performance: Override .elementAt in CachingIterable (#152477)

Add a more efficient override of `Iterable.elementAt` in `CachingIterable`.

Closes #152476

packages/flutter/lib/src/foundation/basic_types.dart

@@ -181,6 +181,22 @@ class CachingIterable<E> extends IterableBase<E> {
     return _results.length;
   }
 
+  @override
+  E elementAt(int index) {
+    RangeError.checkNotNegative(index, 'index');
+    while (_results.length <= index) {
+      if (!_fillNext()) {
+        throw IndexError.withLength(
+          index,
+          _results.length,
+          indexable: this,
+          name: 'index',
+        );
+      }
+    }
+    return _results[index];
+  }
+
   @override
   List<E> toList({ bool growable = true }) {
     _precacheEntireList();

packages/flutter/test/foundation/caching_iterable_test.dart

@@ -107,4 +107,19 @@ void main() {
     expect(expanded2, equals(<int>[1, 1, 2, 2, 3, 3, 4, 4, 5, 5]));
     expect(yieldCount, equals(5));
   });
+
+  test('The Caching Iterable: elementAt correctness', () {
+    final Iterable<int> integers = CachingIterable<int>(range(1, 5).iterator);
+    expect(yieldCount, equals(0));
+
+    expect(() => integers.elementAt(-1), throwsRangeError);
+
+    expect(integers.elementAt(1), equals(2));
+    expect(integers.elementAt(0), equals(1));
+    expect(integers.elementAt(2), equals(3));
+    expect(integers.elementAt(4), equals(5));
+    expect(integers.elementAt(3), equals(4));
+
+    expect(() => integers.elementAt(5), throwsRangeError);
+  });
 }