Replace O(N) recursive sequence_map_inverse with O(1) pack expansion

projects/composablekernel/include/ck/utility/sequence.hpp

@@ -597,31 +597,52 @@ struct is_valid_sequence_map : is_same<typename arithmetic_sequence_gen<0, SeqMa
 {
 };
 
-template <typename SeqMap>
-struct sequence_map_inverse
+// Invert a permutation sequence: given X2Y = {a, b, c, ...}, compute Y2X where Y2X[X2Y[i]] = i
+// Example: Sequence<2,0,1> (meaning pos0->2, pos1->0, pos2->1) inverts to Sequence<1,2,0>
+//
+// Why this implementation is faster to compile than recursive templates:
+//
+// The old recursive approach created a new template type for each element:
+//   sequence_map_inverse<Seq<2,0,1>> -> sequence_map_inverse<Seq<0,1>> ->
+//   sequence_map_inverse<Seq<1>>
+// Each "->" is a new type the compiler must create, track, and manage. For N elements, that's
+// N template types, each with overhead (name mangling, debug info, symbol table entries).
+//
+// This implementation uses a constexpr for loop to build the inverse in O(N) operations:
+// For input Sequence<2,0,1>, the loop sets result[input[pos]] = pos for each position:
+//   pos=0: result[2]=0, pos=1: result[0]=1, pos=2: result[1]=2
+// This builds the inverse permutation in a single pass with O(1) template instantiation depth.
+//
+template <index_t... Is>
+struct sequence_map_inverse<Sequence<Is...>>
 {
-    template <typename X2Y, typename WorkingY2X, index_t XBegin, index_t XRemain>
-    struct sequence_map_inverse_impl
+    private:
+    struct InverseArray
     {
-        static constexpr auto new_y2x =
-            WorkingY2X::Modify(X2Y::At(Number<XBegin>{}), Number<XBegin>{});
-
-        using type =
-            typename sequence_map_inverse_impl<X2Y, decltype(new_y2x), XBegin + 1, XRemain - 1>::
-                type;
+        index_t data[sizeof...(Is)] = {};
     };
 
-    template <typename X2Y, typename WorkingY2X, index_t XBegin>
-    struct sequence_map_inverse_impl<X2Y, WorkingY2X, XBegin, 0>
+    static constexpr auto build_inverse()
     {
-        using type = WorkingY2X;
-    };
+        InverseArray result{};
+        constexpr index_t input[] = {Is...};
+        for(index_t pos = 0; pos < static_cast<index_t>(sizeof...(Is)); ++pos)
+        {
+            result.data[input[pos]] = pos;
+        }
+        return result;
+    }
 
-    using type =
-        typename sequence_map_inverse_impl<SeqMap,
-                                           typename uniform_sequence_gen<SeqMap::Size(), 0>::type,
-                                           0,
-                                           SeqMap::Size()>::type;
+    static constexpr InverseArray inverse = build_inverse();
+
+    template <index_t... Positions>
+    static constexpr auto compute(Sequence<Positions...>)
+    {
+        return Sequence<inverse.data[Positions]...>{};
+    }
+
+    public:
+    using type = decltype(compute(make_index_sequence<sizeof...(Is)>{}));
 };
 
 template <index_t... Xs, index_t... Ys>