#include <stddef.h> /* For offsetof */
#include "_map.h"


/*
This file provides an implemention of an immutable mapping using the
Hash Array Mapped Trie (or HAMT) datastructure.

This design allows to have:

1. Efficient copy: immutable mappings can be copied by reference,
   making it an O(1) operation.

2. Efficient mutations: due to structural sharing, only a portion of
   the trie needs to be copied when the collection is mutated.  The
   cost of set/delete operations is O(log N).

3. Efficient lookups: O(log N).

(where N is number of key/value items in the immutable mapping.)


HAMT
====

The core idea of HAMT is that the shape of the trie is encoded into the
hashes of keys.

Say we want to store a K/V pair in our mapping.  First, we calculate the
hash of K, let's say it's 19830128, or in binary:

    0b1001011101001010101110000 = 19830128

Now let's partition this bit representation of the hash into blocks of
5 bits each:

    0b00_00000_10010_11101_00101_01011_10000 = 19830128
          (6)   (5)   (4)   (3)   (2)   (1)

Each block of 5 bits represents a number betwen 0 and 31.  So if we have
a tree that consists of nodes, each of which is an array of 32 pointers,
those 5-bit blocks will encode a position on a single tree level.

For example, storing the key K with hash 19830128, results in the following
tree structure:

                     (array of 32 pointers)
                     +---+ -- +----+----+----+ -- +----+
  root node          | 0 | .. | 15 | 16 | 17 | .. | 31 |   0b10000 = 16 (1)
  (level 1)          +---+ -- +----+----+----+ -- +----+
                                      |
                     +---+ -- +----+----+----+ -- +----+
  a 2nd level node   | 0 | .. | 10 | 11 | 12 | .. | 31 |   0b01011 = 11 (2)
                     +---+ -- +----+----+----+ -- +----+
                                      |
                     +---+ -- +----+----+----+ -- +----+
  a 3rd level node   | 0 | .. | 04 | 05 | 06 | .. | 31 |   0b00101 = 5  (3)
                     +---+ -- +----+----+----+ -- +----+
                                      |
                     +---+ -- +----+----+----+----+
  a 4th level node   | 0 | .. | 04 | 29 | 30 | 31 |        0b11101 = 29 (4)
                     +---+ -- +----+----+----+----+
                                      |
                     +---+ -- +----+----+----+ -- +----+
  a 5th level node   | 0 | .. | 17 | 18 | 19 | .. | 31 |   0b10010 = 18 (5)
                     +---+ -- +----+----+----+ -- +----+
                                      |
                       +--------------+
                       |
                     +---+ -- +----+----+----+ -- +----+
  a 6th level node   | 0 | .. | 15 | 16 | 17 | .. | 31 |   0b00000 = 0  (6)
                     +---+ -- +----+----+----+ -- +----+
                       |
                       V -- our value (or collision)

To rehash: for a K/V pair, the hash of K encodes where in the tree V will
be stored.

To optimize memory footprint and handle hash collisions, our implementation
uses three different types of nodes:

 * A Bitmap node;
 * An Array node;
 * A Collision node.

Because we implement an immutable dictionary, our nodes are also
immutable.  Therefore, when we need to modify a node, we copy it, and
do that modification to the copy.


Array Nodes
-----------

These nodes are very simple.  Essentially they are arrays of 32 pointers
we used to illustrate the high-level idea in the previous section.

We use Array nodes only when we need to store more than 16 pointers
in a single node.

Array nodes do not store key objects or value objects.  They are used
only as an indirection level - their pointers point to other nodes in
the tree.


Bitmap Node
-----------

Allocating a new 32-pointers array for every node of our tree would be
very expensive.  Unless we store millions of keys, most of tree nodes would
be very sparse.

When we have less than 16 elements in a node, we don't want to use the
Array node, that would mean that we waste a lot of memory.  Instead,
we can use bitmap compression and can have just as many pointers
as we need!

Bitmap nodes consist of two fields:

1. An array of pointers.  If a Bitmap node holds N elements, the
   array will be of N pointers.

2. A 32bit integer -- a bitmap field.  If an N-th bit is set in the
   bitmap, it means that the node has an N-th element.

For example, say we need to store a 3 elements sparse array:

   +---+  --  +---+  --  +----+  --  +----+
   | 0 |  ..  | 4 |  ..  | 11 |  ..  | 17 |
   +---+  --  +---+  --  +----+  --  +----+
                |          |           |
                o1         o2          o3

We allocate a three-pointer Bitmap node.  Its bitmap field will be
then set to:

   0b_00100_00010_00000_10000 == (1 << 17) | (1 << 11) | (1 << 4)

To check if our Bitmap node has an I-th element we can do:

   bitmap & (1 << I)


And here's a formula to calculate a position in our pointer array
which would correspond to an I-th element:

   popcount(bitmap & ((1 << I) - 1))


Let's break it down:

 * `popcount` is a function that returns a number of bits set to 1;

 * `((1 << I) - 1)` is a mask to filter the bitmask to contain bits
   set to the *right* of our bit.


So for our 17, 11, and 4 indexes:

 * bitmap & ((1 << 17) - 1) == 0b100000010000 => 2 bits are set => index is 2.

 * bitmap & ((1 << 11) - 1) == 0b10000 => 1 bit is set => index is 1.

 * bitmap & ((1 << 4) - 1) == 0b0 => 0 bits are set => index is 0.


To conclude: Bitmap nodes are just like Array nodes -- they can store
a number of pointers, but use bitmap compression to eliminate unused
pointers.


Bitmap nodes have two pointers for each item:

  +----+----+----+----+  --  +----+----+
  | k1 | v1 | k2 | v2 |  ..  | kN | vN |
  +----+----+----+----+  --  +----+----+

When kI == NULL, vI points to another tree level.

When kI != NULL, the actual key object is stored in kI, and its
value is stored in vI.


Collision Nodes
---------------

Collision nodes are simple arrays of pointers -- two pointers per
key/value.  When there's a hash collision, say for k1/v1 and k2/v2
we have `hash(k1)==hash(k2)`.  Then our collision node will be:

  +----+----+----+----+
  | k1 | v1 | k2 | v2 |
  +----+----+----+----+


Tree Structure
--------------

All nodes are PyObjects.

The `MapObject` object has a pointer to the root node (h_root),
and has a length field (h_count).

High-level functions accept a MapObject object and dispatch to
lower-level functions depending on what kind of node h_root points to.


Operations
==========

There are three fundamental operations on an immutable dictionary:

1. "o.assoc(k, v)" will return a new immutable dictionary, that will be
   a copy of "o", but with the "k/v" item set.

   Functions in this file:

        map_node_assoc, map_node_bitmap_assoc,
        map_node_array_assoc, map_node_collision_assoc

   `map_node_assoc` function accepts a node object, and calls
   other functions depending on its actual type.

2. "o.find(k)" will lookup key "k" in "o".

   Functions:

        map_node_find, map_node_bitmap_find,
        map_node_array_find, map_node_collision_find

3. "o.without(k)" will return a new immutable dictionary, that will be
   a copy of "o", buth without the "k" key.

   Functions:

        map_node_without, map_node_bitmap_without,
        map_node_array_without, map_node_collision_without


Further Reading
===============

1. http://blog.higher-order.net/2009/09/08/understanding-clojures-persistenthashmap-deftwice.html

2. http://blog.higher-order.net/2010/08/16/assoc-and-clojures-persistenthashmap-part-ii.html

3. Clojure's PersistentHashMap implementation:
   https://github.com/clojure/clojure/blob/master/src/jvm/clojure/lang/PersistentHashMap.java
*/


#define IS_ARRAY_NODE(node)     (Py_TYPE(node) == &_Map_ArrayNode_Type)
#define IS_BITMAP_NODE(node)    (Py_TYPE(node) == &_Map_BitmapNode_Type)
#define IS_COLLISION_NODE(node) (Py_TYPE(node) == &_Map_CollisionNode_Type)


/* Return type for 'find' (lookup a key) functions.

   * F_ERROR - an error occurred;
   * F_NOT_FOUND - the key was not found;
   * F_FOUND - the key was found.
*/
typedef enum {F_ERROR, F_NOT_FOUND, F_FOUND} map_find_t;


/* Return type for 'without' (delete a key) functions.

   * W_ERROR - an error occurred;
   * W_NOT_FOUND - the key was not found: there's nothing to delete;
   * W_EMPTY - the key was found: the node/tree would be empty
     if the key is deleted;
   * W_NEWNODE - the key was found: a new node/tree is returned
     without that key.
*/
typedef enum {W_ERROR, W_NOT_FOUND, W_EMPTY, W_NEWNODE} map_without_t;


/* Low-level iterator protocol type.

   * I_ITEM - a new item has been yielded;
   * I_END - the whole tree was visited (similar to StopIteration).
*/
typedef enum {I_ITEM, I_END} map_iter_t;


#define HAMT_ARRAY_NODE_SIZE 32


typedef struct {
    PyObject_HEAD
    MapNode *a_array[HAMT_ARRAY_NODE_SIZE];
    Py_ssize_t a_count;
} MapNode_Array;


typedef struct {
    PyObject_VAR_HEAD
    uint32_t b_bitmap;
    PyObject *b_array[1];
} MapNode_Bitmap;


typedef struct {
    PyObject_VAR_HEAD
    int32_t c_hash;
    PyObject *c_array[1];
} MapNode_Collision;


static MapNode_Bitmap *_empty_bitmap_node;
static MapObject *_empty_map;


/* Create a new HAMT immutable mapping. */
static MapObject *
map_new(void);

/* Return a new collection based on "o", but with an additional
   key/val pair. */
static MapObject *
map_assoc(MapObject *o, PyObject *key, PyObject *val);

/* Return a new collection based on "o", but without "key". */
static MapObject *
map_without(MapObject *o, PyObject *key);

/* Check if "v" is equal to "w".

   Return:
   - 0: v != w
   - 1: v == w
   - -1: An error occurred.
*/
static int
map_eq(MapObject *v, MapObject *w);

static map_find_t
map_find(MapObject *o, PyObject *key, PyObject **val);

/* Return the size of "o"; equivalent of "len(o)". */
static Py_ssize_t
map_len(MapObject *o);


static MapObject *
map_alloc(void);