * one), AlmostEquals(-90. * deg));
+      REQUIRE_THAT(si::asin(0 * one), AlmostEquals(0. * deg));
+      REQUIRE_THAT(si::asin(1 * one), AlmostEquals(90. * deg));
+    }
+
+    SECTION("atan")
+    {
+      REQUIRE_THAT(si::atan(-1 * one), AlmostEquals(-45. * deg));
+      REQUIRE_THAT(si::atan(0 * one), AlmostEquals(0. * deg));
+      REQUIRE_THAT(si::atan(1 * one), AlmostEquals(45. * deg));
+    }
+  }
+
+  SECTION("SI atan2 functions")
+  {
+    SECTION("atan2 should work on the same quantities")
+    {
+      REQUIRE_THAT(si::atan2(-1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(-45. * deg));
+      REQUIRE_THAT(si::atan2(0. * isq::length[km], 1. * isq::length[km]), AlmostEquals(0. * deg));
+      REQUIRE_THAT(si::atan2(1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(45. * deg));
+    }
+    SECTION("atan2 should work with different units of the same dimension")
+    {
+      REQUIRE_THAT(si::atan2(-1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(-45. * deg));
+      REQUIRE_THAT(si::atan2(0. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(0. * deg));
+      REQUIRE_THAT(si::atan2(1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(45. * deg));
+    }
+  }
+
+  SECTION("Angle trigonometric functions")
+  {
+    using namespace mp_units::angular;
+    using namespace mp_units::angular::unit_symbols;
+    using mp_units::angular::unit_symbols::deg;
+
+    SECTION("sin")
+    {
+      REQUIRE_THAT(sin(0 * angle[deg]), AlmostEquals(0. * one));
+      REQUIRE_THAT(sin(90 * angle[deg]), AlmostEquals(1. * one));
+      REQUIRE_THAT(sin(180 * angle[deg]), AlmostEquals(0. * one));
+      REQUIRE_THAT(sin(270 * angle[deg]), AlmostEquals(-1. * one));
+
+      REQUIRE_THAT(sin(0 * angle[grad]), AlmostEquals(0. * one));
+      REQUIRE_THAT(sin(100 * angle[grad]), AlmostEquals(1. * one));
+      REQUIRE_THAT(sin(200 * angle[grad]), AlmostEquals(0. * one, 2));
+      REQUIRE_THAT(sin(300 * angle[grad]), AlmostEquals(-1. * one));
+    }
+
+    SECTION("cos")
+    {
+      REQUIRE_THAT(cos(0 * angle[deg]), AlmostEquals(1. * one));
+      REQUIRE_THAT(cos(90 * angle[deg]), AlmostEquals(0. * one));
+      REQUIRE_THAT(cos(180 * angle[deg]), AlmostEquals(-1. * one));
+      REQUIRE_THAT(cos(270 * angle[deg]), AlmostEquals(0. * one));
+
+      REQUIRE_THAT(cos(0 * angle[grad]), AlmostEquals(1. * one));
+      REQUIRE_THAT(cos(100 * angle[grad]), AlmostEquals(0. * one));
+      REQUIRE_THAT(cos(200 * angle[grad]), AlmostEquals(-1. * one));
+      REQUIRE_THAT(cos(300 * angle[grad]), AlmostEquals(0. * one));
+    }
+
+    SECTION("tan")
+    {
+      REQUIRE_THAT(tan(0 * angle[deg]), AlmostEquals(0. * one));
+      REQUIRE_THAT(tan(45 * angle[deg]), AlmostEquals(1. * one));
+      REQUIRE_THAT(tan(135 * angle[deg]), AlmostEquals(-1. * one));
+      REQUIRE_THAT(tan(180 * angle[deg]), AlmostEquals(0. * one));
+
+      REQUIRE_THAT(tan(0 * angle[grad]), AlmostEquals(0. * one));
+      REQUIRE_THAT(tan(50 * angle[grad]), AlmostEquals(1. * one));
+      REQUIRE_THAT(tan(150 * angle[grad]), AlmostEquals(-1. * one));
+      REQUIRE_THAT(tan(200 * angle[grad]), AlmostEquals(0. * one, 2));
+    }
+  }
+
+  SECTION("Angle inverse trigonometric functions")
+  {
+    using namespace mp_units::angular;
+    using namespace mp_units::angular::unit_symbols;
+    using mp_units::angular::unit_symbols::deg;
+
+    SECTION("asin")
+    {
+      REQUIRE_THAT(asin(-1 * one), AlmostEquals(-90. * angle[deg]));
+      REQUIRE_THAT(asin(0 * one), AlmostEquals(0. * angle[deg]));
+      REQUIRE_THAT(asin(1 * one), AlmostEquals(90. * angle[deg]));
+    }
+
+    SECTION("acos")
+    {
+      REQUIRE_THAT(asin(-1 * one), AlmostEquals(-90. * angle[deg]));
+      REQUIRE_THAT(asin(0 * one), AlmostEquals(0. * angle[deg]));
+      REQUIRE_THAT(asin(1 * one), AlmostEquals(90. * angle[deg]));
+    }
+
+    SECTION("atan")
+    {
+      REQUIRE_THAT(atan(-1 * one), AlmostEquals(-45. * angle[deg]));
+      REQUIRE_THAT(atan(0 * one), AlmostEquals(0. * angle[deg]));
+      REQUIRE_THAT(atan(1 * one), AlmostEquals(45. * angle[deg]));
+    }
+  }
+
+  SECTION("Angle atan2 functions")
+  {
+    using namespace mp_units::angular;
+    using namespace mp_units::angular::unit_symbols;
+    using mp_units::angular::unit_symbols::deg;
+
+    SECTION("atan2 should work on the same quantities")
+    {
+      REQUIRE_THAT(atan2(-1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(-45. * angle[deg]));
+      REQUIRE_THAT(atan2(0. * isq::length[km], 1. * isq::length[km]), AlmostEquals(0. * angle[deg]));
+      REQUIRE_THAT(atan2(1. * isq::length[km], 1. * isq::length[km]), AlmostEquals(45. * angle[deg]));
+    }
+    SECTION("atan2 should work with different units of the same dimension")
+    {
+      REQUIRE_THAT(atan2(-1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(-45. * angle[deg]));
+      REQUIRE_THAT(atan2(0. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(0. * angle[deg]));
+      REQUIRE_THAT(atan2(1. * isq::length[km], 1000. * isq::length[m]), AlmostEquals(45. * angle[deg]));
+    }
  }
 }
--- a/test/runtime/quantity_test.cpp
+++ b/test/runtime/quantity_test.cpp
@@ -60,22 +60,25 @@ constexpr bool within_4_ulps(T a, T b)

 }  // namespace

-// conversion requiring radical magnitudes
-TEST_CASE("unit conversions support radical magnitudes", "[conversion][radical]")
+TEST_CASE("quantity operations", "[quantity]")
 {
-  REQUIRE(within_4_ulps(sqrt((1.0 * m) * (1.0 * km)).numerical_value_in(m), sqrt(1000.0)));
-}
+  // conversion requiring radical magnitudes
+  SECTION("unit conversions support radical magnitudes")
+  {
+    REQUIRE(within_4_ulps(sqrt((1.0 * m) * (1.0 * km)).numerical_value_in(m), sqrt(1000.0)));
+  }

-// Reproducing issue #474 exactly:
-TEST_CASE("Issue 474 is fixed", "[conversion][radical]")
-{
-  constexpr auto val_issue_474 = 8.0 * si::si2019::boltzmann_constant * 1000.0 * K / (std::numbers::pi * 10 * Da);
-  REQUIRE(within_4_ulps(sqrt(val_issue_474).numerical_value_in(m / s),
-                        sqrt(val_issue_474.numerical_value_in(m * m / s / s))));
-}
+  // Reproducing issue #474 exactly:
+  SECTION("Issue 474 is fixed")
+  {
+    constexpr auto val_issue_474 = 8.0 * si::si2019::boltzmann_constant * 1000.0 * K / (std::numbers::pi * 10 * Da);
+    REQUIRE(within_4_ulps(sqrt(val_issue_474).numerical_value_in(m / s),
+                          sqrt(val_issue_474.numerical_value_in(m * m / s / s))));
+  }

-TEST_CASE("Volatile representation type", "[volatile]")
-{
-  volatile std::int16_t vint = 123;
-  REQUIRE(quantity(vint * m).numerical_value_in(m) == 123);
+  SECTION("Volatile representation type")
+  {
+    volatile std::int16_t vint = 123;
+    REQUIRE(quantity(vint * m).numerical_value_in(m) == 123);
+  }
 }
--- a/test/static/cgs_test.cpp
+++ b/test/static/cgs_test.cpp
@@ -25,24 +25,28 @@
 #include <mp-units/systems/isq/mechanics.h>
 #include <mp-units/systems/isq/space_and_time.h>
 #include <mp-units/systems/si/units.h>
-
-template<class T>
-  requires mp_units::is_scalar<T>
-constexpr bool mp_units::is_vector<T> = true;
+#if MP_UNITS_HOSTED
+#include <mp-units/cartesian_vector.h>
+#endif

 namespace {

 using namespace mp_units;
 using namespace mp_units::cgs;
 using namespace mp_units::cgs::unit_symbols;
+#if MP_UNITS_HOSTED
+using v = cartesian_vector<double>;
+#endif

 // https://en.wikipedia.org/wiki/Centimetre%E2%80%93gram%E2%80%93second_system_of_units#Definitions_and_conversion_factors_of_CGS_units_in_mechanics
 static_assert(isq::length(100 * cm) == isq::length(1 * si::metre));
 static_assert(isq::mass(1000 * g) == isq::mass(1 * si::kilogram));
 static_assert(isq::time(1 * s) == isq::time(1 * si::second));
 static_assert(isq::speed(100 * cm / s) == isq::speed(1 * si::metre / si::second));
-static_assert(isq::acceleration(100 * Gal) == isq::acceleration(1 * si::metre / square(si::second)));
-static_assert(isq::force(100'000 * dyn) == isq::force(1 * si::newton));
+#if MP_UNITS_HOSTED
+static_assert(isq::acceleration(v{100} * Gal) == isq::acceleration(v{1} * si::metre / square(si::second)));
+static_assert(isq::force(v{100'000} * dyn) == isq::force(v{1} * si::newton));
+#endif
 static_assert(isq::energy(10'000'000 * erg) == isq::energy(1 * si::joule));
 static_assert(isq::power(10'000'000 * erg / s) == isq::power(1 * si::watt));
 static_assert(isq::pressure(10 * Ba) == isq::pressure(1 * si::pascal));
--- a/test/static/math_test.cpp
+++ b/test/static/math_test.cpp
@@ -237,17 +237,17 @@ static_assert(compare(round<si::second>(-1999. * isq::time[ms]), -2. * isq::time
 #endif

 // non-truncating
-static_assert(compare(inverse<us>(250 * Hz), 4000 * us));
-static_assert(compare(inverse<us>(250 * kHz), 4 * us));
-static_assert(compare(inverse<ks>(250 * uHz), 4 * ks));
+static_assert(compare(kind_of<isq::time>(inverse<us>(250 * Hz)), 4000 * us));
+static_assert(compare(kind_of<isq::time>(inverse<us>(250 * kHz)), 4 * us));
+static_assert(compare(kind_of<isq::time>(inverse<ks>(250 * uHz)), 4 * ks));

 // truncating
-static_assert(compare(inverse<s>(1 * kHz), 0 * s));
+static_assert(compare(kind_of<isq::time>(inverse<s>(1 * kHz)), 0 * s));

 // floating-point representation does not truncate
-static_assert(compare(inverse<s>(1. * kHz), 0.001 * s));
+static_assert(compare(kind_of<isq::time>(inverse<s>(1. * kHz)), 0.001 * s));

 // check if constraints work properly for a derived unit of a narrowed kind
-static_assert(compare(inverse<Hz>(1 * s), 1 * Hz));
+static_assert(compare(kind_of<isq::frequency>(inverse<Hz>(1 * s)), 1 * Hz));

 }  // namespace
--- a/test/static/reference_test.cpp
+++ b/test/static/reference_test.cpp
@@ -378,4 +378,14 @@ static_assert(invalid_comparison<frequency(1 * hertz), activity(1 * becquerel)>)
 static_assert(invalid_comparison<angular_measure(1 * radian), solid_angular_measure(1 * steradian)>);
 static_assert(invalid_comparison<angular_measure(1 * radian), storage_capacity(1 * bit)>);

+// make_reference
+static_assert(is_of_type<make_reference(length, metre), reference<length_, metre_>>);
+static_assert(is_of_type<make_reference(width, metre), reference<width_, metre_>>);
+static_assert(is_of_type<make_reference(kind_of<length>, metre), metre_>);
+static_assert(is_of_type<make_reference(get_quantity_spec(metre), metre), metre_>);
+static_assert(is_of_type<make_reference(get_quantity_spec(hertz), hertz), hertz_>);
+static_assert(is_of_type<make_reference(kind_of<frequency>, hertz), hertz_>);
+static_assert(is_of_type<make_reference(get_quantity_spec(watt), watt), watt_>);
+static_assert(is_of_type<make_reference(kind_of<power>, watt), reference<kind_of_<power_>, watt_>>);
+
 }  // namespace