hamt.c

#include "Python.h"

#include "pycore_bitutils.h"      // _Py_popcount32
#include "pycore_hamt.h"
#include "pycore_initconfig.h"    // _PyStatus_OK()
#include "pycore_object.h"        // _PyObject_GC_TRACK()
#include <stddef.h>               // offsetof()

/*
This file provides an implementation 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 between 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 `PyHamtObject` object has a pointer to the root node (h_root),
and has a length field (h_count).

High-level functions accept a PyHamtObject 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:

        hamt_node_assoc, hamt_node_bitmap_assoc,
        hamt_node_array_assoc, hamt_node_collision_assoc

   `hamt_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:

        hamt_node_find, hamt_node_bitmap_find,
        hamt_node_array_find, hamt_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:

        hamt_node_without, hamt_node_bitmap_without,
        hamt_node_array_without, hamt_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


Debug
=====

The HAMT datatype is accessible for testing purposes under the
`_testcapi` module:

    >>> from _testcapi import hamt
    >>> h = hamt()
    >>> h2 = h.set('a', 2)
    >>> h3 = h2.set('b', 3)
    >>> list(h3)
    ['a', 'b']

When CPython is built in debug mode, a '__dump__()' method is available
to introspect the tree:

    >>> print(h3.__dump__())
    HAMT(len=2):
        BitmapNode(size=4 count=2 bitmap=0b110 id=0x10eb9d9e8):
            'a': 2
            'b': 3
*/


#define IS_ARRAY_NODE(node)     Py_IS_TYPE(node, &_PyHamt_ArrayNode_Type)
#define IS_BITMAP_NODE(node)    Py_IS_TYPE(node, &_PyHamt_BitmapNode_Type)
#define IS_COLLISION_NODE(node) Py_IS_TYPE(node, &_PyHamt_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} hamt_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} hamt_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} hamt_iter_t;


#define HAMT_ARRAY_NODE_SIZE 32


typedef struct {
    PyObject_HEAD
    PyHamtNode *a_array[HAMT_ARRAY_NODE_SIZE];
    Py_ssize_t a_count;
} PyHamtNode_Array;


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


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


static PyHamtNode_Bitmap *_empty_bitmap_node;
static PyHamtObject *_empty_hamt;


static PyHamtObject *
hamt_alloc(void);

static PyHamtNode *
hamt_node_assoc(PyHamtNode *node,
                uint32_t shift, int32_t hash,
                PyObject *key, PyObject *val, int* added_leaf);

static hamt_without_t
hamt_node_without(PyHamtNode *node,
                  uint32_t shift, int32_t hash,
                  PyObject *key,
                  PyHamtNode **new_node);

static hamt_find_t
hamt_node_find(PyHamtNode *node,
               uint32_t shift, int32_t hash,
               PyObject *key, PyObject **val);

#ifdef Py_DEBUG
static int
hamt_node_dump(PyHamtNode *node,
               _PyUnicodeWriter *writer, int level);
#endif

static PyHamtNode *
hamt_node_array_new(Py_ssize_t);

static PyHamtNode *
hamt_node_collision_new(int32_t hash, Py_ssize_t size);

static inline Py_ssize_t
hamt_node_collision_count(PyHamtNode_Collision *node);


#ifdef Py_DEBUG
static void
_hamt_node_array_validate(void *obj_raw)
{
    PyObject *obj = _PyObject_CAST(obj_raw);
    assert(IS_ARRAY_NODE(obj));
    PyHamtNode_Array *node = (PyHamtNode_Array*)obj;
    Py_ssize_t i = 0, count = 0;
    for (; i < HAMT_ARRAY_NODE_SIZE; i++) {
        if (node->a_array[i] != NULL) {
            count++;
        }
    }
    assert(count == node->a_count);
}

#define VALIDATE_ARRAY_NODE(NODE) \
    do { _hamt_node_array_validate(NODE); } while (0);
#else
#define VALIDATE_ARRAY_NODE(NODE)
#endif


/* Returns -1 on error */
static inline int32_t
hamt_hash(PyObject *o)
{
    Py_hash_t hash = PyObject_Hash(o);

#if SIZEOF_PY_HASH_T <= 4
    return hash;
#else
    if (hash == -1) {
        /* exception */
        return -1;
    }

    /* While it's somewhat suboptimal to reduce Python's 64 bit hash to
       32 bits via XOR, it seems that the resulting hash function
       is good enough (this is also how Long type is hashed in Java.)
       Storing 10, 100, 1000 Python strings results in a relatively
       shallow and uniform tree structure.

       Also it's worth noting that it would be possible to adapt the tree
       structure to 64 bit hashes, but that would increase memory pressure
       and provide little to no performance benefits for collections with
       fewer than billions of key/value pairs.

       Important: do not change this hash reducing function. There are many
       tests that need an exact tree shape to cover all code paths and
       we do that by specifying concrete values for test data's `__hash__`.
       If this function is changed most of the regression tests would
       become useless.
    */
    int32_t xored = (int32_t)(hash & 0xffffffffl) ^ (int32_t)(hash >> 32);
    return xored == -1 ? -2 : xored;
#endif
}

static inline uint32_t
hamt_mask(int32_t hash, uint32_t shift)
{
    return (((uint32_t)hash >> shift) & 0x01f);
}

static inline uint32_t
hamt_bitpos(int32_t hash, uint32_t shift)
{
    return (uint32_t)1 << hamt_mask(hash, shift);
}

static inline uint32_t
hamt_bitindex(uint32_t bitmap, uint32_t bit)
{
    return (uint32_t)_Py_popcount32(bitmap & (bit - 1));
}


/////////////////////////////////// Dump Helpers
#ifdef Py_DEBUG

static int
_hamt_dump_ident(_PyUnicodeWriter *writer, int level)
{
    /* Write `'    ' * level` to the `writer` */
    PyObject *str = NULL;
    PyObject *num = NULL;
    PyObject *res = NULL;
    int ret = -1;

    str = PyUnicode_FromString("    ");
    if (str == NULL) {
        goto error;
    }

    num = PyLong_FromLong((long)level);
    if (num == NULL) {
        goto error;
    }

    res = PyNumber_Multiply(str, num);
    if (res == NULL) {
        goto error;
    }

    ret = _PyUnicodeWriter_WriteStr(writer, res);

error:
    Py_XDECREF(res);
    Py_XDECREF(str);
    Py_XDECREF(num);
    return ret;
}

static int
_hamt_dump_format(_PyUnicodeWriter *writer, const char *format, ...)
{
    /* A convenient helper combining _PyUnicodeWriter_WriteStr and
       PyUnicode_FromFormatV.
    */
    PyObject* msg;
    int ret;

    va_list vargs;
#ifdef HAVE_STDARG_PROTOTYPES
    va_start(vargs, format);
#else
    va_start(vargs);
#endif
    msg = PyUnicode_FromFormatV(format, vargs);
    va_end(vargs);

    if (msg == NULL) {
        return -1;
    }

    ret = _PyUnicodeWriter_WriteStr(writer, msg);
    Py_DECREF(msg);
    return ret;
}

#endif  /* Py_DEBUG */
/////////////////////////////////// Bitmap Node


static PyHamtNode *
hamt_node_bitmap_new(Py_ssize_t size)
{
    /* Create a new bitmap node of size 'size' */

    PyHamtNode_Bitmap *node;
    Py_ssize_t i;

    assert(size >= 0);
    assert(size % 2 == 0);

    if (size == 0 && _empty_bitmap_node != NULL) {
        Py_INCREF(_empty_bitmap_node);
        return (PyHamtNode *)_empty_bitmap_node;
    }

    /* No freelist; allocate a new bitmap node */
    node = PyObject_GC_NewVar(
        PyHamtNode_Bitmap, &_PyHamt_BitmapNode_Type, size);
    if (node == NULL) {
        return NULL;
    }

    Py_SET_SIZE(node, size);

    for (i = 0; i < size; i++) {
        node->b_array[i] = NULL;
    }

    node->b_bitmap = 0;

    _PyObject_GC_TRACK(node);

    if (size == 0 && _empty_bitmap_node == NULL) {
        /* Since bitmap nodes are immutable, we can cache the instance
           for size=0 and reuse it whenever we need an empty bitmap node.
        */
        _empty_bitmap_node = node;
        Py_INCREF(_empty_bitmap_node);
    }

    return (PyHamtNode *)node;
}

static inline Py_ssize_t
hamt_node_bitmap_count(PyHamtNode_Bitmap *node)
{
    return Py_SIZE(node) / 2;
}

static PyHamtNode_Bitmap *
hamt_node_bitmap_clone(PyHamtNode_Bitmap *node)
{
    /* Clone a bitmap node; return a new one with the same child notes. */

    PyHamtNode_Bitmap *clone;
    Py_ssize_t i;

    clone = (PyHamtNode_Bitmap *)hamt_node_bitmap_new(Py_SIZE(node));
    if (clone == NULL) {
        return NULL;
    }

    for (i = 0; i < Py_SIZE(node); i++) {
        Py_XINCREF(node->b_array[i]);
        clone->b_array[i] = node->b_array[i];
    }

    clone->b_bitmap = node->b_bitmap;
    return clone;
}

static PyHamtNode_Bitmap *
hamt_node_bitmap_clone_without(PyHamtNode_Bitmap *o, uint32_t bit)
{
    assert(bit & o->b_bitmap);
    assert(hamt_node_bitmap_count(o) > 1);

    PyHamtNode_Bitmap *new = (PyHamtNode_Bitmap *)hamt_node_bitmap_new(
        Py_SIZE(o) - 2);
    if (new == NULL) {
        return NULL;
    }

    uint32_t idx = hamt_bitindex(o->b_bitmap, bit);
    uint32_t key_idx = 2 * idx;
    uint32_t val_idx = key_idx + 1;
    uint32_t i;

    for (i = 0; i < key_idx; i++) {
        Py_XINCREF(o->b_array[i]);
        new->b_array[i] = o->b_array[i];
    }

    assert(Py_SIZE(o) >= 0 && Py_SIZE(o) <= 32);
    for (i = val_idx + 1; i < (uint32_t)Py_SIZE(o); i++) {
        Py_XINCREF(o->b_array[i]);
        new->b_array[i - 2] = o->b_array[i];
    }

    new->b_bitmap = o->b_bitmap & ~bit;
    return new;
}

static PyHamtNode *
hamt_node_new_bitmap_or_collision(uint32_t shift,
                                  PyObject *key1, PyObject *val1,
                                  int32_t key2_hash,
                                  PyObject *key2, PyObject *val2)
{
    /* Helper method.  Creates a new node for key1/val and key2/val2
       pairs.

       If key1 hash is equal to the hash of key2, a Collision node
       will be created.  If they are not equal, a Bitmap node is
       created.
    */

    int32_t key1_hash = hamt_hash(key1);
    if (key1_hash == -1) {
        return NULL;
    }

    if (key1_hash == key2_hash) {
        PyHamtNode_Collision *n;
        n = (PyHamtNode_Collision *)hamt_node_collision_new(key1_hash, 4);
        if (n == NULL) {
            return NULL;
        }

        Py_INCREF(key1);
        n->c_array[0] = key1;
        Py_INCREF(val1);
        n->c_array[1] = val1;

        Py_INCREF(key2);
        n->c_array[2] = key2;
        Py_INCREF(val2);
        n->c_array[3] = val2;

        return (PyHamtNode *)n;
    }
    else {
        int added_leaf = 0;
        PyHamtNode *n = hamt_node_bitmap_new(0);
        if (n == NULL) {
            return NULL;
        }

        PyHamtNode *n2 = hamt_node_assoc(
            n, shift, key1_hash, key1, val1, &added_leaf);
        Py_DECREF(n);
        if (n2 == NULL) {
            return NULL;
        }

        n = hamt_node_assoc(n2, shift, key2_hash, key2, val2, &added_leaf);
        Py_DECREF(n2);
        if (n == NULL) {
            return NULL;
        }

        return n;
    }
}

static PyHamtNode *
hamt_node_bitmap_assoc(PyHamtNode_Bitmap *self,
                       uint32_t shift, int32_t hash,
                       PyObject *key, PyObject *val, int* added_leaf)
{
    /* assoc operation for bitmap nodes.

       Return: a new node, or self if key/val already is in the
       collection.

       'added_leaf' is later used in '_PyHamt_Assoc' to determine if
       `hamt.set(key, val)` increased the size of the collection.
    */

    uint32_t bit = hamt_bitpos(hash, shift);
    uint32_t idx = hamt_bitindex(self->b_bitmap, bit);

    /* Bitmap node layout:

    +------+------+------+------+  ---  +------+------+
    | key1 | val1 | key2 | val2 |  ...  | keyN | valN |
    +------+------+------+------+  ---  +------+------+
    where `N < Py_SIZE(node)`.

    The `node->b_bitmap` field is a bitmap.  For a given
    `(shift, hash)` pair we can determine:

     - If this node has the corresponding key/val slots.
     - The index of key/val slots.
    */

    if (self->b_bitmap & bit) {
        /* The key is set in this node */

        uint32_t key_idx = 2 * idx;
        uint32_t val_idx = key_idx + 1;

        assert(val_idx < (size_t)Py_SIZE(self));

        PyObject *key_or_null = self->b_array[key_idx];
        PyObject *val_or_node = self->b_array[val_idx];

        if (key_or_null == NULL) {
            /* key is NULL.  This means that we have a few keys
               that have the same (hash, shift) pair. */

            assert(val_or_node != NULL);

            PyHamtNode *sub_node = hamt_node_assoc(
                (PyHamtNode *)val_or_node,
                shift + 5, hash, key, val, added_leaf);
            if (sub_node == NULL) {
                return NULL;
            }

            if (val_or_node == (PyObject *)sub_node) {
                Py_DECREF(sub_node);
                Py_INCREF(self);
                return (PyHamtNode *)self;
            }

            PyHamtNode_Bitmap *ret = hamt_node_bitmap_clone(self);
            if (ret == NULL) {
                return NULL;
            }
            Py_SETREF(ret->b_array[val_idx], (PyObject*)sub_node);
            return (PyHamtNode *)ret;
        }

        assert(key != NULL);
        /* key is not NULL.  This means that we have only one other
           key in this collection that matches our hash for this shift. */

        int comp_err = PyObject_RichCompareBool(key, key_or_null, Py_EQ);
        if (comp_err < 0) {  /* exception in __eq__ */
            return NULL;
        }
        if (comp_err == 1) {  /* key == key_or_null */
            if (val == val_or_node) {
                /* we already have the same key/val pair; return self. */
                Py_INCREF(self);
                return (PyHamtNode *)self;
            }

            /* We're setting a new value for the key we had before.
               Make a new bitmap node with a replaced value, and return it. */
            PyHamtNode_Bitmap *ret = hamt_node_bitmap_clone(self);
            if (ret == NULL) {
                return NULL;
            }
            Py_INCREF(val);
            Py_SETREF(ret->b_array[val_idx], val);
            return (PyHamtNode *)ret;
        }

        /* It's a new key, and it has the same index as *one* another key.
           We have a collision.  We need to create a new node which will
           combine the existing key and the key we're adding.

           `hamt_node_new_bitmap_or_collision` will either create a new
           Collision node if the keys have identical hashes, or
           a new Bitmap node.
        */
        PyHamtNode *sub_node = hamt_node_new_bitmap_or_collision(
            shift + 5,
            key_or_null, val_or_node,  /* existing key/val */
            hash,
            key, val  /* new key/val */
        );
        if (sub_node == NULL) {
            return NULL;
        }

        PyHamtNode_Bitmap *ret = hamt_node_bitmap_clone(self);
        if (ret == NULL) {
            Py_DECREF(sub_node);
            return NULL;
        }
        Py_SETREF(ret->b_array[key_idx], NULL);
        Py_SETREF(ret->b_array[val_idx], (PyObject *)sub_node);

        *added_leaf = 1;
        return (PyHamtNode *)ret;
    }
    else {
        /* There was no key before with the same (shift,hash). */

        uint32_t n = (uint32_t)_Py_popcount32(self->b_bitmap);

        if (n >= 16) {
            /* When we have a situation where we want to store more
               than 16 nodes at one level of the tree, we no longer
               want to use the Bitmap node with bitmap encoding.

               Instead we start using an Array node, which has
               simpler (faster) implementation at the expense of
               having preallocated 32 pointers for its keys/values
               pairs.

               Small hamt objects (<30 keys) usually don't have any
               Array nodes at all.  Between ~30 and ~400 keys hamt
               objects usually have one Array node, and usually it's
               a root node.
            */

            uint32_t jdx = hamt_mask(hash, shift);
            /* 'jdx' is the index of where the new key should be added
               in the new Array node we're about to create. */

            PyHamtNode *empty = NULL;
            PyHamtNode_Array *new_node = NULL;
            PyHamtNode *res = NULL;

            /* Create a new Array node. */
            new_node = (PyHamtNode_Array *)hamt_node_array_new(n + 1);
            if (new_node == NULL) {
                goto fin;
            }

            /* Create an empty bitmap node for the next
               hamt_node_assoc call. */
            empty = hamt_node_bitmap_new(0);
            if (empty == NULL) {
                goto fin;
            }

            /* Make a new bitmap node for the key/val we're adding.
               Set that bitmap node to new-array-node[jdx]. */
            new_node->a_array[jdx] = hamt_node_assoc(
                empty, shift + 5, hash, key, val, added_leaf);
            if (new_node->a_array[jdx] == NULL) {
                goto fin;
            }

            /* Copy existing key/value pairs from the current Bitmap
               node to the new Array node we've just created. */
            Py_ssize_t i, j;
            for (i = 0, j = 0; i < HAMT_ARRAY_NODE_SIZE; i++) {
                if (((self->b_bitmap >> i) & 1) != 0) {
                    /* Ensure we don't accidentally override `jdx` element
                       we set few lines above.
                    */
                    assert(new_node->a_array[i] == NULL);

                    if (self->b_array[j] == NULL) {
                        new_node->a_array[i] =
                            (PyHamtNode *)self->b_array[j + 1];
                        Py_INCREF(new_node->a_array[i]);
                    }
                    else {
                        int32_t rehash = hamt_hash(self->b_array[j]);
                        if (rehash == -1) {
                            goto fin;
                        }

                        new_node->a_array[i] = hamt_node_assoc(
                            empty, shift + 5,
                            rehash,
                            self->b_array[j],
                            self->b_array[j + 1],
                            added_leaf);

                        if (new_node->a_array[i] == NULL) {
                            goto fin;
                        }
                    }
                    j += 2;
                }
            }

            VALIDATE_ARRAY_NODE(new_node)

            /* That's it! */
            res = (PyHamtNode *)new_node;

        fin:
            Py_XDECREF(empty);
            if (res == NULL) {
                Py_XDECREF(new_node);
            }
            return res;
        }
        else {
            /* We have less than 16 keys at this level; let's just
               create a new bitmap node out of this node with the
               new key/val pair added. */

            uint32_t key_idx = 2 * idx;
            uint32_t val_idx = key_idx + 1;
            uint32_t i;

            *added_leaf = 1;

            /* Allocate new Bitmap node which can have one more key/val
               pair in addition to what we have already. */
            PyHamtNode_Bitmap *new_node =
                (PyHamtNode_Bitmap *)hamt_node_bitmap_new(2 * (n + 1));
            if (new_node == NULL) {
                return NULL;
            }

            /* Copy all keys/values that will be before the new key/value
               we are adding. */
            for (i = 0; i < key_idx; i++) {
                Py_XINCREF(self->b_array[i]);
                new_node->b_array[i] = self->b_array[i];
            }

            /* Set the new key/value to the new Bitmap node. */
            Py_INCREF(key);
            new_node->b_array[key_idx] = key;
            Py_INCREF(val);
            new_node->b_array[val_idx] = val;

            /* Copy all keys/values that will be after the new key/value
               we are adding. */
            assert(Py_SIZE(self) >= 0 && Py_SIZE(self) <= 32);
            for (i = key_idx; i < (uint32_t)Py_SIZE(self); i++) {
                Py_XINCREF(self->b_array[i]);
                new_node->b_array[i + 2] = self->b_array[i];
            }

            new_node->b_bitmap = self->b_bitmap | bit;
            return (PyHamtNode *)new_node;
        }
    }
}

static hamt_without_t
hamt_node_bitmap_without(PyHamtNode_Bitmap *self,
                         uint32_t shift, int32_t hash,
                         PyObject *key,
                         PyHamtNode **new_node)
{
    uint32_t bit = hamt_bitpos(hash, shift);
    if ((self->b_bitmap & bit) == 0) {
        return W_NOT_FOUND;
    }

    uint32_t idx = hamt_bitindex(self->b_bitmap, bit);

    uint32_t key_idx = 2 * idx;
    uint32_t val_idx = key_idx + 1;

    PyObject *key_or_null = self->b_array[key_idx];
    PyObject *val_or_node = self->b_array[val_idx];

    if (key_or_null == NULL) {
        /* key == NULL means that 'value' is another tree node. */

        PyHamtNode *sub_node = NULL;

        hamt_without_t res = hamt_node_without(
            (PyHamtNode *)val_or_node,
            shift + 5, hash, key, &sub_node);

        switch (res) {
            case W_EMPTY:
                /* It's impossible for us to receive a W_EMPTY here:

                    - Array nodes are converted to Bitmap nodes when
                      we delete 16th item from them;

                    - Collision nodes are converted to Bitmap when
                      there is one item in them;

                    - Bitmap node's without() inlines single-item
                      sub-nodes.

                   So in no situation we can have a single-item
                   Bitmap child of another Bitmap node.
                */
                Py_UNREACHABLE();

            case W_NEWNODE: {