Add unit test for XKCD 3038 alt-text (#377)

See for context: <https://xkcd.com/3038/>.  Presumably, the joke only
works if the speed limit in question corresponds to a realistic speed
limit for American roads, so we take the range to be from 25 MPH (many
residential streets) to 75 MPH (some roads in places I have seen such as
parts of MI or TX).

To make this work, it was convenient to add unit definitions for
`Arcminutes` and `Arcseconds`.  These have various choices for unit
symbol, but I decided to go with `am` and `as` because this will be the
most consistent with users who form symbols for `mas` and `uas`.

For the labels, in any case, I went with `'` and `"`.  I could be
persuaded to go with `''` for arcseconds, but I think `"` is likely to
be better overall.

We also now group all of our XKCD test cases into an `Xkcd` test family,
because of course we do.

au/code/au/CMakeLists.txt

@@ -59,6 +59,10 @@ header_only_library(
     stdx/utility.hh
     units/amperes.hh
     units/amperes_fwd.hh
+    units/arcminutes.hh
+    units/arcminutes_fwd.hh
+    units/arcseconds.hh
+    units/arcseconds_fwd.hh
     units/bars.hh
     units/bars_fwd.hh
     units/becquerel.hh
@@ -306,6 +310,8 @@ gtest_based_test(
   NAME units_test
   SRCS
     units/test/amperes_test.cc
+    units/test/arcminutes_test.cc
+    units/test/arcseconds_test.cc
     units/test/bars_test.cc
     units/test/becquerel_test.cc
     units/test/bits_test.cc

au/code/au/au_test.cc

@@ -14,8 +14,10 @@
 
 #include "au/au.hh"
 
+#include "au/constants/speed_of_light.hh"
 #include "au/prefix.hh"
 #include "au/testing.hh"
+#include "au/units/arcminutes.hh"
 #include "au/units/celsius.hh"
 #include "au/units/fahrenheit.hh"
 #include "au/units/fathoms.hh"
@@ -26,12 +28,19 @@
 #include "au/units/knots.hh"
 #include "au/units/meters.hh"
 #include "au/units/miles.hh"
+#include "au/units/steradians.hh"
 #include "au/units/yards.hh"
 #include "gtest/gtest.h"
 
 using ::testing::StaticAssertTypeEq;
 
 namespace au {
+namespace {
+template <typename T, typename U>
+auto IsBetween(T lower, U upper) {
+    return ::testing::AllOf(::testing::Ge(lower), ::testing::Le(upper));
+}
+}  // namespace
 
 TEST(Conversions, SupportIntMHzToU32Hz) {
     constexpr QuantityU32<Hertz> freq = mega(hertz)(40);
@@ -54,7 +63,7 @@ constexpr auto round_sequentially(Quantity<U, R> q, FirstUnit first_unit, NextUn
     return round_sequentially(round_as(first_unit, q), next_units...);
 }
 
-TEST(RoundAs, ReproducesXkcd2585) {
+TEST(Xkcd, RoundAsReproducesXkcd2585) {
     constexpr auto true_speed = (miles / hour)(17);
 
     const auto rounded_speed = round_sequentially(true_speed,
@@ -86,6 +95,17 @@ TEST(RoundAs, ReproducesXkcd2585) {
     EXPECT_EQ((miles / hour)(45), rounded_speed);
 }
 
+TEST(Xkcd, Xkcd3038GivesReasonableSpeedLimit) {
+    using symbols::h;
+    using symbols::mi;
+
+    constexpr auto c = SPEED_OF_LIGHT;
+    constexpr auto SPEED_LIMIT = make_constant(c * squared(arcminutes) / steradian);
+
+    EXPECT_THAT(SPEED_LIMIT, IsBetween(25.0 * mi / h, 75.0 * mi / h))
+        << SPEED_LIMIT.as<double>(mi / h);
+}
+
 TEST(QuantityPoint, DocumentationExampleIsCorrect) {
     EXPECT_LT(fahrenheit_pt(-40) + celsius_qty(60), kelvins_pt(300));
 }

au/code/au/units/arcminutes.hh

@@ -0,0 +1,44 @@
+// Copyright 2025 Aurora Operations, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include "au/units/arcminutes_fwd.hh"
+// Keep corresponding `_fwd.hh` file on top.
+
+#include "au/quantity.hh"
+#include "au/unit_symbol.hh"
+#include "au/units/degrees.hh"
+
+namespace au {
+
+// DO NOT follow this pattern to define your own units.  This is for library-defined units.
+// Instead, follow instructions at (https://aurora-opensource.github.io/au/main/howto/new-units/).
+template <typename T>
+struct ArcminutesLabel {
+    static constexpr const char label[] = "'";
+};
+template <typename T>
+constexpr const char ArcminutesLabel<T>::label[];
+struct Arcminutes : decltype(Degrees{} / mag<60>()), ArcminutesLabel<void> {
+    using ArcminutesLabel<void>::label;
+};
+constexpr auto arcminute = SingularNameFor<Arcminutes>{};
+constexpr auto arcminutes = QuantityMaker<Arcminutes>{};
+
+namespace symbols {
+constexpr auto am = SymbolFor<Arcminutes>{};
+}
+
+}  // namespace au

au/code/au/units/arcminutes_fwd.hh

@@ -0,0 +1,21 @@
+// Copyright 2025 Aurora Operations, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+namespace au {
+
+struct Arcminutes;
+
+}  // namespace au

au/code/au/units/arcseconds.hh

@@ -0,0 +1,44 @@
+// Copyright 2025 Aurora Operations, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include "au/units/arcseconds_fwd.hh"
+// Keep corresponding `_fwd.hh` file on top.
+
+#include "au/quantity.hh"
+#include "au/unit_symbol.hh"
+#include "au/units/degrees.hh"
+
+namespace au {
+
+// DO NOT follow this pattern to define your own units.  This is for library-defined units.
+// Instead, follow instructions at (https://aurora-opensource.github.io/au/main/howto/new-units/).
+template <typename T>
+struct ArcsecondsLabel {
+    static constexpr const char label[] = "\"";
+};
+template <typename T>
+constexpr const char ArcsecondsLabel<T>::label[];
+struct Arcseconds : decltype(Degrees{} / mag<3600>()), ArcsecondsLabel<void> {
+    using ArcsecondsLabel<void>::label;
+};
+constexpr auto arcsecond = SingularNameFor<Arcseconds>{};
+constexpr auto arcseconds = QuantityMaker<Arcseconds>{};
+
+namespace symbols {
+constexpr auto as = SymbolFor<Arcseconds>{};
+}
+
+}  // namespace au

au/code/au/units/arcseconds_fwd.hh

@@ -0,0 +1,21 @@
+// Copyright 2025 Aurora Operations, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+namespace au {
+
+struct Arcseconds;
+
+}  // namespace au

au/code/au/units/test/arcminutes_test.cc

@@ -0,0 +1,34 @@
+// Copyright 2025 Aurora Operations, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "au/units/arcminutes.hh"
+
+#include "au/testing.hh"
+#include "au/units/degrees.hh"
+#include "gtest/gtest.h"
+
+namespace au {
+
+using ::testing::Eq;
+
+TEST(Arcminutes, HasExpectedLabel) { expect_label<Arcminutes>("'"); }
+
+TEST(Arcminutes, RelatesCorrectlyToDegrees) { EXPECT_THAT(arcminutes(120.0), Eq(degrees(2.0))); }
+
+TEST(Arcminutes, HasExpectedSymbol) {
+    using symbols::am;
+    EXPECT_THAT(5.f * am, SameTypeAndValue(arcminutes(5.f)));
+}
+
+}  // namespace au

au/code/au/units/test/arcseconds_test.cc

@@ -0,0 +1,34 @@
+// Copyright 2025 Aurora Operations, Inc.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "au/units/arcseconds.hh"
+
+#include "au/testing.hh"
+#include "au/units/degrees.hh"
+#include "gtest/gtest.h"
+
+namespace au {
+
+using ::testing::Eq;
+
+TEST(Arcseconds, HasExpectedLabel) { expect_label<Arcseconds>("\""); }
+
+TEST(Arcseconds, RelatesCorrectlyToDegrees) { EXPECT_THAT(arcseconds(7200.0), Eq(degrees(2.0))); }
+
+TEST(Arcseconds, HasExpectedSymbol) {
+    using symbols::as;
+    EXPECT_THAT(5.f * as, SameTypeAndValue(arcseconds(5.f)));
+}
+
+}  // namespace au