From 409aaf463665f8f3945fef456e9dac2db2861732 Mon Sep 17 00:00:00 2001
From: Chip Hogg <chogg@aurora.tech>
Date: Sat, 8 Jan 2022 19:34:21 -0500
Subject: [PATCH] Generalize inverse() to pow<...>()

---
 src/core/include/units/magnitude.h        | 23 +++++++++++++----------
 test/unit_test/runtime/magnitude_test.cpp | 17 +++++++++++++++++
 2 files changed, 30 insertions(+), 10 deletions(-)

diff --git a/src/core/include/units/magnitude.h b/src/core/include/units/magnitude.h
index f50ca775..c4964337 100644
--- a/src/core/include/units/magnitude.h
+++ b/src/core/include/units/magnitude.h
@@ -126,11 +126,11 @@ constexpr bool operator==(T t, U u) {
 }
 
 /**
- * @brief  The (multiplicative) inverse of a BasePower.
+ * @brief  A BasePower, raised to a rational power E.
  */
-template<BasePower BP>
-constexpr auto inverse(BP bp) {
-  bp.power = -bp.power;
+template<ratio E>
+constexpr auto pow(BasePower auto bp) {
+  bp.power = bp.power * E;
   return bp;
 }
 
@@ -220,8 +220,8 @@ constexpr bool strictly_increasing(Ts&&... ts) {
 /**
  * @brief  A representation for positive real numbers which optimizes taking products and rational powers.
  *
- * Magnitudes can be treated as values.  Each type encodes exactly one value.  Users can multiply, divide, and compare
- * for equality.
+ * Magnitudes can be treated as values.  Each type encodes exactly one value.  Users can multiply, divide, raise to
+ * rational powers, and compare for equality.
  */
 template<BasePower auto... BPs>
   requires ((detail::is_valid_base_power(BPs) && ... && detail::strictly_increasing(BPs.get_base()...)))
@@ -274,10 +274,13 @@ constexpr bool operator==(magnitude<LeftBPs...>, magnitude<RightBPs...>) {
 }
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
-// Magnitude inverse implementation.
+// Magnitude rational powers implementation.
 
-template<BasePower auto... BPs>
-constexpr auto inverse(magnitude<BPs...>) { return magnitude<inverse(BPs)...>{}; }
+template<ratio E, BasePower auto... BPs>
+constexpr auto pow(magnitude<BPs...>) {
+  if constexpr (E == 0) { return magnitude<>{}; }
+  else { return magnitude<pow<E>(BPs)...>{}; }
+}
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 // Magnitude product implementation.
@@ -322,7 +325,7 @@ constexpr auto operator*(magnitude<H1, T1...>, magnitude<H2, T2...>) {
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 // Magnitude quotient implementation.
 
-constexpr auto operator/(Magnitude auto l, Magnitude auto r) { return l * inverse(r); }
+constexpr auto operator/(Magnitude auto l, Magnitude auto r) { return l * pow<-1>(r); }
 
 ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
 // `as_magnitude()` implementation.
diff --git a/test/unit_test/runtime/magnitude_test.cpp b/test/unit_test/runtime/magnitude_test.cpp
index 0750a4b5..b32d2928 100644
--- a/test/unit_test/runtime/magnitude_test.cpp
+++ b/test/unit_test/runtime/magnitude_test.cpp
@@ -181,6 +181,23 @@ TEST_CASE("Division works for magnitudes")
   }
 }
 
+TEST_CASE("Can raise Magnitudes to rational powers")
+{
+  SECTION("Anything to the 0 is 1") {
+    CHECK(pow<0>(as_magnitude<1>()) == as_magnitude<1>());
+    CHECK(pow<0>(as_magnitude<123>()) == as_magnitude<1>());
+    CHECK(pow<0>(as_magnitude<ratio{3, 4}>()) == as_magnitude<1>());
+    CHECK(pow<0>(pi_to_the<ratio{-1, 2}>()) == as_magnitude<1>());
+  }
+
+  SECTION("Anything to the 1 is itself") {
+    CHECK(pow<1>(as_magnitude<1>()) == as_magnitude<1>());
+    CHECK(pow<1>(as_magnitude<123>()) == as_magnitude<123>());
+    CHECK(pow<1>(as_magnitude<ratio{3, 4}>()) == as_magnitude<ratio{3, 4}>());
+    CHECK(pow<1>(pi_to_the<ratio{-1, 2}>()) == pi_to_the<ratio{-1, 2}>());
+  }
+}
+
 namespace detail
 {