Cache island topology data

Store island topology in `mjData` so repeated island solves can reuse stable connect/weld equality partitions. Add cache invalidation checks for active equality changes and cover the fast path with an island regression test.

Signed-off-by: teerthsharma <teerths57@gmail.com>

include/mujoco/mjdata.h

@@ -198,6 +198,11 @@ typedef struct mjData_ {
   // sleep state
   int*    tree_asleep;       // <0: awake; >=0: index cycle of sleeping trees    (ntree x 1)
 
+  // opaque internal island topology cache; users must not modify
+  int* island_cache_tree;    // tree and island topology                         (ntree x 28)
+  int* island_cache_dof;     // DOF topology                                     (nv x 8)
+  int* island_cache_eq;      // equality topology                                (neq x 40)
+
   // plugins
   int*       plugin;         // copy of m->plugin, required for deletion         (nplugin x 1)
   uintptr_t* plugin_data;    // pointer to plugin-managed data structure         (nplugin x 1)

include/mujoco/mjxmacro.h

@@ -929,7 +929,10 @@
     X   ( mjtNum,    qfrc_inverse,      nv,          1           ) \
     X   ( mjtNum,    cacc,              nbody,       6           ) \
     X   ( mjtNum,    cfrc_int,          nbody,       6           ) \
-    X   ( mjtNum,    cfrc_ext,          nbody,       6           )
+    X   ( mjtNum,    cfrc_ext,          nbody,       6           ) \
+    XIC ( int,       island_cache_tree, ntree,       28          ) \
+    XIC ( int,       island_cache_dof,  nv,          8           ) \
+    XIC ( int,       island_cache_eq,   neq,         40          )
 
 
 // macro for annotating that an array size in an X macro is a member of mjData
@@ -1080,5 +1083,6 @@
 // to obtain only X macros for fields that are relevant for mjvScene creation,
 // redefine XNV to expand to nothing
 #define XNV X
+#define XIC(type, name, nr, nc)
 
 #endif  // MUJOCO_MJXMACRO_H_