Address review feedback

src/core/include/units/magnitude.h

@@ -427,6 +427,18 @@ constexpr auto pow(magnitude<BPs...>)
   }
 }
 
+template<BasePower auto... BPs>
+constexpr auto sqrt(magnitude<BPs...> m)
+{
+  return pow<ratio{1, 2}>(m);
+}
+
+template<BasePower auto... BPs>
+constexpr auto cbrt(magnitude<BPs...> m)
+{
+  return pow<ratio{1, 3}>(m);
+}
+
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 // Magnitude product implementation.
 
@@ -569,18 +581,14 @@ constexpr auto common_magnitude(magnitude<H1, T1...> m1, magnitude<H2, T2...> m2
 {
   using detail::remove_positive_power;
 
-  // Case for when H1 has the smaller base.
   if constexpr (H1.get_base() < H2.get_base()) {
+    // When H1 has the smaller base, prepend to result from recursion.
     return remove_positive_power(magnitude<H1>{}) * common_magnitude(magnitude<T1...>{}, m2);
-  }
+  } else if constexpr (H2.get_base() < H1.get_base()) {
-
+    // When H2 has the smaller base, prepend to result from recursion.
-  // Case for when H2 has the smaller base.
-  if constexpr (H2.get_base() < H1.get_base()) {
     return remove_positive_power(magnitude<H2>{}) * common_magnitude(m1, magnitude<T2...>{});
-  }
+  } else {
-
+    // When the bases are equal, pick whichever has the lower power.
-  // Case for equal bases.
-  if constexpr (H1.get_base() == H2.get_base()) {
     constexpr auto common_tail = common_magnitude(magnitude<T1...>{}, magnitude<T2...>{});
     if constexpr (H1.power < H2.power) {
       return magnitude<H1>{} * common_tail;

src/core/include/units/quantity_cast.h

@@ -62,10 +62,7 @@ inline constexpr Magnitude auto quantity_magnitude<quantity<D, U, Rep>> = [] {
 }();
 
 template<typename T>
-inline constexpr ratio quantity_ratio = std::enable_if_t<!Quantity<T>>{};
+inline constexpr ratio quantity_ratio = as_ratio(quantity_magnitude<T>);
-
-template<typename D, typename U, typename Rep>
-inline constexpr ratio quantity_ratio<quantity<D, U, Rep>> = as_ratio(quantity_magnitude<quantity<D, U, Rep>>);
 
 template<typename QFrom, typename QTo>
 inline constexpr Magnitude auto cast_magnitude = [] {
@@ -119,17 +116,14 @@ template<Quantity To, typename D, typename U, scalable_with_<typename To::rep> R
   using traits = detail::cast_traits<Rep, typename To::rep>;
   using ratio_type = TYPENAME traits::ratio_type;
   using rep_type = TYPENAME traits::rep_type;
-  constexpr Magnitude auto c_mag = detail::cast_magnitude<quantity<D, U, Rep>, To>;
 
-  if constexpr (treat_as_floating_point<rep_type>) {
+  constexpr Magnitude auto c_mag = detail::cast_magnitude<quantity<D, U, Rep>, To>;
-    return To(
+  constexpr Magnitude auto num = numerator(c_mag);
-      static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.number()) * (get_value<ratio_type>(numerator(c_mag)) /
+  constexpr Magnitude auto den = denominator(c_mag);
-                                                                         get_value<ratio_type>(denominator(c_mag)))));
+  constexpr Magnitude auto irr = c_mag * (den / num);
-  } else {
+
-    return To(
+  constexpr auto val = [](Magnitude auto m) { return get_value<ratio_type>(m); };
-      static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.number()) * get_value<ratio_type>(numerator(c_mag)) /
+  return To(static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.number()) * val(num) / val(den) * val(irr)));
-                                    get_value<ratio_type>(denominator(c_mag))));
-  }
 }
 
 /**

src/core/include/units/ratio.h

@@ -61,6 +61,8 @@ struct ratio {
 
   [[nodiscard]] friend constexpr bool operator==(const ratio&, const ratio&) = default;
 
+  [[nodiscard]] friend constexpr auto operator<=>(const ratio& lhs, const ratio& rhs) { return (lhs - rhs).num <=> 0; }
+
   [[nodiscard]] friend constexpr ratio operator-(const ratio& r) { return ratio(-r.num, r.den, r.exp); }
 
   [[nodiscard]] friend constexpr ratio operator+(ratio lhs, ratio rhs)
@@ -81,8 +83,6 @@ struct ratio {
 
   [[nodiscard]] friend constexpr ratio operator-(const ratio& lhs, const ratio& rhs) { return lhs + (-rhs); }
 
-  [[nodiscard]] friend constexpr auto operator<=>(const ratio& lhs, const ratio& rhs) { return (lhs - rhs).num <=> 0; }
-
   [[nodiscard]] friend constexpr ratio operator*(const ratio& lhs, const ratio& rhs)
   {
     const std::intmax_t gcd1 = std::gcd(lhs.num, rhs.den);

test/unit_test/static/ratio_test.cpp

@@ -108,4 +108,10 @@ static_assert(numerator(ratio(3, 7, 2)) == 300);
 static_assert(denominator(ratio(3, 4)) == 4);
 static_assert(denominator(ratio(3, 7, -2)) == 700);
 
+// comparison
+static_assert((ratio(3, 4) <=> ratio(6, 8)) == (0 <=> 0));
+static_assert((ratio(3, 4) <=> ratio(-3, 4)) == (0 <=> -1));
+static_assert((ratio(-3, 4) <=> ratio(3, -4)) == (0 <=> 0));
+static_assert((ratio(1, 1, 1) <=> ratio(10)) == (0 <=> 0));
+
 }  // namespace

test/unit_test/static/si_fps_test.cpp

@@ -31,6 +31,7 @@
 #include <units/isq/si/pressure.h>
 #include <units/isq/si/speed.h>
 #include <units/isq/si/time.h>
+#include <units/math.h>
 
 namespace {
 
@@ -113,6 +114,13 @@ static_assert(1_q_pdl_per_ft2 > 1.4881639435_q_Pa && 1_q_pdl_per_ft2 < 1.4881639
 }  // namespace fps_plus_si_literals
 
 namespace fps_test {
+namespace {
+constexpr bool is_near(auto a, auto b, auto tol)
+{
+  const auto diff = a - b;
+  return (diff <= tol) && (-diff <= tol);
+}
+}  // namespace
 
 using namespace units::isq::si::fps::literals;
 using namespace units::isq::si::fps::references;
@@ -121,10 +129,12 @@ using namespace units::isq::si::fps::references;
 
 static_assert(si::length<si::metre>(1) + 1 * ft == si::length<si::metre>(1.3048));
 static_assert(1 * ft + si::length<si::metre>(1) == si::length<si::metre>(1.3048));
-static_assert(quantity_cast<si::length<si::metre>>(1. * ft / 0.3048) + si::length<si::metre>(1) ==
+static_assert(is_near(quantity_cast<si::length<si::metre>>(1. * ft / 0.3048) + si::length<si::metre>(1),
-              si::length<si::metre>(2));  // 1 m in ft + 1 m
+                      si::length<si::metre>(2),
-static_assert(si::length<si::metre>(1) + quantity_cast<si::length<si::metre>>(1. * ft / 0.3048) ==
+                      si::length<si::femtometre>(1)));  // 1 m in ft + 1 m
-              si::length<si::metre>(2));  // 1 m + 1 m in ft
+static_assert(is_near(si::length<si::metre>(1) + quantity_cast<si::length<si::metre>>(1. * ft / 0.3048),
+                      si::length<si::metre>(2),
+                      si::length<si::femtometre>(1)));  // 1 m + 1 m in ft
 static_assert(1 * ft + quantity_cast<si::fps::length<si::fps::foot>>(si::length<si::metre>(0.3048)) ==
               2 * ft);  // 1 ft + 1 ft in m
 static_assert(quantity_cast<si::fps::length<si::fps::foot>>(si::length<si::metre>(0.3048)) + 1 * ft ==