Merge pull request #354 from chiphogg/chiphogg/num-den-conv

Support seamless interop between `ratio` and rational `Magnitude`

src/core/include/units/magnitude.h

@@ -392,7 +392,7 @@ template<typename T, BasePower auto... BPs>
 constexpr T get_value(const magnitude<BPs...>&)
 {
   // Force the expression to be evaluated in a constexpr context, to catch, e.g., overflow.
-  constexpr auto result = detail::checked_static_cast<T>((detail::compute_base_power<T>(BPs) * ...));
+  constexpr auto result = detail::checked_static_cast<T>((detail::compute_base_power<T>(BPs) * ... * T{1}));
 
   return result;
 }
@@ -480,6 +480,51 @@ constexpr auto operator*(magnitude<H1, T1...>, magnitude<H2, T2...>)
 
 constexpr auto operator/(Magnitude auto l, Magnitude auto r) { return l * pow<-1>(r); }
 
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Magnitude numerator and denominator implementation.
+
+namespace detail {
+
+// The largest integer which can be extracted from any magnitude with only a single basis vector.
+template<BasePower auto BP>
+constexpr auto integer_part(magnitude<BP>)
+{
+  constexpr auto power_num = numerator(BP.power);
+  constexpr auto power_den = denominator(BP.power);
+
+  if constexpr (std::is_integral_v<decltype(BP.get_base())> && (power_num >= power_den)) {
+    constexpr auto largest_integer_power = [=](BasePower auto bp) {
+      bp.power = (power_num / power_den);  // Note: integer division intended.
+      return bp;
+    }(BP);  // Note: lambda is immediately invoked.
+
+    return magnitude<largest_integer_power>{};
+  } else {
+    return magnitude<>{};
+  }
+}
+
+}  // namespace detail
+
+template<BasePower auto... BPs>
+constexpr auto numerator(magnitude<BPs...>)
+{
+  return (detail::integer_part(magnitude<BPs>{}) * ... * magnitude<>{});
+}
+
+constexpr auto denominator(Magnitude auto m) { return numerator(pow<-1>(m)); }
+
+// Implementation of conversion to ratio goes here, because it needs `numerator()` and `denominator()`.
+constexpr ratio as_ratio(Magnitude auto m)
+  requires(is_rational(decltype(m){}))
+{
+  return ratio{
+    get_value<std::intmax_t>(numerator(m)),
+    get_value<std::intmax_t>(denominator(m)),
+  };
+}
+
+
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 // `as_magnitude()` implementation.
 

src/core/include/units/ratio.h

@@ -87,6 +87,24 @@ struct ratio {
   }
 
   [[nodiscard]] friend constexpr ratio operator/(const ratio& lhs, const ratio& rhs) { return lhs * inverse(rhs); }
+
+  [[nodiscard]] friend constexpr std::intmax_t numerator(const ratio& r)
+  {
+    std::intmax_t true_num = r.num;
+    for (auto i = r.exp; i > 0; --i) {
+      true_num *= 10;
+    }
+    return true_num;
+  }
+
+  [[nodiscard]] friend constexpr std::intmax_t denominator(const ratio& r)
+  {
+    std::intmax_t true_den = r.den;
+    for (auto i = r.exp; i < 0; ++i) {
+      true_den *= 10;
+    }
+    return true_den;
+  }
 };
 
 [[nodiscard]] constexpr ratio inverse(const ratio& r) { return ratio(r.den, r.num, -r.exp); }

test/unit_test/runtime/magnitude_test.cpp

@@ -63,6 +63,18 @@ void check_same_type_and_value(T actual, U expected)
   CHECK(actual == expected);
 }
 
+template<ratio R>
+void check_ratio_round_trip_is_identity()
+{
+  constexpr Magnitude auto m = as_magnitude<R>();
+  constexpr ratio round_trip = ratio{
+    get_value<std::intmax_t>(numerator(m)),
+    get_value<std::intmax_t>(denominator(m)),
+  };
+  CHECK(round_trip == R);
+}
+
+
 TEST_CASE("base_power")
 {
   SECTION("base rep deducible for integral base")
@@ -351,6 +363,33 @@ TEST_CASE("can distinguish integral, rational, and irrational magnitudes")
   }
 }
 
+TEST_CASE("Constructing ratio from rational magnitude")
+{
+  SECTION("Round trip is identity")
+  {
+    // Note that not every Magnitude can be represented as a ratio.  However, if we _start_ with a
+    // ratio, we must guarantee to recover the same ratio in a round trip.
+    check_ratio_round_trip_is_identity<1>();
+    check_ratio_round_trip_is_identity<9>();
+    check_ratio_round_trip_is_identity<ratio{5, 8}>();
+  }
+
+  SECTION("Rational magnitude converts to ratio")
+  {
+    constexpr ratio r = as_ratio(as_magnitude<ratio{22, 7}>());
+    CHECK(r == ratio{22, 7});
+  }
+
+  SECTION("Irrational magnitude does not convert to ratio")
+  {
+    // The following code should not compile.
+    // as_ratio(pow<ratio{1, 2}>(as_magnitude<2>()));
+
+    // The following code should not compile.
+    // as_ratio(as_magnitude<180>() / pi_to_the<1>());
+  }
+}
+
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 // Detail function tests below.
 
@@ -374,6 +413,34 @@ TEST_CASE("int_power computes integer powers")
   }
 }
 
+TEST_CASE("integer_part picks out integer part of single-basis magnitude")
+{
+  SECTION("integer_part of non-integer base is identity magnitude")
+  {
+    CHECK(integer_part(pi_to_the<1>()) == magnitude<>{});
+    CHECK(integer_part(pi_to_the<-8>()) == magnitude<>{});
+    CHECK(integer_part(pi_to_the<ratio{3, 4}>()) == magnitude<>{});
+  }
+
+  SECTION("integer_part of integer base to negative power is identity magnitude")
+  {
+    CHECK(integer_part(magnitude<base_power{2, -8}>{}) == magnitude<>{});
+    CHECK(integer_part(magnitude<base_power{11, -1}>{}) == magnitude<>{});
+  }
+
+  SECTION("integer_part of integer base to fractional power is identity magnitude")
+  {
+    CHECK(integer_part(magnitude<base_power{2, ratio{1, 2}}>{}) == magnitude<>{});
+  }
+
+  SECTION("integer_part of integer base to power at least one takes integer part")
+  {
+    CHECK(integer_part(magnitude<base_power{2, 1}>{}) == magnitude<base_power{2, 1}>{});
+    CHECK(integer_part(magnitude<base_power{2, ratio{19, 10}}>{}) == magnitude<base_power{2, 1}>{});
+    CHECK(integer_part(magnitude<base_power{11, ratio{97, 9}}>{}) == magnitude<base_power{11, 10}>{});
+  }
+}
+
 TEST_CASE("Prime helper functions")
 {
   SECTION("multiplicity")

test/unit_test/static/ratio_test.cpp

@@ -102,4 +102,10 @@ static_assert(common_ratio(ratio(100, 1), ratio(1, 10)) == ratio(1, 10));
 static_assert(common_ratio(ratio(1), ratio(1, 1, 3)) == ratio(1));
 static_assert(common_ratio(ratio(10, 1, -1), ratio(1, 1, -3)) == ratio(1, 1, -3));
 
+// numerator and denominator
+static_assert(numerator(ratio(3, 4)) == 3);
+static_assert(numerator(ratio(3, 7, 2)) == 300);
+static_assert(denominator(ratio(3, 4)) == 4);
+static_assert(denominator(ratio(3, 7, -2)) == 700);
+
 }  // namespace