+bool aff_combination_constant_multiple_p (aff_tree *, aff_tree *, double_int *);
+void aff_combination_expand (aff_tree *, struct pointer_map_t **);
+void tree_to_aff_combination_expand (tree, tree, aff_tree *,
+ struct pointer_map_t **);
+void get_inner_reference_aff (tree, aff_tree *, double_int *);
+void free_affine_expand_cache (struct pointer_map_t **);
+
+/* Debugging functions. */
+void print_aff (FILE *, aff_tree *);
+void debug_aff (aff_tree *);