Double prev pointer seems to allow traversing list in one direction only, while allowing easy deletion (because even though you can't access the previous element (easily), you can access the next pointer of previous element, and set it to new correct value when deleting a node.
Without seeing other related functions, it's hard to see why it is done this way. I've not seen this done, and can't immediately think of any really useful benefit.
I think this allows having simpler node deletion code, because node does not need to care if it first or not, because node's prev pointer will always have non-NULL value to a pointer it needs to modify when deleting itself. And same simplicity for insertion before a current node. If these operations are what dominate the use pattern, then this could be seen as minor optimization, I suppose, especially in older CPUs where branches might have been much more expensive.
How to traverse list
This was the question, right? You can only traverse it forward, in a very simple manner, here's a for loop to traverse entire list:
struct r *node;
for (node = rlist ; node ; node = node->next) {
// assert that prev points to pointer, which should point to this node
assert(*(node->prev) == node);
// use node
printf("node at %p with data at %p\n", node, node->d);
}
Example insertion function
This example insertion function demonstrates how insertion before a node needs no branches (untested):
struct r *rinsert(struct r *nextnode, data *d) {
// create and initialize new node
struct r *newnode = xmalloc(sizeof(struct r));
newnode->d = d;
newnode->next = nextnode;
newnode->prev = nextnode->prev;
// set next pointer of preceding node (or rlist) to point to newnode
*(newnode->prev) = newnode;
// set prev pointer of nextnode to point to next pointer of newnode
nextnode->prev = &(newnode->next);
return newnode;
}